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3 years ago

1. Consider the following system of equations.

Mathematics

1 answer:

Ivenika [448]3 years ago

7 0

Answer:

x + 5 = 5

Step-by-step explanation:

Solution doesn't change as the x in the equation is 0 and the answer totals as 5 due to 5 plus 0 being 5

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HURRYYYYYYYYY!! What is the equation of the quadratic function with a vertex at (2, 25) and an x-intercept at (7,0)?

tangare [24]

Answer:

$y=-(x-7)(x+3)$

which is none of the choices provided.

Are you sure the question is right or even the choices?

You can even write it as:

$y=-(x+3)(x-7)$ but this is still not a choice.

Step-by-step explanation:

The vertex form of a quadratic is $y=a(x-h)^2+k$ .

This is called vertex form because it gives you the vertex is $(h,k)$ .

We are given that $(h,k)=(2,25)$ which makes our equation:

$y=a(x-2)^2+25$ .

We can find the value of $a$ by plugging in the x-intercept (7,0) for $(x,y)$ into:

$y=a(x-2)^2+25$

$0=a(7-2)^2+25$

$0=a(5)^2+25$

Subtract 25 on both sides:

$-25=a(5)^2$

$-25=a(25)$

Divide both sides by 25:

$\frac{-25}{25}=a$

$-1=a$ .

So the equation for the quadratic is:

$y=-1(x-2)^2+25$

Let's put this into factored form since all the choices are in factored form.

This will require us to multiply the (x-2)(x-2) out:

$y=-1(x-2)(x-2)+25$

$y=-1(x^2-2x-2x+4)+25$

$y=-1(x^2-4x+4)+25$

$y=-x^2+4x-4+25$

$y=-x^2+4x+21$

Factor out -1:

$y=-(x^2-4x-21)$

WE need to find two numbers that multiply to be -21 and add to be -4:

$y=-(x-7)(x+3)$

8 0

3 years ago

Read 2 more answers

Find the midpoint of the segment from point a (6,3) to point B (8,1)

velikii [3]

Answer: $M=(7,2)$

Step-by-step explanation:

You need to use the following formula:

$M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})$

Given the points A(6,3) and B(8,1), you can identify that:

$x_A=6\\x_B=8\\y_A=3\\y_B=1$

Now, you can substitute these values into the formula $M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})$ .

Therefore, you get this result:

$M=(\frac{6+8}{2},\frac{3+1}{2})$

$M=(7,2)$

5 0

3 years ago

Read 2 more answers

Power set of {e,f,m,n,o}

Nastasia [14]

$\{\emptyset,\{e\},\{f\},\{m\},\{n\},\{o\},\{e,f\},\{e,m\},\{e,n\},\{e,o\},\{f,m\},\{f,n\},\\
\{f,o\},\{m,n\},\{m,o\},\{n,o\},\{e,f,m\},\{e,f,n\},\{e,f,o\},\{e,m,n\},\\
\{e,m,o\},\{e,n,o\},\{f,m,n\},\{f,m,o\},\{f,n,o\},\{m,n,o\},\{e,f,m,n\},\\
\{e,f,m,o\},\{e,f,n,o\},\{e,m,n,o\},\{f,m,n,o\},\{e,f,m,n,o\}\}$

5 0

3 years ago

Read 2 more answers

James is making a paper chain from different colored paper strips. He joins the links in the following pattern: red, blue, red,

Whitepunk [10]

Answer:

red

Step-by-step explanation:

1-red

2-blue

3-red

4-blue

5-red

6-blue

7-red

8-blue

9-red

10-blue

11-red

12-blue

13-red

14-blue

15-red

16-blue

17-red

18-blue

19-red

20-blue

21-red

22-blue

23-red

im so smart fr

8 0

2 years ago

A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data

LuckyWell [14K]

Answer:

(25.53, 37.87): 95% CI

(23.59, 39.81): 99% CI

Step-by-step explanation:

The margin of error of a confidence interval is given by:

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

z is related to the confidence level. The higher the confidence level, the higher the values of z, and thus, we wider the confidence interval is.

In this question:

The narrower C.I. is the 95%, and the wider is the 99%. So

(25.53, 37.87): 95% CI

(23.59, 39.81): 99% CI

4 0

3 years ago