Rectangle A'B'C'D' was created by dilation Rectangle ABCD using D as the center of dilation.
What is the scale factor of the dilation?
Based on the scale factor, how many copies of ABCD, including the original, should fit inside A'B'C'D?

The roots of the given quadratic equation are 6 and -4.

The given quadratic equation is:

[tex](x-4)(x+2)=16[/tex]

Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where [tex]a\neq 0[/tex].

[tex]x^{2} -2x-8=16[/tex]

[tex]x^2-2x-24=0[/tex]

[tex]x^{2} -6x+4x-24=0[/tex]

[tex]x(x-6)+4(x-6)=0[/tex]

[tex](x-6)(x+4)=0[/tex]

[tex]x=6[/tex]

[tex]x=-4[/tex]

Hence, the roots of the given quadratic equation are 6 and -4.

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Answer:

The factored form of the equation is (x + 4)(x – 6) = 0.

(option C)

Answer:

Mitch did not make a mistake

Step-by-step explanation:

The -2 and 2 on the right side cancel out and so you are left with 7.7-2=w. Combine like terms and your left with 5.7=w

Answer:

x: {-3, 5}

Step-by-step explanation:

Step 1. Find least common denominator

Step 2. Multiply missing factors on top AND bottom

Step 3. Combine like terms

Step 4. Simplify (get rid of denominator)

Step 5. Solve for x

[tex]\frac{x}{x-5} +\frac{3}{x+2} =\frac{7x}{x^2-3x-10}[/tex]            LCD = [tex]x^2-3x-10[/tex]   OR  [tex](x-5)(x+2)[/tex]

[tex]\frac{x}{x-5}(\frac{x+2}{x+2}) +\frac{3}{x+2}(\frac{x-5}{x-5}) =\frac{7x}{x^2-3x-10}[/tex]

[tex]\frac{x(x+2)}{(x-5)(x+2)} +\frac{3(x-5)}{(x+2)(x-5)} =\frac{7x}{(x-5)(x+2)}[/tex]

[tex]\frac{x(x+2)+3(x-5)}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}[/tex]

[tex]\frac{x^2+2x+3x-15}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}[/tex]

[tex]\frac{x^2+5x-15}{(x-5)(x+2)} =\frac{7x}{(x-5)(x+2)}[/tex]

[tex]x^2+5x-15=7x[/tex]

[tex]x^2-2x-15[/tex]

[tex](x-5)(x+3)[/tex]

x = -3, 5

The Inference that can be made from the survey is: B. On average, it will take 4 hours to complete a round of golf at Green Tee's golf course.

Survey can be defined as the process of collecting data or informationso as to reach or draw a conclusion.

The survey analysis shows that it will take an average of 4 hours for an experience golfers to complete or finish a round of golf based on the fact that the golfers all had previous experience.

Therefore on average, it will take 4 hours to complete a round of golf at Green Tee's golf course.

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The total score of Melissa and Tomas who are playing a game with complex numbers is 8-2i.

A complex number is the combination of real and imaginary number. It can be written as,

[tex]a+bi[/tex]

Here, (a) is a real number and (b) is an imaginary number.

Melissa and Tomas are playing a game with complex numbers.  Melissa has a score of 5 – 4i and Tomas has a score of 3 2i. The sum of their score is,

[tex]S=5 -4i +(3+2i)\\S=5+3-4i+2i\\S=8-2i[/tex]

Hence, the total score of Melissa and Tomas who are playing a game with complex numbers is 8-2i.

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Answer:

8-2i

Step-by-step explanation:

c

Answer:

the median is 15, there is no mode.

Step-by-step explanation:

to find the median- put the numbers in order from least to greatest (13,14,14,16,16,19) use a sheet of paper and cross off each number on the ends until you get to the middle. Once you have reached the middle you should have the two numbers 14, 16. Take 14 and 16, add them together and you will get 30. Divide 30 by 2 because there is two numbers for the median. You should end with 15 as your median.

to find the mode- find the number that occurs the most in the set of numbers, in this case all numbers occur the same amount of times, so therefor there is no mode.

happy to help<33.

Answer:

The circumference is 125.7cm

Answer:

-4 and 4

Step-by-step explanation:

Method 1

Apply Difference of Two Squares Formula: [tex]a^2-b^2=(a+b)(a-b)[/tex]

Given  [tex]x^2-16=0[/tex]

Rewrite 16 as 4²

Therefore, [tex]a^2=x^2[/tex] and [tex]b^2=4^2[/tex]

[tex]\implies a = \sqrt{x^2}=x[/tex]

[tex]\implies b=\sqrt{4^2} =4[/tex]

[tex]\implies x^2-16^2=(x+4)(x-4)[/tex]

[tex]\implies (x+4)(x-4)=0[/tex]

[tex]\implies (x+4)=0 \implies x=-4[/tex]

[tex]\implies (x-4)=0 \implies x=4[/tex]

Method 2

Given equation:

[tex]x^2-16=0[/tex]

Add 16 to both sides:

[tex]\implies x^2-16+16=0 + 16[/tex]

[tex]\implies x^2=16[/tex]

Square root both sides:

[tex]\implies \sqrt{x^2}=\sqrt{16}[/tex]

[tex]\implies x=\pm4[/tex]

Therefore, x = -4, x = 4

Answer:

B

Step-by-step explanation:

Because 0.75 is less than 1, the bigger x is, the smaller the whole thing will get. And the 4.1 in front is the starting point on the left side of the graph. Like on an actual graph with numbers:

If x is 0, f(x) is 4.1

If x is 5, f(x) is 0.97

The graph is decreasing. This is an equation and graph for "decay"

Answer:

3x2+9x−5

Step-by-step explanation:

You just have to add the like terms

Answer:

3x² + 9x - 5

Step-by-step explanation:

Group like terms:

3x² + 6x - 10 + 3x + 5

3x² + 9x -5

hope this helps :)

Answer:

A

Step-by-step explanation:

Answer:

Correct answer is: B: y ≤ 0

Step-by-step explanation:

[tex] \huge\fbox\green{ANSWER} [/tex]

Area is the amount of space taken up by a 2D shape

Answer:

The area is the extent or measurement of a surface or piece of land. You find out the area by doing the height x the Width.

Hope this helps..

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

2x = 84

x = roses

x = 84/2

x = 42

Answer:

$42.00

Step-by-step explanation:

You divide 84 by 2 and find the answer 42. Therefore, each rose is 42 dollars.

Answer:

1440 square inches of fabric

Step-by-step explanation:

Answer:

1440 square inches of fabric

Step-by-step explanation:

Solve for 1 banner

Area of 1 banner:

12*20/2

12*10

120.

12 banners,

12*120

= 1440 square inches of fabric

(or other types of material)

Answer:

385 cubes

Step-by-step explanation:

11*7*5=385 cubes

Answer:

Part A=7

Part B=7

Step-by-step explanation:

Part A = 7+9=16

Part B = 4 times 7= 28

Answer:

should be a. took the test and It was horrible. I remember trying and forgot how to do everything beother

Step-by-step explanation:

no balls

Melanie write the quadratic equation x^2 + 4x - 2 according to the directions that write a trinomial that could not be factored using integers.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

Patricia wrote:

[tex]\rm x^2+5x-14=0\\\\\rm x^2 -2x+7x-14=0\\\\\rm (x-2)(x+7)[/tex]

Shelly wrote:

[tex]\rm x^2-x-30=0\\\\\rm x^2-6x+5x-30=0\\\\\rm (x-6)(x+5)=0[/tex]

Melanie wrote:

[tex]\rm x^2+4x-2=0[/tex]

Here is the value of D:

[tex]\rm D = \sqrt{4^2-4(1)(-2)}[/tex]

D = √24

Lisa wrote:

[tex]\rm x^2+4x-5=0\\\\\rm x^2-x+5x-5=0\\\\\rm (x-1)(x+5)[/tex]

Thus, Melanie write the quadratic equation x^2 + 4x - 2 according to the directions that write a trinomial that could not be factored using integers.

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The sections of the garden is an illustration of fractions

The number sentence best shows whether Imelda is correct is 1/2 ÷ 3

From the question, we understand that she plants in 1/2 of the garden

Then 1/2 of the garden is divided into 3 sections, one of which is used to plant tulips

So, the area in which tulips are planted is:

Tulip = 1/2 ÷ 3

Hence, the number sentence best shows whether Imelda is correct is 1/2 ÷ 3

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The resulting equation of that step is the square root of  (x + 2)²  is  (x + 2).

A square root function is defined as a one-to-one function that takes a positive number as an input and returns the square root of the given input number.

From there, it was pretty easy for Theo to find the solutions

to the original equation.

If  (x + 2) = +2 , then  x = 0 .

If  (x + 2) = -2 , then  x = -4

Hence, the resulting equation of that step is the square root of  (x + 2)²  is  (x + 2).

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Answer:

no idea sorry

Step-by-step explanation:

.... .. . .... ...... . . .   .     ..      ...     ..        .         .

Answer:

huhh

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Answer: just graph it using the x and y coordinate points

Step-by-step explanation:

Answer:

(-4, -2)

Step-by-step explanation:

Rewrite the equations to make y the subject, so that it's easier to calculate the points on each line:

Equation 1

x - y = -2

⇒ x + 2 = y

⇒ y = x + 2

Equation 2

2x - 3y = -2

⇒ 2x + 2 = 3y

⇒ y = (2/3)x + 2/3

Calculate 2 points on each line:

Equation 1  (blue line on attached graph)

Substitute x = 0 and x = -2 into Equation 1 to create 2 points:

x = 0:   y = 0 + 2  ⇒ (0, 2)

x = -2:   y = -2 + 2  ⇒ (-2, 0)

Plot the points and draw a line through them.

Equation 2 (red line on attached graph)

Substitute x = 2 and x = -1 into Equation 1 to create 2 points:

x = 2:   y = (2/3)(2) + 2/3  ⇒ (2, 2)

x = -1:   y = (2/3)(-1) + 2/3  ⇒ (-1, 0)

Plot the points and draw a line through them.

Solution

The solution is the point where the two lines intersect.

Therefore, the point of intersection is (-4, -2)

Answer:

Instructions on making a parallelogram is stated below!

Step-by-step explanation:

To create a parallelogram with base measuring 6 units and the height 4 units:

Note: The height of the parallelogram must be perpendicular to the base.

Answer:

D + E = 2x⁴ + x³ –  3x²   + x + 1

D - E  = 9x³ +  x²   + x – 3

Step-by-step explanation:

D = x⁴ + 5x³ – x² + x – 1

E = x⁴ – 4x³ – 2x² + 2

D + E :                                                   D - E :

 x⁴ + 5x³ –  x²   + x – 1                          x⁴ + 5x³ –  x²   + x – 1  

+                                                         –                                                                  

 x⁴ – 4x³ – 2x² + 0 + 2                         x⁴ – 4x³ – 2x² + 0 + 2

_________________                      _________________

2x⁴ + x³ –  3x²   + x + 1                          0  +  9x³ +  x²   + x – 3

Answer:

i think its y=-1

Step-by-step explanation:

hope u get it right

The range of the frame width for the considered case is 0.5 (feet), because for this case, it can be at max of 0.5 feet, and at minimum of 0 feet.

For a set of data, the range is the difference between the maximum and minimum value. It sort of gives an idea of spread of the data.

For this case, we're given that:

Perimeter of a rectangle = 2(length + width)

Let 'l' denotes length, and 'w' denotes width, then we get:

[tex]Perimeter \leq 4\\2(l+w) \leq 4\\2(1.5 + w) \leq 4\\\\\text{Dividing both the sides by 2}\\\\1.5 + w \leq 2\\\\\text{Subtracting 1.5 from both the sides so as to get 'w' on one side}\\\\w \leq 0.5[/tex]

Now since the lowest value of width of a frame can be zero only, therefore, we get:

[tex]0 \leq w \leq 0.5[/tex]

Thus, the range of values 'w' can assume is: 0.5 - 0 = 0.5

Thus, the range of the frame width for the considered case is 0.5 (feet), because for this case, it can be at max of 0.5 feet, and at minimum of 0 feet.

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