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Romashka [77]
3 years ago
6

Which of these linear functions has a greater rate of change than a linear function with a slope of 6 and a y–intercept of 3? Se

lect three that apply.
A)
y = 5x + 2

B)
y = 7x + 4

C)
y = 2x + 8

D)
y = 9x + 1

E)
y = 6x + 3

F)
y = 8x + 5
Mathematics
1 answer:
valentinak56 [21]3 years ago
8 0

Answer: the correct options are B, D and F

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

m = slope = rate of change

Looking at the equations given, the three that apply are

B) slope = 7

y intercept = 4

It has a greater rate of change than a linear function with a slope of 6 and a y–intercept of 3

D) y = 9x + 1

slope = 9

y intercept = 1

It has a greater rate of change than a linear function with a slope of 6 and a y–intercept of 3

F) y = 8x + 5

slope = 8

y intercept = 5

It has a greater rate of change than a linear function with a slope of 6 and a y–intercept of 3

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The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 se
kakasveta [241]
Let:
x = cost of senior citizen ticket
y = cost of student ticket

4x + 5y = 102
7x + 5y = 126

4x + 5y = 102
4x = 102 - 5y
x = (102 - 5y)/4
x = 102/4 - 5y/4

7x + 5y = 126
7(102/4 - 5y/4) + 5y = 126
(714/4 - 35y/4) + 5y = 126
-35y/4 + 5y = 126 - 714/4

note:
-35y/4 = -8.75y
714/4 = 178.5

-8.75y + 5y = 126 - 178.5
-3.75y = -52.5
y = -52.5/-3.75
y = 14


x = 102/4 - 5y/4
x = 102/4 - 5(14)/4
x = 8

x = cost of senior citizen ticket = $8/ea
y = cost of student ticket = $14/ea



6 0
3 years ago
Mackenzie built the small LEGO set. It cost $5.49.
EleoNora [17]
$5.49 + $10.49=$15:49 there’s your answer
6 0
2 years ago
How do you find the center of dilation for a negetive dilation?​
Andrei [34K]

the Answer:

Notice that the "image" triangles are on the opposite side of the center of the dilation (vertices are on opposite side of O from the preimage). Also, notice that the triangles have been rotated 180º.

Step-by-step explanation:

A dilation is a transformation that produces an image that is the same shape as the original but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. The center of dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

Note:

A dilation is NOT referred to as a rigid transformation (or isometry) because the image is NOT necessarily the same size as the pre-image (and rigid transformations preserve length).

What happens when scale factor k is a negative value?

If the value of scale factor k is negative, the dilation takes place in the opposite direction from the center of dilation on the same straight line containing the center and the pre-image point. (This "opposite" placement may be referred to as being a " directed segment" since it has the property of being located in a specific "direction" in relation to the center of dilation.)

Let's see how a negative dilation affects a triangle:

Notice that the "image" triangles are on the opposite side of the center of the dilation (vertices are on opposite side of O from the preimage). Also, notice that the triangles have been rotated 180º.

5 0
2 years ago
Read 2 more answers
According to the article "Characterizing the Severity and Risk of Drought in the Poudre River, Colorado" (J. of Water Res. Plann
mihalych1998 [28]

Answer:

(a) P (Y = 3) = 0.0844, P (Y ≤ 3) = 0.8780

(b) The probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.

Step-by-step explanation:

The random variable <em>Y</em> is defined as the number of consecutive time intervals in which the water supply remains below a critical value <em>y₀</em>.

The random variable <em>Y</em> follows a Geometric distribution with parameter <em>p</em> = 0.409<em>.</em>

The probability mass function of a Geometric distribution is:

P(Y=y)=(1-p)^{y}p;\ y=0,12...

(a)

Compute the probability that a drought lasts exactly 3 intervals as follows:

P(Y=3)=(1-0.409)^{3}\times 0.409=0.0844279\approx0.0844

Thus, the probability that a drought lasts exactly 3 intervals is 0.0844.

Compute the probability that a drought lasts at most 3 intervals as follows:

P (Y ≤ 3) =  P (Y = 0) + P (Y = 1) + P (Y = 2) + P (Y = 3)

              =(1-0.409)^{0}\times 0.409+(1-0.409)^{1}\times 0.409+(1-0.409)^{2}\times 0.409\\+(1-0.409)^{3}\times 0.409\\=0.409+0.2417+0.1429+0.0844\\=0.8780

Thus, the probability that a drought lasts at most 3 intervals is 0.8780.

(b)

Compute the mean of the random variable <em>Y</em> as follows:

\mu=\frac{1-p}{p}=\frac{1-0.409}{0.409}=1.445

Compute the standard deviation of the random variable <em>Y</em> as follows:

\sigma=\sqrt{\frac{1-p}{p^{2}}}=\sqrt{\frac{1-0.409}{(0.409)^{2}}}=1.88

The probability that the length of a drought exceeds its mean value by at least one standard deviation is:

P (Y ≥ μ + σ) = P (Y ≥ 1.445 + 1.88)

                    = P (Y ≥ 3.325)

                    = P (Y ≥ 3)

                    = 1 - P (Y < 3)

                    = 1 - P (X = 0) - P (X = 1) - P (X = 2)

                    =1-[(1-0.409)^{0}\times 0.409+(1-0.409)^{1}\times 0.409\\+(1-0.409)^{2}\times 0.409]\\=1-[0.409+0.2417+0.1429]\\=0.2064

Thus, the probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.

6 0
3 years ago
At the school book sale, Michael bought 3 books for $6. Darnell bought 5 books for $10. Are these rates equivalent? Explain your
Inessa [10]

Answer:

yes they are

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