Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided. 4(7 - 3x) = 7(4 - 2x)

Answer:

Y'=(2,-4)

Z'=(8,0)

Step-by-step explanation:

X + T = X'

(2,3) + (T) = (5,-2)

T = (3,-5)

Y' = Y + T = (2,-4)

Z' = Z + T = (8,0)

Answer:

C=10

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

here b = 16 and h = 8 , then

A = \(\frac{1}{2}\) × 16 × 8 = 8 × 8 = 64 ft²

Answer:

x = - 7, y = 6

Step-by-step explanation:

7x + 7y = - 7 -----> equation 1

- 10x - 7y = 28 -----> equation 2

Add equations 1 & 2,

7x + 7y = - 7

- 10x - 7y = 28

___________

- 3x + 0 = 21

- 3x = 21

x = 21 / - 3

x = - 7

Substitute x = - 7 in equation 1,

7x + 7y = - 7

7y + 7x = - 7

7y + 7 ( - 7 ) = - 7

7y - 49 = - 7

7y = - 7 + 49

7y = 42

y = 42 / 7

y = 6

Answer:

x = -7

y = 6

Step-by-step explanation:

7x + 7y = -7  ------------------(I)

-10x - 7y = 28 ----------------(II)

Add both the equation and so y will be eliminated and we can find the value of x

(I)           7x + 7y = -7

(II)        -10x - 7y = 28 {Now add}

            -3x         = 21              {Divide both sides by (-3)}

                      x = 21/-3

x = -7

Plugin x = -7 in equation (I)

7*(-7) + 7y = -7

-49   + 7y = -7

           7y = -7 + 49

           7y = 42

             y = 42/7

y = 6

The element of A n B is { 7, 8}

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind.

For example, if the element of P is even numbers from 1 to 20 and element of Q is factor of 6 from 1 to 20 then we can say that set Q is a subset of set P.

The sign 'n' means intersection and this means what is common to two or more set.

If set A = { 1,2,5,7,8}

set B = { 6,7,8,9}

then we can see that 7 and 8 are common to both sides, then

A n B = { 7,8}

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The simple interest on a principal, P can be obtained using the formula

Total amount = $2000 + $720

=> $ 2720

hello

negative 33 = -33

Answer:

d. 108 °

Step-by-step explanation:

(2x + 3x) * 2 = 360

4x + 6x = 360

10x = 360

x = 36

Angle DAB = 3x = 36 * 3 = 108°

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Answer:

1. Natural Number

2. Integer

3. Rational Number

4. Rational Number

5. Irrational Number

6. Rational Number

7. Rational Number

8. Natural Number

9. Irrational Number

10. Integer

11. Irrational Number

12. Natural Number

Answer:

Sum of −42 and −147

=−42+(−147)=−42−147=−189

Difference of −283 and −415

=greater number−smaller number=−283−(−415)=415−283=132

Subtracting −189 from 132

=132−(−189)=132+189=321

Answer:

512 ft and 1,232 ft

Step-by-step explanation:

area is length x width

the pool's area can be calculated doing 32ft x 16ft

the area of the pool is 512 ft

the deck's area can be calculated doing 28ft x 44ft

the area of the deck is 1,232 ft

you're welcome<3

Answer:

Step-by-step explanation:

Percentage change= New number/ original x 100

3/5=0.6

0.6 x 100= 60%

100-60=40%

Answer:

\(m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} \)

\(7 = - \frac{8}{3} ( - 3) + b\)

\(7 = 8 + b\)

\(b = - 1\)

\(y = - \frac{8}{3} x - 1\)

The y-intercept is -1.

The amount of work done is Option A) 12 N/m

Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.

It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.

Work done on a body is equivalent  to the increase in the energy of the body, because it transfers energy to the body.

The formula for work done is;

W = fd

Where, 'f' is the applied force and d is the distance

Substitute the values

Work done = 6(2)

Work done = 12 N/m

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Answer:

C: One soda cost $2

Step-by-step explanation:

One soda costs $2. As you can see, which each soda you buy, X and Y go up by two. The relationship of X and Y is x=2y, with X being sodas and Y being dollars

Given the expression:

5x + 6 (x-2) -8 (x-3)

Let's simplify the exression using the following steps:

Step 1.

Apply distributive property:

5x + 6x + 6(-2) - 8x - 8(-3)

5x + 6x - 12 - 8x + 24

Step 2.

Combine like terms:

5x + 6x - 8x - 12 + 24

3x + 12

Therefore, the simplified expression is:

3x + 12

ANSWER:

D. 3x + 12

Answer:

m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Step-by-step explanation:

2m³ - 5m² - 7m = 0 ← factor out common factor m from each term

m(2m² - 5m - 7) = 0

factorise the quadratic 2m² - 5m - 7

consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × - 7 = - 14 and sum = - 5

the factors are + 2 and - 7

use these factors to split the m- term

2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )

2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term

(m + 1)(2m - 7)

then

2m³ - 5m² - 7m = 0

m(m + 1)(2m - 7) = 0 ← in factored form

equate each factor to zero and solve for m

m = 0

m + 1 = 0 ( subtract 1 from both sides )

m = - 1

2m - 7 = 0 ( add 7 to both sides )

2m = 7 ( divide both sides by 2 )

m = \(\frac{7}{2}\)

solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Answer:

104ft

Step-by-step explanation:

First - find the area of triangles.

h = hight

b = base
h • b / 2

5 • 8 /2 = 20ft

And

4 • 6 /2 = 12ft

And then area of the rectangle.
l • w

9 • 8 = 72 ft

Than add. Them all together

Answer:

Sarah is paid $20 an hour at her new job. She wishes to graph her total pay y, as a function of the number of hours, x. She wants to be sure her graph shows her pay for 10 and 20 hours of work.

a. What is a good scale to use for the x-axis? Explain your reasoning.

b. What is a good interval to use for the y-axis? Explain your r

Step-by-step explanation:

the perimeter of the polygon is: \(5 + 5 + 6 = 16\)  So, the perimeter of the polygon with vertices at   \((1, 2), (4, 6),\) and  \((7, 2)\) is \(16\)  units.

To find the perimeter of the polygon with vertices at   \((1, 2), (4, 6),\) and  \((7, 2),\) we need to find the length of each side of the polygon and add them up.

Using the distance formula, we can find the length of each side:

The length of the side connecting (1, 2) and (4, 6) is:

\(\sqrt((4-1)^2 + (6-2)^2) = \sqrt(3^2 + 4^2) = 5\)

The length of the side connecting \((4, 6) and (7, 2) is:\sqrt((7-4)^2 + (2-6)^2) = \sqrt(3^2 + (-4)^2) = 5\)

The length of the side connecting \((7, 2) and (1, 2) \ is:\ \sqrt((1-7)^2 + (2-2)^2) = \sqrt((-6)^2 + 0^2) = 6\)

Therefore, the perimeter of the polygon is:  \(5 + 5 + 6 = 16\) So, the perimeter of the polygon with vertices at \((1, 2), (4, 6),\) and \((7, 2) \ is \ 16\) units.

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The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.

After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.

However, Caesar, true to his word, had the pirates crucified on his own authority.

This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

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Using the volume of the sphere, it is found that 445.1 in³ of the ball is occupied by water.

The volume of a sphere of radius r is given by:

\(V = \frac{4\pi}{3}r^3\)

In this problem, the radius is of r = 5 in, hence the volume in cubic inches is given by:

\(V = \frac{4\pi}{3}(5)^3 = 523.6\)

85% of this is filled by water, hence the space occupied by water, in cubic inches, is of:

0.85 x 523.6 = 445.1.

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Answer:

Jerry

Step-by-step explanation:

As you are able to see exactly how many students travel whatever distance to get into school. As in Katys study, you will not be able to see exactly how many people travel 0 miles for example.

Answer:

Yes

Step-by-step explanation:

Because 9/12 and 6/8 are both equivalent to 3/4 of the total.

The rational equation to represent the students average cycling speed is  105 = 26.25x.

A student taking part in a cross country endurance race was required to cycle 70 km then run for 7 km. Her average cycling speed was five times as fast as her average running speed. She completed the course in 5 hours and 15 minutes.

Therefore, the equation to represent the students average cycling speed can be calculated as follows:

speed  = distance / time

average running speed = x

Hence,

x = 7 / time

time = 7 / x

Hence,

average cycling speed = 5x

time = 70 / 5x

Therefore, she completed the course for 5 hours 15 minutes.

Hence,

5 hours 15 minutes = 5.25 hours

Therefore,

7 / x + 70 / 5x =  5.25

35 + 70 / 5x = 5.25

105 / 5x = 5.25

cross multiply

Therefore,

105 = 26.25x

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