MATHEMATICS HIGH SCHOOL

Write an equation in slope-intercept form of the line through point P(6, –1) with slope 4.A. y = 4x – 25
B. y = 4x – 1
C. y + 1 = 4(x – 6)
D. y + 6 = 4(x – 1)

Answers

Answer 1
Answer:

Answer:

The answer is the option A

y=4x-25

Step-by-step explanation:

we know that

The equation of the line into slope-intercept form is equal to

y=mx+b

where

m is the slope

b is the y-coordinate of the y-intercept of the line

In this problem we have

m=4

point(6,-1)

substitute the values in the equation and solve for b

-1=4*6+b

b=-1-24=-25

The equation of the line is equal to

y=4x-25
Answer 2
Answer: y = mx+b

m= 4 

y= 4x+b

solve for b using (6,-1)

-1 = 4 (-1)+b
b=3

therefore equation is y=4x+3

same as (y+1)=4(x-6)

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If p(x) = x +9, and q(x) = 2x² + 3x, find p(2a) - q(a)

Answers

Answer:

p(2a) - q(a) = -2a² + 2a + 9

Step-by-step explanation:

Given;

p(x) = x + 9 and q(x) = 2x² + 3x,

we can replace 2a and a for p(x) and q(x).

p(2a) = 2a + 9 and q(a) = 2a² + 3a are the substituted values.

Now we can evaluate p(2a) - q(a):

p(2a) - q(a) = (2a + 9) - (2a² + 3a)

= 2a + 9 - 2a² - 3a

= -2a² + 2a + 9

p(2a) - q(a) = -2a² + 2a + 9

Hope this helps!

A bus and a car leave from the same city traveling in opposite directions. The bus leaves 2 hours before the car does. The bus travels at a steady speed of 50 mph while the car travels at 70 mph. After how many hours will the bus and car be 800 miles apart?

Answers


Normally, I would pass right by this question, because it is so complicated
and there are so many numbers in it.  But I've allowed myself to become
seduced by the bounty of a full 5 points waiting at the end of the rainbow,
and I decided to rush in where more reasonable people would rightly fear
to tread.

The answer is a number, that represents "after how many hours".  So we
need to know how many hours AFTER WHAT.  The question is not very
clear on when the beginning of time is, so I need to decide.  I'm going to
say that the time when the bus leaves is the beginning of time.  And I'm
going to call  ' H '  the number of hours AFTER the bus leaves.

-- The bus covers 50 miles every hour.  So 'H' hours after the bus leaves,
the bus is  50H  miles away from the city, in some direction.

-- The car leaves 2 hours later.  So 'H' hours after the bus leaves, the car
has only been traveling for  (H-2)  hours.

-- The car covers 70 miles every hour.  So 'H' hours after the bus leaves,
the car is  (70)x(H-2)  miles away from the city, in the OTHER direction.

-- Since the bus and the car are moving in opposite directions, the distance
between the bus and the car is the SUM of the distances each one covers.

     'H' hours after the bus leaves, they are  (50H) plus (70)(H-2) miles apart.

What we need to figure out is:  When is that distance 800 miles ?


The distance between them at 'H' hours after the bus leaves is

                                                            (50H) plus (70)(H-2) miles

Eliminate the first parentheses:             50H  +  (70)(H-2)

Eliminate the rest of the parentheses:   50H  +  70H - 140

Combine the terms with 'H' in them:         120H - 140

So here's the equation:                            120H - 140 = 800

Add  140  to each side:                            120H          =  940

Divide each side by  120 :                             H  =  7.8333 hours
                                                                           =  7 and 5/6 hours
                                                                           =  7 hours and 50 minutes
                                                                                 after the bus leaves.

Check:

Assume that  H = 7 hrs 50 minutes  (7 and 5/6 hours)
The bus has covered  (50 x 7-5/6) = 391 and 2/3 miles.
 
The car has been traveling for only  5 and 5/6 hours
The car has covered   (70) x (5-5/6) =  408 and 1/3 miles

How far apart are they ?   (391-2/3) + (408-1/3) =  800 miles !           YAY!   


Note:  If the book or the homework sheet wants to count the hours
after the CAR leaves, then the answer is  5-5/6 hours, not 7-5/6 . 

Simplifying radicals: √196s²

Answers

√196s² = √196 times √s²

s² is the square of 's'
196 is the square of 14
So both can easily come out of the radical.

√196s² = 14s

Enter the values for a and b that complete

the sum:

3/x + 5/x^{2} =ax+b/x^{2}

Answers

ANSWER

a=3, b=5

EXPLANATION

The given equation is

(3)/(x) + \frac{5}{ {x}^(2) } = \frac{ax + b}{ {x}^(2) }

We simplify the left hand side.

We collect LCD to obtain:

\frac{3x + 5}{ {x}^(2) } = \frac{ax + b}{ {x}^(2) }

Both sides of the equation are now the same.

By comparing the coefficients of x, we have

a = 3

By comparing the constant terms

b = 5

Answer:

For the first part

A=3

B=5

For the second part

M=3

N=14

P=2

Step-by-step explanation:

Right on edge 2020

June has 42 sports books, 85 mystery books, and 69 nature books. She arranged her books equally on 7 shelves. How many books are on each shelf.

Answers

Answer:

28

Step-by-step explanation:

We are given that

June has sports books=42

June has mystery books=85

June has nature books=69

Total number of shelves=7

We have to find the number of books are on each shelf.

Total number of books=42+85+69=196

To find the number of books on each shelf we will divide the total number of books by 7.

Number of books on each shelf=(196)/(7)

Number of books on each shelf=28

Hence, number of books on each shelf=28

Answer:

28

Step-by-step explanation:

Add 42, 85, and 69 together and you get 196 but you need to divide that by 7 and you get 28

Solve: 2x-7>3 or 4-x≤-4

Answers

Steps to solve:

2x - 7 > 3

~Add 7 to both sides

2x > 10

~Divide 2 to both sides

x > 5

Steps to solve:

4 - x <= -4

~Subtract 4 to both sides

-x <= -8

~Divide -1 to both sides

x >= 8

Best of Luck!

Answer:

2x-7>3     ----->     x>5

4-x≤-4      ------>    x\geq 8

Step-by-step explanation:

2x-7>3

2x-7+7>3+7

2x>10

2x/2 > 10/2

x>5

4-x≤-4    

4-x-4 \leq -4-4

-x \leq -8

(-x)(-1) \geq (-8) (-1)

x \geq 8
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