For the first equation, we can use the product rule. Let f(x) = 2x+ and g(x) = 5x+2. Then, f'(x) = 2 and g'(x) = 5. Using the product rule formula, we get:
k'(x) = f(x)g'(x) + g(x)f'(x)
k'(x) = (2x+)(5) + (5x+2)(2)
k'(x) = 10x+ + 4x+10
For the profit function, P(x) = -2x^2 + 6x + 7, we can use the derivative to find the marginal profit. The derivative of P(x) is:
P'(x) = -4x + 6
To find the marginal profit when 4 units are produced and sold, we plug in x = 4 into P'(x):
P'(4) = -4(4) + 6
P'(4) = -10
Therefore, the marginal profit when 4 units are produced and sold is -10 hundred dollars or -$1,000. This means that for each additional unit produced and sold beyond the initial 4 units, the profit will decrease by $1,000.
Hi! It seems that your question has some missing information and typos, but I'll try my best to help you with the given data. The main task here is to find the marginal profit when 4 units are produced and sold, and interpret the answer.
The profit function P(x) appears to be incomplete. However, since we're asked to find the marginal profit, we need to take the derivative of the profit function with respect to x. Marginal profit is the derivative of the profit function with respect to the number of units sold (x). We can use the chain rule, product rule, or quotient rule to find the derivative, depending on the given profit function.
Once we have the derivative, we can evaluate it at x = 4 to find the marginal profit when 4 units are produced and sold. The result will indicate how much additional profit (in hundreds of dollars) the company will gain for producing and selling one more unit.
Please provide the complete profit function P(x), and I will be glad to help you find the marginal profit and interpret the answer.
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Q11
A ball is thrown vertically upward. After t seconds, its height, h (in feet), is given by the function h left parenthesis t right parenthesis equals 76 t minus 16 t squared. After how long will it reach its maximum height?
Round your answer to the nearest hundredth.
Group of answer choices
90 seconds
1.2 seconds
0.17 seconds
2.38 seconds
Answer:
Step-by-step explanation:
To find when the ball reaches its maximum height, we need to find the vertex of the quadratic function h(t) = 76t - 16t^2.
The vertex of a quadratic function of the form y = ax^2 + bx + c is at the point (-b/2a, f(-b/2a)), where f(x) = ax^2 + bx + c.
In this case, a = -16 and b = 76, so the time at which the ball reaches its maximum height is given by:
t = -b/2a = -76/(2*(-16)) = 2.375
Rounded to the nearest hundredth, the ball reaches its maximum height after 2.38 seconds (Option D).
Tanisha is playing a game with two different types of fair geometric objects. One object has eight faces numbered from 1 to 8. The other has six faces labeled M, N, oh, P, Q, and R. What is the probability of rolling a number greater than three and the R on the first role of both objects?
A. 1/8
B. 1/14
C. 5/48
D. 43/48
The probability of rolling a number greater than three and an R on the first roll of both objects is 5/48. The answer is C.
What's P(rolling >3 and R on the first roll of both objects)?
The probability of rolling a number greater than three on the eight-faced object is 5/8 because there are five numbers greater than three (4, 5, 6, 7, and 8) out of eight possible outcomes. The probability of rolling an R on the six-faced object is 1/6 because there is only one R out of six possible outcomes.
To find the probability of both events occurring simultaneously, we multiply the probabilities together:
P(rolling a number > 3 and rolling an R) = P(rolling a number > 3) x P(rolling an R)
= (5/8) x (1/6)
= 5/48
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Assume that a simple random sample has been selected from a normally distributed population and test the given claim. identify the null and alternative hypotheses, test statistic, p-value, and state the final conclusion that addresses the original claim.
a simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. the sample has a mean of 19.8 mg and a standard deviation of 3.21 mg. use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes.
required:
what do the results suggest, if anything, about the effectiveness of the filters?
The results suggest that the mean tar content of filtered 100 mm cigarettes is significantly lower than 21.1 mg, which is the mean for unfiltered king size cigarettes. This indicates that the filters are effective in reducing the tar content of cigarettes.
Null hypothesis: The mean tar content of filtered 100 mm cigarettes is greater than or equal to 21.1 mg.
Alternative hypothesis: The mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.
The test statistic to use is the t-statistic, since the population standard deviation is not known.
t = (19.8 - 21.1) / (3.21 / sqrt(25)) = -2.03
Using a t-table with degrees of freedom of 24 and a significance level of 0.05, the critical t-value is -1.711. Since our test statistic is less than the critical t-value, we reject the null hypothesis.
The p-value can also be calculated using the t-distribution with degrees of freedom of 24 and the t-statistic of -2.03. The p-value is 0.029, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis.
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The quantity of a product manufactured by a company is given by Q = aK^{0.6}L^{0.4}
where a is a positive constant, Kis the quantity of capital and Listhe quantity of labor used. Capital costs are $44 per unit, labor costs are $11 per unit, and the company wants costs for capital and labor combined to be no higher than $330. Suppose you are asked to consult for the company, and learn that 6 units each of capital and labor are being used, (a) What do you advise? Should the company use more or less labor? More or less capital? If so, by how much?
The company should increase the quantity of capital used from 6 units to 3 units, an increase of 3 units.
The cost of capital and labor can be expressed as:
C = 44K + 11L
The company wants to limit the cost of capital and labor to $330:
44K + 11L ≤ 330
Substituting Q = aK^{0.6}L^{0.4} into the inequality, we get:
44K + 11L ≤ 330
44K + 11(Q/aK^{0.6})^{0.4} ≤ 330
44K^{1.6} + 11(Q/a)^{0.4}K ≤ 330
Solving for K, we get:
K ≤ (330 - 11(Q/a)^{0.4}) / 44K^{1.6}
Substituting K = 6, Q = aK^{0.6}L^{0.4}, and solving for L, we get:
Q = aK^{0.6}L^{0.4}
Q/K^{0.6} = aL^{0.4}
L = (Q/K^{0.6})^{2.5}/a
Substituting Q = a(6)^{0.6}(6)^{0.4} = 6a into the equation, we get:
L = (6/a)^{0.4}(6)^{2.5} = 9.585a^{0.6}
Therefore, the company is currently using 6 units each of capital and labor, and the total cost of capital and labor is:
C = 44(6) + 11(6) = 330
This means that the company is already using the maximum allowable cost. To reduce the cost, the company should use less labor or less capital.
To determine whether to use more or less labor, we can take the derivative of Q with respect to L:
∂Q/∂L = 0.4aK^{0.6}L^{-0.6}
This is a decreasing function of L, so as L increases, the quantity of product Q produced will decrease. Therefore, the company should use less labor.
To determine how much less labor to use, we can find the value of L that would reduce the cost to the maximum allowable level of $330:
44K + 11L = 330
44(6) + 11L = 330
L = 18
Therefore, the company should reduce the quantity of labor used from 6 units to 18 units, a decrease of 12 units.
To determine whether to use more or less capital, we can take the derivative of Q with respect to K:
∂Q/∂K = 0.6aK^{-0.4}L^{0.4}
This is an increasing function of K, so as K increases, the quantity of product Q produced will increase. Therefore, the company should use more capital.
To determine how much more capital to use, we can find the value of K that would reduce the cost to the maximum allowable level of $330:
44K + 11L = 330
44K + 11(18) = 330
K = 3
Therefore, the company should increase the quantity of capital used from 6 units to 3 units, an increase of 3 units.
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WORK OUT THE SIZE OF AN EXTERIOR ANGLE OF A REGULAR HEXAGON
Answer:
60°
Step-by-step explanation:
A hexagon has 6 angles
The sum of the measures of the exterior angles of a hexagon is equal to 360°
So, measure of each exterior angle = 360∘ / 6 = 60∘
If the arc length of a circle with a radius of 5 cm is 18.5 cm, what is the area of the sector, to the nearest hundredth
i need it quick please
The area of the sector, to the nearest hundredth, is 45.87 cm^2.
The formula for the length of an arc of a circle is L = rθ, where L is the arc length, r is the radius, and θ is the angle in radians subtended by the arc.
We solve for θ by dividing both sides by r: θ = L/r.
In this case, r = 5 cm and L = 18.5 cm, so θ = 18.5/5 = 3.7 radians.
The formula for the area of a sector of a circle is A = (1/2)r^2θ.
Plugging in the values, we get A = (1/2)(5^2)(3.7) ≈ 45.87 cm^2.
Therefore, the area of the sector, to the nearest hundredth, is 45.87 cm^2.
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Find the function, f, that satisfies the following conditions f"(x)=-sin x/2, f'(π) = 0, f(π/3)=-3
The function f(x) = -4*sin(x/2) - 1 is the solution that meets the specified conditions.
To find the function, f, that satisfies the given conditions f"(x) = -sin(x/2), f'(π) = 0, and f(π/3) = -3, we need to integrate the given second derivative twice and apply the boundary conditions. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x).
1. Integrate f"(x) = -sin(x/2) with respect to x to find f'(x):
f'(x) = ∫(-sin(x/2)) dx = -2*cos(x/2) + C1, where C1 is the integration constant
2. Apply the boundary condition f'(π) = 0:
0 = -2*cos(π/2) + C1
C1 = 0, since cos(π/2) = 0.
3. Now, f'(x) = -2*cos(x/2).
4. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x):
f(x) = ∫(-2*cos(x/2)) dx = -4*sin(x/2) + C2, where C2 is the integration constant.
5. Apply the boundary condition f(π/3) = -3:
-3 = -4*sin(π/6) + C2
-3 = -4*(1/2) + C2
C2 = -1.
So, the function f(x) that satisfies the given conditions is f(x) = -4*sin(x/2) - 1.
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During the holiday season Andrew has to help his mother wrap the candy that she makes. The number of pieces that she can wrap (y) can be described as
y = 73. Andrew takes a lot more breaks to eat pieces of the candy, so he wraps at a rate of y = 3x + 8.
At how many minutes (s) have Andrew and his mother wrapped the same number of candy pieces?
2 minutes
O 3 minutes
0 4 minutes
t
8 minutes
Andrew and his mother will have wrapped the same number of candy pieces in 21.6 minutes.
We need to find out how many minutes (s) Andrew and his mother wrapped the same number of candy pieces.
Given data:
The number of pieces that Andrew’s mother can wrap is y = 73.
Andrew wraps at a rate of y = 3x + 8.
To find the number of minutes (s) at which Andrew and his mother have wrapped the same number of candy pieces, we need to equate both equations and then find the value of x the equation is given as,
73 = 3x + 8
65 = 3x
x = 21.6
Therefore, Andrew and his mother will have wrapped the same number of candy pieces after 21.6 minutes.
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John is planning an end of the school year party for his friends he has $155 to spend on soda and pizza he knows he has to buy 10 2 L bottles of soda choose the any quality and calculate the greatest number of pizzas he can buy
If John has to buy 10 "2-Liter" bottles of soda, then the inequality representing this situation is "10(1.50) + 7.50p ≤ 150" and greatest number of pizzas he can buy is 18, Correct option is (d).
Let "p" denote the number of "large-pizzas" that John can buy.
One "2-liter" bottle of soda cost is = $1.50,
So, the cost of the 10 bottles of soda is : 10 × $1.50 = $15,
one "large-pizza's cost is = $7.50,
So, the cost of p large pizzas is : $p × $7.50 = $7.50p,
The "total-cost" of the soda and pizza must be less than or equal to $150, so we can write the inequality as :
10(1.50) + 7.50p ≤ 150
Simplifying the left-hand side of the inequality,
We get,
15 + 7.50p ≤ 150
7.50p ≤ 135
p ≤ 18
Therefore, John can buy at most 18 large pizzas with his remaining budget, the correct option is (d).
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The given question is incomplete, the complete question is
John is planning an end of the school year party for his friends he has $150 to spend on soda and pizza.
Soda (2-liter) costs $1.50;
large pizza cost $7.50;
He knows he has to buy 10 "2-Liter" bottles of soda.
Choose the inequality and calculate the greatest number of pizzas he can buy.
(a) 10(1.50) + 7.50p ≥ 150; 54 pizzas
(b) 10(7.50) + 1.50p ≤ 150; 53 pizzas
(c) 10(7.50) + 1.50p ≥ 150; 19 pizzas
(d) 10(1.50) + 7.50p ≤ 150; 18 pizzas
At the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter, i. e. the minimum of the three. what is the variance of the actuary's wait time
The variance of the actuary's wait time is 36 / 121.
How to calculate the varianceFrom the information, at the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter,
From the complete question, the variance of the actuary's wait time will be:
= 1 / (11/6)²
= (6/11)²
= 36 / 121
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The original price of an item is $25, but after the discount, you only have to pay $18.50. What is the discount (as a percent)
The discount is 26%.
What is Discount?The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
Given:
[tex]\bold{Marked} \ \text{price} = \$25[/tex]
[tex]\bold{Selling} \ \text{price} = \$18.50[/tex]
So,
[tex]\text{Discount = MP - SP}[/tex]
[tex]\text{Discount} = 25-18.50[/tex]
[tex]\bold{Discount} = 6.50[/tex]
Now,
[tex]\text{D}\% = \dfrac{\text{D}}{\text{MP}} \times100[/tex]
[tex]\text{D}\% = \dfrac{6.5}{25} \times100[/tex]
[tex]\text{D}\% = 26\%[/tex]
Hence, the discount percent is 26%.
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Factorize completely the expression (m+n)(2x-y)-x(m+n)
The complete factorization of the expression is (m+n)(x-y).
What is the complete factorization of the expression?The complete factorization of the expression is determined as follows;
To factorize the expression (m+n)(2x-y)-x(m+n), we can first factor out the common factor (m+n):
(m+n)(2x-y)-x(m+n) = (m+n)(2x-y-x)
Next, we will factorize completely as follows;
2x - x - y = x - y
(m+n)(2x-y-x) = (m+n)(x-y)
Therefore, the fully factorized form of the expression is (m+n)(x-y).
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find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→5 x2 − 25 x2 − 5x
The limit is equal to 10. We didn't need to use L'Hospital's rule or any other advanced method, as the limit was easily evaluate through simplification and direct substitution.
We can simplify the expression as follows:
[tex]lim x→5 (x + 5) x = lim x→5 (10) = 10[/tex]
Now, we can directly evaluate the limit by substituting 5 for x:
[tex]lim x→5 (x + 5) x = lim x→5 (10) = 10[/tex]
Therefore, the limit is equal to 10. We didn't need to use L'Hospital's rule or any other advanced method, as the limit was easily evaluatable through simplification and direct substitution.
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Guadalupe models the volume of a popcorn box as a right rectangular prism and the box can hold 46 cubic inches of popcorn when it is full. Its length is 2 3 4 2 4 3 in and its height is 7 1 2 7 2 1 in. Find the width of the popcorn box in inches. Round your answer to the nearest tenth if necessary.
The width of the rectangular prism popcorn box is approximately 2.27 inches when rounded to the nearest tenth.
How to Find the Width of a Rectangular Prism?The volume of a right rectangular prism is given by:
V = lwh
where V is the volume, l is the length, w is the width, and h is the height.
We are given that the box can hold 46 cubic inches of popcorn, the length is 2¾ inches, and the height is 7½ inches. Let's use w to represent the width we are trying to find.
So we have:
46 = (2¾)w(7½)
To solve for w, we can divide both sides of the equation by (2¾)(7½):
46 / ((2¾)(7½)) = w
Simplifying the right-hand side, we get:
w ≈ 2.27
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Complete Question:
Guadalupe models the volume of a popcorn box as a right rectangular prism and the box can hold 46 cubic inches of popcorn when it is full. Its length is 2¾ inches and its height is 7½ inches. Find the width of the popcorn box in inches. Round your answer to the nearest tenth if necessary.
3. The scale of a room in a blueprint is 2 inches : 1 foot. A window in the same blueprint is 12 inches. Complete the table. Blueprint Length (in.) Actual Length (ft) a. How long is the actual window? 2 1 4 3 4 10 12 5 6 b. A mantel in the room has an actual width of 8 feet. What is the width of the mantel in the blueprint?
Therefor, the length of mantel in blueprint is > 30 ft
width of the mantel in the blueprint 8ft×2inc/1ft=16inch
what is width?The term "width" refers to the length from side to side of anything. For instance, the shorter side of a rectangle would be the width.
we know that
[scale]=[blueprint]/[actual]-------> [actual]=[blueprint]/[scale]
[scale]=3/5 in/ft
for [wall blueprint]=18 in
[wall actual]=[wall blueprint]/[scale]-------> 18/(3/5)----> 30 ft
Part A)
the actual wall is 30 ft long
Part B) window has actual width of 2.5 ft
[ window blueprint]=[scale]*[actual window]-----> (3/5)*2.5----> 1.5 in
the width of the window in the blueprint is 1.5 in
Part C) Complete the table
For [blueprint length]=4 in
[actual length]=[blueprint length]/[scale]-------> 4/(3/5)----> 20/3 ft
For [blueprint length]=5 in
[actual length]=[blueprint length]/[scale]-------> 5/(3/5)----> 25/3 ft
For [blueprint length]=6 in
[actual length]=[blueprint length]/[scale]-------> 6/(3/5)----> 30/3=10 ft
For [blueprint length]=7 in
[actual length]=[blueprint length]/[scale]-------> 7/(3/5)----> 35/3 ft
For [actual length]=6 ft
[blueprint length]=[actual length]*[scale]-------> 6*(3/5)----> 18/5 in
For [actual length]=7 ft
[blueprint length]=[actual length]*[scale]-------> 7*(3/5)----> 21/5 in
For [actual length]=8 ft
[blueprint length]=[actual length]*[scale]-------> 8*(3/5)----> 24/5 in
For [actual length]=9 ft
[blueprint length]=[actual length]*[scale]-------> 9*(3/5)----> 27/5 in
B) width of the mantel in the blueprint 8ft×2inc/1ft=16inch
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Find the derivative y = cot (sen x/X + 14)
To find the derivative of y = cot(sen x/X + 14), we need to use the chain rule and the derivative of cot(x) which is -csc^2(x).
First, we let u = sen x/X + 14.
Then, we can rewrite y as y = cot(u).
Using the chain rule, the derivative of y with respect to x is:
dy/dx = dy/du * du/dx
To find dy/du, we need to use the derivative of cot(u) which is -csc^2(u).
So,
dy/du = -csc^2(u)
To find du/dx, we need to use the quotient rule.
Let v = X, so u = sen x/v + 14.
Then,
du/dx = (v*cos x - sen x * 0)/(v^2)
du/dx = cos x/v
Now we can substitute the values of dy/du and du/dx:
dy/dx = dy/du * du/dx
dy/dx = (-csc^2(u)) * (cos x/v)
But u = sen x/X + 14, so we substitute this in:
dy/dx = (-csc^2(sen x/X + 14)) * (cos x/X)
Therefore, the derivative of y = cot(sen x/X + 14) is
dy/dx = (-csc^2(sen x/X + 14)) * (cos x/X).
To find the derivative of y = cot(sen(x)/(x + 14)), we will use the quotient rule and the chain rule.
Let u = sen(x) and v = x + 14, then y = cot(u/v).
First, find the derivatives of u and v:
du/dx = cos(x) (since the derivative of sen(x) is cos(x))
dv/dx = 1 (since the derivative of x is 1, and the derivative of a constant is 0)
Now, apply the quotient rule for cotangent:
d(cot(u/v))/dx = -1/(sin^2(u/v)) * (du/dv - u*dv/dx) / (v^2)
Substitute the expressions for u, v, du/dx, and dv/dx:
dy/dx = -1/(sin^2(sen(x)/(x + 14))) * ((cos(x)*(x + 14) - sen(x)*1) / (x + 14)^2)
This is the derivative of y with respect to x.
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Lesley needs to spend at least $15 at the grocery store to use a coupon. She buys 1 container of tomatoes and needs to buy some potatoes. One container of tomatoes costs $2. 75 and one pound of potatoes costs $2. 45. How may pounds of potatoes, p, does Lesley need to buy to use the coupon? write your answer using an inequality symbol
Answer: 5
2.75+(2.45x5) = 15
Please help!!! Simplify[tex]\frac{\sqrt 7 + \sqrt 3}{2\sqrt 3 - \sqrt 7}[/tex]
The simplified rational expression for this problem is given as follows:
[tex]\frac{3\sqrt{21} + 13}{12}[/tex]
How to simplify the rational expression?The rational expression in the context of this problem is defined as follows:
[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}}[/tex]
The first step in simplifying the expression is removing the root from the denominator, multiplying numerator and denominator by the conjugate, as follows:
[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}} \times \frac{2\sqrt{3} + \sqrt{7}}{2\sqrt{3} + \sqrt{7}}[/tex]
Applying the subtraction of perfect squares, the denominator is given as follows:
2² x 3 - 7 = 12.
The numerator is:
[tex](\sqrt{7} + \sqrt{3})(2\sqrt{3} + \sqrt{7}) = 2\sqrt{21} + 7 + 6 + \sqrt{21} = 3\sqrt{21} + 13[/tex]
Thus the simplified expression is:
[tex]\frac{3\sqrt{21} + 13}{12}[/tex]
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I NEED HELP UNDER 30 MINS PLEASE!!!!
The total number of gifts is given as follows:
439 gifts.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For a single gift, the number of options is given as follows:
10 + 4 + 7 = 21 gifts.
For two gifts, the number of options is given as follows:
10 x 4 + 10 x 7 + 7 x 4 = 138 gifts.
For three gifts, the number of options is given as follows:
10 x 4 x 7 = 280 gifts.
Hence the total number of gifts is obtained as follows:
280 + 138 + 21 = 439 gifts.
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3x + 5y = -59 complete the solution of the equation
The solutions of the equation are y = (-3/5)x - 59/5 and x = (-5/3)y - 59/3
Completing the solution of the equationTo solve for one variable in terms of the other, we can rearrange the equation to isolate one of the variables. For example, solving for y in terms of x:
3x + 5y = -59
5y = -3x - 59
y = (-3/5)x - 59/5
So the solution of the equation is:
y = (-3/5)x - 59/5
Alternatively, we could solve for x in terms of y:
3x + 5y = -59
3x = -5y - 59
x = (-5/3)y - 59/3
So another possible solution of the equation is:
x = (-5/3)y - 59/3
Note that both solutions represent the same line in the xy-plane, since they are equivalent equations.
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Annie wrote the equation y= 175x +3375 where x represents the number of hours of classwork a college student is
taking per semester and y represents their total fee for the semester including housing.
What does the number 175 represent in Annie's equation?
The total number of hours of classwork a college student is taking per semester
The cost per hour per semester for classwork
© The cost per week for housing
The total cost for housing per semester
The number 175 in Annie's equation represents the cost per hour per semester for classwork.
This means that for every additional hour of classwork a college student takes per semester, their fee increases by $175. It is important to note that this cost does not include the cost for housing, which is represented by the constant term of the equation, 3375. Therefore, the equation allows us to calculate the total fee a college student would pay for a semester based on the number of hours of classwork they take and the cost per hour.
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Susan got a prepaid debit card with 20 on it.For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 16 cents per yard. If after that purchase there was 14.88 left on the card, how many yards of ribbon did Susan buy?
Answer:
32 yards
Step-by-step explanation:
Let's see, the card started out with $20 on it, and ended up with $14.88.
To find how much she spent on ribbon, we can first subtract the 2 amounts:
20-14.88
=5.12
So, Susan spent $5.12 on ribbon. We also know that each yard of ribbon was $0.16, so we can divide the spent amount ($5.12) by $0.16 to find out how many yards she bought:
5.12/0.16
=32
So, Susan bought 32 yards of ribbon.
Hope this helps :)
Find the angle between the planes 8x + y = - 7 and 4x + 9y + 10z = - 17. The radian measure of the acute angle is = (Round to the nearest thousandth.)
Angle between the planes is 0.978 radians
To find the angle between the planes 8x + y = -7 and 4x + 9y + 10z = -17, we need to follow these steps:
Step 1: Find the normal vectors of the planes. The coefficients of the variables in the plane equation (Ax + By + Cz = D) represent the components of the normal vector (A, B, C).
For the first plane (8x + y = -7), the normal vector is N1 = (8, 1, 0).
For the second plane (4x + 9y + 10z = -17), the normal vector is N2 = (4, 9, 10).
Step 2: Calculate the dot product of the normal vectors.
N1 · N2 = (8 * 4) + (1 * 9) + (0 * 10) = 32 + 9 + 0 = 41
Step 3: Calculate the magnitudes of the normal vectors.
|N1| = √(8² + 1² + 0²) = √(64 + 1) = √65
|N2| = √(4² + 9² + 10²) = √(16 + 81 + 100) = √197
Step 4: Find the cosine of the angle between the planes.
cos(angle) = (N1 · N2) / (|N1| * |N2|) = 41 / (√65 * √197)
Step 5: Calculate the angle in radians.
angle = arccos(cos(angle)) = arccos(41 / (√65 * √197))
Using a calculator, we find the acute angle between the planes to be approximately 0.978 radians (rounded to the nearest thousandth).
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(a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1, 2, 3) x + 3y + 22 = 14 14 (b) Find a set of symmetric equations for the normal line to the surface at the given point. Ox - 1 = y - 2 = z - 3 OX-1-y-2-2-3 14 14 Y Y 2 3 X-1 _ y - 2 2-3 2 3 y 14 14 14 o 1 2
An equation of the tangent plane to the surface at the given point is x + 2y + 3z = 14. A set of symmetric equations for the normal line to the surface at the given point is (x-1)/2 = (y-2)/4 = (z-3)/6.
The gradient of the surface is given by
∇f(x, y, z) = <2x, 2y, 2z>
At point (1, 2, 3), the gradient is
∇f(1, 2, 3) = <2, 4, 6>
The equation of the tangent plane can be found using the formula
f(x, y, z) = f(a, b, c) + ∇f(a, b, c) · <x-a, y-b, z-c>
Plugging in the values we have
x + 2y + 3z = 14
The direction vector of the normal line is the same as the gradient of the surface at the given point
<2, 4, 6>
To find symmetric equations for the line, we can use the parametric equations
x = 1 + 2t
y = 2 + 4t
z = 3 + 6t
Eliminating the parameter t, we get the symmetric equations
(x-1)/2 = (y-2)/4 = (z-3)/6
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Sabine rode on a passenger train for 480 miles between 10:30 A. M. And 6:30 P. M. A friend in a different city
The speed of the train is 60 miles per hour.
Sabine travel 480 miles on a passenger train between 10:30 A.M. and 6:30 P.M. What is speed of train?We calculate in two steps:
Calculate the speed of the trainTo calculate the speed of the train, we need to use the formula:
Speed = Distance / Time
Here, the distance travelled by the train is 480 miles, and the time taken is 8 hours (from 10:30 A.M. to 6:30 P.M.). So, we can calculate the speed of the train as:
Speed = 480 miles / 8 hours
Speed = 60 miles per hour
Therefore, the speed of the train is 60 miles per hour.
Explain the solutionSabine rode on a passenger train for 480 miles between 10:30 A.M. and 6:30 P.M.
To calculate the speed of the train, we used the formula Speed = Distance / Time, where Distance is 480 miles and Time is 8 hours (since the journey was between 10:30 A.M. and 6:30 P.M.).
Substituting the values, we get the speed of the train as 60 miles per hour.
This means that the train travelled at a speed of 60 miles per hour throughout the journey, covering a distance of 480 miles in 8 hours.
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find the length of the third side if necessary round to the nearest tenth
The third side that we can not see in the image that is shown has a size of 15.
How do you find the hypotenuse of a right triangle when other sides are given?The hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
If c^2 = a^2 + b^2
c = √a^2 + b^2
c = √12^2 + 9^2
c = 15
Thus the missing side is 15 from the calculation.
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Mr. Vega is going to buy a blue tractor that weighs 3/5 of a ton or a red tractor weighs 4/6 of a ton. Which tractor is heavier
The red tractor is heavier.
To determine which tractor is heavier, Mr. Vega needs to compare the weights of the blue and red tractors. The blue tractor weighs [tex]\frac{3}{5}[/tex] of a ton, and the red tractor weighs [tex]\frac{4}{6}[/tex] of a ton.
First, we need to simplify the fractions if possible. In this case, we can simplify the red tractor's fraction by dividing both the numerator and denominator by 2:
[tex]\frac{4}{6} = \frac{\frac{4}{2} }{\frac{6}{2} } = \frac{2}{3}[/tex]
Now we can compare the simplified fractions:
[tex]Blue tractor: \frac{3}{5}[/tex]
[tex]Red tractor: \frac{2}{3}[/tex]
To compare these fractions, we can find a common denominator. The least common multiple of 5 and 3 is 15. To convert the fractions to the same denominator, we multiply the numerators and denominators by the necessary factors:
[tex]Red tractor: (\frac{2}{3}) (\frac{5}{5}) = \frac{10}{15}[/tex]
[tex]Blue tractor: (\frac{3}{5}) (\frac{3}{3}) = \frac{9}{15}[/tex]
Now we can easily compare the weights:
[tex]Blue tractor: \frac{9}{15}[/tex]
[tex]Red tractor: \frac{10}{15}[/tex]
Since [tex]\frac{10}{15}[/tex] is greater than [tex]\frac{9}{15}[/tex] , the red tractor is heavier.
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A brick wall be shaped like a rectangular prism.the wall needs to be 3 feet tall, and the builder have enough bricks for the wall to have a volumn of 330 cubic feet.
we need to find two numbers whose product is 110. Possible combinations include L = 10 feet and W = 11 feet or L = 11 feet and W = 10 feet. Therefore, the dimensions of the brick wall can be either 10 feet by 11 feet or 11 feet by 10 feet.
A brick wall can be shaped like a rectangular prism, and in this case, the wall needs to be 3 feet tall. With the builder having enough bricks for the wall to have a volume of 330 cubic feet, we can calculate the area of the base of the wall.
To find the base area, we can use the formula for the volume of a rectangular prism: Volume = Base Area × Height. In this situation, we know the volume (330 cubic feet) and the height (3 feet), so we can solve for the base area.
330 cubic feet = Base Area × 3 feet
Dividing both sides of the equation by 3, we get:
Base Area = 110 square feet
So, the base area of the brick wall that is shaped like a rectangular prism with a height of 3 feet and a volume of 330 cubic feet will be 110 square feet.
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In the shown figure, DE←→
is parallel to side BC¯¯¯¯¯¯¯¯
in triangle ABC
. If m∠B=52
°, what is m∠DAB
?
m∠DAB
=
°
Answer:
In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC =
Answer:
52 degrees
Step-by-step explanation: because i looked and they looked the same so i put 52 and it was right
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Answer:
Angle C also measures 64°.