Answer:
55 degrees
Step-by-step explanation:
sin Φ = cos 35
sin Φ = .81915
Φ = arc sin (.81915) = 55 degrees
Or you could just know that the cos of an angle is equal to the sin of its comeplement
suppose a piece of dust finds itself on a cd. if the spin rate of the cd is 500 rpm, and the piece of dust is 2.1 cm from the center, what is the total distance traveled by the dust in 4.0 minutes?
The total distance travelled by dust in the given time of 4.0 minutes at the spin rate of 500rpm is equal to 26,400cm.
Spin rate of the cd is equal to 500rpm
distance of piece of dust from the center = 2.1 cm
Distance traveled by a point on the CD that is 2.1 cm from the center in one revolution = circumference of the circle with a radius of 2.1 cm,
C = 2πr
= 2π(2.1 cm)
≈ 13.2 cm
Distance traveled by the dust in one revolution is 13.2 cm.
Calculate the number of revolutions that the CD makes in 4.0 minutes.
1 minute = 60 seconds
⇒ 4.0 minutes = 4.0 x 60
⇒4.0 minutes = 240 seconds
The CD rotates at a rate of 500 revolutions per minute,
In 4.0 minutes it will rotate,
500 x 4.0
= 2000 times.
The total distance traveled by the dust in 4.0 minutes is,
distance traveled per revolution x number of revolutions
= 13.2 cm/rev x 2000 rev
= 26,400 cm
Therefore, the total distance traveled by the dust in 4.0 minutes is 26,400 cm.
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Hillary used her credit card to buy a $804 laptop, which she paid off by making identical monthly payments for two and a half years. Over the six years that she kept the laptop, it cost her an average of $0. 27 of electricity per day. Hillary's credit card has an APR of 11. 27%, compounded monthly, and she made no other purchases with her credit card until she had paid off the laptop. What percentage of the lifetime cost of the laptop was interest? Assume that there were two leap years over the period that Hillary kept the laptop and round all dollar values to the nearest cent)
14.33% of the lifetime cost of Hillary's laptop was interest.
Since Hillary paid off her laptop in two and a half years, and kept it for six years, we need to calculate the compound interest over six years. Accounting for two leap years, there were 365 * 6 + 2 = 2192 days over the period that Hillary kept the laptop. Therefore, the total cost of electricity over that period was 2192 * 0.27 = $592.64.
Plugging in the values, we get:
A = 804 * (1 + 0.1127/12)³⁰= 1003.94
Hillary paid $1003.94 for her laptop, including interest. Subtracting the original cost of the laptop, we get:
Interest = 1003.94 - 804 = 199.94
So Hillary paid $199.94 in interest on her credit card over two and a half years. To calculate what percentage of the lifetime cost of the laptop was interest, we need to divide the interest paid by the total cost of the laptop and electricity:
Lifetime cost = 804 + 592.64 = 1396.64
Percentage of lifetime cost that was interest = (199.94 / 1396.64) * 100% = 14.33%
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The value of a sculpture depreciates by 20% each year. Today it is worth £650. How much was it worth 3 years ago? Give your newer to the nearest penny.
The sculpture was worth £332.80 three years ago when it depreciates by 20% each year
To determine how much the sculpture was worth 3 years ago, we need to apply the depreciation rate of 20% per year for the past three years.
First, we need to calculate how much the sculpture would be worth after one year of depreciation:
650 - (0.20)(650) = 520
This means that after the first year, the sculpture would be worth £520.
Next, we can calculate the value of the sculpture after the second year of depreciation:
520 - (0.20)(520) = 416
After two years, the sculpture would be worth £416.
Finally, we can calculate the value of the sculpture after the third year of depreciation:
416 - (0.20)(416) = 332.8
Therefore, the sculpture was worth £332.80 three years ago.
To check this answer, we can also use another method: We can calculate the value of the sculpture using the compound interest formula, where the initial value is £x, the annual depreciation rate is 20%, and the time period is three years:
650 = x[tex](1-0.20)^{2}[/tex]
Simplifying this equation, we get:
x = 650 / [tex]0.80^{2}[/tex] = 332.80
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Write and simplify the integral that gives the arc length of the following curve on the given integral. b. If necessary, use technology to evaluate or approximate the integral. y = -x² -5 on [-1,2]
To find the arc length of the curve y = -x² -5 on the interval [-1,2], we use the formula to evaluate:
L = ∫√(1 + (dy/dx)²) dx
where dy/dx is the derivative of y with respect to x.
First, we find dy/dx:
dy/dx = -2x
Next, we substitute dy/dx into the formula and simplify:
L = ∫√(1 + (-2x)²) dx
L = ∫√(1 + 4x²) dx
To evaluate this integral, we can use a trigonometric substitution. Let x = (1/2)tanθ, then dx = (1/2)sec²θ dθ. Substituting, we get:
L = ∫√(1 + 4(1/2)²tan²θ)(1/2)sec²θ dθ
L = (1/2)∫sec³θ dθ
To integrate sec³θ, we use integration by parts:
u = secθ, du/dθ = secθ tanθ
dv/dθ = sec²θ, v = tanθ
∫sec³θ dθ = secθ tanθ - ∫tan²θ secθ dθ
= secθ tanθ - ∫secθ dθ + ∫sec³θ dθ
Rearranging, we get:
2∫sec³θ dθ = secθ tanθ + ln|secθ + tanθ|
Therefore:
L = (1/2)(secθ tanθ + ln|secθ + tanθ|) + C
To evaluate L on the interval [-1,2], we need to find θ when x = -1 and x = 2. Using the substitution x = (1/2)tanθ:
When x = -1, θ = -π/4
When x = 2, θ = π/3
Substituting these values into the equation for L and simplifying, we get:
L = (1/2)(2√2 + ln(3 + 2√3) + π/4)
Therefore, the integral that gives the arc length of the curve y = -x² -5 on the interval [-1,2] is:
L = (1/2)(2√2 + ln(3 + 2√3) + π/4)
Note: If technology is used to evaluate or approximate the integral, the answer may differ slightly due to rounding errors.
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Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y) = 3ex sin(y), (0, 1/3), v = (-5, 12) V = D,FO, 1/3) = 12-973 10 x Need Help? Read It Watch
The directional derivative of the function f(x,y) in the direction of the vector v at the point (0,1/3) is:
Duf(0,1/3) = ∇f(0,1/3) · u = [0, 3e/2] · [-5/13, 12/13] = (3e/2)(12/13) ≈ 1.38
To find the directional derivative of the function f(x, y) = 3e^x sin(y) at the point (0, 1/3) in the direction of the vector v = (-5, 12), we first need to calculate the gradient of the function, which is a vector containing the partial derivatives with respect to x and y.
The partial derivative with respect to x:
∂f/∂x = 3eˣ sin(y)
At point (0, 1/3), ∂f/∂x = 3e⁰ sin(1/3) = 3 sin(1/3)
The partial derivative with respect to y:
∂f/∂y = 3eˣ cos(y)
we first need to find the gradient of f at that point:
∇f = [∂f/∂x, ∂f/∂y] = [3ex sin(y), 3ex cos(y)]
Evaluated at (0,1/3), we get:
∇f(0,1/3) = [0, 3e/2
At point (0, 1/3), ∂f/∂y = 3e⁰ cos(1/3) = 3 cos(1/3)
So the gradient vector is ∇f = (3 sin(1/3), 3 cos(1/3)).
Next, we need to normalize the direction vector v:
|v| = √((-5)² + (12)²) = 13
Normalized vector v: (-5/13, 12/13)
Finally, we calculate the directional derivative (D_vf) as the dot product of the gradient vector and the normalized direction vector:
D(vf)= ∇f • (-5/13, 12/13) = (3 sin(1/3) × (-5/13)) + (3 cos(1/3) × (12/13))
D(vf) = (-15/13) sin(1/3) + (36/13) cos(1/3)
That is the directional derivative of the function at the given point in the direction of the vector v
Duf(0,1/3) = ∇f(0,1/3) · u = [0, 3e/2] · [-5/13, 12/13] = (3e/2)(12/13) ≈ 1.38
Therefore, the directional derivative of f(x, y) in the direction of v at the point (0,1/3) is approximately 1.38.
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This question is kinda confusing :(
state the parent function of g(x) and describe how the graph of (x) is related to its parent function (questions 3,4,5)
The parent functions of the function equations are x³, x⁴ and x²
Stating the parent functionsThe transformed functions 3 - 5 represent the given parameter
To derive the parent functions, we need to determine the degree of the transformed and use this degree as a guide
By definition, the degree of a function is the highest power in the function
So, we have
Question 3
g(x) = (1/2x + 2)³ + 5
The degree here is 3
This means that the function is a cube function
The parent function of a cube function is y = x³
So, the parent function is g(x) = x³
Question 4
g(x) = x⁴ - 4
The degree here is 4
This means that the function is a polynomial function shifted down by 4 units
The parent function of this is y = x⁴
So, the parent function is g(x) = x⁴
Question 5
g(x) = 1/2(x - 1)² - 4
The degree here is 2
This means that the function is a quadratic function
The parent function of a quadratic function is y = x²
So, the parent function is g(x) = x²
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two players simultaneously toss (independently) a coin each. both coins have a chance of heads p. they keep on performing simultaneous tosses till they end up with different. what is the expected number of trials (simultaneous tosses) before they stop?
The expected number of tosses until two players get different results when simultaneously tossing a coin each with a chance of heads p is (1-2p)/(2p-2p²).
The probability that both players get the same result (either both heads or both tails) on any given toss is p² + (1-p)² = 2p² - 2p + 1. The probability that they get different results (one head and one tail) is therefore 1 - (2p² - 2p + 1) = 2p - 2p².
Let E be the expected number of tosses until they end up with different results. If they get different results on the first toss, the game ends after 1 toss.
Otherwise, they have to repeat the process again, and the expected number of tosses is increased by 1. Therefore, we can express E in terms of the probabilities of getting different or same results on the first toss
E = (2p - 2p²)1 + (1 - 2p + 2p²)(1 + E)
Simplifying, we get
E = 1 + 2pE - 2p + 2p²
Rearranging and solving for E, we get
E = (1 - 2p) / (2p - 2p²)
Therefore, the expected number of tosses before the players end up with different results is (1 - 2p) / (2p - 2p²).
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A company claims that the mean monthly residential electricity consumption in a certain region is more than 880 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 64 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 124 kWh. At a = 0. 01, can you support the claim? Complete parts (a) through (e)
(a) State the null and alternative hypotheses.
Null Hypothesis: The mean monthly residential electricity consumption in the region is less than or equal to 880 kWh.
Alternative Hypothesis: The mean monthly residential electricity consumption in the region is greater than 880 kWh.
(b) Determine the test statistic.
We need to use a one-tailed t-test because the alternative hypothesis is one-tailed.
t = (x - μ) / (σ / √n) = (900 - 880) / (124 / √64) = 2.581
(c) Find the p-value.
Using a t-table or a calculator, we can find the p-value associated with a t-value of 2.581 and 63 degrees of freedom: p-value = 0.007
(d) State the conclusion.
The p-value is less than the significance level of 0.01, which means that we reject the null hypothesis. We have enough evidence to support the claim that the mean monthly residential electricity consumption in the region is more than 880 kWh.
(e) Interpret the conclusion in the context of the problem.
Based on the sample data, we can conclude that the mean monthly residential electricity consumption in the region is likely to be greater than 880 kWh. However, we cannot say for sure whether this conclusion would hold true for the entire population.
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1. A company is testing a new energy drink. Volunteers are asked to rate their energy one hour
after consuming a beverage. Unknown to them, some volunteers are given the real energy
drink and some are given a placebo-a drink that looks and tastes the same, but does not have
the energy-producing ingredients. Show your work using the following list of random digits to
assign each participant listed either the real drink or the placebo.
We can assign each participant the real drink or placebo by assigning a drink based on the next random digit.
How to assign to the real and placebo ?One method for assigning participants their drink is to utilize a basic rule predicated on the oddness or evenness of specific digits. In this scenario, you may reserve “odd” numbers strictly for real drinks and “even” numbers exclusively for placebos.
To execute this procedure, we will begin at the left-hand side of our precomputed list of randomized digits and work to identify the subsequent digit in order to assign each participant with their corresponding drink:
Abby - Real (6)Barry - Placebo (9)Callie - Real (4)Dion - Placebo (2)Ernie - Real (9)Falco - Placebo (8)Garrett - Real (6)Hallie - Placebo (1)Indigo - Real (1)Jaylene - Real (6)How to assign numbers to each division ?Assign numbers to each of the houses in every subdivision, ranging from 1 through to 100. Utilize an online random number generator or a table containing random numbers within the range of 1 and 100 to construct a list of such randomly generated figures.
Choose the initial 20 unique figures from said list for both subdivisions selectively. Proceed with visiting those particular homes denoted by these chosen numbers, then examine and test their water sources accordingly.
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Find the area of a regular decagon with an apothem of 6. 2 units. Round your answer to the nearest hundredth.
The approximate area of the regular decagon, rounded to the nearest hundredth, is 190.78 square units.
What is the area of a regular decagon with an apothem of 6.2 units, rounded to the nearest hundredth?To find the area of a regular decagon with an apothem of 6.2 units, we can use the formula:
Area = (1/2) × apothem × perimeter
To find "s", we can use the fact that a regular decagon can be divided into 10 congruent triangles, where each triangle has an interior angle of 144 degrees. We can use trigonometry to find the length of the side "s" using one of these triangles:
tan(72) = (s/2.6)s = 2.6 × tan(72)s ≈ 6.16Now we can find the perimeter of the decagon:
Perimeter = 10 × sPerimeter = 10 × 6.16Perimeter ≈ 61.62Finally, we can substitute the apothem and perimeter into the formula to find the area:
Area = (1/2) × 6.2 × 61.62Area ≈ 190.78Rounding to the nearest hundredth, the area of the regular decagon is approximately 190.78 square units.
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A cylinder has a radius of 2 ft and a hight of 6 ft. What is the total surface area using 3.14 as pi.
The total surface area of a cylinder is the sum of the areas of its top and bottom circles, along with the area of its lateral surface (the curved surface that connects the two circles).
The formula for the lateral surface area of a cylinder is:
Lateral surface area = 2πrh
where r is the radius of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.
The formula for the area of a circle is:
Area of circle = πr^2
Using these formulas, we can calculate the total surface area of the cylinder as follows:
Area of top and bottom circles = 2 × π × r^2
= 2 × 3.14 × 2^2
= 25.12 square feet
Lateral surface area = 2 × π × r × h
= 2 × 3.14 × 2 × 6
= 75.36 square feet
Total surface area = Area of top and bottom circles + Lateral surface area
= 25.12 + 75.36
= 100.48 square feet
Therefore, the total surface area of the cylinder is 100.48 square feet.
In a student poll of 38 boys and 42 girls,
15 boys and 20 girls said they like science
fiction books. Based on this information,
Answer:40-45 percent
Step-by-step explanation:
explenation
If Ethan’s monthly expenses are $1160 and his debt to income ratio is 0. 8, what is his monthly salary?
Ethan's monthly salary is $1450.
Ethan's monthly salary, we can use the debt to income ratio formula, which is calculated by dividing monthly debt expenses by monthly income.
Given:
Monthly expenses = $1160
Debt to income ratio = 0.8
Let's assume Ethan's monthly salary as S.
We can set up the equation using the debt to income ratio formula:
Debt to income ratio = Monthly expenses / Monthly income
0.8 = $1160 / S
To solve for S (monthly salary), we can rearrange the equation:
S = $1160 / 0.8
Dividing $1160 by 0.8 gives us:
S ≈ $1450
Therefore, Ethan's monthly salary is approximately $1450.
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252-(18x8)
Ross says that he does not need parenthesis. Is he correct?
Yes
Step-by-step explanation:PEMDAS explains the order that operations are done.
PEMDAS
PEMDAS stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. This is the order of operations. Always start with operations inside parentheses, then exponents, then multiplication and division, and the last operations are addition and subtraction. In the problem above, parentheses come first, so means start with 18 x 8 and then do subtraction afterward.
Without Parentheses
Take the new expression, 252 - 18 x 8. Following the order of operations, multiplication goes first. This means multiply 18 x 8 first and then subtract. This order of operations is the same with or without parentheses. Since multiplication comes before subtraction, parentheses are not needed.
Can someone please help me ASAP? It’s due tomorrow.
Answer: m*n
Step-by-step explanation:
based on a random sample of 1505 us adults, we built a confidence interval for the proportion of us adults that say the country's best days are still ahead The 95% confidence interval is from 0.588 to 0.612. Select the statement below that correctly interprets this confidence interval. We are 95% confident that the sample proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612 We are 95% confident that the population proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612. 95% of the population proportions of US adults that believe owning a house is very important to their quality of life will fall within this interval. The probability that the population proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612 is 0.95.
The correct interpretation of the given confidence interval is: We are 95% confident that the population proportion of US adults that say the country's best days are still ahead is between 0.588 and 0.612.
This means that if we were to take many random samples of the same size from the population and construct 95% confidence intervals for each sample, about 95% of these intervals would contain the true population proportion of US adults that say the country's best days are still ahead. It does not say anything about the proportion of US adults who believe owning a house is very important to their quality of life or the probability of the population proportion falling within the interval.
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(−2x−1)(−3x 2 +6x+8)
solve for the value of x .
80(x+15)
=60
Answer:
x = [tex]\frac{-57}{4}[/tex]
Step-by-step explanation:
solve for the value of x .
80(x+15)=60
80(x + 15) = 60
80x + 1200 - 60 = 0
80x + 1140 = 0
80x = -1140
x = -1140/80
x = [tex]\frac{-57}{4}[/tex]
Answer:
-14.25
Step-by-step explanation:
Given: 80 (x+15) = 60
Solution: On opening the brackets, we get
> 80x + 80 * 15 = 60
> 80x + 1200 = 60
Then, taking 1200 to the other side of the equation,
80x = 60 - 1200
Therefore, 80x = -1140
Now, dividing both sides by 80, we get:
80x/80 = -1140/80
So, x= -14.25
Hope this helps!
Untitled Question
14 points
2 Chelsea sprinted 120 yards in 18. 5
seconds. One meter is approximately equal
to 1. 1 yards. Which measurement is closest
to the number of meters Chelsea sprinted?
F 109. 1 yd H 64. 9 yd
G 132 yd J 90. 6 yd
7. 4E
G
The measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.
To determine the number of meters Chelsea sprinted, we need to convert the distance she sprinted from yards to meters.
Given:
Chelsea sprinted 120 yards.
Conversion:
1 meter is approximately equal to 1.1 yards.
To convert yards to meters, we divide the distance in yards by the conversion factor:
120 yards / 1.1 yards/meter ≈ 109.1 meters.
Therefore, the measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.
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During a survey of 240 people who own cats, 188 people preferred cat food A to cat food B. Based on these results, in the second survey of 60 people, how many people can be predicted to prefer cat food A?
Based on the first survey results, we can predict that around 47 people in the second survey of 60 people will prefer cat food A over cat food B.
Based on the results of the first survey, 188 out of 240 people preferred cat food A over cat food B. To predict the preference for cat food A in the second survey, we can calculate the proportion of people who preferred cat food A in the first survey and apply it to the sample size of the second survey.
First, find the proportion of people preferring cat food A in the first survey:
Proportion = (Number of people preferring cat food A) / (Total number of people surveyed)
Proportion = 188 / 240
Proportion ≈ 0.7833
Now, apply this proportion to the second survey's sample size of 60 people:
Predicted preference = Proportion × (Sample size of the second survey)
Predicted preference = 0.7833 × 60
Predicted preference ≈ 47
Therefore, based on the first survey results, we can predict that around 47 people in the second survey of 60 people will prefer cat food A over cat food B.
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QUESTION 5/10
24-136
If Chris has car liability insurance, what damage would he be covered for?
HATA
EAN
A. Repairing damage to his own car that was caused by storms
or theft.
C. Repairing damage to his own car that was caused by
another driver who does not have car insurance.
B. Repairing damage to other cars if he got into an accident
that was his fault.
D. Repairing damage to his own car if he got into an accident
that was his fault
Answer:
Step-by-step explanation:
Pythagorean theorem
1. a surveyor walked eight miles north, then three miles west. how far was she from her starting point?
2. a four meter ladder is one meter from the base of a building. how high up the building will the ladder reach?
3. what is the longest line you can draw on a paper that is 15 cm by 25 cm?
4. how long a guy wire is needed to support a 10 meter tall tower if it is faster
the foot of the tower?
5. the hypotenuse of a right triangle is twice as long as one of its legs.the other leg is nine inches long. find the length of the hypotenuse.
The distance traveled by the surveyor is √73 miles. The height of the building that the ladder reaches is √15 meters. The longest line that can be drawn is 5√34 cm. The length of the guy wire that is needed is 5√5 meters. The length of the hypotenuse of the given right triangle is 6√3 inches.
In a right-angled triangle that is a triangle with one of the angles with magnitude 90° following is true according to Pythogaras' Theorem:
[tex]A^2=B^2+C^2[/tex]
where A is the hypotenuse
B is the base
C is the height
1. According to the question,
the distance between the starting and the ending point is the hypotenuse of a right-angled triangle
B = 8 miles
C = 3 miles
A = √(64 + 9)
= √73 miles
2. Hypotenuse in the given question is the length of the ladder, thus,
A = 4 m
B = 1 m
16 = 1 + [tex]C^2[/tex]
C = √15 meters
3. The longest line that can be drawn on the paper is described as the hypotenuse of the triangle
C = √225 + 625
= 5√34 cm
4. The length of the guy wire is the hypotenuse of the triangle.
C = √100 + 25
= 5√5 meters
5. Let the base of the triangle be x
the hypotenuse be 2x
height = 9 inches
[tex]4x^2=x^2[/tex] + 81
[tex]3x^2[/tex] = 81
x = 3√3 inches
Hypotenuse = 2x = 6√3 inches
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The sixth-graders at Ayana's school got to choose between a field trip to a museum and a field trip to a factory. 39 sixth-graders picked the museum. If there are 50 sixth-graders in all at Ayana's school, what percentage of the sixth-graders picked the museum?
Answer:
78% of sixth-graders picked a field trip to a museum.
Step-by-step explanation:
39 out of 50 kids picked the museum field trip. This is 39/50. We can change this like so:
39/50 × 2/2
= 78/100
78/100 is 78% (because percent literally means "per hundred)
Another way is to just divide. 39/50 means 39 ÷ 50.
39 ÷ 50 is .78 then times by 100 to change to a percent. This works for all kinds of fractions.
78% of sixth graders at Ayana's school selected the museum field trip.
Consider the following 8 numbers, where one labelled
x
is unknown. 32
,
46
,
46
,
x
,
35
,
9
,
4
,
38
Given that the range of the numbers is 55, work out 2 values of
x
Two possible values of x are 10 and 40.
To find two possible values of x, we need to first determine the highest and lowest numbers in the set.
Highest number: 46
Lowest number: 4
To get a range of 55, we need the highest number minus the lowest number to equal 55.
46 - 4 = 42
But we know that there are 8 numbers in the set, so the range must be spread out over those 8 numbers. To get an idea of how much each number should increase, we can divide 42 by 7 (the number of gaps between the numbers) to get an average increase of 6.
Now we can use this average increase to find two possible values of x.
1) If x is 6 more than the lowest number (4 + 6 = 10), then the set becomes:
4, 9, 10, 32, 35, 38, 46, 46
And the range is:
46 - 4 = 42
2) If x is 6 less than the highest number (46 - 6 = 40), then the set becomes:
4, 9, 35, 38, 40, 46, 46, 32
And the range is:
46 - 4 = 42
Therefore, two possible values of x are 10 and 40.
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19. Write a proof in two-column form for the Corresponding Angles Theorem. Given: pill q Prove: m/1 = m/5 Statements Pll q given Reasons aler
Corresponding Angles Theorem: If a transversal intersects two parallel lines, then the corresponding angles formed are congruent.
Statements Reasons
1. ∠1 and ∠3 are corresponding angles Given
2. m//n Given
3. ∠1 and ∠2 are congruent Alternate Interior Angles Theorem
4. ∠2 and ∠3 are congruent Alternate Interior Angles Theorem
5. ∠1 ≅ ∠2 and ∠2 ≅ ∠3 Substitution (from statements 3 and 4)
6. ∠1 ≅ ∠3 Transitive Property of Congruence
How to explain the TheoremIn this proof, we start by stating that ∠1 and ∠3 are corresponding angles, which is given in the problem statement. We also know that m and n are parallel lines, which is also given.
Then, we apply the Alternate Interior Angles Theorem to show that ∠1 and ∠2, as well as ∠2 and ∠3, are congruent.
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Please i cant find the answer to this
Answer:
9
Step-by-step explanation:
First, let's move the variables to one side and the numbers to the other side:
[tex]\frac{2}{3}b+5=20-b\\[/tex]
subtract 5 from both sides:
[tex]\frac{2}{3}b=15-b\\[/tex]
add b to both sides:
[tex]\\1\frac{2}{3}b=15\\[/tex]
divide both sides by [tex]1\frac{2}{3}[/tex]:
[tex]b=9[/tex]
Hope this helps :)
A triangle with area 28 square inches has a height that is six less than twice the width. Find the height and width of the triangle. [Hint: For a triangle with base b and height h , the area, A , is given by the formula
The height of the triangle is 8 inches and the width is 7 inches.
Find the height and width of a triangle with area 28 square inches, where the height is six less than twice the width.Let's start by using the formula for the area of a triangle:
A = (1/2)bh
where A is the area of the triangle, b is the base, and h is the height.
We are given that the area of the triangle is 28 square inches, so we can write:
28 = (1/2)bh
Next, we are given that the height h is six less than twice the width w. In other words:
h = 2w - 6
Now we can substitute this expression for h into the formula for the area:
28 = (1/2)bw(2w - 6)
Simplifying this equation, we get:
56 = bw(2w - 6)
28 = w(w - 3)
w^2 - 3w - 28 = 0
We can solve this quadratic equation using the quadratic formula:
w = [3 ± √ ([tex]3^2[/tex] - 4(1)(-28))] / 2
w = [3 ± √ (121)] / 2
w = (3 + 11) / 2 or w = (3 - 11) / 2
w = 7 or w = -4
Since a negative width doesn't make sense in this context, we can ignore the second solution and conclude that the width of the triangle is 7 inches.
Now we can use the expression for h in terms of w to find the height:
h = 2w - 6
h = 2(7) - 6
h = 8
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Harvey won some money on a
scratch-and-win ticket. Then, he won a
$2 bonus. When he arrived at the counter,
he noticed that he had also won a "triple
your winnings" ticket. As Harvey was
cashing in his prize, the cashier told him
he was the 100th customer, so his total
winnings were automatically doubled. Write two algebraic expressions to
describe Harvey’s winnings
First algebraic expression: x + 2. Second algebraic expression: 6x + 12.
We can represent Harvey's winnings using algebraic expressions.
Let's use the variable 'x' to represent the amount Harvey won on the scratch-and-win ticket. Harvey then won a $2 bonus, so we add 2 to 'x':
1) x + 2
Next, Harvey won a "triple your winnings" ticket, so we need to multiply the current winnings by 3:
2) 3(x + 2)
Finally, as the 100th customer, Harvey's total winnings were doubled:
3) 2 * 3(x + 2)
So, the two algebraic expressions to describe Harvey's winnings are:
1) x + 2 (initial winnings with the $2 bonus)
2) 2 * 3(x + 2) (total winnings after tripling and doubling)
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Kevin and his family are going camping.the tent has a width of 20ft,and the sides are 12ft long.how high is the tent in the middle?round to nearest tenth
Therefore , the solution of the given problem of unitary method comes out to be length (12 ft) that is less than its width (20 ft), which is the case with the tent.
What is a unitary method?The well-known simple approach, real variables, and any crucial elements from the very initial And specialised inquiry can all be used to finish the work. Customers may then be given another chance to try the product in response. If not, significant impacts on our understanding of algorithms will vanish.
Here,
The hypotenuses of two right triangles created by halving the triangle can be viewed as the two sides of the triangle. Next, we have
=> h² = (12/2)² - (20/2)²
=> h² = 36 - 100
=> h² = -64
The fact that the outcome is bad indicates that we made a mistake. In this instance, it is because a legitimate triangular prism cannot be formed using the specified dimensions.
A triangular prism cannot have a length (12 ft) that is less than its width (20 ft), which is the case with the tent.
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