To calculate the arc length, multiply the angle in radians (7pi/3) by the radius (3 inches). After simplifying, the arc length for this circle is 21 inches.
To find the arc length for a central angle of 7pi/3 radians in a circle with a radius of 3 inches, we use the formula for arc length, which is the product of the central angle in radians and the radius of the circle.
The formula for the arc length (As) is given by:
As = r times theta
Where:
r is the radius of the circle.
theta is the central angle in radians.
Substituting the given values, we get:
As = 3 inches times 7pi/3 radians
The 7pi/3 terms cancel out the pi/3 from the angle and /3 from the radius, giving us:
As = 3 times 7 inches
The arc length is therefore 21 inches.
Given that the two triangles shown are congruent, explain one way to verify that the corresponding angles of the two triangles are congruent.
A) reflect triangle 1 across the y-axis
B) reflect triangle 2 across the y-axis
C) rotate triangle 2 counter-clockwise 90° about the origin
D) reflect triangle 2 across the y axis and rotate 90° about the origin at
Answer:
The correct option is C.
Step-by-step explanation:
From the given graph it is noticed that the vertices of triangle 1 are P'(-2,2), Q'(-4,4) and R'(-2,4). The vertices of triangle 2 are P(2,2), Q(4,4) and R(4,2).
If a figure rotated counter-clockwise 90° about the origin, then
[tex](x,y)\rightarrow (-y,x)[/tex]
If we rotate triangle 2 counter-clockwise 90° about the origin, then[
[tex]P(2,2)\rightarrow P'(-2,2)[/tex]
[tex]Q(4,4)\rightarrow Q'(-4,4)[/tex]
[tex]R(4,2)\rightarrow R'(-2,4)[/tex]
If we rotate triangle 2 counterclockwise, then we get the triangle 1.
Therefore the correct option is C.
Troy has a box of 600 tiny blocks. Each block is a cube with dimensions of 1 cm x 1cm x 1cm. The blocks are arranged in the box in rows and layers so that there are no gaps. Which could be the dimensions of the box?
a. 5 cm x 10 cm x 12 cm
b. 5 cm x 10 cm x 10 cm
c. 10 cm x 10 cm x 12 cm
d. 200 cm x 200 cm x 200 cm
divide r+5/ r^2+5r-14 by r^2+4-21/r-2
Given y = 4x + 3, what effect does changing the equation to y = 2x + 3 have on the slope?
Changing the slope of the equation from 4 to 2 reduces the steepness of the line in the graph, with the y-intercept remaining constant at 3.
Explanation:The student asked about the effect on the slope of the linear equation when changing from y = 4x + 3 to y = 2x + 3. The slope of the first equation is 4, which can be seen from the coefficient of x, indicating a rise of 4 on the vertical axis for every increase of 1 on the horizontal axis. When the equation changes to y = 2x + 3, the slope is reduced to 2, which means there is a rise of 2 on the vertical axis for every increase of 1 on the horizontal axis. This change in the slope would cause the line to rotate clockwise when graphed on a coordinate plane. The y-intercept remains the same at 3 since it is unchanged in both equations. Therefore, changing the equation has the effect of decreasing the steepness of the line, but the location where the line crosses the y-axis does not change.
amanda is shipping a package, which is in the shape of a cube. To determine the cost of shipping, she must determine the side length of the packages She knows that the volume of the package is V cubic inches
Which of the follow functions would best model this situation above?
Cube root
Polynomial
Piecewise
Absolute Value
A bowl contains 24 marbles consisting of 6 white marbles, 8 blue marbles, 7 black marbles, 3 red marbles. What is the probability of drawing a red marble?
a. 6/24B.5/25C.1/8D.7/8
Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of α if α < β. sin(2x − 8) = cos(6x − 6)
i really need help. please help
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^−x and y = 8^(−x−1) intersect are the solutions of the equation 4^−x = 8^(−x−1). (4 points)
Part B: Make tables to find the solution to 4^−x = 8^(−x−1). Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4^−x = 8^(−x−1) graphically? (2 points)
The product of a number (n) and 12 is 64. Which equation shows this relationship
12+n=64
64n=12
12n=64
64-n=12
The equation that shows the relationship between the number (n) and 12 being multiplied to equal 64 is 12n = 64, the correct option is C.
In this equation, the variable n represents the number we are trying to find. The equation states that when we multiply 12 and n together, the result is 64.
To solve this equation and find the value of n, we divide both sides of the equation by 12:
(12n)/12 = 64/12
n = 64/12
Which can be further simplified to:
n = 16/3
Therefore, the equation that represents the relationship between the number (n) and 12 being multiplied to equal 64 is 12n = 64.
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A pet store has 12 puppies, including 3 poodles, 5 terriers, and 4 retrievers. if rebecka and aaron, in that order, each select one puppy at random without replacement, find the probability that aaron selects a retriever, given that rebecka selects a poodle.
The probability that Aaron will select a retriever given that Rebecka has selected a poodle is 4/11.
To calculate the probability that Aaron selects a retriever given that Rebecka selects a poodle, we will use the concept of conditional probability. The total number of puppies is 12, and the number of poodle puppies is 3.
When Rebecka selects a poodle, one puppy is removed from the total, leaving 11 puppies, including the same 4 retrievers (since she did not pick a retriever).
The probability that Aaron picks a retriever given Rebecka has picked a poodle is:
P(Aaron picks a retriever | Rebecka picks a poodle) = P(Rebecka picks a poodle and Aaron picks a retriever) / P(Rebecka picks a poodle)
Since Rebecka has already picked a poodle, we focus only on the event where Aaron picks a retriever. So the probability becomes:
P(Aaron picks a retriever | Rebecka picks a poodle) = Number of retrievers left / Total number of puppies left
= 4 retrievers / 11 total puppies
= 4/11
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:f(t) = −16t2 + 48t + 100The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.
The scale of a map is 0.5 inch : 20 miles. on the map, the distance between two cities is 1.5 inches. what is that actual distance between the two cities? select one:
a. 30 miles
b. 150 miles
c. 60 miles
d. 110 miles
Write the inverse function for the function, ƒ(x) = x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.
ƒ -1(x) = _________ x ___________ ______
ƒ -1(4) = _____________
Answer: The required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
Step-by-step explanation: We are given the following function f(x) :
[tex]f(x)=x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the values of [tex]f^{-1}(x)[/tex] and [tex]f^{-1}(4).[/tex]
Let us consider that
[tex]y=f(x)~~~~~~~~\Rightarrow x=f^{-1}(y).[/tex]
So, from equation (i), we get
[tex]f(x)=x+4\\\\\Rightarrow y=f^{-1}(y)+4\\\\\Rightarrow f^{-1}(y)=y-4\\\\\Rightarrow f^{-1}(x)=x-4.[/tex]
Substituting x = 4 in the above equation, we get
[tex]f^{-1}(4)=4-4=0\\\\\Rightarrow f^{-1}(4)=0.[/tex]
Thus, the required values are
[tex]f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.[/tex]
A field goal post in football is 3.33 yards above the ground. If a football player kicks the ball at a 10 degree square angle in a straight line toward the goal post what is the distance away in yards where the ball barely goes over the goal post
Use the given graph to determine the limit, if it exists.
Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.
Factor this trinomial completely.
–6x2 + 26x + 20
A. –6x2 + 26x + 20
–2(3x2 – 13x – 10)
–2(3x + 2)(x – 5)
B. –6x2 + 26x + 20
–2(3x2 + 11x + 10)
–2(3x + 5)(x + 2)
C. –6x2 + 26x + 20
–2(3x2 – 13x – 10)
–2(3x – 10)(x + 1)
D. –6x2 + 26x + 20
–2(3x2 – 13x + 10)
–2(3x – 5)(x – 2)
First, factor out -2 from the trinomial, and then factor the resulting quadratic expression by grouping. The correct factored form is -2(3x + 2)(x - 5).
To factor the trinomial “6x² + 26x + 20 completely, follow these steps:
First, factor out the greatest common factor, which is -2:Therefore, the correct factored form is (Option A) “2(3x + 2)(x – 5).
On a scatter plot what does it mean when both variables are increasing
I NEED HELP CAN SOMEONE HELP ME GET THIS?? ILL GIVE POINTS!!
Answer:
[tex]a^{9}b^{6}[/tex]
Step-by-step explanation:
What is the best estimate of the mean price of all the sunglasses on the rack?
What is the value of x?
a. 6
b. 6√3
c. 12
d. 12√3
Help with algebra 2 please!!!!!!!
The population of a city is 578,992. The land area of the city is 67.2 mi². What is the population density of the city? Enter your answer in the box. Round your answer to the nearest whole number.
Just took the K12 test and the correct answer is 8616 people/mi²
(please give the other person brainliest-thanks!!!)
A. 3
B. 26
C. 36
D. 51
If the ratio of the radii of two spheres is 8:9, what is the ratio of the volumes of the two speheres
∠ACE is formed by two secants intersecting outside of a circle. If minor arc BD = 28°, minor arc AB = 112°, and minor arc DE = 112°, what is the measure of ∠ACE? A) 14° B) 28° C) 40° D) 54°
Answer:
its 40 degrees
Step-by-step explanation:
rata ta taaa
Blue marbles, green marbles and red marbles are in a ratio of 5 to 7 to 8 in a box. if the total number of marbles is 240, how many green marbles are in the box?
Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inches? Check all that apply.
-
A cross section parallel to the base is a rectangle measuring 15 inches by 8 inches.
A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches.
A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
Answer:
A cross-section parallel to the base is a rectangle measuring 15 inches by 8 inches.
A cross-section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross-section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.
the cross sections that are parallel and perpendicular will have the same measurements as the non-intersected sides. the last one will be a diagonal so the intersected edge is 6 and it creates a right triangle so it must be larger than 15 inches.
Step-by-step explanation:
50 Points and will mark Brainiest.
Draw four different triangles with the following two side lengths (you decide the length of side c). Be sure to label the sides and their lengths.
Side a = 2 cm
Side b = 5 cm
Look at the triangles you created. What do you notice about the different lengths of line c?
Write an inequality that shows the possible lengths for line c (the triangle inequality theorem will help you):
Answer:
As we can observe from the drawing that with increasing length of side C the angle C also increases.
On a map, 1 inch equals 9.2 miles. two houses are 3.5 inches apart on the map. what is the actual distance between the houses? use pencil and paper. show how you can represent the scale with two different ratios. what ratio is more helpful for solving the problem? explain.
The actual distance between the houses is 18.9 miles.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
Given that On a map, 1 inch equals 9.2 miles. Two houses are 3.5 inches apart on the map.
To find the actual distance between the houses.
Given that,
1 inch = 9.2 miles
Therefore,
∴ we get
3.5 inches = 3.5 × 9.2 miles
= 13.8 miles
The actual distance is 13.8 miles.
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Final answer:
To find the actual distance between the houses, we can set up a proportion using the given map scale. The actual distance between the houses is 32.2 miles. Using the ratio 1 inch/9.2 miles = 3.5 inches/x is more helpful in solving the problem.
Explanation:
To find the actual distance between the houses, we need to use the scale of 1 inch equals 9.2 miles. We are given that the two houses are 3.5 inches apart on the map.
First, we can set up a proportion to find the actual distance:
1 inch / 9.2 miles = 3.5 inches / x
Cross-multiplying, we have:
1x = 3.5 * 9.2 miles
Simplifying, we get:
x = 32.2 miles
The actual distance between the houses is 32.2 miles.
To represent the scale with two different ratios, we can use the proportion:
1 inch / 9.2 miles = 3.5 inches / x
This ratio is more helpful for solving the problem as it allows us to directly calculate the actual distance using the given map distance and the scale ratio.
solve for A
R=x(A+B)
To solve the equation R=x(A+B) for A, divide both sides by x to get R/x = A+B. Then, subtract B from both sides to isolate A. The final equation is A = R/x - B.
Explanation:The goal is to solve for A in the equation R=x(A+B). It's a simple problem of algebraic manipulation. Here's how to do it step by step:
First, divide both sides of the equation by x to isolate the term (A+B). This gives R/x = A+B.Next, subtract B from both sides of the newly formed equation to isolate A on one side. This gives us A = R/x - B.And there you have it! The value of A in terms of R, x, and B is A = R/x - B.
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