Given that △A′B′C′ is a dilation of △ABC, how are the angles and side lengths of the preimage and image related?


The angles are proportional and the side lengths are proportional.


The angles are congruent and the side lengths are congruent.


The angles are proportional and the side lengths are congruent.


The angles are congruent and the side lengths are proportional.

The solution of the equation Bx =     1       2       3   is    x =        2      6      4.

To find the solution of the equation Bx =
1
2
3
, we can multiply both sides of the equation by the inverse of B, B^-1. This will give us:

B^-1 Bx = B^-1
1
2
3


Since the product of a matrix and its inverse is the identity matrix, I, we can simplify the left side of the equation to:

Ix = B^-1
1
2
3


And since the product of the identity matrix and any vector is just the vector itself, we can simplify further to:

x = B^-1
1
2
3


Now, we can plug in the given values for B^-1 and the right side of the equation to find the solution for x:

x =
-1 0 1
2 2 0
1 0 1
*
1
2
3


Multiplying the matrices gives us:

x =
(-1)(1) + (0)(2) + (1)(3)
(2)(1) + (2)(2) + (0)(3)
(1)(1) + (0)(2) + (1)(3)


Simplifying further gives us:

x =
2
6
4


So, the solution of the equation Bx =     1       2       3   is    x =        2      6      4

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The distance across the lake is 120 feet.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given is a right angled triangle.

Pythagoras theorem states that,

Square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the two legs of the triangle.

The distance across the lake is one of the leg of the right triangle.

Length of hypotenuse = 208 feet + 104 feet

                                     = 312 feet

Length of other leg = 192 feet + 96 feet

                                = 288 feet

Distance across the lake = √(312² - 288²)

                                         = √14,400

                                         = 120 feet

Hence 120 feet is the distance across the lake.

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Simplified expression of (5t^(3))/(-25t)| is (1/5)( [tex]t^{2}[/tex] ).

To simplify the expression |(5[tex]t^{(3))}[/tex]/(-25t)|, we need to follow these steps:

1. Start by simplifying the fraction inside the absolute value signs.

2. The 5 in the numerator and the 25 in the denominator can be reduced to 1/5.

3. The t in the denominator can be reduced with one of the t's in the numerator, leaving us with [tex]t^{2}[/tex] in the numerator. This gives us |(1/5)( [tex]t^{2}[/tex]))|.

5. The absolute value signs mean that we need to take the positive value of whatever is inside.

6. Since both 1/5 and [tex]t^{2}[/tex] are positive, we can remove the absolute value signs.

   This leaves us with (1/5)( [tex]t^{2}[/tex])) as our simplified expression.

So the final answer is (1/5)( [tex]t^{2}[/tex] ).

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40 adult tickets were sold and 80 student tickets were sold.

What is an equation?

An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations.

Let's use algebra to solve this problem.

Let's call the number of student tickets sold "s" and the number of adult tickets sold "a".

From the problem, we know two things:

The total number of tickets sold was 120:

s + a = 120

The total amount of money made from ticket sales was $1,400:

10s + 15a = 1400

Now we have two equations with two variables, so we can solve for "a" and "s".

Let's start by solving for "s" in the first equation:

s + a = 120

s = 120 - a

Now we can substitute this expression for "s" into the second equation:

10s + 15a = 1400

10(120 - a) + 15a = 1400

1200 - 10a + 15a = 1400

5a = 200

a = 40

So 40 adult tickets were sold.

Now we can substitute this value of "a" into the first equation to find "s":

s + a = 120

s + 40 = 120

s = 80

So 80 student tickets were sold.

Therefore, 40 adult tickets were sold and 80 student tickets were sold.

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Answer:

5 (3x+2)

Step-by-step explanation:

Hope this helps! :)

Answer: A

Step-by-step explanation:

You can prove it by Pythagorean's Theorem, a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

It has to be a right triangle.

Applying the definition of complementary angles, the measures are:

7. m<DBE = 64°; m<CBE = 26°

8. m<WVZ = 84°; m<XVW = 96°

9. m<RTS = 63°; m<PTQ = 27°

10. m<EFG = 139°

m<IFH = 49°

Complementary angles are two angles whose sum is equal to 90 degrees. In other words, when two angles are placed side by side, forming a right angle, they are said to be complementary.

7. Angles DBE and CBE are complementary angles, therefore:

17x + 13 + 32 - 2x = 90

15x + 45 = 90

15x = 90 - 45

15x = 45

x = 3

m<DBE = 17x + 13 = 17(3) + 13 = 64°

m<CBE = 32 - 2x = 32 - 2(3) =  26°

8. 5x + 29 = 9x - 15 [vertical angles are equal]

5x - 9x = -29 - 15

-4x = -44

x = 11

m<WVZ = 9x - 15 = 9(11) - 15 = 84°

m<XVW = 180 - 84 = 96° [linear pair]

9. 8x - 17 = 5x + 13 [vertical angles]

8x - 5x = 17 + 13

3x = 30

x = 10

m<RTS = 5x + 13 = 5(10) + 13 = 63°

m<PTQ = 180 - 90 - 63 = 27°

10. (2x + 3) + (6x + 25) = 180 [linear pair]

8x + 28 = 180

8x = 180 - 28

8x = 152

x = 19

m<EFG = 6x + 25 = 6(19) + 25 = 139°

m<IFH = 90 - (2x + 3) = 90 - (2(19) + 3)

m<IFH = 49°

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The sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.

The power of a test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, we wish to find the power of the z-test to detect a difference of δ1 - δ2 = 0.1 when the sample size is 100 and the significance level is 0.05.

a) First, we need to find the critical value for the z-test at a significance level of 0.05. This can be found using a z-table or a calculator. The critical value is 1.645.

Next, we need to find the standardized difference between the two means, which is (δ1 - δ2)/√(2δ^2/n) = (0.1)/√(2(1)^2/100) = 0.1/√(0.02) = 0.7071.

Finally, we can find the power of the test by subtracting the standardized difference from the critical value and finding the corresponding probability from a z-table or calculator. The power is 1 - P(Z < 1.645 - 0.7071) = 1 - P(Z < 0.9379) = 1 - 0.8264 = 0.1736.

Therefore, the power of the z-test to detect a difference of δ1 - δ2 = 0.1 with a sample size of 100 and a significance level of 0.05 is 0.1736.

b) To find the sample size needed to detect µ1 - µ2 = 1 with power at least 80%, we can use the formula for power:

Power = 1 - P(Z < (critical value - standardized difference))

We can rearrange this formula to solve for the sample size:

Standardized difference = (critical value - Z value corresponding to power)/√(2δ^2/n)

n = (2δ^2(critical value - Z value corresponding to power)^2)/(standardized difference)^2

Plugging in the values for critical value (1.645), Z value corresponding to power (0.8416), and standardized difference (1), we get:

n = (2(1)^2(1.645 - 0.8416)^2)/(1)^2 = 322.69

Therefore, the sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.

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The correlation coefficient relating is 0.76 thath mean  the accompaniment rates for wives and sons is the accompaniment rate for wives increases, the accompaniment rate for sons also tends to increase.

To find the correlation coefficient relating the accompaniment rates for wives and sons, we can use the formula:

r = (nΣxy - (Σx)(Σy)) / √[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

Where:
- r is the correlation coefficient
- n is the number of observations (in this case, 9)
- x and y are the accompaniment rates for wives and sons, respectively
- Σxy is the sum of the products of x and y
- Σx and Σy are the sums of x and y, respectively
- Σx^2 and Σy^2 are the sums of x squared and y squared, respectively

Using the data from the table, we can calculate the following:

Σx = 27.2 + 40.1 + 35.7 + 37.8 + 38 + 38.4 + 38.7 + 29.8 + 23.8 = 309.5
Σy = 2.2 + 1.5 + 0.3 + 3.5 + 5.4 + 11 + 11.9 + 8.6 + 7.4 = 51.8
Σxy = (27.2)(2.2) + (40.1)(1.5) + (35.7)(0.3) + (37.8)(3.5) + (38)(5.4) + (38.4)(11) + (38.7)(11.9) + (29.8)(8.6) + (23.8)(7.4) = 1164.41
Σx^2 = 27.2^2 + 40.1^2 + 35.7^2 + 37.8^2 + 38^2 + 38.4^2 + 38.7^2 + 29.8^2 + 23.8^2 = 11491.89
Σy^2 = 2.2^2 + 1.5^2 + 0.3^2 + 3.5^2 + 5.4^2 + 11^2 + 11.9^2 + 8.6^2 + 7.4^2 = 349.98

Plugging these values into the formula, we get:

r = (9)(1164.41) - (309.5)(51.8) / √[(9)(11491.89) - (309.5)^2][(9)(349.98) - (51.8)^2] = 0.76

This value of r indicates a strong positive correlation between the accompaniment rates for wives and sons. This means that as the accompaniment rate for wives increases, the accompaniment rate for sons also tends to increase.

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Answer:

Awnser "y = 10x + 60"

Step-by-step explanation:

So, the chart coordinate should looks like this:

(1, 75)

(2, 70)

(3, 80)

(4, 95)

(4, 100)

And there is a line passing (0, 60) and (2, 80)

So we just need to find the y-intercept and the slope by the line:

Slope: [change in x over change in y] = 20 ÷ 2 = 10

y-intercept: [the value of y when x equal 0] = 60 (because the line passed through (0, 60) )

Step-by-step explanation:

Answer; 10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test

Step-by-step explanation:

Answer:4

Step-by-step explanation:

The length of MN, to the nearest tenth of a unit is equal to: C. 14.4 units.

In order to determine the missing side length of a geometric figure with the adjacent and hypotenuse side lengths given, you should apply the law of cosine:

C² = A² + B² - 2(A)(B)cosθ

Where:

A, B, and C is the length of side of a given triangle.

By substituting the given side lengths and angle into the law of cosine formula, we have the following;

MN² = LM² + LN² - 2(LM)(LN)cosθ

MN² = 12² + 10² - 2(12)(10)cos(52)

MN² = 144 + 100 - 147.76

MN = √96.24

MN = 9.8 units.

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The value of the expression 7₂ + 3₃ is 10₅.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

An expression is 7₂ + 3₃.

To find the value of the expression, first, add 7 and 3.

That means, 7 + 3 = 10.

Now add 2 and 3,

2 +3 = 5

So, the value of the expression is 10₅.

Therefore, the result is 10₅.

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The permutation ([1,2,3,4,5,6],[6,5,4,3,1,2]) can be written as a product of disjoint cycles as (A) ([1,6,2,5])([3,4]).

To find the product of disjoint cycles, we can start by looking at the first element in the first cycle, which is 1. We see that 1 maps to 6 in the given permutation, so we write ([1,6. Next, we see that 6 maps to 2, so we write ([1,6,2. Finally, 2 maps to 5, so we write ([1,6,2,5. Since 5 maps back to 1, we can close the cycle and write ([1,6,2,5]).

Next, we look at the remaining elements, which are 3 and 4. We see that 3 maps to 4 and 4 maps back to 3, so we write ([3,4]).

Therefore, the permutation ([1,2,3,4,5,6],[6,5,4,3,1,2]) can be written as a product of disjoint cycles as ([1,6,2,5])([3,4]). The correct answer is (A) ([1,6,2,5])([3,4]).

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By those 2 ways of solution, a total of 3,105 packs of juice drinks were distributed to different schools.

To find out how many packs of juice drinks were distributed to different schools, we need to add the number of packs given to each school.

950 (La Paz Elementary School) + 785 (Igdarapdap Elementary School) + 1,370 (Cabalaynan Elementary School) = 3,105 packs of juice drinks

So, a total of 3,105 packs of juice drinks were distributed to different schools.

To find out how many packs of juice drinks were not given, we need to subtract the number of packs distributed to different schools from the total number of packs available.

5,000 (total number of packs) - 3,105 (number of packs distributed to different schools) = 1,895 packs of juice drinks

So, a total of 1,895 packs of juice drinks were not given.

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The correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.

The standard equation of an ellipse is (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1, where (h,k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the covertices.

In this case, the center of the ellipse is the midpoint of the vertices and covertices, which is (7, -2). The distance from the center to the vertices is 5 (12-7) and the distance from the center to the covertices is 3 (1-(-2)).

Therefore, the standard equation of the ellipse is (x-7)^2 / 25 + (y+2)^2 / 9 = 1, which corresponds to answer choice (a).

So the correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.

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Yes, Tanner has enough spray paint for his arrow.

What is an Area?

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. A planar figure's area is the area that its perimeter encloses. The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square measurements for area include cm2 and m2.

Given : paint available in can = 12 ft²

We know that the arrow is comprised of a triangle and a rectangle.

So, the area of given arrow = area of rectangle + area of triangle

Now, area of triangle = 1/2 ×base × height

                                   = 1/2 × 3 × (6 - 5 1/3)

                                   = 3/2 × ( 6 - 16/3)

                                   = 3/2 × ( 18-16)/3

                                   = 3/2 × 2/3

                                    = 1 ft²

Similarly, area of rectangle =  length × breadth

                                            = 5 1/3 × 2

                                            = 16/3 × 2

                                            = 32/3 ft²

Hence, area of arrow = area of triangle +area of rectangle

                                   = 1 + 32/3

                                   = 35/3 ft²

                                   = 11.67 ft²

So, he has sufficient paint to cover the arrow.

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1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,

Here, we have

Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any​ direction.

Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.

The area of a circle is given as:

Area = πr²

Radius = 24 feet

Area = 3.14(24)²

Area = 1808.64

Hence, 1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

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Answer:

1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

What is an area of a circle?

The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,

Here, we have

Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any​ direction.

Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.

The area of a circle is given as:

Area = πr²

Radius = 24 feet

Area = 3.14(24)²

Area = 1808.64

Hence, 1808.64  is the area formed by the water pattern if it can spray out 24 feet in any​ direction.

The value in the red box would be 19√7.

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is a pyramid as shown in the image.

We can write -

b{4} = 2√7 - 4√7 = - 2√7

b{4} = - 2√7

- 4√7 + b{9} = 3√28

b{9} = 3√28 + 4√7

b{9} = 6√7 + 4√7

b{9} = 10√7

b{6} = 10√7 - √7

b{6} = 9√7

b{2} =  - 2√7 + 6√7

b{2} = 4√7

b{3} = 3√28 + 9√7

b{3} = 6√7 + 9√7

b{3} = 15√7

b{1} = 4√7 + 15√7

b{1} = 19√7

Therefore, the value in the red box would be 19√7.

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{QUESTION IN ENGLISH -

Look at the following pyramid, in which each box has a number that is formed by adding the two bottom boxes.

What is the number that occupies the red box?}

Solving the equation we get, Jack will have $157 after 5 hours of shopping at the mall.

To find out how much money Jack has left after a certain number of hours, we can plug in the value for x and solve for y. For example, if Jack spends 5 hours at the mall, we would plug in 5 for x:

y = -7(5) + 192
y = -35 + 192
y = 157

We can use this equation to find out how much money Jack has left after any number of hours at the mall.

Jack starts with $192. He spends $7 every hour. Jack is left with $157 at the end of 5 hours.  

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This distribution of inequities ensures that the total amount of ticket sales revenue stays within the budget, that no more than 150 tickets are sold overall, and that no negative ticket sales occur.

Let x represent the quantity of single tickets sold and y represent the quantity of pair tickets sold. The entire revenue from ticket sales, R, is then calculated as follows:

R = 45x + 70y

The entire amount of ticket sales revenue is limited by the budget to $5000:

45x + 70y ≤ 5000

No more than 150 tickets may be sold in total.

x + y ≤ 150

X and Y must both be non-negative since we cannot sell negative tickets:

x ≥ 0\sy ≥ 0

As a result, the system of disparities that best captures this circumstance is:

5000 x + y 45x + 70y 150x 0y 0

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Answer:

C.

Step-by-step explanation:

C. show the undulating forms of fabric.

The radius of the circle is 13 units

From the question, we have the following parameters that can be used in our computation:

The circle

Where we have

Center = (0, 0)

Point - (-5, 12)

The radius of the circle is the distance between the point and the center

So, we have

Radius = √[(0 + 5)² + (0 - 12)²]

Evaluate

Radius = 13

Hence, the radius is 13 units

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Cost of 75 pound of candy = 75×6 = $450

Additional fee for each bulk = $250

Total = $700

Therefore, $700 is the correct answer.

The slope of the curve at a particular point on the hyperbolic spiral, we need to take the derivative of the equation with respect to θ and evaluate it at the given value of θ. Slope of the curve found to be = 2pi. The correct answer is option C

The equation of the hyperbolic spiral is given by: r = 1/θ To express this equation in terms of x and y, we use the polar-to-rectangular coordinate transformation: x = r cos(θ) y = r sin(θ)

Substituting the equation for r, we get: x = (cos(θ))/θ y = (sin(θ))/θ Taking the derivative of y with respect to x using the chain rule, we get:

[tex](dy/dx) = (dy/dθ)/(dx/dθ) (dy/dx) = [(cos(θ)/θ^2) + (sin(θ)/θ)] / [(-sin(θ)/θ^2) + (cos(θ)/θ)] At t = π, θ = π/2.[/tex]

Therefore, the slope of the hyperbolic spiral at t = π is: (dy/dx) = 2/π The correct option to this value is C. 2pi

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