Find the scale factors for the dilation of the small quadrilateral to the large

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Rewrite the fol

never [62]

Vertex Form: y = a(x - h)^2 + k, with (h,k) as the vertex.

To convert it into vertex form, we are going to be completing the square. Firstly, subtract 56 on both sides: $y-56=2x^2-32x$

Next, factor out the GCF, or greatest common factor, of the right side. To find the GCF, list the factors of both terms and the greatest one they share is their GCF. In this case, the GCF is 2: $y-56=2(x^2-16x)$

Next, we want to make what's inside the parentheses a perfect square. To find the constant of the perfect square, divide the x term by 2 and square the quotient. In this case:

-16 ÷ 2 = -8, (-8)² = 64

So you're gonna have to add 64 to the inside of the parentheses. To cancel this out, you will need to add to the other side the product of 64 and 2 (since 64 is inside the parentheses), which is 128: $y+72=2(x^2-16x+64)$

Next, factor the polynomial inside the parentheses: $y+72=2(x-8)^2$

Next, subtract 72 on both sides and your vertex form is $y=2(x-8)^2-72$

Now looking at this vertex form, the vertex is (8,-72), which means that the x-coordinate of the vertex is 8.

6 0

2 years ago

Help me on this question! Jake can carry 6 1/4 pounds of wood in from the barn.His father can carry 1 5/7 times as much as jake.

ioda

$\text{ Jake father can carry } 10\frac{5}{7} \text{ or } \frac{75}{7} \text{ pounds }$

Solution:

From given question,

Number of pounds Jake carry = $6\frac{1}{4} \text{ pounds }$

Number of pounds his father carry is $1\frac{5}{7}$ times as much as jake

To find: Number of pounds Jake father can carry

Convert the mixed fractions to improper fractions

Multiply the whole number part by the fraction's denominator.

Add that to the numerator.

Then write the result on top of the denominator

$\rightarrow 6\frac{1}{4} = \frac{4 \times 6+1}{4} = \frac{25}{4}\\\\\rightarrow 1\frac{5}{7} = \frac{7 \times 1+5}{7} = \frac{12}{7}$

Then according to question,

$\text{Pounds father carry } = \frac{12}{7} \text{ times the pounds jake carry }\\\\\text{Pounds father carry } = \frac{12}{7} \times \frac{25}{4}\\\\\text{Pounds father carry } = \frac{75}{7}\\\\\text{In terms of mixed fractions, }\\\\\text{Pounds father carry } = \frac{75}{7} = 10\frac{5}{7}$

$\text{ Thus, Jake father can carry } 10\frac{5}{7} \text{ or } \frac{75}{7} \text{ pounds }$

3 0

2 years ago

What is the solution of 3x=67 ?

natta225 [31]

Answer:

22.3 repeating

Step-by-step explanation:

3x divided by 3x equals 1x or just x but to divide this you also have to divide the other side of the equals sign by 3 as well therefore the answer is 22.3 repeating

You might find it easy by putting it in fractions such as 3x/3x = 67/3 so x =22.3 repeating

8 0

3 years ago

Read 2 more answers

Solve the system by substitution. -2x-10y=-2 -4y=x

Julli [10]

maybe xd ad something else please

8 0

3 years ago

7. Jane is at the amusement park. The admission is $25, and the rides are $2 each. If Jane

Vedmedyk [2.9K]

Answer:

Jane got on 16 rides

Step-by-step explanation:

r= numbers of rides

25 + 2r

25 + 2r = 57

-25 -25

_____________

2r\2 32/2

r=16

6 0

3 years ago