Averi was trying to factor 4x2 + 20x - 16. She found
that the greatest common factor of these terms was 4
and made an area model:


What is the width of Averi's area model?​

Answer:

x > -3/14

Step-by-step explanation:

Step 1:  Subtract 2x from both sides

16x - 2x > 2x - 3 - 2x

14x > -3

Step 2:  Divide both sides by 14

14x / 14 > -3 / 14

x > -3/14

Answer:  x > -3/14

Answer:

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Answer:

d = 17

Step-by-step explanation:

d = √ (9 − 1) 2 + (15− 0)^2

d = √ (8) ^2 + (15) ^2

d = √ 64 + 225

d = √289

d = 17

Answer:

17

Step-by-step explanation:

i got it right on a quiz

C. Coordinates of D' (-6,3)

Step-by-step explanation:

When any figure is rotated 180° in the counterclockwise direction, then the coordinates of the vertices is changed into its opposite sign.

(x, y) → (-x, -y)

The coordinates of the vertices of quadrilateral ABCD is changed when it is rotated 180 degrees counterclockwise about the origin as,

A (7,-7) → A'(-7,7)

B (4,-10) → B' (-4,10)

C (1.5, -2.5) → C' (-1.5, 2.5)

D (6, -3) → D'(-6,3)

So the coordinates of D' will be (-6,3)

Answer:

  $361,223

Step-by-step explanation:

Each year, the value is multiplied by 1+5% = 1.05. After 51 years, it has been multiplied by that factor 51 times, so is now ...

  $30,000×1.05^51 ≈ $361,223

Final answer:

To find the approximate value of land purchased for $30,000 in 1960 with a 5% annual increase by 2011, we use the compound interest formula which results in an approximate value of $447,187.25.

Explanation:

To determine the approximate value of land in the year 2011, which was purchased for $30,000 in 1960 with an average annual increase of 5%, we will use the formula for compound interest. This situation can be treated as a compound interest problem where the initial principal is the initial land value, the rate is the annual increase, and the time is the number of years the land has appreciated.

The compound interest formula is [tex]A = P(1 + r/n)^(nt),[/tex] where A is the future value of the investment/loan, including interest, P is the principal investment amount (initial value of land), r is the annual interest rate (annual increase in value), n is the number of times that interest is compounded per year, and t is the time the money is invested or borrowed for, in years.

In this scenario, P is $30,000, r is 0.05 (5% expressed as a decimal), n is 1 since we are compounding annually, and t is 51 (2011 - 1960).

Therefore,

[tex]A = 30,000(1 + 0.05/1)^(1*51).[/tex]

Carrying out the calculation gives us the approximate value of the land in 2011.

[tex]A = 30,000(1.05)^51[/tex]
Approximate value of the land in 2011 = $447,187.25

The other measurement of the golden rectangle is approximately 9.1 inches.

A golden rectangle is defined by the property that the ratio of its length to its width is equal to the golden ratio, which is approximately 1.61803398875. This ratio is often denoted by the Greek letter phi (φ).

Given that one measurement of the golden rectangle is 5.7 inches, we can denote this as the width, w. To find the length, l, we use the golden ratio formula:

[tex]\[ l = w \times \phi \][/tex]

Substituting the given width and the value of φ:

[tex]\[ l = 5.7 \text{ inches} \times 1.61803398875 \][/tex]

[tex]\[ l \approx 9.1 \text{ inches} \][/tex]

Therefore, the other measurement of the golden rectangle, which is the length, is approximately 9.1 inches.

Answer:78

Step-by-step explanation:

77+67+99+79+100+65+79+89+58+67 = 780

Divide this number by the toal number of factor,which here is 10:

780/10 = 78

Answer:

25 in

Step-by-step explanation:

Answer:

25 miles

Step-by-step explanation:

If 1 inch equals 5 miles, which I wrote like 1in/5mi = 5in/x.

To find our answer we just multiply 5 miles by 5 inches to get 25 miles.

Answer:

Step-by-step explanation:

B

for a square diagonal is found by using pythagoras theorem.

(30)²+30²=900+900=1800≠45²

The best describes the shape of the baseball field would be; B Not square (30)² + 30² ≠45².

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Giselle is building a small baseball infield for her brother.

The infield should be in the shape of a square.

Each side of the infield, between bases, measures 30 feet.

The distance between home plate and second base, as shown in the picture, is 45 feet.

A square diagonal can be calculated by using the Pythagoras theorem.

|AC|^2 = |AB|^2 + |BC|^2    

= (30)² + 30²

= 900 + 900

= 1800

≠45²

Learn more about Pythagoras' theorem here:

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Answer:

195?

Step-by-step explanation:

Answer:

v = 8

Step-by-step explanation:

-v -7-3 = -26+v

2v = -10+26

2v = 16

v = 8

Height of the cone is 9.99 in

Step-by-step explanation:

512.87 = 1/3 × 22/7 × 7² × h

512.87 × 3 = 22 × 7 × h

1538.61 = 154h

∴ h = 1538.61/154 = 9.99 in

Answer:

350 *100 /50 = 700

Step-by-step explanation:

Basically 350 is 50 percent of the total. What u need to do is find the 100 percent. Just use this formula

Discounted price *100 / (what was the discount percentage when it was bought)

Answer:

original price is $525

Step-by-step explanation:

Answer:

(8,15)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that,

x^8/x^a=x²

Applying indices

Division rule a^m ÷ a^n = a^(m-n)

Then,

x^8/x^a=x²

x^(8-a)=x²

For this to be equal means that, the power are equals since they have the same base

Then, 8-a=2

8+2=a

So, a=10

Taking the second equation

(x^6)^b=x¹²

Using indices again

x^(6b)=x¹²

Also, for this to be equal

6b=12

Then, b=12/6

b=2

Then, b=2 and =10

We need to find b-a.

b-a=2-10=-8

Then, the answer to b-a is -8

Answer:

it depends on how big the floors are.

Step-by-step explanation:

x + y = 9

x = 9 - y

2x - y = 0

2(9 - y) - y = 0

18 - 2y - y = 0

-3y = -18

y = 6

x = 9 - y

x = 9 - 6

x = 3

The value of x and y are 3 and 3 respectively in the given system of equations.

A system of equations is a set of two or further equations that own an identical set of unknowns. The thing of solving a system of equations is to determine the values for the unknowns that quench all of the equations in the system.

It is given that the system of equations is,

2x - y = 0

x + y = 9

Now, from the first equation, we get

y = 2x

On putting the above value of y in the second equation, we get

x + 2x = 9,

3x = 9,

x = [tex]\frac{9}{3}[/tex]

x = 3.

Now putting this value of x in the first equation, we get

2 [tex]\times[/tex] 3 + y = 9

6 + y = 9

y = 9 - 6

y = 3.

So, x = 3 and y = 3 in the above system of equations.

Learn more about the system of equations here:

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Answer:

y = -5x + 9

Step-by-step explanation:

Hello!

Here is a chart on the slope intercept.

Hope This Helps!

Answer:

The dryer would cost 318 and the washer would cost 636

Step-by-step explanation:

954 divided by 3 = 318  318x2=636     318+638=954

Answer:

The correct answer is first option

(t + p, r)

Step-by-step explanation:

Points to remember

midpoint formula

Length of a line segment with endpoints (x1, y1) and (x2, y2) is given by,

Midpoint= [(x2 + x1)/2 , (y2 + y1)/2]

To find the midpoint of EC

Let   (x1, y1) = E(2t, 0) and  (x2, y2) = C(2p, 2r)

Midpoint = [(2t + 2p)/2 , (0 + 2r)/2]

= (2(t + p)/2 , 2r/2)

= (t + p, r)

Therefore midpoint of EC = (t + p, r)

The correct answer is first option

Answer:

36 cubed pieces of fudge

Step-by-step explanation:

9 x 12 = 108

108 ÷ 3 = 36

Answer:

AC=96 units

Step-by-step explanation:

x^2 - 16 = 6x

x^2 - 6x - 16 = 0

(x - 8)(x + 2) = 0

x - 8 + 8 = 0 + 8

x = 8 WORKS

x + 2 - 2 = 0 - 2

x = -2 CANT WORK BECAUSE IS NEG

CE = 6(8)

48

AC = AE + CE

AC = 48 + 48

AC = 96

Answer:  AC = 96

Answer:

4a² + 4ab + b² units²

Step-by-step explanation:

Area of a square = Length²

ER is a length of the square

ER = (2a + b)

Area of a square = (2a + b)² = (2a + b)(2a + b) = (2a)(2a) + (2a)(b) + (2a)(b) + (b)(b) = 4a² + 4ab + b²

The area of the square OSER = [tex]4a^{2}+4ab+b^{2}[/tex] sq unit

Step-by-step explanation:

Given,

Length of each side(ER) = (2a+b) unit

To find the area of the square OSER.

Formula

The area of a square with each side a unit is [tex]a^{2}[/tex] sq unit

[tex](a+b)^{2}= a^{2} +b^{2} +2ab[/tex]

Now,

The area of the square OSER = [tex](2a+b)^{2}[/tex] sq unit

= [tex]4a^{2}+4ab+b^{2}[/tex] sq unit [ by using the formula of ([tex]a+b)^{2}[/tex]]

Answer:

Step-by-step explanation:

24

Answer:

I think the answer would be C.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

it is the cost  in dollars to rent the bowling lane for 14 hrs.

The function f(14) represents that the number of dollars it costs to rent the bowling lane for 14 hours and this can be determined by using the given data.

Given :

The total cost f(x), in dollars, for renting a bowling lane for x hours is shown:  f(x) = 2x + 12.

The following steps can be used in order to determine the correct statement:

Step 1 - The arithmetic operations can be used in order to determine the value of f(14).

Step 2 - Write the given function.

f(x) = 2x + 12

Step 3 - Substitute the value of 'x' in the above function.

f(14) = 2(14) + 12

f(14) = 40

Therefore, the correct option is A) The number of dollars it costs to rent the bowling lane for 14 hours.

For more information, refer to the link given below:

https://brainly.com/question/5245372

Answer:

Real number is any number. This includes integers, rational, and irrational numbers.

While integers are just positive or negative whole numbers that also includes 0.

Hope this helps!

Answer:

2000

Step-by-step explanation: