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2 years ago

Write in slope-intercept form an equation of a line that passes through the points (-1,2) and (1,-6)

Mathematics

1 answer:

creativ13 [48]2 years ago

3 0

Answer: y = 6 - 4x

Step-by-step explanation: Find the slope: (y2-y1) / (x2-x1). In this case, [2-(-6)] / (-1-1) = 8/-2 = -4. Then write it in intercept form, substituting in a point for y and x: 2 = a -4(-1). Then balance to get a = 6. So y = 6 - 4x

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At a competition with 8 runners, 2 medals are awarded for first and second

Dafna1 [17]

Answer: Option 'A' is correct.

Step-by-step explanation :

Since we have given that

Number of medals = 2

Number of runners = 8

We need to find the number of ways to award the medals.

We would use "fundamental theorem of counting" to find the number of ways.

So, number of ways is given by

8 × 7 = 56

Hence, option 'A' is correct.

4 0

2 years ago

Read 2 more answers

Consider the parent function f(x) = x^2 and the transformed function f(x) =- 5(x - 4)^2 – 8. Identify the

madam [21]

Given:

The parent function is

$f(x)=x^2$

Consider the transformed function is g(x) instead of f(x) because both functions are different.

$g(x)=-5(x-4)^2-8$

Step-by-step explanation:

We have,

$f(x)=x^2$

$g(x)=-5(x-4)^2-8$

It can be written as

$g(x)=-5f(x-4)-8$ ...(i)

The translation is defined as

$g(x)=kf(x+a)+b$ .... (ii)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<|k|<1, then the graph compressed vertically by factor k and if |k|>1, then the graph stretch vertically by factor k.

If k is negative, then f(x) is reflected across the x-axis to get g(x).

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (i) and (ii), we get

$a=-4$ , f(x) shifts 4 units right.

$b=-8$ , f(x) shifts 8 units down.

$k=-5$ , it is negative so f(x) reflected across the x-axis.

$|k|=|-5|=5>1$ , so f(x) stretched vertically by factor 5.

Therefore, the function f(x) reflected across the x-axis, stretched vertically by factor 5 and shifted 4 units right 8 units down to get g(x).

8 0

2 years ago

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

zepelin [54]

Answer:

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

As we know the given points

Center = (5, -4)

and

Point on circle = (-3,2)

The distance between point on circle and center will give us the radius of circle

So,

The formula for distance is:

$\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}\\Taking\ center\ as\ point\ 1\ and\ the\ other\ point\ as\ point\ 2\\d=\sqrt{(-3-5)^{2}+(2-(-4))^{2}}\\d=\sqrt{(-8)^{2}+(2+4)^{2}}\\d=\sqrt{(-8)^{2}+(6)^{2}}\\\\d=\sqrt{64+36}\\d=\sqrt{100} \\ d=10\\So\ the\ radius\ is\ 10$

The standard form of equation of circle is:

$(x-h)^{2}+(y-k)^{2}=r^{2}$

where h and k are the coordinates of the center. So putting in the value:

$(x-5)^{2}+(y-(-4))^{2}=(10)^{2}\\(x-5)^{2}+(y+4)^{2}=100$

8 0

2 years ago

Combine like terms 1,17-0,07a+(-3,92a).<br><br> HELPPPPPPP!!!

Anna35 [415]

Answer:

$=1.17-3.99a$

Step-by-step explanation:

$1.17-0.07a+\left(-3.92a\right)$

$=1.17-0.07a-3.92a$

$=1.17-3.99a$

8 0

2 years ago

Which of the following statements is not true? a) The standard deviation of the sampling distribution of sample mean = σ/√n b) T

I am Lyosha [343]

Answer:

e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken.

Step-by-step explanation:

The central limit theorem states that

"Given a population with a finite mean μ and a finite non-zero variance σ2, the sampling distribution of the mean approaches a normal distribution with a mean of μ and a variance of σ2/N as N, the sample size, increases."

This means that as the sample size increases, the sample mean of the sampling distribution of means approaches the population mean. This does not state that the sample mean will always be the same as the population mean.

6 0

2 years ago