Sarah has a brother who is 5 years younger than herself and another brother who is 8 years younger than herself. She observes that the product of her brothers ages is equal to the age of her 40 year old father. How old is Sarah? How do we setup an equation for this using null factor law presumably.

Answers

Answer 1

Answer:

Sarah is 13 years old

Step-by-step explanation:

Represent Sarah's age with S

Her first brother's age with F

Her second brother's age with B

So, we have:

From the first statement, we have:

[tex]S - F = 5[/tex] ---- (1)

From the second, we have:

[tex]S - B = 8[/tex] ---- (2)

The product of their ages is 40.

First, we make F the subject in (1) and B the subject in (2)

[tex]F = S - 5[/tex]

[tex]B = S - 8[/tex]

Their product is represented as follows:

[tex]F * B = 40[/tex]

Substitute values for F and B

[tex](S - 5) * (S - 8)=40[/tex]

Open bracket

[tex]S^2 - 5S -8S + 40 = 40[/tex]

[tex]S^2 - 13S + 40 = 40[/tex]

Subtract 40 from both sides

[tex]S^2 - 13S = 0[/tex]

Factorize:

[tex]S(S - 13) = 0[/tex]

Split:

[tex]S = 0[/tex] or [tex]S - 13 = 0[/tex]

But Sarah's age can't be 0 because she has two younger brothers.

So, we stick to

[tex]S - 13 = 0[/tex]

Make S the subject

[tex]S = 13[/tex]

Hence, Sarah is 13 years old


Related Questions

Tiana's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 50 espressos in all, 60% of which were single-shot. How many single-shot espressos did the cafe sell?

Answers

Answer:

I am pretty sure its 43.48%

Calc how much interest you would earn on a deposit of $8500 at 2.75%,
compounded annually, for a term of 4 years?

Answers

9514 1404 393

Answer:

  $974.28

Step-by-step explanation:

The formula for the account balance is ...

  A = P(1 +r)^t

Subtracting the principal gives the amount of interest.

  I = P((1 +r)^t -1)

  i = $8500(1.0275^4 -1) ≈ $974.28

You would earn $974.28 in interest over that time period.

Which equation in standard form has a graph that passes through the point (5, −2) and has a slope of 72 ?

A. 7x − 2y = 35
A. 7x − 2y = 35

B. 7x − 2y = 39
B. 7x − 2y = 39

C. 7x − 2y = −31
C. 7x − 2y = −31

D. 7x − 2y = −24
D. 7x − 2y = −24

Answers

Given:

Consider the graph passes through the point (5, −2) and has a slope of [tex]\dfrac{7}{2}[/tex].

To find:

The equation of graph in standard form.

Solution:

Point slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

where, m is slope and [tex](x_1,y_1)[/tex] is the point lies on the line.

Slope is [tex]\dfrac{7}{2}[/tex] and graph passes through (5,-2), so the equation of line is

[tex]y-(-2)=\dfrac{7}{2}(x-5)[/tex]

[tex]y+2=\dfrac{7}{2}(x-5)[/tex]

Multiply both sides by 2.

[tex]2(y+2)=7(x-5)[/tex]

[tex]2y+4=7x-35[/tex]

[tex]4+35=7x-2y[/tex]

[tex]39=7x-2y[/tex]

The required equation is [tex]7x-2y=39[/tex].

Therefore, the correct option is B.

please help find the volume of the sphere and show work

Answers

Answer:

1436.76

Step-by-step explanation:

I think so

Answer: V≈1436.76

[tex]V=\frac{4}{3} \pi r^3[/tex]

4/3×π=4.1887902047863909846168578443727

r=7

7^3=343

4.1887902047863909846168578443727×343=1,436.7550402417321077235822406198

1,436.7550402417321077235822406198=1436.76

I hope this is good enough:

Find an equation relating x and y

Answers

Answer:

(3,3) is a 3rd of (6,9)

Step-by-step explanation:

A runner's racecourse has a total distance of . Race officials want to mark the course every with a flag, including one at the finish line. (The starting line does not need a flag.) How many flags are needed? First fill in the blanks on the left side of the equation using three of the ratios shown. Then write your answer on the right side of the equation.

Answers

Complete question :

A runner's racecourse has a total distance of 2.5 mi. Race officials want to mark the course every 200 yd with a flag, including one at the finish line. (The starting line does not need a flag. How many flags are needed?

Answer:

22 flags

Step-by-step explanation:

Given that total distance = 2.5 miles

Marked distance = every 200 yards

Ratio of yard to miles:

1 mile = 1760 yards

Total distance in yards :

Note :

1 mile = 5280 feet

1 yard = 3 feet

Given that:

1 flag per 200 yards

Number of flags :

2.5 miles * (5280 / 1 ) * (1 /3) * (1 / 200) = 22 flags

Similarly ;

Since 1 mile = 1760 yards

Total distance in yards : (2.5 * 1760) = 4400 yards

Number of flags :

Total distance in yards / marked distance

= 4400 / 200

= 22 flags

find the slope between the points (5,6) and (9,6)

Answers

Answer:

the slope is m=0

Step-by-step explanation:

when I put it in the graph and slope calculator I got 0

Answer:0

Step-by-step explanation:

The slope equation is y2-y1/x2-x1 so it would look like this: 6-6/5-9. If you simplify, the slope equals 0

The slope of a line is 1, and the y-intercept is -1. What is the equation of the line written in slope-intercept form?

Answers

Answer:

y = x - 1

Step-by-step explanation:

Slope intercept form is y = mx + b

m is the slope and b is the y-intercept so it would be:

y = x -1 but u don't have to write 1x just x will do

Answer:

y = x - 1

Step-by-step explanation:

slope intercept form

y = mx + b

where m = 1

          y-intercept = b = -1

therefore:

y = x - 1

To celebrate the first day of school, Reagan brought in a tray of caramel brownies and walnut brownies. The tray had a total of 20 brownies, of which 10% were caramel. How many caramel brownies did Reagan bring?

Answers

Answer:

18 I think

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Reagan brought 2 caramel brownies.

Solve using a proportion.

[tex]\frac{?}{20}[/tex]=[tex]\frac{10}{100}[/tex]

You're trying to find how many brownies he brought were caramel. We know Reagan brought a total of 20 brownies. Therefore since you don't know how many caramel brownies he brought, the fraction would be ?/20. Next, you know he brought brownies in which 10% were caramel. In proportions, the denominator would be 100% since that is the total percentage. Therefore, the proportion would be 10%/100%. Now we just have to cross multiply.

Proportion:

[tex]\frac{?}{20}[/tex]=[tex]\frac{10}{100}[/tex]

10 x 20 = 200

200/100= 2

Thus, Reagan brought 2 caramel brownies.

Not an important question, but math is only something we made, we can change the rules of it and/or how to solve it. So my question is, why do we only have so few people who fully understand all of the math we know of?

Answers

Answer:

HELLO KYRAH IT'S DAISY

Step-by-step explanation:

IM IN UR CLASS

Answer:

We change the rules due to the human mind always wanting to understand though very few people acutall gets its our way of iterperting things that makke sense. The human mind will never take no as a complete answer and willlkeepwondering no matter what

Step-by-step explanation:

Jonathan wants to the new baseball game for his game console. The game costs $45.99. If sales tax is 6%, write an equation to find the total cost of the game, represented as P.

Answers

Answer:

45.99*1.06=P

Step-by-step explanation:

please help me solve this as soon as possible.

Answers

Answer:because they are both interscting DUUUUUUUUHHHHHHH

Step-by-step explanation:

Find y-intercept for 9x-5y=0.

Answers

Answer:

y=-9/5x+0  the y intercept would simply be 0

Step-by-step explanation:

Answer:

y=0

Step-by-step explanation:

9x-5y=0

9(0)-5y=0

-5y=0

-5y/-5=0/-5

y=0 (y intercept)

9x-5y=0

9x-5(0)= 0

9x=0

9x/9=0/9

x=0 (x intercept)

Hope this Helps :)

Have a good day :)

what is the missing part​

Answers

Answer: the missing part is 45

suppose:  the missing part is x

we use Thales theorem:

[tex]\frac{x}{18}=\frac{20}{8}\\\\=> x = \frac{20.18}{8}=45[/tex]

Step-by-step explanation:

use thales theorem to solve this question

What is the value of a in the right triangle shown below?
15
12
O aſ
O Q=3
Oa=9
O G = 81

Answers

can you put a picture of the triangle?

Solve the inequality 5x-6<=2+(3x-4)

Answers

Answer:

x =< 2

Step-by-step explanation:

5x - 6 =< 2 + (3x - 4)

5x - 6 =< 2 + 3x - 4

5x - 3x =< 2 - 4 + 6

2x =< 4

x =< 2

Marla owes her sister $15. She pays her $6 today. Which integer represents the amount of debt she has remaining?

Answers

Answer:

The integer that represents the amount of debt she has remaining is $9

Step-by-step explanation:

$15 - $6 = $9

please help i’ll mark brainliest

Answers

Answer:

b

Step-by-step explanation:

its a straigt line thats what linear means (line)

The Population in Corpus Christi in 1970 was 204,525. The population in 2002 was 276,877. Create an
exponential equation and find out what the population will be in 2017?
When solving for b round it to the 4 decimals to use in the Equation. WHAT WILL BE THE POPULATION IN
2017?

Answers

Answer:

The population is 2017 is 291,254

Step-by-step explanation:

The exponential equation will be in the form

P = I( 1 + r)^t

where P is the present population

I is the population initially at 1970

r is the annual growth percentage

t is the number of years since 1970

So for 2002, we have

r in this case will be 2002-1970 = 32

277,877 = 204,525(1 + r)^32

(1 + r)^32 = 1.3586

1 + r = 1.0096

r = 1.0096-1

r = 0.0096

So the growth percentage is 0.96% annually

So the population in 2017 where t will be 2017-1970 = 37 will be

P = 204,525(1 + 0.0096)^37

P = 204,525(1.0096)^37

P = 291,254

One year, the population of a city was 130,000. Several years later it was 135,200.
Find the percent increase.

Answers

Answer:

Increase in percent = 4%

Step-by-step explanation:

Given:

Present population = 130,000

Future population = 135,200

Find:

Increase in percent

Computation:

Increase in population = Future population - Present population

Increase in population = 135,200 - 130,000

Increase in population = 5,200

Increase in percent = [Increase in population / Present population]100

Increase in percent = [5,200/130,000] 100

Increase in percent = 4%

On neatly scaled axes, graph and then write an equation in terms of u and y for the distance Leslie travels. Let I represent time in seconds and y represent distance in meters. Then do the same for Kristin and Erie using the same set of axes.​

Answers

Leslie: y= 2x

Kristin: y= 2/5x + 8

Erie: y= 5/4x + 6

For the graph, find attached below. Thanks and if you could mark me as brainliest.

PLEASE HELP ASAP:(....

Answers

Answer:

A

Step-by-step explanation:

7 x 1/3 = 7/3

Evaluate g(x)=6x when x=-3,0, and 4 .

Answers

Answer:

-3 = -18

0 = 0

4 = 24

Step-by-step explanation:

-3... so 6(-3) equals -18 because a positive times a negative equals a negative

0... so 6 (0) equals 0 because anything multiplied by 0 equals 0

4... so 6 (4) equals 24

() means multiplied by so if it’s y(x) then that means y is multiplied by x :)

How many times does 17 go into 65 no decimals please only remainders if there is one.

Answers

Answer:  3.82

Step-by-step explanation: there is a decimal

Do you have a picture

A cook has a scoop that measures ¼ cup. A bread recipe calls for 1 ¼ cups of sugar and 2 ½ cups of flour. The cook uses the scoop to measure and put both ingredients into a bowl. How many total scoops of both ingredients does the cook put into the bowl?

Answers

Given:

A cook has a scoop that measures [tex]dfrac{1}{4}[/tex] cup.

Required sugar for bread recipe = [tex]1\dfrac{1}{4}[/tex] cups

Required flour for bread recipe = [tex]2\dfrac{1}{2}[/tex] cups

To find:

The total number of scoops of both ingredients does the cook put into the bowl.

Solution:

Required amount of sugar and flour for the bread recipe is

[tex]=1\dfrac{1}{4}+2\dfrac{1}{2}[/tex]

[tex]=\dfrac{1\times 4+1}{4}+\dfrac{2\times 2+1}{2}[/tex]

[tex]=\dfrac{4+1}{4}+\dfrac{4+1}{2}[/tex]

[tex]=\dfrac{5}{4}+\dfrac{5}{2}[/tex]

Taking LCM, we get

[tex]=\dfrac{5+10}{4}[/tex]

[tex]=\dfrac{15}{4}[/tex]

Now,

[tex]\text{Number of scoops}=\dfrac{\text{Total amount of sugar and flour}}{\dfrac{1}{4}}[/tex]

[tex]\text{Number of scoops}=\dfrac{\dfrac{15}{4}}{\dfrac{1}{4}}[/tex]

[tex]\text{Number of scoops}=\dfrac{15}{4}\times \dfrac{4}{1}[/tex]

[tex]\text{Number of scoops}=15[/tex]

Therefore, the required number of scoops is 15.

simplify these like terms please 1-1-1+5x

Answers

Answer:

5x - 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Combining like terms

Step-by-step explanation:

Step 1: Define expression

1 - 1 - 1 + 5x

Step 2: Simplify

Subtract:                    -1 + 5xRewrite:                     5x - 1

And we have our final answer!

Answer: -1 + 5x

Step-by-step explanation: you have to simplify hope you understand

what is reminder if you devide 786 to 6?​

Answers

Answer:

There is no reminder as the answer will be an integer 131.

Thank you and please rate me as brainliest as it will help me to level up

The north pole is in the middle of the ocean. A person at sea level at the north pole would be 3,949 miles from the center of Earth. The sea floor below the north pole is at an elevation of approximately -2.7 miles. The elevation of the south pole is about 1.7 miles. How far is a person standing on the south pole from a submarine at the sea floor below the north pole?

Answers

Answer:

I LOVE YOU

Step-by-step explanation:

HOOIIIIIIIIIIIIIIIIII

A line has the equation y =1/3 x - 5.
Find the equation of a
perpendicular line passing through
(3,2).

Answers

the answer is y -2 = -3x -3

PLEASE HELP:( asapp!!!!!!!! i’ll mark brainlest

Answers

Answer:

6 * 1/9

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

6/9 = 0.66666666666666666666666666666667

6 * 1/9 = 0.66666666666666666666666666666667

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