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3 years ago

If the graph of the following parabola is shifted two units left and three units down, what is the resulting equation?

Mathematics

1 answer:

mafiozo [28]3 years ago

7 0

Answer:

$x=-8\left(y+3\right)^2-2$

Step-by-step explanation:

Because the x and y have been reversed in this equation, shifting the parabola to the left will be outside of the exponent and shifting up and down will be inside with the exponent.

The equation becomes $x=-8\left(y+3\right)^2-2$ .

Where subtracting by 2 moves it two units to the left and adding by 3 moves it 3 units down.

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Darina [25.2K]

Answer:

Part 1) The rate of change is $\frac{17}{15}$

Part 2) The initial value is 68

Part 3) The function rule to the linear model is $y=\frac{17}{15}x+68$

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

step 1

Find the slope

take two points from the table

(0,68) and (15,85)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{85-68}{15-0}$

$m=\frac{17}{15}$

In a linear function , the slope is the same that the rate of change

therefore

The rate of change is $\frac{17}{15}$

step 2

Find the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

Looking at the table

For x=0, y=68

therefore

The y-intercept is

$b=68$

The y-intercept is also called the initial value

therefore

The initial value is 68

step 3

Determine the function rule to the linear model

$y=mx+b$

we have

$m=\frac{17}{15}$

$b=68$

substitute

$y=\frac{17}{15}x+68$

8 0

3 years ago

At eagle bay, it cost $12 per hour to rent a canoe. Nate and his friends rented a canoe for 4 hours and paid $68. Write and solv

Rus_ich [418]

Answer:84

Step-by-step explanation:because 7x12=84

6 0

4 years ago

A train travels 3.5 kilometers on a straight track with grade of 1 degree 10'. What is the vertical rise of the train distance?

denpristay [2]

The answer is
h = AB sin tetha,
tetha is <span>1 degree 10' = 1.1°, and AB = 3.5km

the vertical rise is h = 4.7</span>

3 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. Based on the Pythagorean theorem, find the missing length fo

Neporo4naja [7]

Answer: See below

Step-by-step explanation:

The Pythagorean Theorem is a²+b²=c². Since each problem gives us the length of a, b, or c, we can directly plug them into this equation and solve.

Triangle EFG

9²+b²=41²

81+b²=1681

b²=1600

b=√1600

b=40

----------------------------------------------------------------------

Triangle PQR

20²+21²=c²

400+441=c²

c²=841

c=√841

c=29

----------------------------------------------------------------------

Triangle XYZ

a²+24²=25²

a²+576=625

a²=49

a=√49

a=7

6 0

3 years ago

in 1991, a gallup poll reported this percent to be 79%. using the data from this poll, test the claim that the percent of driver

snow_lady [41]

We reject our null hypothesis, H₀, at a level of significance of =0.01 since the P-value is less than that threshold. There is compelling statistical data to indicate that since 1991, the proportion of drivers who love driving has decreased.

Given,

The Pew Research Center recently polled n=1048 U.S. drivers and found that 69% enjoyed driving their automobiles.

In 1991, a Gallup poll reported this percentage to be 79%. using the data from this poll, test the claim that the percentage of drivers who enjoy driving their cars has declined since 1991.

To report the large-sample z statistic and its p-value,

Null hypothesis,

H₀ : p = 0.79

Alternative hypothesis,

Ha : p < 0.79

Level of significance, α = 0.01

Under H₀

Test statistic,

$Z_0= \frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n} } }$

Z₀ = -7.948

The alternative hypothesis(Ha) is left-tailed, so the P-value of the test is given by

P-value = P(z <-7.945)

= 0.000 (from z-table)

Since the P-value is smaller than given level of significance, α=0.01 we reject our null hypothesis, H₀, at α=0.0.1 level Strong statistical evidence to conclude that the percentage of drivers who enjoy driving their cars has declined since 1991.

To learn more about hypothesis click here:

brainly.com/question/17173491

#SPJ4

5 0

2 years ago