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1 year ago

What is the location of A’ and did the figure get larger or smaller?

Mathematics

1 answer:

storchak [24]1 year ago

3 0

Scale Factor is defined as the ratio of the size of the new image to the size of the old image. The center of dilation is a fixed point in the plane.

If the scale factor is more than 1, then the image stretches. If the scale factor is between 0 and 1, then the image shrinks. If the scale factor is 1, then the original image and the image produced are congruent.

To dilate a figure by a scale factor, all the coordinates are multiplied by the scale factor.

The coordinates of point A are (8, 6). A dilation by a scale factor of 0.5 means that the figure will be reduced. The new coordinates will be:A

$\begin{gathered} A^{\prime}=(0.5\times8,0.5\times6) \\ A^{\prime}=(4,3) \end{gathered}$

Therefore, the FIRST OPTION is correct.

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F(x)=2x^2-x-10 part a: what are the X intercepts of the graph of f(x)? Show your work

Genrish500 [490]

A. x intercepts are where the graph hits the x axis or where f(x)=0
0=2x^2-x-10
solve
hmm
we can use the ac method
multiply 2 and -10 to get -20
what 2 numbers muliply to get -20 and add to get -1 (the coefint of the x term)
-5 and 4
split the midd into that
0=2x^2+4x-5x-10
group
0=(2x^2+4x)+(-5x-10)
factor
0=2x(x+2)-5(x+2)
undistribute
0=(x+2)(2x-5)
set each to 0
0=x+2
0=-2

0=2x-5
5=2x
5/2=x

x intercepts are at x=-2 and 5/2 or the points (-2,0) and (5/2,0)

B. ok, so for f(x)=ax^2+bx+c
if a>0, then the parabola opens up and the vertex is a minimum
if a<0 then the parabola opens down and the vertex is a max

f(x)=2x^2-x-10
2>0
opoens up
vertex is minimum

ok, the vertex

the x value of the vertex in f(x)=ax^2+bx+c= is -b/(2a)
the y value of the vertex is f(-b/(2a)) so
given
f(x)=2x^2-x-10
a=2
b=-1
-b/2a=-(-1)/(2*2)=1/4
f(1/4)=2(1/4)^2-(1/4)-10
f(1/4)=2(1/16)-1/4-10
f(1/4)=1/8-1/4-10
f(1/4)=1/8-2/8-80/8
f(1/4)=-81/8
so the vertex is (1/4,-81/8) or (0.25,-10.125)

C. graph the x intercepts and the vertex
the vertex is min and the graph goes through the x intercepts

4 0

2 years ago

Kayla is on level 12 of a new game. Everyday she completes 6 new levels. Maddy is on level 28 of the same game. Everyday she com

ankoles [38]

Answer:

Kayla and Maddy will be in the same level in 4 days.

Step-by-step explanation:

Kayla: y = 6x + 12

Maddy: y = 2x + 28

6x + 12 = 2x + 28

Subtract 2x from both sides;

4x + 12 = 28

Subtract 12 from both sides;

4x = 16

Divide both sides by 4;

x = 4

3 0

2 years ago

Read 2 more answers

Here is a diagram and its corresponding equation. Find the solution to the equation and explain your reasoning 38 x+7 x+7 x+7 x+

QveST [7]

Answer:

x = (-158)/87

Step-by-step explanation:

Solve for x:

38 x + 7 x + 7 x + 7 x + 7×4 (x + 7) = 38

Hint: | Multiply 7 and 4 together.

7×4 = 28:

38 x + 7 x + 7 x + 7 x + 28 (x + 7) = 38

Hint: | Group like terms in 38 x + 7 x + 7 x + 7 x + 28 (x + 7).

Grouping like terms, 38 x + 7 x + 7 x + 7 x + 28 (x + 7) = 28 (x + 7) + (38 x + 7 x + 7 x + 7 x):

28 (x + 7) + (38 x + 7 x + 7 x + 7 x) = 38

Hint: | Add like terms in 38 x + 7 x + 7 x + 7 x.

38 x + 7 x + 7 x + 7 x = 59 x:

28 (x + 7) + 59 x = 38

Hint: | Distribute 28 over x + 7.

28 (x + 7) = 28 x + 196:

28 x + 196 + 59 x = 38

Hint: | Add like terms in 59 x + 28 x + 196.

28 x + 59 x = 87 x:

87 x + 196 = 38

Hint: | Isolate terms with x to the left hand side.

Subtract 196 from both sides:

87 x + (196 - 196) = 38 - 196

Hint: | Look for the difference of two identical terms.

196 - 196 = 0:

87 x = 38 - 196

Hint: | Evaluate 38 - 196.

38 - 196 = -158:

87 x = -158

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 87 x = -158 by 87:

(87 x)/87 = (-158)/87

Hint: | Any nonzero number divided by itself is one.

87/87 = 1:

Answer: x = (-158)/87

5 0

3 years ago

Between 2000 and 2010, the percentage of fatal automobile accidents due to speeding decreased by 34% to 16%. What percentage of

docker41 [41]

Answer: 50%

Step-by-step explanation:

In 2010 the percentage of fatal accidents was 16%.

This is 34% less than it was in 2000 because the text says that the 2010 percentage was 16% after being reduced by 34% from 2010.

The percentage of fatal accidents in 2000 is therefore:

= 2010 fatal percentage + Percentage reduced from 2000

= 16% + 34%

= 50%

6 0

2 years ago

6=2(y+2) what is the value of y in the equation

uysha [10]

Answer: y = 1

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers