MATHEMATICS HIGH SCHOOL

Which equation describes the line that contains (1,5) and has a slope of 2

Answers

Answer 1

Answer:

The equation that describes the line that contains (1,5) and has a slope of 2 is y = 3x + 2

The equation of a line in point slope form is expressed as;

y-y0 = m(x - x0)

m is the slope of the line

(x0, y0) is the point on the line

Given the following parameters;

Slope = 2

Point on the line is (1, 5)

Substitute the given parameters into the formula to have:

y - 5 = 3(x-1)

y - 5 = 3x - 3

y = 3x + 2

Hence the equation that describes the line that contains (1,5) and has a slope of 2 is y = 3x + 2

Learn more on equation of a line here: brainly.com/question/18831322

Answer 2

Answer: in order to write an equation you need to find the y-intercept. the way you do this is by plugging in the value 2 and the point into y=mx+b and solving for b. once you plug everything in you get 5=2(1)+b. solving from here you get b=3. putting everything together you get y=2x+3

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In how many ways can a committee of 6 be chosen from 5 teachers and 4 students if the committee must include 3 teachers and 3 students?

Answers

[5! / 3! * 2!] *[4! / 3! * 1!] = ( 20 / 2 ) * 4 = 40 ways;

One number is 1 more than 2 times another. Their product is 10. Find the numbers.

Answers

whenever a problem says "one number" and "another number" we can substitute x and y. for this we have x=2y+1 and xy=1. since we know the value of x (2y+1) we can substitute it for the other equation to get (2y+1)y=10. simplify to get 2y^2+y=10. from here you can do a few methods to solve this, but the simplest in my opinion is by factoring.

In order to factor it must be equal to 0, so we have 2y^2+y-10=0. We factor this and get y=5 (we also get y=-4 but it is an extraneous root). now we can plug that into either equation and find that x=2.

this means our two numbers are 5 and 2

What is the average rate of change of f(x), represented by the table of values, over the interval [-3, 2]?

Answers

Average rate of change is: $(f(x2)-f(x1))/(x2-x1) = (4-(-36))/(2-(-3))= (4+36)/(2+3)= (40)/(5) =8$
Answer:C) 8

Find the area of the figure. Round decimal answers to the nearest tenth.

Answers

The base is 8 and the height is 8.
8x8 = 64
64 divided by 2 is 32
The area is 32 ft squared

I got this answer by using the formula for finding the area of a triangle. Base x height divided by 2

What are the roots of the polynomial equation x^3-7x=6x-12? a. –6, 6
b. –4, 1, 3
c. –3, –1, 4
d. 1, 3

Answers

Hello,

Answer B

P(x)=x^3-13x+12
P(1)=1-13+12=0 ==>1 is root
P(3)=3^3-13*3+12=0 ==>3 is root
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P(x)=(x-1)(x-3)(x+4)

Answer:

Step-by-step explanation:

What is the solution to the system of equations

Answers

Step-by-step explanation:

$5x + 3y = 13 \n 7x + 8y = - 16 \n 5x = 13 - 3y \n x = (13 - 3y)/(5) \n 7( (13 - 3y)/(5) ) + 8y = - 16 \n 18.2 - 4.2y + 8y = - 16 \n 3.8y = - 34.2 \n y = - 9 \n$

$x = (13 - 3( - 9))/(5) = (13 + 27)/(5) = (40)/(5) = 8 \n x = 8 \n y = - 9$

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