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sertanlavr [38]
3 years ago
14

The system of equations y = –2x + 1 and y = x + 5 is shown on the graph below. Which statement is true about the solution to the

system of equations?
A. The x-value is between –1 and –2, and the y-value is between 3 and 4.
B. The x-value is between 3 and 4 , and the y-value is between –1 and –2.
C. The x-value is between 1 and 2, and the y-value is between –3 and –4.
D.The x-value is between –3 and –4, and the y-value is between 1 and 2.
Mathematics
1 answer:
Semenov [28]3 years ago
8 0

Answer:

the answer is a

Step-by-step explanation:

y = -2x +1

y = x + 5

-2x+1=x+5

-3x = 4

x= -4/3

y = -1 1/3 + 5= 3 2/3

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What is the equation of the circle that has its center at -26,120 and passed through the origin
OlgaM077 [116]

well, first off let's check those two points, we know it's centerd at (-26 , 120) and we also know it passes through (0 , 0), so the distance between those two points is its radius

~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-26}~,~\stackrel{y_2}{120})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(~~-26 - 0~~)^2 + (~~120 - 0~~)^2} \implies r=\sqrt{(-26)^2 + (120 )^2} \\\\\\ r=\sqrt{( -26 )^2 + ( 120 )^2} \implies r=\sqrt{ 676 + 14400 } \implies r=\sqrt{ 15076 } \\\\[-0.35em] ~\dotfill

\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-26}{h}~~,~~\underset{120}{k})}\qquad \stackrel{radius}{\underset{\sqrt{15076}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-26) ~~ )^2 ~~ + ~~ ( ~~ y-120 ~~ )^2~~ = ~~(\sqrt{15076})^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (x+26)^2+(y-120)^2 = 15076~\hfill

3 0
1 year ago
Question: Consider the similarity transformation of ΔABC to produce ΔEDF.
german

Answer:

see the explanation

Step-by-step explanation:

we have triangle  ΔABC

step 1

Rotate 90 degrees clockwise ΔABC about point C to obtain ΔA'B'C'

Remember that

A rotation is a rigid transformation

An object and its rotation are the same shape and size, but the figures may be turned in different directions

so

ΔABC and ΔA'B'C' are congruent

ΔABC≅ ΔA'B'C

step 2

Dilate the triangle ΔA'B'C' to obtain triangle ΔEDF

Remember that

A dilation is a non rigid transformation

A dilation produces similar figures

If two figures are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent

Find the scale factor of the dilation

The scale factor is equal to the ratio of corresponding sides

In this problem

Let

z ----> the scale factor

so

z=\frac{ED}{AB}=\frac{DF}{BC}=\frac{EF}{AC}

Multiply the length sides of triangle ΔA'B'C' by the scale factor z to obtain the length sides of triangle ΔEDF

Note: in this problem the scale factor z is less than 1

That means ----> the dilation is a reduction

3 0
3 years ago
The table shows the height of a ball that was dropped from a 380-foot tower. What was the ball's rate of fall during the first 3
Alex

Answer:

60ft/s

Step-by-step explanation:

To find the rate

rate = f(3) - f(0)

         -------------

         3-0

rate = 200-380

         ---------------

         3-0

rate = -180/3   = -60 ft/s

The negative tells us it is falling

The fall falls 60ft/s

8 0
3 years ago
Read 2 more answers
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