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3 years ago

This system has one solution. {y=5x−9y=x2−3x+7 What is the y-coordinate of the solution?

1 answer:

3 0

The y-coordinate of the solution is 11.

Both equations have y isolated. We will use substitution for this system:

5x-9=x²-3x+7

We want to gather all of the variables on one side, so we will subtract 5x from each side:

5x-9-5x=x²-3x+7-5x
-9=x²-8x+7

We want the equation to be equal to 0 to solve it, so we will add 9 to both sides:

-9+9=x²-8x+7+9
0=x²-8x+16

This is easy to factor; factors of 16 that sum to -8 are -4 and -4:
0=(x-4)(x-4)

Since these are the same factor, we solve it to get our answer:
x-4=0
x-4+4=0+4
x=4

Substitute this into the first, linear, equation:
y=5(4)-9=20-9=11

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Which statement is true about the equations 3x + 4y = 12 and ¿-X- = = 1?

jarptica [38.1K]

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Step-by-step explanation:

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3 years ago

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

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".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$

Now we have everything in order to replace into formula (1):

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

7 0

3 years ago

Anyone willing to help?? thank u to whoever does help :))

blsea [12.9K]

Answer and Step-by-step explanation:

Yes, the three side lengths could form a triangle.

To find out if the sides can form a triangle, you take the lowest side lengths and add them together. If they are greater than the longest side, then they can form a triangle. If it is equal or less than the longest side, then it CAN NOT form a triangle.

7.8 + 10.4 > 13

18.2 > 13

So, the answer is Yes.

#teamtrees #PAW (Plant And Water)

4 0

3 years ago

Read 2 more answers

In the diagram below, triangle abc ~ triangle dec . What is the value of x? A. 28 b. 24 c. 22 d. 26

Lesechka [4]

Answer:

Option A.

Step-by-step explanation:

From the figure attached,

Given : ΔABC ~ ΔDEC

By the property of similarity,

"Corresponding sides of the similar triangles are proportional"

$\frac{\text{AB}}{ED}=\frac{BC}{EC}=\frac{AC}{DC}$

Since, $\frac{\text{AB}}{ED}=\frac{AC}{DC}$

$\frac{42}{6}=\frac{x}{(32-x)}$

6x = 42(32 - x)

6x = 1344 - 42x

6x + 42x = 1344

48x = 1344

x = $\frac{1344}{48}$

x = 28 units

Therefore, Option (A). x = 28 units will be the answer.

4 0

3 years ago

Solve for the variable 7/28 = 25/?

ICE Princess25 [194]

Let x be the unknown number. The equation is going to be 7/28=25/x, now we cross multiply. 7*x=25*28, 7x=700, divide both sides by 7 and you should get 100, So, x=100 and 7/28=25/100

7 0

3 years ago