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3 years ago

Describe how to translate the graph of y=√x to obtain the graph of y=√x-4

Mathematics

2 answers:

Korvikt [17]3 years ago

4 0

Answer:

Shifted to right by 4 units.

Step-by-step explanation:

We have been given a function $y=\sqrt{x}$ . We are asked to find the translation rule to obtain the function $y=\sqrt{x-4}$ from $y=\sqrt{x}$ .

Let us recall translation rules.

$f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}$

$f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}$

$f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}$

$f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}$

We can see that $-4$ is under radical, therefore, the function $y=\sqrt{x}$ is shifted to right by 4 units to obtain the graph of $y=\sqrt{x-4}$ .

Genrish500 [490]3 years ago

3 0

If the -4 is NOT under the radical sign the graph would move DOWN four units on the y axis.

If the -4 is under the radical sign the graph would move 4 units to the RIGHT on the x-axis.

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Alfred has 10 more tokens than Clarissa. Clarissa has twice as many tokens as Benji. They have 85 tokens altogether. How many to

marysya [2.9K]

Answer:

Alfred has 40 tokens

Clarissa has 30 tokens

Benji has 15 tokens

Step-by-step explanation:

Let's give each person a variable:

A for Alfred

C for Clarissa

B for Benji

Now, we can take what the question is saying and convert them into equations:

Alfred has 10 more tokens than Clarissa can look like this:

A = C + 10

Since Alfred has 10 more coins than Clarissa we can take C and add 10 to find how many tokens Alfred has.

Clarissa has twice as many tokens as Benji looks like this:

C = 2B

Since Clarissa has twice as many tokens as Benji we can multiply B (how many tokens Benji has) by 2.

Lastly, they have 85 tokens all together:

A + B + C = 85

We have these 3 equations:

A = C + 10

C = 2B

A + B + C = 85

Now, we can substitute some variables:

A = (2B) + 10 Since C is equal to 2B we can substitute 2B in for C in the first equation.

We have found what A equals, we can plug that in to the last equation:

(2B) + 10 + B + C = 85

We can also substitute the second equation into the third equation:

(2B) + 10 + B + 2B = 85

Combine like terms:

5B + 10 = 85

Solve

5B = 75

B = 15

This means that Benji has 15 tokens. Now we can find how much the other children have:

C = 2(15) = 30

Clarissa has 30 tokens

A = 30 + 10

A = 40

Alfred has 40 tokens.

Answer:

Alfred has 40 tokens

Clarissa has 30 tokens

Benji has 15 tokens

Checking the Answer

A + B + C = 85

40 + 15 + 30 = 85

85 = 85

I hope this helps!!

- Kay :)

6 0

3 years ago

15 points answer ,,,,,,,,,,,,,,,,,,,,,,,,

densk [106]

6/16 is the correct answer enjoy

6 0

4 years ago

A 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender selecti

Andrews [41]

Answer:

(a) Null Hypothesis, $H_0$ : p = 0.50

Alternate Hypothesis, $H_A$ : p > 0.50

(b) The value of level of significance (α) given in the question is 0.10.

(c) The sampling distribution of the sample statistic is Normal distribution.

(d) This test is right-tailed.

(e) The value of z test statistics is 0.96.

(f) The P-value is 0.1685.

(g) At 0.10 significance level the z table gives critical value of 1.282 for right-tailed test.

(h) We conclude that the proportion of baby girls is equal to 0.50.

Step-by-step explanation:

We are given that a 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender selection, the proportion of baby girls is greater than 0.5.

Assume that sample data consists of 78 girls in 144 births.

Let p = population proportion of baby girls

(a) So, Null Hypothesis, $H_0$ : p = 0.50 {means that the proportion of baby girls is equal to 0.50}

Alternate Hypothesis, $H_A$ : p > 0.50 {means that the proportion of baby girls is greater than 0.50}

(b) The value of level of significance (α) given in the question is 0.10.

(c) The sampling distribution of the sample statistic is Normal distribution.

(d) This test is right-tailed as in the alternative hypothesis we are concerned for proportion of baby girls that is greater than 0.50.

(e) The test statistics that would be used here One-sample z test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of baby girls = $\frac{78}{144}$ = 0.54

n = sample of births = 144

So, the test statistics = $\frac{0.54-0.50}{\sqrt{\frac{0.54(1-0.54)}{144} } }$

= 0.96

The value of z test statistics is 0.96.

(f) The P-value of the test statistics is given by;

P-value = P(Z > 0.96) = 1 - P(Z < 0.96)

= 1 - 0.8315 = 0.1685

(g) Now, at 0.10 significance level the z table gives critical value of 1.282 for right-tailed test.

(h) Since our test statistic is less than the critical value of z as 0.96 < 1.282, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region (which was to the right of value of 1.282) due to which we fail to reject our null hypothesis.

Therefore, we conclude that the proportion of baby girls is equal to 0.50.

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3 years ago

Kevin is planting 15 bushes and 9 trees in rows. If he wants all the rows to be exactly the same, with no plants left over, what

Alexandra [31]

Answer:

why is Kevin planting all those trees Kevin should get a job

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3 years ago

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yulyashka [42]

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