Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks

Mrs. McMillan, the PE, teacher, is pairing off students to race against each other. Heather can
run 4 meters per second, and Erin can run 5 meters per second, Mrs. McMillan decides to give Heather a head start of 23 meters since she runs more slowly. Once the students start
running, Erin will quickly catch up to Heather. How far will Erin have to run? How long will
that take?

Please help.

Answer:

x = 0

y = -1

Step-by-step explanation:

Multiply second equation with -1

(-1) * (-3x - 8y) = 8

3x + 8y = -8 now find its sum with the first equation

2x - 8y + 3x + 8y = 8 - 8 add like terms (note that minus 8y will eliminate +8y)

x = 0 to find the value  of y replace the x with 0 in the first equation

2*0 - 8y = 8

-8y = 8 divide both sides by -8

y = -1

Answer:

( 4 x − 7 ) ( 16 x 2 + 28 x + 49 )

Step-by-step explanation:

Answer:

(4x - 7) (16x^2 + 28x + 49)

Step-by-step explanation:

Since both terms are perfect cubes, factor using the difference of cubes formula, a^3 - b^3 = (a - b) (a^ 2  +  a b  +  b^ 2 )  where  a  =  4 x  and  b  =  7 .

Answer:

x²+1/x² = 51

Explanation:

Given x - 1/x = 7 ---(1)

We know the algebraic identity:

a²+b²-2ab = (a-b)²

Or

a²+b² = (a-b)²+2ab

Now,

x²+1/x²

= (x-1/x)²+2*x*(1/x)

= (x-1/x)²+2

:7²+2 [ from (1)] =

= 49+2

= 51

Therefore,

x²+1/x² = 51

Answer:

A. sec =12/13×

B. COS =12/13×

C. tan =12/5✓

D. sin =12/13 ✓

Step-by-step explanation:

we know,

using Pythagoras formula,

p=12,h=13 ,b=?

h^2 =p^2 +b^2

b=5

so tan = p/b

=12/5

sin=p/h and cosec= h/p

D. sin =12/13

The amount Billy has at the end of the 15 years is $9,377.73.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P[tex](1 + r/n)^{nt}[/tex]

P = principal

r = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $5000

r = 4.2%

t = 15 years

n = 12

A = P[tex](1 + r/n)^{nt}[/tex]

A = 5000 [tex](1 + 0.0035)^{180}[/tex]

A = 5000 x [tex]1.0035^{180}[/tex]

A = $9,377.73

Thus,

Billy has $9,377.73 at the end of the 15 years.

Learn more about compound interest here:

https://brainly.com/question/13155407

#SPJ2

Answer:

3 (B)

Step-by-step explanation:

rise/run

rise=3

run=1

3/1=3

Answer:

C)105

Step-by-step explanation:

sizde benim sorduğum soruları cevaplarsanız sevinirim doğru ve hızlı bir şekilde

Answer:

[tex]\boxed{\tt \frac{40}{9}} \ \sf or \ \boxed{\tt 4 \frac{4}{9}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for the sum of 2 fractions.}[/tex]

[tex]\large\underline{\textsf{What are Fractions?}}[/tex]

[tex]\textsf{Fractions are representations of rational numbers that can be represented as part}[/tex]

[tex]\textsf{of a whole number.}[/tex]

[tex]\underline{\textsf{What are the parts of a fraction?}}[/tex]

[tex]\textsf{Fractions have 2 parts, they're called the Numerator and the Denominator.}[/tex]

[tex]\frac{\sf Numerator}{\sf Denominator}[/tex]

[tex]\textsf{The Numerator represents the amount of equal parts a certain rational number}[/tex]

[tex]\textsf{has compared to the Denominator. The Denominator represents the total amount}[/tex]

[tex]\textsf{of parts that make a fraction equal to 1. If the Numerator is the same as the}[/tex]

[tex]\textsf{Denominator, then the fraction is just 1. If the Numerator is greater than 1, then}[/tex]

[tex]\textsf{this kind of fraction is considered an Improper Fraction, and improper fractions}[/tex]

[tex]\textsf{are fractions that are improper due to the Numerator being greater than the}[/tex]

[tex]\textsf{Denominator, which means these fractions shouldn't be represented as fractions,}[/tex]

[tex]\textsf{but there's nothing wrong with representing it as a fraction.}[/tex]

[tex]\textsf{Since we know what majority of fractions are, we may begin adding these fractions}[/tex]

[tex]\textsf{which are improper.}[/tex]

[tex]\large\underline{\textsf{How are we able to Add Fractions?}}[/tex]

[tex]\textsf{Adding Fractions is simply adding the Numerators together since the Denominator}[/tex]

[tex]\textsf{can't be changed, if so then the equation won't be equal.}[/tex]

[tex]\textsf{*Remember that when adding fractions we must have common denominators.}[/tex]

[tex]\textsf{This means that we should find the LCM (Least Common Multiple) of the}[/tex]

[tex]\textsf{Denominators.}[/tex]

[tex]\underline{\textsf{For our problem;}}[/tex]

[tex]\textsf{Since we already have Common Denominators, we are able to simply add the}[/tex]

[tex]\textsf{Numerators.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Add the Numerators together.}[/tex]

[tex]\tt \frac{\boxed{\tt 23}}{9} + \frac{\boxed{\tt 17}}{9} =\boxed{\tt \frac{40}9}[/tex]

[tex]\tt \frac{40}{9} \ \textsf{can be our final answer. However, since our sum is an Improper Fraction, it's}[/tex]

[tex]\textsf{greater than 1. Since 40 can divide into 9 about 4 times, our whole number will}[/tex]

[tex]\textsf{be 4, and the remainder will be our fraction.}[/tex]

[tex]\underline{\textsf{Explained in numerical;}}[/tex]

[tex]\tt \frac{40}{9} = \frac{9}{9} + \frac{9}{9} + \frac{9}{9} + \frac{9}{9} + \frac{4}{9} = \boxed{\tt 4 \frac{4}{9}}[/tex]

[tex]*\tt \frac{36}{9} = \frac{4}{1}[/tex]

[tex]\textsf{These are called Whole Number Fractions.}[/tex]

[tex]\large\underline{\textsf{Hence;}}[/tex]

[tex]\tt \frac{23}{9} + \frac{17}{9} = \boxed{\tt \frac{40}{9}} \ \sf or \ \boxed{\tt 4 \frac{4}{9}}[/tex]

[tex]\large\underline{\textsf{Learn more about Fractions;}}[/tex]

https://brainly.com/question/26180542

[tex]\textsf{This answer will give you a great review of how to turn word-form problems into}[/tex]

[tex]\textsf{fractions, and how to simpify those fractions.}[/tex]

Answer:

C=50.27mm

Step-by-step explanation:

C=2πr=2·π·8≈50.26548mm

[tex]\mathfrak{5x + 15 = 28} [/tex]

[tex]\mathfrak{5x = 28-15} [/tex]

[tex]\mathfrak{5x = 13} [/tex]

[tex]\boxed{\mathfrak{x = \dfrac{13}{5}}} [/tex] → option B.

[tex]\mathbb{MIREU} [/tex]

Answer:

B

Step-by-step explanation:

The first thing you need to do is,

28 - 15

which is 13.

Now look at the answer choices and multiply them by 5.

It cannot be C or D because it would not fit the equation.

If anyone of them equal 13 then it is the answer.

Now lets try it.

43/5 = 8.6

13/5 = 2.6

8.6 times 5 is way to big so A is not it.

2.6 times 5 is 13.

So it is B.

Answer:

7=4m +c( y intercept)

Step-by-step explanation:

use the formula y= mx +c

Answer:

2/7÷3/4=2/7×4/3=8/21

[tex] \rm \ \blue{ \overbrace{ \underbrace{ \tt \color{hotpink} \: \: \: \: \: \: \: \: \: \: answer \: \: \: \: \: \: \: \: \: }}}[/tex]

[tex]\large \color{pink} \frac{8}{21} [/tex]

Step-by-step explanation:

[tex] \huge \color{brown} \frac{2}{7} \div \frac{3}{4} [/tex]

[tex] \large \color{hotpink} \frac{2}{7} \div \frac{4}{3} [/tex]

[tex] \huge \color{darkblue} \frac{8}{21} [/tex]

Answer:

ok first we round them both

386230 is rounded to 386k

59250 is rounded to 59 k

386+59=445

445,000

Hope This Helps!!!

Answer:

Slope=0.12   power is down by 28%

Step-by-step explanation:

:)

Answer:

x=17.333

Step-by-step explanation:

3x+8=60

3x=60-8

3x=52

x=52\3

x=17.333

we know that $1290 is to be divided on a 7:8 ratio, so we'll start off by dividing 1290 by (7+8) and give each person accordingly

[tex]1290~~ at~~ 7:8\implies 7\cdot \cfrac{1290}{7+8}~~ :~~8\cdot \cfrac{1290}{7+8} \\\\\\ 7\cdot 86~~:~~8\cdot 86\implies 602~~ :~~688[/tex]

Answer:

x < - 1

Step-by-step explanation:

You have to treat it is a linear equation.

First, - 5 from both sides, resulting in -2x < 2.

Lastly, you need to find x on it's own so you have to divide by - 2.

Therefore, the answer would be x < -1.

Hope this helps :)

The inverse of an implication p ⇒ q is ¬p ⇒ ¬q.

The converse of p ⇒ q is q ⇒ p.

The contrapositive of p ⇒ q is ¬q ⇒ ¬p.

Then

• the inverse of the inverse of p ⇒ q is p ⇒ q

• the inverse of the the converse of p ⇒ q is ¬q ⇒ ¬p

• the inverse of the contrapositive of p ⇒ q is q ⇒ p

Answer:

Since the logarithmic function is define for ×>-3,thus,the graph has a vertical asymptote at ×=-3.

Answer:

try for an answer: 6ab • (18ab + a - 6b)

Answer:

$30.46

Step-by-step explanation:

Total payment = down payment + interest fee + 24 equal payments

980 = 200 + 49 + 24 equal payments

24 equal payments = 24 * p, as we add p 24 times

980 = 249 + 24p

subtract 249 from both sides to isolate p and its coefficient

731 = 24p

divide both sides by 24 to isolate p

p = 30.46

Answer: B)1/4

Step-by-step explanation: If you divide a pizza into 4 pieces, each person will get a fourth of the pizza.

Answer:

 (c)  p = vm

Step-by-step explanation:

Momentum, represented by 'p', is the product of mass and velocity. It is a vector quantity, just as velocity is a vector quantity.

  p = vm

Answer:

[tex]y'= \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]

Step-by-step explanation:

We have [tex]e^{2x} = \ln(y^3)[/tex] and we want the implicit differentiation [tex]\dfrac{dy}{dx}f(x) = y'[/tex]

Therefore, we want to separate the [tex]y[/tex] from the equation.

[tex]\ln(y^3) =e^{2x} \implies 3 \ln(y) = e^{2x} \implies \ln(y) = \dfrac{e^{2x} }{3}[/tex]

[tex]\implies e^{\ln(y)} = e^{e^{2x}/3} \implies \boxed{y = e^{e^{2x}/3}}[/tex]

Now we can calculate the derivative. By the chain rule,

[tex]y' = \dfrac{d}{dx}\left(e^{e^{2x}/3}\right) = e^{e^{2x}/3}\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right)[/tex]

Now

[tex]\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right) =\dfrac{1}{3}\dfrac{d}{dx}\left(e^{2x}\right) = \dfrac{2}{3}e^{2x}[/tex]

Therefore

[tex]y' = e^{e^{2x}/3}\cdot \dfrac{2}{3}e^{2x} = \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]

Answer:

1/28

Step-by-step explanation:

Answer:

[tex]b=-a^2-c[/tex]

Step-by-step explanation: