Mary’s bedroom rug is shown below. Find the perimeter and area of the rug.

Given:

The given functions are:

[tex]f(x)=x^2[/tex]

[tex]g(x)=3(x+5)^2-2[/tex]

To find:

The transformations performed of f(x) to create g(x).

Solution:

The translation is defined as

[tex]g(x)=kf(x+a)+b[/tex]                .... (i)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

We have,

[tex]f(x)=x^2[/tex]

[tex]g(x)=3(x+5)^2-2[/tex]

Using these two function, we get

[tex]g(x)=3f(x+5)-2[/tex]                 ...(ii)

On comparing (i) and (ii), we get

[tex]k=3,a=5,b=-2[/tex]

It means the graph of f(x) is vertically stretched with a scale factor of 3, shifts 5 units left and 2 units down to get g(x).

Therefore, the correct options are A and C.

Answer:

1200*0.70=840

840*0.70=588

588*0.70=411.60

411.60*0.70=288.12

Answer:

D. 95.476.

Step-by-step explanation:

sin 33 = 52/h

h =  52/sin 33

h = 95.476.

Answer:

Step-by-step explanation:

We will use right triangle trig and SohCahToa here to solve this. The side across from the angle marked as 33 degrees is given as 52; we are looking for h, the hypotenuse. The trig ratio that uses the the side across from the reference angle along with the hypotenuse is the sin ratio. Setting up the equation:

[tex]sin33=\frac{52}{h}[/tex]. Multiply both sides by h and then divide by sin(33) to get

[tex]h=\frac{52}{sin33}[/tex] so

h = 95.476, choice D.

Make sure your calculator is in degree mode and not radians when your angles are given in degrees

Answer:

125.7 inches cubed.

Step-by-step explanation:

πr^h is the formula for volume of cylinder.

Answer:

tdxutdxfhdxfhx hd tudbtd tudbytd

Step-by-step explanation:

fc fcgbtufnyufnutfiygniygmyufniygnyigfntudb rsdut rd utddutestur dutrd uttu uhgugfutfuy8. f utfuy. dutugvu v gigv. uvv gihg ihg igg gv ugv vug ugf ugv ugv v igiugigougojgohgiohgk h. i gigiy gygiygiytiy

Answer:

See below.

Step-by-step explanation:

Expected number = probability x 96 (the number of rolls)

Outcome    Probability    Expected Value

1                   1/3                  (1/3)(96) = 32

2                  1/12                 8

3                  1/12                 8

4                  1/12                  8

5                  1/12                  8

6                  1/3                    32

Answer:

6

Step-by-step explanation:

385/65= about 6 but technically its like 5.92307...

Step-by-step explanation:

Price of glove with tax = 385

Money saved per month = 65

Months needed for Derek to save enough money

= 385/65

= 5.923 months

Answer:

The answer is "16, 43, and 96".

Step-by-step explanation:

Given:

[tex]\sigma = 0.20\\\\c = 95\% = 0.95\\\\\therefore \alpha = 1- c = 1- 0.95 = 0.05\\\\\therefore \frac{\alpha}{2} = 0.025\\\\[/tex]

Using Z table:

[tex]\therefore Z_{\frac{\alpha}{2}} = 1.96\\\\[/tex]

For point a:

[tex]E = 0.10\\\\n=(\frac{Z_{\frac{\alpha}{2} \times \sigma}}{E})^2[/tex]

    [tex]= (\frac{(1.96\times 0.20)}{0.10})^2\\\\= 15.3664 \approx 16[/tex]

so, The Sample size (n) = 16

For point b:

[tex]E = 0.06\\\\n=(\frac{Z_{\frac{\alpha}{2} \times \sigma}}{E})^2[/tex]

   [tex]= (\frac{(1.96\times 0.20)}{0.06})^2\\\\= 42.6844444444\approx 43[/tex]

For point c:

[tex]E = 0.04\\\\n=(\frac{Z_{\frac{\alpha}{2} \times \sigma}}{E})^2[/tex]

    [tex]= (\frac{(1.96\times 0.20)}{0.04})^2\\\\= 96.04\approx 96[/tex]

Answer:

I believe that the question is "A puppy weighs 5 3/4 pounds. How many ounces does the puppy weigh."

Step-by-step explanation:

The answer is 23 ounces.

Step-by-step explanation:

if x is from B to D then it's 12-2= 10

x= 10

Answer:

(x + 4)² + (y - 7)² = 20²

Step-by-step explanation:

Graphing form

(x - h)² + (y - k)² = r²

(h, k) is the center = (-4, 7)

r is the radius = 20

-----------------------------------

Plug in the givens

(x + 4)² + (y - 7)² = 20²

Answer:

2

Step-by-step explanation:

Answer:

96 i think

Step-by-step explanation:

Answer:

96 I think

Step-by-step explanation:

Answer:

HL

Step-by-step explanation:

The two larger triangles shown in the diagram above each has a corresponding leg that is congruent to each other (BC = BC).

Also, we are given that the hypotenuse AC of one is congruent to the hypotenuse DB of the other.

This satisfy the Hypotenuse-Leg Congruence Theorem. Thus, the two larger triangles are congruent based on the HL Congruence Criterion which says two triangles are congruent if the leg and hypotenuse of one is congruent to the corresponding leg and hypotenuse of the other.

=======================================================

Explanations:

Problem 5)

Assuming HEFG is a parallelogram, this means the opposite sides are the same length.

EH = GF

x-3 = 4x-15

x-4x = -15+3

-3x = -12

x = -12/(-3)

x = 4

--------------------------

Problem 6)

We'll use the same idea from problem 5. The opposite sides EF and HG are congruent

EF = HG

3y = 3x+12

3y = 3*4+12

3y = 24

y = 24/3

y = 8

--------------------------

Problem 7)

For any parallelogram, the diagonals always cut each other in half.

Therefore HK = 2z+3 is exactly half that of segment HF = 22

Put another way, HF is twice as long as HK

2*(HK) = HF

2*(2z+3) = 22

4z+6 = 22

4z = 22-6

4z = 16

z = 16/4

z = 4

Answer:

Explanation:

Both of these inequalities are describing that the value of x is less than negative four, as observable by the solution set graphed on the number line.

Answer:

Step-by-step explanation:

the least common denominator for the fraction is

7*5=35

since there is no any number that ca divide both the number so multiply them.

Answer:

134.04

hope this helps

have a good day :)

Step-by-step explanation:

Answer: w=9/8

Step-by-step explanation:

Answer:

w=9/8

Hope I got it right

Answer:

a. Flipping a coin

b. heads ⇒ boy   tails ⇒ girl

c. Flip 4 coins (1 for each child) ten times

Step-by-step explanation:

Answer:

Step-by-step explanation:

D. On a coordinate plane, a straight line with positive slope goes through points (3, 3) and (4, 4).

Explanation:

For a relationship to be proportional it needs to meet two conditions:

1) its graph needs to be a straight line

2) every point of the graph needs to satisty the equation y = k•x, or, in other words k has to be equal for every point

Now, let's check the answers;

A) we have two points: A (2, 6) and B (4, 5). For point A, x is 2 and y is 6, so:

y = k•x

6 = k•2

k = 3

For point B, x is 4 and y is 5, so:

y = k•x

5 = k•4

k= 5/4

Since k isn't the same value for these two points, this isn't proprtional relationship.

B) this graph is curve, so since it's not a straight line it can't be proportional relationship.

C) similarly to graph A we have point A (5, 2) and point B (6, 3).

For point A, x is 5 and y is 2, so:

y = k•x

2 = k•5

k = 2/5

For point B, x is 6 and y is 3, so:

y = k•x

3 = k•6

k = 1/2

Again values of k aren't the same, so this isn't a proportional relationship.

D) Point A (3, 3) and point B (4, 4). For point A, x is 3 and y is 3, so:

y = k•x

3 = k•3

k = 1

For point B, x is 4 and y is 4, so:

y = k•x

4 = k•4

k = 1

Since value of k is the same for both points, this graph shows the proportional relationship.

Answer:

a

Step-by-step explanation: the line goes thru the origin

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

We want the solution to ...

  [tex]\dfrac{1}{x}=\dfrac{x+3}{2x^2}\\\\2x=x+3\qquad\text{multiply by $2x^2$}\\\\\boxed{x=3}\qquad\text{subtract $x$}[/tex]

Answer:

We have to find the value of x in

[tex] \sf \: \dfrac{1}{x} = \dfrac{x + 3}{2x {}^{2} } [/tex]

On cross multiplication

2x² × 1 = x × (x + 3)

2x² = x² + 3x

2x² - x² = 3x

x² = 3x

x × x = 3 × x

x = 3

Answer:

3. x=50, y=80, 4. x=6.5, y=5

Step-by-step explanation:

I think, not entirely sure.