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For which value of x must the expression square root of 19x be further simplified? A. 15. B 21. C 28. D 41

algol [13]

<span>The expression of the square root of 19x must be simplified when x is equal to 28. This is because possible factors of 28 can be seen to be 4 and 7, and 4 is a perfect square. This means it can be pulled outside of the square root when evaluated. The other options include only prime factors that could not be pulled out. (3,5), (3,7), (1,41)
28 simplifies as such:
Sqrt(19*28) = Sqrt(19*4*7) = 2*Sqrt(19*7) = 2*Sqrt(133).</span>

5 0

3 years ago

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Helppppppppppppppppppppppppppppp

KonstantinChe [14]

Answer:

None of these

Step-by-step explanation:

This polynomial is a quartic (4th degree polynomial), and it is not linear, cubic, or quadratic.

5 0

3 years ago

Jennifer hit a golf ball from the ground and it followed the projectile ℎ(t)= −15t^2+100t, where t is the time in seconds, and ℎ

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

In order to find the max height the ball reached, we have to complete the square on that quadratic. That will also, conveniently so, give us the number of seconds it will take the ball to reach that max height, that answer to part b. Let's begin to complete the square. Normally, you would move the constant over to the other side of the equals sign, but there is no constant here. The next step is to get the leading coefficient to be a 1, and ours right now is a -15. So we have to factor it out. Here's where we start the process of completing the square.

$-15(t^2-\frac{20}{3}t)=0$ Next step is to take half the linear term, square it, and add it to both sides. Our linear term is 20/3. Half of 20/3 is 20/6, and 20/6 squared is 400/36.

$-15(t^2-\frac{20}{3}t+\frac{400}{36})=0+???$ Because this is an equation, what we add to the left side also has to be added to the right. BUT we didn't just add in 400/36, because we have that -15 out front as a multiplier that refuses to be ignored. What we actually added in was -15(400/36):

$-15(t^2-\frac{20}{3}t+\frac{400}{36})=0-\frac{500}{3}$

The reason we do this is to create a perfect square binomial on the left which will serve as the number of seconds, h, in the vertex (h, k), where h is the number of seconds it takes the ball to reach its max height, k. Simplifying both sides then gives us:

$-15(t-\frac{20}{6})^2=-\frac{500}{3}$ Finally, we will move the right side over by the left and set the quadratic back equal to h(t):

$h(t)=-15(t^2-\frac{20}{3})^2+\frac{500}{3}$ and from that you can determine that the vertex is $(\frac{20}{3},\frac{500}{3})$ .

The answer to a. is vound in the second number of our vertex: k, the max height. The max of the golf ball was 500/3 feet or 166 2/3 feet.

Part b is found in the first number of the vertex: h, the number of seconds it took the golf ball to reach that max height. The time it took was 3 1/3 seconds.

Part c. is to state the domain (the time) and the range (the height) of the ball.

Domain is

D: {x | 0 ≤ x ≤ 3 1/3} and

Range is

R: {y | 0 ≤ y ≤ 166 2/3}

8 0

3 years ago

Julie buys a pair of earrings for $7. Now she would like to the same earrings for 2 friends. How much will she spend for all 3 p

ankoles [38]

The easiest way to do this is to multiple 7 and 3, which gives you 21. Julie will spend $21 on the gifts.

5 0

3 years ago

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The mean consumption of water per household in a city was 1425 cubic feet per month. Due to a water shortage because of a drough

liberstina [14]

Answer:

a) $t=\frac{1175-1425}{\frac{250}{\sqrt{100}}}=-10$

The degrees of freedom are given by:

$df=n-1=100-1=99$

The p value for this case would be given by:

$p_v =P(t_{99}$

Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425

b) For this case we need to find a critical value in the t distribution with 99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:

$t_{\alpha/2}=1.984$

Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425

Step-by-step explanation:

Information given

$\bar X=1175$ represent the sample mean for the cubic feets of households

$\sigma=250$ represent the population standard deviation

$n=100$ sample size

$\mu_o =1425$ represent the value to verify

$\alpha=0.025$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Part a

We want to test that the mean consumption of water per household has decreased due to the campaign by the city council, the system of hypothesis would be:

Null hypothesis: $\mu \geq 1425$

Alternative hypothesis: $\mu < 1425$

Since we don't know the deviation the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The statistic is given by:

$t=\frac{1175-1425}{\frac{250}{\sqrt{100}}}=-10$

The degrees of freedom are given by:

$df=n-1=100-1=99$

The p value for this case would be given by:

$p_v =P(t_{99}$

Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425

Part b

For this case we need to find a critical value in the t distribution with 99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:

$t_{\alpha/2}=1.984$

Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425

6 0

3 years ago