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The coordinates of the vertices of △PQR are P(4, −2) , Q(6, −4) , and R(8, 0) .

The coordinates of the vertices of △P′Q′R′ are P′(−4, 3) , Q′(−6, 5) , and R′(−8, 1) .

The approximate number of guests that were children are 172 and adults are 278

From the complete question, we have the following system of equations

25x + 12y = 9014

x + y = 450

Make y the subject in x + y = 450

y = 450 -x

Substitute y = 450 - x in 25x + 12y = 9014

25x + 12(450 - x) = 9014

Expand the expression

25x + 5400 - 12x = 9014

Evaluate the like terms

13x = 3614

Divide both sides by 12

x = 278

Substitute x = 278 in y = 450 -x

y = 450 - 278

Evaluate

y = 172

Hence, the approximate number of guests that were children are 172 and adults are 278

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Add -9 to both sides.

Solve Absolute Value.

No solutions. (Absolute value cannot be less than 0.)

Step-by-step explanation:

The absolute value of x is g(x)=f(x)+k.

Answer: B. 24

Step-by-step explanation:



Answer:

y=-7/2

Step-by-step explanation:

1=|8-2y|

1=8+2y

-7=2y

2y=-7

y=-7/2

Answer :  7.5 ft

Step-by-step explanation:

when the length of the shadow is 8ft, the actual height of the man = 5ft

8:5

let the giraffe be 'x' ft tall.

if the length of the shadow is 12ft, actual height = x ft

12:x

8:5 x 12:x

[tex]\frac{8}{5}[/tex] × [tex]\frac{12}{x}[/tex]

x= [tex]\frac{15}{2}[/tex]

x=7.5 ft

Therefore, the giraffe is 7.5ft tall.

Answer:

[tex]7.5\; {\rm ft}[/tex].

Step-by-step explanation:

The height of objects nearby under the sun are approximately proportional to the length of their shadows.

In other words, if the man and the giraffe are near each other and under the sun:

[tex]\begin{aligned} \frac{\text{height of man}}{\text{length of shadow of man}} = \frac{\text{height of giraffe}}{\text{length of shadow of giraffe}}\end{aligned}[/tex].

Given that:

Rearrange the equation to find [tex](\text{height of giraffe})[/tex]:

[tex]\begin{aligned} (\text{height of giraffe}) &= (\text{length of shadow of giraffe})\times \frac{\text{height of man}}{\text{length of shadow of man}} \\ &= 12\; {\rm ft} \times \frac{5\; {\rm ft}}{8\; {\rm ft}} \\ &= 7.5\; {\rm ft}\end{aligned}[/tex].

Answer:

37.9 units (nearest tenth)

Step-by-step explanation:

As ABCD is a rectangle, AD = BC and AB = DC.

Find the length of AD and AB using the distance formula.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}}[/tex]

From inspection of the given diagram:

Therefore:

[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(-7-(-5))^2+(-3-(-9))^2}\\& =\sqrt{(-2)^2+(6)^2}\\& =\sqrt{4+36}\\& =\sqrt{40}\end{aligned}[/tex]

[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(7-(-5))^2+(-5-(-9))^2}\\& =\sqrt{(12)^2+(4)^2}\\& =\sqrt{144+16}\\& =\sqrt{160}\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Perimeter of a rectangle} & = \sf 2(length + width)\\& = 2(AB+AD)\\& = 2(\sqrt{160}+\sqrt{40})\\& = 2(18.97366596...)\\& = 37.94733192...\\& = 37.9\: \sf units\:(nearest\:tenth)\end{aligned}[/tex]

Therefore, the perimeter of the rectangle ABCD is 37.9 units (nearest tenth).

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[tex]\sqrt{10^2 - 3^2}=\boxed{\sqrt{91} \text{ ft}}[/tex]

The slope of Line 1 is m = -2

The slope of Line 2 is m = -2

For Line 1;

(x₁, y₁) = (1, 1);

(x₂, y₂) = (-2, 7);

m₁ = (7-1)/(-2-1) = -2;

For Line 2;

(x₃, y₃) = (-1, 4);

(x₄, y₄) = (1, 0);

m₂ = (4-0)/(-1-1) = -2;

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Answer:

[tex]-1t+31 +3 \geq -4[/tex]

[tex]-1t +34 \geq -4[/tex]

[tex]-1t \geq 30[/tex]

[tex]t \geq -30[/tex]

Answer:

x = 3.25

Step-by-step explanation:

Use the Rule of 3 to solve this

Work in picture

Step-by-step explanation:

the average change rate for a function g(x) is defined for an interval of x values as

(g(interval end) - g(interval begin))/(interval end - interval begin)

in our case that is

(g(2013) - g(2008))/(2013 - 2008) =

= (24 mil. - 186 mil)/5 = -162 mil./5 =

= -162,000,000 / 5 = -32,400,000

that means that as a mean value there were 32,400,000 digital cameras shipped less every year.

in other words, fewer and fewer digital cameras are sold. the demand is strongly declining.

actually, following the mean values and their trend, there should have been no new digital cameras shipped in 2014 anymore (as 24 mil. - 32.4 mil is less than 0).

Answer: $52 is your new balance

Step-by-step explanation: -12+60=52

If points E,F,G are collinear, then,

EF+FG = EG

5x+10 = 10x

10 = 10x-5x

10 = 5x

5x = 10

x = 10/5

x = 2

So,

As a check, EF+FG = 10+10 = 20 = EG to help confirm the answer

Answer:

EF = 10

Step-by-step explanation:

EF = 5x

FG = 10

EG = 10x

Answer:

x^21/5

Step-by-step explanation:

To change this expression to an expression with a rational exponent, we need to change the radical to a rational (fractional) exponent. Just as square root is a one half power and cuberoot is a one-third power, a fifth root is a one-fifth power.

Once the radical is changed to a fraction, we will just use the exponent rule that says when you raise a power to a power, you multiply exponents.

see image.

Answer:

x = 7, y = 45

Step-by-step explanation:

[tex]7x+13=6x+20[/tex]

[tex]x=20-13\\x=7[/tex]

Angle

[tex]7(7)+13=49+13=62^{0}[/tex]

supplementary angle

180 - 62 = 118°

[tex]3y-17=118[/tex]

[tex]y=\frac{118+17}{3} =135/3=45[/tex]

Hope this helps

Answer:

12.50m/s

in 2 seconds: 25

im not really good at math but i tried

An equation that relates the number of bags, x, to the cost, y is y = 5x.

An equation is a mathematical statement that claims that the two sides are equal.

An equation involves two or more variables that require some mathematical operations to obtain their equivalent value.

Therefore, an equation contains numbers, variables, and operators, which show a value after the mathematical operations.

Let the number of bags for the class = x (number of students)

Let the unit cost of a bag = $5

Let y = the total cost

Equation, y = 5x

Thus, an equation that relates the number of bags, x, to the cost, y is y = 5x.

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Answer:

b= p-(a+c)

Step-by-step explanation:

Answer: 3.32  

Step-by-step explanation:

√11=

3.3166=

3.3166=3.32      ==>When rounding to the hundredth place, if the thousandth's digit is 5 or greater, increase the hundredth's digit by 1.

Answer:y=mx+b

Step-by-step explanation:

Answer:

Let x be the amount invested in funds that earned 8%.

Then the amount invested in stock that suffered 3% loss is 18,000 - x.

The profit from investment in funds is 8%x

The loss from investment in stock is 3%(18,000 - x).

The net profit is 8%x - 3%(18,000 - x).

As the net profit given in the problem is $780, we have:

8%x - 3%(18,000 - x) = 780

Step-by-step explanation:

Answer:

The length should equal 27.

The width should equal 13.

A: P= 2L+ 2W

B: L=2W+1

Step-by-step explanation:

Perimeter is always equal to all of the sides added up.

You can find out the width and length by subsititution.

80=2(2W+1) +2W

80=4W+2+2W

80=6W+2

78=6W

W=13

L=(13*2)+1

L=27

Answer:

Flying Disc should be 72

Step-by-step explanation:

circumference = πd

HD Coin    C = 3π

                  9.42477796077

Flying Disc.  C = 23π
                      72.2566310326

Jar Lid      C = 8π

                  25.1327412287

Flower Pot     C = 15π

                        47.1238898038

Answer:

21

Step-by-step explanation:

Just substitute -3 in for a and 2 in for b

[tex]a^2 + 6b\\-3^2 + 6(2)\\9 + 6(2)\\9 + 12\\21[/tex]

When you square a negative number, the answer is positive. Good luck, and have a great day!

Also, Jesus loves you!!!!

Step-by-step explanation:

complementary means together they are 90°.

x = 3y - 6

x + y = 90

(3y - 6) + y = 90

4y - 6 = 90

4y = 96

y (the smaller angle) = 24°

x (the larger angle) = 3y - 6 = 3×24 - 6 = 72 - 6 = 66°

The probability that at least one of the births requires a cesarean delivery is 0.897.

To calculate prob(x >= 1):

prob(x>=1) = 1 - prob(x = 0)

                  = 1 - (1-0.248)^8

                  = 0.897

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