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Yanka [14]
3 years ago
11

The graph below shows two functions: function f of x is a straight line which joins the ordered pairs negative 2.5, 9 and 2.5, n

egative 1. Function g of x is a curved line which joins the ordered pairs negative 1.4, 6.8 and 2, 0.2 Based on the graph, what are the approximate solutions to the equation −2x + 4 = (0.25)x?

Mathematics
2 answers:
7nadin3 [17]3 years ago
7 0

just took the test and this is the correct answer -1.4, 2.

weqwewe [10]3 years ago
6 0
We are looking for the approximate solution of -2x+4=(0.25)^x, that is, we are looking for the solution of the equation f(x)=g(x).

The solution of this equation are represented by the intersecting points (x, y) of the graphs of these functions, because the intersecting points (x, y) are such that 

                    y=f(x), but also y=g(x).


From the graph, we can see that there are two solutions, one is at approximately x=2, and the other is approximately -1.4.


Answer: -1.4, 2.

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Triangle QRS is dilated according to the rule DO,2 (x,y).
Gemiola [76]

The correct options about the dilation are; Options A, B and E

<h3>How to interpret Dilated Objects?</h3>

From the given information, find attached a dilated image.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS are; Q (-3, 3), R (2, 4) and S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In other words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2(x, y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes: Q' (-6, 6), R' (4, 8), S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

A) DO, 2 (x, y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

Thus Option A is correct.

B) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

m = 4/(-6+2) = 4/-4

m = -1

Option B is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

Option C is false

d) The vertices of the image are closer to the origin than those of the pre-image.

From the diagram, the vertices of the preimage are closer to the origin than those of the dilation image.

Option D is False

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

Option E is correct.

Read more about Dilated Objects at; brainly.com/question/10253650

#SPJ1

8 0
2 years ago
A restaurant manager recorded the number of people in different age groups who attended her food festival. She then created the
Andre45 [30]

Answer:

Option: B

There are three times as many participants in the 40-59 age group than in the 0-19 age group.

Step-by-step explanation:

From the histogram we have following observations:

Number of people in the age group  0-19= 20

Number of people in the age group 20-39=40

Number of people in the age group 40-59=60

Number of people in the age group 60-79=50

Hence, from the data we could say that  there are three times as many participants in the 40-59 age group( which is 60) than in the 0-19 age group(which is 20).

Hence, option B is correct.


4 0
3 years ago
Read 2 more answers
Please help i don't get it
Ivan
The perimeter is just all the lines around the outside of the shape so basically take all the numbers and add them together to get the answer
3 0
3 years ago
Read 2 more answers
What is the sum of 1+3+5+7+...1209
Natalka [10]

the sum of 1+3+5+7+1209 is.....1225

8 0
3 years ago
A magazine has 96 pages. There are ads on 75% of the pages. How many pages don't have ads?
abruzzese [7]

Hey there! :)

Answer:

24 pages.

Step-by-step explanation:

Calculate how many pages 75% of 96 is:

96 × 0.75 = 72 pages.

Find how many pages do not have ads by subtracting the amount that have ads from the total:

96 - 72 = 24 pages.

Therefore, 1/4 of 96 or 24 pages do not have ads.

4 0
4 years ago
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