The vertices of triangle ABC are A(-2, 3), B(3, 3), and C(-2, -7). The triangle is dilated with a scale factor of 2. Estimate the perimeter of the dilated figure to the nearest whole number.

Answer:

(3, 6)

Step-by-step explanation:

1. If any factors can be cancelled out, then this indicates that there are holes in the graph.

2. To find the x-coordinate of the hole, set the factor equal to zero and solve for x.

3. Find the y-coordinate by substituting the x-coordinate back into the "reduced" function.

Here are the steps:

[tex]f(x) = \dfrac{ { x }^{ 2 } -9 }{ x-3 }[/tex]

Factor the top part of the function

x² - 9

Since both terms are perfect squares, factor using the difference of squares formula, a² - b² = (a + b) (a - b) where a = x and b = 3

(x + 3) (x - 3)

Now that we have the top part of the function factored, we can solve the rest of the problem:

[tex]f \left( x \right) = \dfrac{ \left( x+3 \right) \left( x-3 \right) }{ x-3 }[/tex]

Set the factor "x - 3" equal to zero and solve for x

x - 3 = 0

Add 3 to both sides

x - 3 + 3 = 0 + 3

Simplify

x = 3

Now we need to solve for "y"

[tex]f \left( x \right) = \dfrac{ \left( x+3 \right) \left( x-3 \right) }{ x-3 }[/tex]

We change "f(x)", to "y"

[tex]y = \dfrac{ \left( x+3 \right) \left( x-3 \right) }{ x-3 }[/tex]

The two "x - 3" cancel out

y = x + 3

Substitute the x-value into the equation

y = 3 + 3

Add 3 and 3

y = 6

Now that we have our coordinates, we can write it as:

(x, y) = (3, 6)

So the answer is (3, 6)

Answer:

35.283

Step-by-step explanation:

Let's put it in a vertical format;

35

0.283

35 plus 0 = 35, and the rest will remain same, so the answer is 35.283

Answer:

B) 0.42

Step-by-step explanation:

population density=number of people/square units

we plug in 2,100 for the first one but we don't know the second one for that we need the area which is A=π[tex]r^{2}[/tex] so the radius is 40 millimeters so [tex]40^{2}[/tex] =1600 1600*π=5024

2,100/5024=0.417 round it up and it is 0.42

so B) 0.42 is the answer

Answer:

Step-by-step explanation:

STEP

1

:

           x

Simplify   —

           x

Equation at the end of step

1

:

 (3•(x2))

 ————————+((6•1)-8)

  (x-8)  

STEP

2

:

Equation at the end of step

2

:

   3x2      

 ——————— +  -2

 (x - 8)    

STEP

3

:

            3x2

Simplify   —————

           x - 8

Equation at the end of step

3

:

  3x2    

 ————— +  -2

 x - 8    

STEP

4

:

Rewriting the whole as an Equivalent Fraction

4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  (x-8)  as the denominator :

         -2     -2 • (x - 8)

   -2 =  ——  =  ————————————

         1        (x - 8)  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

4.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3x2 + -2 • (x-8)     3x2 - 2x + 16

————————————————  =  —————————————

   1 • (x-8)          1 • (x - 8)

Trying to factor by splitting the middle term

4.3     Factoring  3x2 - 2x + 16

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  +16

Step-1 : Multiply the coefficient of the first term by the constant   3 • 16 = 48

Step-2 : Find two factors of  48  whose sum equals the coefficient of the middle term, which is   -2 .

     -48    +    -1    =    -49

     -24    +    -2    =    -26

     -16    +    -3    =    -19

     -12    +    -4    =    -16

     -8    +    -6    =    -14

     -6    +    -8    =    -14

Answer:

98 cm

Step-by-step explanation:

sum the parts of the ratio , 2 + 4 + 7 = 13 parts

divide perimeter by 13 to find the value of one part of the ratio.

182 ÷ 13 = 14 cm ← value of 1 part of the ratio , then

2 parts = 2 × 14 = 28 cm

4 parts = 4 × 14 = 56 cm

7 parts = 7 × 14 = 98 cm

the longest side is 98 cm

Answer: a) y= 2,170,000(1+0.04)^10
b)  3,212,130 U.S. workers working at home.

Step-by-step explanation:

Step-by-step explanation:

initial amount: 2,170,000

rate of growth: 4%, or 0.04

time: 10 years

Using this information we can use the formula y=a(1+r)^t to figure out the answer.

After plugging in the amounts, we end up with the equation: 2,170,000(1+0.04)^10

Now, all that's left is to calculate. The final amount is 3,212,130

Answer:

169

Step-by-step explanation:

Use a proportion:

72/85=x/200

Solve for x

(72)(200)=85x

x=(72)(200)/85

x=169.41≈ 169

She can make 169 of 200 free throws.

Answer:

Use a simple random sampling technique.

Step-by-step explanation:

Sampling is a procedure applied in statistical analysis where a fixed number of data (observations or individuals) are selected from a superior population. The approach used to select a sample from a population is determined on the basis of the type of analysis being executed.

To test for defective bulbs the store manager has to select a sample. She can select a sample of size n from the 1000 bulbs using the simple random sampling technique.

A simple random sample is a part of a statistical population in which every individual of the population has an equal probability of being selected.

Assigning each individual of the population a unique number and using a computer or random number generator for selection is a procedure to select a simple random sample.

Answer:

1,000g:60sec

or 10 gram every singular second.

Step-by-step explanation:

Answer:

Go to symbolab . com and enter in the problems, it will give you the answers and show you the steps it took to solve them

Step-by-step explanation:

Answer:

The answer is 1

Step-by-step explanation:

Answer:

Dave had most fun for 1.5 minutes.

explanation:

Let the "fun time" be f

total time * portion of time fun  = fun time

[tex]\sf t * p = f[/tex]

[tex]\sf 6 \ * \frac{1}{4} = f[/tex]

[tex]\sf \frac{6}{4} = f[/tex]

[tex]\sf f = 1.5 \ minutes[/tex]

Question was for how many minutes, Dave had fun, so he had fun for 1.5 minutes

Let that half be x

So

[tex]\\ \rm\Rrightarrow x(4)=6min[/tex]

[tex]\\ \rm\Rrightarrow x=6/4[/tex]

[tex]\\ \rm\Rrightarrow x=1.5min[/tex]

9514 1404 393

Answer:

  5x + 12 = 5x - 7

Step-by-step explanation:

There will be no solution when the coefficients of x are the same on both sides of the equal sign and the constants are different. That is the case for ...

  5x + 12 = 5x - 7

This reduces to ...

  19 = 0 . . . . . no value of x will make this be true: NO SOLUTION

Answer:

20:28 and 30:42

Step-by-step explanation:

Answer:

[see below]

Step-by-step explanation:

10/2 : 14/2 = 5:7

10 * 2 : 14 * 2 = 20:28

Hope this helps.

Step-by-step explanation:

-3/8 × 1 × -9/10 × -8/3

we know

- × - = +

+ × - = -

therefore, since we have 3 negative factors we get a negative result.

we can ignore the completely neutral multiplication by 1.

-3/8 × -9/10 × -8/3 = -(3×9×8)/(8×10×3) = -9/10

Answer:

d) 168 in.³

Step-by-step explanation:

volume = length × width × height

volume = 6 in. × 4 in. × 7 in.

volume = 168 in.³

Answer: d) 168 in³

Step-by-step explanation:

        The volume of a right rectangular prism can be found by multiplying the base (the length times the width) by the height. Since we are given all the values needed, we can multiply them all together and find our answer.

                 V = length * width * height

                 V = 4 in * 6 in * 7 in

                 V = 168 in³

  This gives us an answer of "d) 168 in³"

Answer:

y=10

Step-by-step explanation:

y=4x+2

y=4(2)+2

y=8+2

y=10

Answer:

y=10

Step-by-step explanation:

plug-in 2 to x

[tex]y=4(2)+2[/tex]

multiply 4 and 2

[tex]y=8+2[/tex]

add 8 and 2

[tex]y=10[/tex]

Answer:

3/2

Step-by-step explanation:

"Negative" means take the opposite sign.

"reciprocal" means flip it over.

Answer:

I think the last one?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the exponential function:

P(t) = 500,000 * e^(-0.099t)

P(t) = population t years later

When population will be one-half the initial amount

Half the initial amount = 500000/2 = 250,000

250000 = 500000 * e^(-0.099t)

250000/50000 = e^(-0.099t)

0.5 = e^(-0.099t)

Take the In of both sides

In(0.5) = - 0.099t

−0.693147 = - 0.099t

0.693147 / 0.099 = t

t =

Answer:

[tex]2\frac{5}{9}[/tex]

Step-by-step explanation:

Hi !

2.(5) = 2 5/9

Good luck !

Step-by-step explanation:

please mark me as brainlest chelli

Answer:

Can I see a picture? Or the angle diagram?

Answer: I think 288

Step-by-step explanation:

Answer:

A. 3680.32 inches³

Step-by-step explanation:

To find the volume of this shape, all we have to do is multiply the length width and height together:

v = l × w × h = 15.5 × 11.2 × 21.2 = 3680.32 inches³

Hope this helps!

Answer:

Well the only answer to this question that I can think of is 360 that's because all of the angles in a circle are equal to 360.

Step-by-step explanation:

Answer:

it will travel 9 hour in 600miles

it will take 4 men to weed the same compound in 2 days

it will take 2 men to now a large piece of law in 3 days

Step-by-step explanation:

it

Answer:

Step-by-step explanation:

Circumference: Pi(D)

Circumference: 3.14x30

Circumference: 94.2

Area: Pi(R)^2

Area: 3.14x15^2

Area: 3.14x225

Area: 706.5

Answer:

3

Step-by-step explanation:

2y - 6y = 5 - 17

-4y = -12

y = 3