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3 years ago

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The graph of F(x) shown below, has the same shape as the graph of G(x)=x^ 2 , but it is shifted down 3 units and to the left 2 u

nits. What is its equation?

1 answer:

MakcuM [25]3 years ago

4 0

Answer:

y = (x+2)^2 - 3

Step-by-step explanation:

Because you are shifting the graph down, the y-coordinate is being changed, so you subtract 3 from the original equation. Because you are shifting to the left, you have to add to the x-value. (It's kind of backwards from what you'd think.)

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Y = 3x +1; domain = {-1, 0, 1}<br> HELP PLEASE

ser-zykov [4K]

We have to put values of domain to find range

$\\ \ast\sf\longmapsto y=3x+1$

$\\ \ast\sf\longmapsto D_R=[-1,0,1]$

$\\ \ast\sf\longmapsto y=3(-1)+1=-3+1=-2$

$\\ \ast\sf\longmapsto y=3(0)+1=0+1=1$

$\\ \ast\sf\longmapsto y=3(4)+1=12+1=13$

Now

$\\ \ast\sf\longmapsto R_R=[-2,1,13]$

6 0

3 years ago

Read 2 more answers

The coordinates below represent two linear equations.

Alexxx [7]

So solve for the equations of the lines
y=mx+b
m=slope
b=y intercept

line 1=
(-4,5)
(0,2)
(x,y)
slope=(y1-y2)/(x1-x2)
x1=-4
y1=5
x2=0
y2=2
subsitute
(5-2)/(-4-0)=3/-4=-3/4
slope=-3/4
subsitute
y=-3/4x+b
subsitute one of the points
(0,2)
x=0 and y=2 is one solution
2=-3/4(0)+b
2=0+b
2=b
the equation is y=-3/4x+2

other line
(0,5)
(4,2)
x1=0
y1=5
x2=4
y2=2
sybsitute
(5-2)/(0-4)=3/-4=-3/4
slope=-3/4
subsitute
y=-3/4x+b
now subsitute one of the points to solve for b
(0,5)
x=0 and y=5 is one solution
5=-3/4(0)+b
5=0+b
5=b
y=-3/4x+5

so we have the lines/equations
y=-3/4x+2 and y=-3/4x+5
(at this point we can see that since slopes are the same and the y intercepts are different, they are paralell and therefor have 0 solutions, but for those who don't know paralellline thingie read on)

solve for common (x,y)
y=-3/4x+2
y=-3/4x+5
subsitute
-3/4x+2=y=-3/4x+5
-3/4x+2=-3/4x+5
subtract 2 from both sides
-3/4x=-3/4x+5
add 3/4x to both sides
0=5
fasle
there are no solutions

the answer is A: 0 solutions

6 0

3 years ago

2 ⋅ √ 2 + √ 8 - simplify

Ivanshal [37]

Answer:

$4\sqrt2$

Step-by-step explanation:

$2\sqrt{2} +\sqrt{8}=2\sqrt{2}+2\sqrt{2}=4\sqrt{2}$

6 0

2 years ago

Read 2 more answers

anna has 300naira and ojo has 1860naira.if anna saves 50 naira a day and ojo spends 70 a day, after how many days will they have

ExtremeBDS [4]

Answer:

Anna and Ojo will have same amount after 13 days.

Step-by-step explanation:

Given that:

Anna has 300 naira

She saves 50 naira per day.

Let,

x be the number of days.

y be the amount saved

y = 50x + 300

Ojo has 1860 naira

He spends 70 naira per day.

Let,

x be the number of days

y be the amount left

y = 1860 - 70x

For equal amount, the equations will be equal

50x +300 = 1860 - 70x

50x + 70x = 1860 - 300

120x = 1560

Dividing both sides by 120

$\frac{120x}{120}=\frac{1560}{120}\\x=13$

Hence,

Anna and Ojo will have same amount after 13 days.

4 0

3 years ago

A sample of 900900 computer chips revealed that 76v% of the chips do not fail in the first 10001000 hours of their use. The comp

Sergio039 [100]

Answer:

Null hypothesis: $p=0.78$

Alternative hypothesis: $p \neq 0.78$

$z=\frac{0.76 -0.78}{\sqrt{\frac{0.78(1-0.78)}{900}}}=-1.448$

$p_v =2*P(Z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of chip that do not fail in the first 1000 hours is not significantly different from 0.78 or 78%.

Step-by-step explanation:

1) Data given and notation

n=900 represent the random sample taken

$\hat p=0.76$ estimated proportion of chips do not fail in the first 1000 hours

$p_o=0.78$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.78:

Null hypothesis: $p=0.78$

Alternative hypothesis: $p \neq 0.78$

When we conduct a proportion test we need to use the z statistic, and the is given by:

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.76 -0.78}{\sqrt{\frac{0.78(1-0.78)}{900}}}=-1.448$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level assumed for this case is $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of chip that do not fail in the first 1000 hours is not significantly different from 0.78 or 78%.

7 0

3 years ago