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2 years ago

A parabola is graphed such that the axis of symmetry is x = 3. One of the x-intercepts is (5, 0). What is the other x-intercept?

Mathematics

1 answer:

Stells [14]2 years ago

6 0

The axis of symmetry is the fold line that splits the parabola down the middle.

Now, since a parabola is symmetrical, every point, except the vertex, will have a mirror image of another point if we folded the parabola over the axis of symmetry.

So if we know the axis of symmetry is x = 3 and one of our points

has the coordinates (5, 0), the other point will have the coordinates (3, 0).

The axis of symmetry is always halfway between the x-intercepts.

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Which point is 7 units from (–2, 4)?

Serjik [45]

The distance formula:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(x_1,y_1)=(-2,4) \\
d=7 \\ \\
7=\sqrt{(x-(-2))^2+(y-4)^2} \\
7=\sqrt{(x+2)^2+(y-4)^2} \ \ \ |^2 \\
49=(x+2)^2+(y-4)^2$
Check which point satisfies the equation:
$(x,y)=(-5,4) \\
49 \stackrel{?}{=} (-5+2)^2+(4-4)^2 \\
49 \stackrel{?}{=} (-3)^2+0^2 \\
49 \stackrel{?}{=} 9 \\
49 \not= 9 \\
doesn't \ satisfy \ the \ equation$

$(x,y)=(-2,3) \\
49 \stackrel{?}{=} (-2+2)^2+(3-4)^2 \\
49 \stackrel{?}{=} 0^2+(-1)^2 \\
49 \stackrel{?}{=} 1 \\
49 \not= 1 \\
doesn't \ satisfy \ the \ equation$

$(x,y)=(5,4) \\
49 \stackrel{?}{=} (5+2)^2+(4-4)^2 \\
49 \stackrel{?}{=} 7^2+0^2 \\
49 \stackrel{?}{=} 49 \\
49=49 \\
satisfies \ the \ equation$

$(x,y)=(9,4) \\
49 \stackrel{?}{=} (9+2)^2+(4-4)^2 \\
49 \stackrel{?}{=} 11^2+0^2 \\
49 \stackrel{?}{=} 121 \\
49 \not= 121 \\
doesn't \ satisfy \ the \ equation$

The answer is C.

3 0

3 years ago

Jenna wants to wrap a shipping box shaped like a rectangular prism. The box is 29 inches tall and has a square base with sides t

AnnyKZ [126]

Answer:

she will use 420 inches of paper with 69 left over

Step-by-step explanation:

It is what it is

6 0

3 years ago

What is the method to the problem

madreJ [45]

I think it might be the 3rd one.

Someone correct me if I'm wrong please.

7 0

3 years ago

5=x+8 (Sorry but i've been on this one for hours)

DENIUS [597]

Answer:

x = -3

Step-by-step explanation:

Subtract 8 from both sides to get x alone.

5 - 8 = x + 8 - 8

-3 = x

3 0

3 years ago

Read 2 more answers

Suppose that a researcher is designing a survey to estimate the proportion of adults in your state who oppose a proposed law tha

irinina [24]

Answer:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Solution to the problem

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

The margin of error desired for this case is $ME= \pm 0.02$ equivalent to 2% points

For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is $\hat p =0.5$

In order to find the critical value we need to take in count that we are finding the margin of error for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.96$

Now we have all the values needed and if we replace into equation (b) we got:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

5 0

3 years ago