All categories

1 year ago

Given that the line y=ax+b passes through the points A(0; 3) and B(-2;7), how do I find the values of a and b?

1 answer:

4 0

First you have find the slope (a) in order to find the value of the y intercept (b).

To compute the slope, you simply have to find the difference of y coordinates and divide them by the difference of x coordinates:

a = (y2-y1)/(x2-x1)
a = (7-3)/(-2–0)
a = 4/-2
a = -2

To compute the y intercept denoted by b, we substitute the value of a with -2 in the formula and choose any point (x,y) and substitute their values in the formula as well. Like so:

I choose point A:

3 = (-2)(0) + b
3 = b

You might be interested in

Adult men have heights with a mean of 69. 0 inches and a standard deviation of 2. 8 inches. find the z-score of a man who is 71.

Anarel [89]

The value of the z score is 1.03.

According to the statement

we have given that the value of mean and standard deviation and we have to find the value of the z score.

So, For this purpose we know that the

Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.

And the given values are:

mean value = 69 inches

s.d value = 2.8 inches

And the value of x is 71.9 inches.

So, The Z score is

z = x - mean / standard deviation

substitute the values in it then

z = 71.9 - 69 / 2.8

then

z = 2.9 /2.8

z = 1.03

So, The value of the z score is 1.03.

Learn more about Z Score here

brainly.com/question/25638875

#SPJ4

8 0

8 months ago

If possible help me in this. I need to find the two odd numbers...

Lelechka [254]

Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

<h3>Answer: x+2</h3>

========================================================

Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

<h3>Answer: x^2 + (x+2)^2 = 394</h3>

========================================================

Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\$

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

<h3>Answer: Either 13, 15 or -15, -13</h3>

4 0

2 years ago

Solve the equation: X to the 4th power - 81=0

Musya8 [376]

$x^4-81=0\\
x^4=81\\
x^4=3^4 \vee x^4=(-3)^4\\x=3 \vee x=-3$

5 0

3 years ago

What is the product of [x-(4+13i)][x-(4+13i)]

Luden [163]

Answer:

x^2 - (4+13i)^2

Step-by-step explanation:

This product has the form (a-b)(a+b), which is a 'special product' equal to a^2 - b^2. Following this pattern, [x-(4+13i)][x-(4+13i)] = x^2 - (4+13i)^2. The 2nd term could be expanded if desired, but the above result is the most compact one possible.

3 0

2 years ago

PLZZZZZ HELPPP ASAPPPP IM FREAKIN OUTTTTTT

Temka [501]

Answer:

1. C) 2 (x-2)(x-1)

2. D) cannot be factored

3. B) (x-8)(x+5)

4. D) 2 (x+5)(x-5)

5. D) (x+5)(x-3)

hope this was helpful! let me know if you needd the steps! c:

3 0

3 years ago