Answer:
530.7 rpm3334.7 rad/minStep-by-step explanation:
You want the angular speed in RPM and in radians per minute for a truck wheel 38 inches in diameter traveling at 60 mph.
RevolutionsThere are 60 minutes in an hour, so a speed of 60 mi/h is a speed of ...
[tex]\dfrac{60\text{ mi}}{1\text{ h}}\times\dfrac{1\text{ h}}{60\text{ min}}\times\dfrac{5280\text{ ft}}{1\text{ mi}}=5280\text{ ft/min}[/tex]
The distance traveled for 1 revolution of the wheel is equal to its circumference:
C = πd
C = π(38 in)/(12 in/ft) = (19/6)π ft ≈ 9.948 ft
Then the number of revolutions in 5280 ft is ...
(5280 ft/min)/(9.948 ft/rev) ≈ 530.7 rev/min
The wheels make about 530.7 revolutions per minute.
RadiansEach revolution is an angle of 2π radians, so the angular speed is ...
ω = 530.7 rev/min × 2π rad/rev
ω = 3334.7 rad/min
can you solve this question?
x=?
the value of this limit=?
y=?
The derivative of f(x) = 3·x² + 7·x + 6, at x = 4, f'(4) is presented as follows;
f'(4) is the limit as x → 4 of the expression 6·x + 7.
The value of this limit is 31
The equation of the tangent line to the parabola y = 3·x² + 7·x + 6 at the point (4, 82) is y = 31·x - 42
What is the derivative of function?The derivative of a function is a measure of how much the output values of the function changes as the input value is changed. The derivative is the limit of the difference quotient as the change in input approaches zero. The limit is the instantaneous rate of change of the function at a specified input variable value.
The value of f'(4) using the definition of derivative, can be obtained using the following definition;
f'(x) = lim(h → 0)[f(x + h) - f(x)]/h
Plugging in x = 4, and f(x) = 3·x² + 7·x + 6, we get;
f'(4) = lim(h → 0)[f(4 + h) - f(4)]/h
f'(4) = lim(h → 0)[3·(4 + h)² + 7·(4 + h) + 6 - (3·(4)² + 7·(4) + 6)]/h
f'(4) = lim(h → 0)[(3·h + 31)·h]/h
f'(4) = lim(h → 0)[(3·h + 31)]
Therefore;
f'(4) = lim(h → 0)[(3·h + 31)] = 31
f'(4) = 31
Therefore; f'(4) is the limit as x → 4 of the expression 6·x + 7, therefore. The value of this limit is 31
The point-slope form of the equation of a line can be used to find the equation of the parabola as follows;
y - y₁ = m·(x - x₁)
The point (x₁, y₁) and the slope of the line is m
The point on the parabola of the tangent is; (4, 82)
The slope of the tangent line at x = 4, f'(4) = 31
The tangent equation is therefore;
y - 82 = 31·(x - 4)
y = 31·(x - 4) + 82 = 31·x - 42
The equation of the tangent line to the parabola, y = 3·x² + 7·x + 6, at the point (4, 82) is; y = 31·x - 42
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Use point-slope form to write the equation of a line that passes through the point (−11,−13) with slope -2/3 .
Answer:
y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - [tex]\frac{2}{3}[/tex] and (a, b ) = (- 11, - 13 ) , then
y - (- 13) = - [tex]\frac{2}{3}[/tex] (x - (- 11) ) , that is
y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)
Is 4p + 7n+ 3p and 14pn equal
Answer:
yes
Step-by-step explanation:
4p+ 3p= 7p
7p+7n=14pn
52. The height of an isosceles triangle is 8 feet. The base of the isosceles triangle is 23 feet. What is the
measure of one of the base angles of the triangle? Round your answer to the nearest degree
As a result, the triangle's base angle is roughly 72 °
What is isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides.. Sometimes it is said that it must have exactly two sides that are the same length, and other times it must have at least two sides that are the same length, with the latter version adding the equilateral triangle as an exception.
Let x represent the size of one of the triangle's base angles.
Hence, we may apply the following equation to determine x:
angle = ((b/2)/h) arccos
where h is the height and b is the length of the base of one of the equal sides.
B in this instance equals 23 feet, while h is 8 feet.
Filling up the formula with these values:
angle = ((23/2)/8) arccosine
angle ≈ 72°
Consequently, one of the triangle's base angles is roughly 72 °
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Use the definition of a logarithm to solve the equation. ln ( − 5 z ) = ln ( z^ 2 − 7 z )
To solve for z, we can subtract 7 from both sides to get -5/z = -6. Finally, we can multiply both sides by -1 to get z = -7. Therefore, the solution to this equation is z = -7.
A logarithm is an equation that expresses the relationship between an exponent and its base. In this equation, we have two logarithms, ln (-5z) and ln [tex](z^2-7z)[/tex], which are both equal to each other. To solve this equation, we can use the properties of logarithms to isolate the variable. First, we can rewrite the equation as ln (-5z) - ln [tex](z^2-7z)[/tex]= 0, which can then be simplified to ln (-5/z+7) = 0. We can then take the inverse of both sides to get -5/z+7 = 1. To solve for z, we can subtract 7 from both sides to get -5/z = -6. Finally, we can multiply both sides by -1 to get z = -7. Therefore, the solution to this equation is z = -7.
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A convenience store sold 14 half-gallon containers of milk and 28 quars of orange juice. Write a sentence comparing the total number of gallons of milk sold to the total number of gallons of orange juice sold. Explain how you know that your comparison is correct without multiplying.
Who ever answers nicely gets 40 points
Answer:
The total number of gallons of milk sold is equal to the total number of gallons of orange juice sold. This is because there are 2 quarts in a half-gallon, so the 14 half-gallon containers of milk sold is equal to 28 quarts. Therefore, the total amount of milk sold is the same as the total amount of orange juice sold, which is 28 gallons.
f(x)=3x^3+5x^2-11x+3
Polynomials are functions that are constructed from a sum of powers of the independent variable x, multiplied by coefficients. In this case, we have powers of x from 0 to 3, and the coefficients are 3, 5, -11, and 3.
To evaluate the function for a particular value of x, we substitute that value in place of x and perform the necessary arithmetic. For example, to find f(2), we substitute x = 2 in the expression for f(x):
f(2) = 3(2)^3 + 5(2)^2 - 11(2) + 3
= 24 + 20 - 22 + 3
= 25
Therefore, f(2) = 25. We can similarly evaluate the function for other values of x.
Find the product.
a.
b.
8 15 19
7 -4 12
1
-15 19
-12-19
0-13
-600 -760
-114 106
-120 -114
-760
106
C.
d.
-354 -406
-111 27
57 71
3
17
The product of the values can be obtained by multiplying as follows:
1. 8 * 15 * 19 = 2280
2. 7 * -4 * 12 = -41
How to find the product of a valueTo find a product simply means to multiply the figures in order to arrive at a value. The question asks that we get the product of some values. To get these values, we are to multiply the numbers given to arrive at the answers.
It is possible to multiply two, three, or more values at the same time. So, another word that is used in place of multiplication is "product" as is the case in the question given.
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A study by the department of education of
a certain state was trying to determine the
mean SAT scores of the graduating high
school seniors. The study examined the
scores of a random sample of 250
graduating seniors and found the mean
score to be 538 with a standard deviation
of 96. Determine a 95% confidence
interval for the mean, rounding all values
to the nearest tenth.
The 95% confidence interval for the mean SAT scores is CI = (526.2, 549.8)
What is confidence interval?It is a statistical tool used in inferential statistics to estimate the unknown population parameter based on the sample data.
According to question:To find the 95% confidence interval for the mean SAT scores, we can use the formula: CI
where:
sample mean (538)
population standard deviation (96)
n = sample size (250)
z = z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96)
Plugging in the values, we get:
CI = 538 ± 1.96*(96/√250)
Simplifying, we get:
CI = 538 ± 11.8
Rounding to the nearest tenth, the 95% confidence interval for the mean SAT scores is:
CI = (526.2, 549.8)
For example, a 95% confidence interval for a population mean means that if we were to repeat the sampling process multiple times and calculate a 95% confidence interval each time, about 95% of the intervals would contain the true population mean.
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can you pls answer this for me im really struggling with this
Answer:
The slope of this line is 2.
Step-by-step explanation:
Start at (1, 0). Go up 4 units, then right 2 units. You will end at (3, 4). The slope of this line is 2.
How do you solve the equation absolute value of K +7 equals three
Answer:
k=-4
Step-by-step explanation:
k+7=3
take way 7 from both sides
k=-4
A sine function has the following key features:
Period = 4
Amplitude = 3
Midline: y=−1
y-intercept: (0, -1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
The resulting graph should have a period of 4, an amplitude of 3, a midline of y=-1, and no reflection over the x-axis.
What are the period and amplitude of a graph?
The period of a function is the smallest distance over which the function repeats itself. In other words, it is the length of one complete cycle of the function. For a sine or cosine function of the form f(x) = a sin(bx) or f(x) = a cos(bx), the period is given by 2π/b.
The most simple sine function considered the parent function, is:
y = sin(x)
That function has:
Midline, also known as rest or equilibrium position: y = 0
Minimum: - 1
Maximum: 1
Amplitude: the distance between a minimum or a maximum and the midline = 1
period: the interval of repetition of the function = 2π
The more general sine function is:
y = Asin(Bx + C) + D
That function has:
Midline: y = D (it is a vertical shift from the parent function)
Minimum: - A + D
Maximum: A + D
Amplitude: A
period: 2π/B
phase shift: C (it is a horizontal shift of from the parent function)
Now, you have to draw the sine function with the given key features:
Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
Amplitude, A = 3
midline y = - 1 ⇒ D = - 1
y-intercept = (0, -1)
Substitute the know values and use the y-intercept to find C:
y = 3sin(2x/π + C) -1
Substitute (0, -1)
-1 = 3sin(2(0)/π + C) -1
3sin(C) = 0
sin(C) = 0
C = 0
Hence, the function to graph is:
y = 3sin(2x/π ) -1
To draw that function use this:
Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
Minima: 3(-1) - 1 = - 3 - 1 = -4
y-intercept: (0, - 1)
x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
first point of the midline: (0, -1) it is the same y-intercept
Hence, the resulting graph should have a period of 4, an amplitude of 3, a midline of y=-1, and no reflection over the x-axis.
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Valeria conducted a survey at the local mall. She
sat and counted 50 people exiting the mall and
noted how many of them were carrying bags of
things they purchased. Using this information,
predict how many of the 4,800 visitors to the
mall on this day purchased something.
With Bag
37
Without Bag
13
We can use the proportion of people carrying bags from the sample of 50 people to estimate the number of visitors who purchased something out of the total 4,800 visitors to the mall.
The proportion of people carrying bags in the sample is:
37/50 = 0.74
This means that 74% of the sample of 50 people were carrying bags.
To estimate the number of visitors who purchased something out of the total 4,800 visitors, we can multiply the proportion by the total number of visitors:
0.74 x 4,800 = 3,552
Therefore, we can predict that approximately 3,552 visitors out of the total 4,800 visitors purchased something on that day.
The outer door of an airplane hangar is in the shape of a parabola. The door is 120 feet wide and 90 feet high. (i)Find the equation describing the door’s shape. (3) (ii)If you are 6 feet tall, how far must you stand from the edge of the door to keep from hitting your head? (2)
Step-by-step explanation:
So this will be an upside down parabola....the leading coefficient (for x^2 ) will be negative ...
Vertex at 60,90 <=====given
Vertex form y = a (x-h) ^2 + k
y = a ( x -60)^2 + 90 to find 'a' substitute in a point on the parabola...I'll use 0,0
0 = a ( 0-60)^2 + 90 shows a = - 1/40
so the equation is y = -1/40 ( x -60)^2 + 90
( or expanded to y= -1/40 x^2 + 3x )
Solve for 'x' when y = 6 ft ( to keep from hitting your head)
6 = -1/40x^2 +3x
0 = -1/40 x^2 + 3x - 6 Use Quadratic Formula to find x = ~ 2 feet
A laboure digs a pit 6.5 m long, 3 m wide and 1.6 m deep. How much earth is du. out from it ?
Answer:
Volume =
Step-by-step explanation:
Volume = length x width x depth
Volume = (6.5 x 3 x 1.6)m
Volume = 31.2m
Will give brainly
Trig
Step-by-step explanation:
angle c = 180 -19 - 139 = 22 degrees ( interior angles of a triangle sum to 180 degrees)
Now you can use law of sines to find the missing side lengths
12 / sin 22 = DC /sin19
DC = sin 19 * 12 / sin 22 = 10.4 units
12/sin 22 = BC / sin 132
BC = sin132 * 12 / sin 22 = 23.8 units
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please try to answer all questions below** TYYY
1.The equation that represents the proportional relationship is y = 4x + 3.
2. The corresponding equation that represents a proportional relationship is y = (1/5)x.
3. y = 7/2x.
4. when y = 21 is x = 6.
5. y = 8 is x = 3.33.
What is slope?The slope of a function is the rate of change in the function's output (y-value) relative to the change in its input (x-value).
The equation that represents a proportional relationship is y = mx + b, where m is the slope of the equation.
In this equation, x and y are in direct proportion.
1.The equation that represents the proportional relationship is y = 4x + 3. This equation is in the form of y = mx + b, with m being the coefficient of x, which is 4, and b being the constant, which is 3.
2. The corresponding equation that represents a proportional relationship is y = (1/5)x.
This equation is in the form of y = mx + b, with m being the coefficient of x, which is 1/5, and b being the constant, which is 0.
3. The equation that represents this relationship is y = 7/2x.
This equation is in the form of y = mx + b, with m being the coefficient of x, which is 7/2, and b being the constant, which is 0.
4. The value of x when y = 21 is x = 6.
This is because the equation representing the proportional relationship is y = 7/2x, and
when y = 21, 21 = 7/2x,
so x = 6.
5. The value of x when y = 8 is x = 3.33.
This is because the equation representing the proportional relationship is y = 12/5x, and when y = 8, 8 = 12/5x, so x = 3.33.
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According to 2015 census data, 40 percent of Colorado residents were born in
Colorado. If a sample of 250 Colorado residents is selected at random, what is
the standard deviation of the number of residents in the sample who were born in
Colorado?
60
12.23
0.24
7.75
10
Option D is correct. The Standard Deviation of the number of residents in the sample who were born in colorado is 7.75
How to find Standard Deviation of a given sample ?
Let x be the standard deviation for the sample, n =250
p = probability of success, q = probability of failure = 1 - p
q = 1 - 0.40 = 0.60
[tex]x = \sqrt{n \times p \times q}\\= \sqrt{250 \times 0.40 \times 0.60}\\= \sqrt{60}\\=7.75[/tex]
Therefore, Option D is correct. Standard Deviation is 7.75.
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option (d) the standard deviation of the number of residents in the sample who were born in Colorado is approximately 7.75.
what is standard deviation formula?The standard deviation of a binomial distribution is given by the formula:
σ = √(np(1-p))
binomial distribution with parameters n = 250 and p = 0.4—where n is the sample size and p is the probability of success—can be used to approximate the distribution of the number of Colorado residents who were born in Colorado in a sample of 250 residents.
Substituting n = 250 and p = 0.4, we get:
σ = √(250 x 0.4 x 0.6) ≈ 7.75
Therefore, the standard deviation of the number of residents in the sample who were born in Colorado is approximately 7.75.
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What is 231 3/25 x .75
to follow the order of operations or PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction) to ensure that we get the correct answer. [tex]231 3/25 \times 0.75 = 4348.5 / 75.[/tex]
What is the improper fraction?To solve this multiplication problem, we can first convert the mixed number 231 3/25 to an improper fraction:
[tex]231 3/25 = (25 \times 231 + 3) / 25 = 5778/25[/tex]
Then, we can multiply this fraction by 0.75:
[tex]5778/25 \times 0.75 = (5778 \times 0.75) / 25[/tex]
To simplify this fraction, we can multiply the numerator and denominator by 3:
[tex](5778 \times 0.75 \times 3) / (25 \times 3) = 4348.5 / 75[/tex]
Therefore, [tex]231 3/25 x\times 0.75 = 4348.5 / 75.[/tex]
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Simplify (Write each expression without using the absolute value symbol)
|x+3| if x>5
we can simplify |x+3| to x+3 when x is greater than 5. This is the final answer.The absolute value of a number is the distance of the number from zero on a number line, regardless of whether the number is positive or negative.
For example, the absolute value of -5 is 5, because 5 is the distance of -5 from zero on the number line.
In this problem, we are asked to simplify the expression |x+3| without using the absolute value symbol. We are also given the condition that x is greater than 5.
When x is greater than 5, we know that x+3 is also greater than 5+3=8. This is because x is already greater than 5, and adding 3 to it makes it even larger. So, we can say that x+3 is positive when x is greater than 5.
Now, let's consider what the absolute value of x+3 means in this context. Since x+3 is positive when x is greater than 5, the absolute value of x+3 is just x+3 itself. This is because the absolute value of a positive number is just the number itself.
Therefore, we can simplify |x+3| to x+3 when x is greater than 5. This is the final answer.
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Which table shows values for the equation y=3x+2
?
Answer:
Answer is option D
Step-by-step explanation:
Hope this helps:)
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x=14
Step-by-step explanation:
80+58=138
180-138=42
42÷3=x
14=x
Answer:
x= 14
Step-by-step explanation:
80 + 58 = 138°
A triangle has 180°
180-138= 42°
Put into equation
42=3x
42/3=14
X=14
Use the Quadratic Formula to solve the equation x² - 6x = - 18.
x = −3+3i or x = -3-3i
x = −3+3√√3 or x = -3-3√3
x = 3 + 3i or x = 3 - 3i
x = 3 + 3√3 or x = 3−3√√3
These are the two complex solutions to the equation [tex]x^{2} - 6x = -18[/tex] is[tex]x = 3 + 3i or x = 3 - 3i[/tex].
What are equations used for?A linear formalism is a statement that two numbers or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account together in order to comprehend or explain the whole situation, this is known as an equation.
What sort of equation would that be?The concept of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 consists of the two numbers 3x + 5 and 14, which are separated by the 'equal' sign.
we have a = 1, b = -6, and c = 18
[tex]x = (-(-6) +- \sqrt{-6^{2} } - 4(1)(18))) / 2(1)[/tex]
[tex]x = (6 +/- \sqrt{36-72} / 2[/tex]
[tex]x = (6 +/- \sqrt{36} / 2[/tex]
[tex]\sqrt{-36} = \sqrt{36} * \sqrt{-1} = 6i[/tex]
Therefore, the solutions are:
[tex]x = (6 + 6i) / 2 or x = (6 - 6i) / 2[/tex]
Simplifying:
[tex]x = 3 + 3i or x = 3 - 3i[/tex]
These are the two complex solutions to the equation [tex]x^{2} - 6x = -18[/tex].
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At the ' Grub shrub, the following orders were placed: 3 burgers and 6 fries, which cost $30 in total 3 burgers and 2 fries, which cost $18 in total Find the cost, in dollars, of 2 burgers and 3 fries.
The total cost of 2 burgers and 3 fries, considering a system of equations, is given as follows:
$17.
How to obtain the costs?The costs are obtained by a system of equations, for which the variables are given as follows:
Variable x: cost of a burger.Variable y: cost of a fry.3 burgers and 6 fries, which cost $30, hence:
3x + 6y = 30
x + 2y = 10
x = 10 - 2y.
3 burgers and 2 fries, which cost $18 in total, hence:
3x + 2y = 18
1.5x + y = 9
Replacing the first equation into the second, the value of y is given as follows:
1.5(10 - 2y) + y = 9
2y = 6
y = 3.
Then the value of x is given as follows:
1.5x + 3 = 9
x = 6/1.5
x = 4.
Then the cost, in dollars, of 2 burgers and 3 fries, is given as follows:
2 x 4 + 3 x 3 = $17.
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If
f(x)
X-5
= 4x + 5, find f(x).
Answer:
f(x) = 4+10/x
Step-by-step explanation:
f(x)x-5 = 4x+5
add 5 to both sides
f(x)x = 4x+10
divide both sides by x
f(x) = 4+10/x
still not sure if its the right problem...
Find the value of t for a t-distribution with 45 degrees of freedom such that the area to the right of t equals 0.010. Round your answer to three decimal places, if necessary.
The value of t for a t-distribution with 45 degrees of freedom such that the area to the right of t equals 0.010 is approximately -2.326.
With its bell-shaped structure and heavier tails, the t-distribution, commonly referred to as the Student's t-distribution, is a kind of probability distribution that resembles the normal distribution. When there are insufficient samples or unknown variances, it is used to estimate population parameters. T-distributions have broader tails than normal distributions because they are more likely to contain extreme values.
To find the value of t for a t-distribution with 45 degrees of freedom such that the area to the right of t equals 0.010, we can use a t-table or a calculator. Using a calculator, we can use the inverse t-distribution function. The inverse t-distribution function gives us the value of t for a given probability and degrees of freedom.
Using this function, we have:
t = invT(0.010, 45) ≈ -2.326
Rounding this to three decimal places gives us the answer:
t ≈ -2.326
Therefore, the value of t for a t-distribution with 45 degrees of freedom such that the area to the right of t equals 0.010 is approximately -2.326.
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Calculate the area of the shape below
Answer:
[tex]225 \: {m}^{2} [/tex]
Step-by-step explanation:
I added a photo of my notes
This figure is formed from a rectangle and a trapezoid
Since the opposite sides of a rectangle are equal, we can find the its area:
A (rectangle) = 9 × 17 = 153 m^2
In order to find the area of a trapezoid, we have to know the length of its altitude:
H = 15 - 9 = 6 m
We know the lengths of both bases, now we can find the area:
A (trapezoid) = 0,5(7 + 17) × 6 = 0,5 × 24 × 6 = 12 × 6 = 72 m^2
Now add these two areas together and we'll get the total area of this figure:
A = 153 + 72 = 225 m^2
Find the missing numbered angle
(5x-2)
The missing numbered angle is 80 degrees.
In the given diagram, we can see that angles A and B form a linear pair (they are adjacent angles whose sum is 180 degrees). So we can write:
A + B = 180 degrees
Substituting the given value of angle A, we get:
(3x + 10) + B = 180 degrees
Simplifying this equation, we get:
3x + B = 170 degrees
We are also given that angle C is a complementary angle to angle B, which means that angle C + angle B = 90 degrees. We can substitute the value of angle B from the above equation to get:
C + (3x + B) = 90 degrees
Simplifying this equation, we get:
C + (3x + 170 - 3x) = 90 degrees
Simplifying further, we get:
C + 170 = 90 degrees
Subtracting 170 from both sides, we get:
C = 80 degrees
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Add 6.034 +10 +0.608
Answer: 16.642
Step-by-step explanation:
I hope this helped you! A brainilist is highly appreciated and helpful! <3
Answer: 16.642
Step-by-step explanation:
10 + 6.034 = 16.034
16.034 + 0.608 = 16.642
Question What is the volume of this figure? Enter your answer in the box. ft³ Three-dimensional figure that could be formed by placing two rectangular prisms together to form an L shape where the wider part of the L is on the bottom and the L extends up from the left side. The wider part of the L has a length of 6 ft and a width of 2 ft and a height of 3 ft. The L extends up on the left side with the total height of the figure labeled 8 ft. The taller part of the L has a length of 4 ft and a width of 2 ft.
The volume of the figure is 76 ft³.
What is a prism?In geometry, a prism is a three-dimensional solid object that has two parallel bases that are congruent polygons, and rectangular faces connecting the bases. The rectangular faces are also called lateral faces or sides, and the edges where the bases and lateral faces meet are called lateral edges. The number of sides in the bases and the shape of the bases determine the name of the prism.
To find the volume of the figure, we can break it down into two rectangular prisms and add their volumes.
The first rectangular prism has dimensions 6 ft x 2 ft x 3 ft, so its volume is:
V1 = 6 ft x 2 ft x 3 ft = 36 ft³
The second rectangular prism has dimensions 4 ft x 2 ft x 5 ft (8 ft - 3 ft), so its volume is:
V2 = 4 ft x 2 ft x 5 ft = 40 ft³
The total volume of the figure is the sum of these volumes:
V = V1 + V2 = 36 ft³ + 40 ft³ = 76 ft³
Therefore, the volume of the figure is 76 ft³.
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