MATHEMATICS HIGH SCHOOL

Levi runs cross country. He runs 5 miles in 45 minutes. He runs 20 miles in 180 minutes. If he keeps the same pace, how long will it take him to run 12 miles?

Answers

Answer 1

Answer:

Answer:

It will take 108 minutes to Levi to run 12 miles

Step-by-step explanation:

Formulas

(1) $velocity=(distance)/(time)$ and (2) $time=(distance)/(velocity)$

Using (1) we can conclude that $velocity=(5miles)/(45minutes)=(1)/(9)mil/min$ in the first case, and for the second $velocity=(20miles)/(180minutes)=(1)/(9)mil/min$ , is the same.

Finally using (2) $time=(12 mil)/((1)/(9)mil/min)=108min$ , is the time that will take to Levi to run 12 miles.

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What is the point-slope form of a line with slope that contains the point (-3, 6)?

Answers

Answer: y-6=2/5(x+3)

Step-by-step explanation:

Add the slope next time 2/5

point slope
y-y1=m(x-x1)
where you are given the point (x1,y1) and the slope is m

we are given the point (-3,6)
x1=-3
y1=6
y-6=m(x-(-3))
y-6=m(x+3) is the point slope form and we don't kn ow the slope yet

Add or subtract the following mixed fractions. all answers must be in simplest form. show all work 7 2/5 - 6 1/5 =

Answers

7 2/5 - 6 1/5
first subtract the fractions, since the denominators are the same.
2/5 - 1/5 = 1/5
Then subtract the whole numbers.
7- 6 = 1
So your answer is 1 1/5
Hope this helps! :)

The answer is: 1 ⅕ .
________________________________________________
7 ⅖ − 6 ⅕ = 1 ⅕ .
________________________________________________

Which is a solution to the equation?(x −2)(x + 5) = 18

x = −10
x = −7
x = −4
x = −2

Answers

If you would like to know the solution to the equation (x - 2) * (x + 5) = 18, you can calculate this using the following steps:

(x - 2) * (x + 5) = 18
x^2 + 5x - 2x - 10 = 18
x^2 + 3x - 28 = 0
(x + 7) * (x - 4) = 0
1. x = - 7
2. x = 4

The correct result would be x = - 7.

The solutions to the equation are x = - 7 and x = 4

What are equation solutions?

Equation solutions are the true values of x in the equation

The equation is given as:

(x - 2)(x + 5) = 18

Expand the equation

x^2 + 5x - 2x - 10 = 18

Subtract 18 from both sides

x^2 + 3x - 28 = 0

Factorize the expression

(x + 7) * (x - 4) = 0

Solve for x

x = - 7 and x = 4

Hence, the solutions to the equation are x = - 7 and x = 4

Read more about quadratic equations at:

brainly.com/question/8649555

Write an equation in point-slope form, y – y1 = m(x – x1), of the line through points (9, –2) and (10, 2). Use (9, –2) as the point (x1, y1).

Answers

The equation written in point-slope form would be:

y+2=1/4(x-9).

Find the next term of the given sequence. 1.31, 2.54, 3.77, ... 4.90 5.00 5.10

Answers

Answer:

Option B is correct.

the next term of the sequence is 5.00

Explanation:

Arithmetic progression(A.P) is a sequence of numbers in which the consecutive terms are formed by adding a constant quantity with the preceding term.

Common difference(d) is the constant quantity stated in the above definition of arithmetic progression. it is given by;

$d=a_(n+1) - a_n$ for all n∈N

Given sequence:- 1.31, 2.54 , 3.77 , ___ ;

we have;

$a_1 = 1.31$ , $a_2= 2.54$ and $a_3 = 3.77$

First find the common difference;

$d =a_2 - a_1$ = $2.54-1.31 = 1.23$

d = $=a_3-a_2 = 3.77-2.54 =1.23$

Therefore, by the definition of arithmetic progression,

the given sequence is Arithmetic progression

Now, to find the fourth term of the sequence, add constant quantity (d) to the third term;

$a_4 = 3.77+1.23 = 5.00$

Therefore, in the given sequence next term will be 5.00.

It is A.P. with common difference = 2.54-1.31 = 1.23

So, next term would be 3.77+1.23 = 5.00

OPTION B IS YOUR ANSWER

"Solving Equations by Completing the Square: m^2+2m-48=-6

Answers

$m^2+2m-48=-6 \n \n m^2+2m-48+6=0\n \nm^2+2m-42=0\n \na=1, \ b= 2, \ c= -42 \n \n\Delta = b^(2)-4ac = 2^(2)-4*1*(-42)= 4+168 =172 \n\n√(\Delta )=√(172) =√(4*43)=2√(43)\n \nx_(1)=(-b-√(\Delta ))/(2a) =(-2-2√(43))/(2)=(2(-1-√(43)))/(2)= -1-√(43) \n \nx_(2)=(-b+√(\Delta ))/(2a) = (-2+2√(43))/(2)=( 2(-1+√(43)))/(2)= -1+√(43)$

$m^2+2m-48=-6\n\nm^2+2m\cdot1+1^2-1^2=-6+48\n\n(m+1)^2-1=42\n\n(m+1)^2=42+1\n\n(m+1)^2=43\iff m+1=-√(43)\ \vee\ m+1=√(43)\n\nm=-1-√(43)\ \vee\ m=-1+√(43)$

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