Jack had $80 more than Eric. When Jack spent $30, he found that the amount of money he had left was twice s much as Eric had. How much did the boys have altogether at the beginning?

Answers

Answer 1

First we define variables:
x: amount of money Jack has
y: amount of money Eric has
We write the system of equations:
x = y + 80
x - 30 = 2y
Solving the system we have:
x = $130
y = $ 50
Therefore, the amount of money they had at the beginning is:
130 + 50 = $ 180
Answer:
the boys had $ 180 altogether at the beginning

Related Questions

The radius of a cone can be found using the formula r=3⁢Vπ⁢h , where V stands for the volume of the cone and h stands for the height. If r=3 , h=8 , and π is 3.14, find the volume (V). Round the answer to the nearest hundredths place.

Answers

The right expression for r is give as follows:

r = Sqrt [(3V)/(πh)]

Making the V the subject of the formula
r^2 = (3V)/(πh)
V = πr^2h/3

Substituting,
V= 3.14*3^2*8/3 = 75.36 sq. units

Using the formula for the radius of a cone and the given values of r = 3, h = 8, and [tex]\pi[/tex] = 3.14, the volume of the cone is calculated to be approximately 25.12 [tex]cm^3[/tex].

To find the volume V of a cone, we need to solve for V in the given formula [tex]$ r = \frac{3V}{\pi h} $. With $ r = 3 $,[/tex] h = 8, and [tex]\pi = 3.14[/tex], let's proceed as follows:

Rearrange the Formula

1. Given that [tex]$ r = \frac{3V}{\pi h} $[/tex], isolate V to get:

[tex]\[ V = \frac{r \cdot \pi \cdot h}{3} \][/tex]

2. Using r=3, h=8, and [tex]$ \pi = 3.14 $[/tex]:

[tex]\[ V = \frac{3 \cdot 3.14 \cdot 8}{3} \][/tex]

3. Simplify and solve:

[tex]\[ V = 3.14 \cdot 8 \approx 25.12 \][/tex]

Rounding to the nearest hundredths place, the value for the volume V is approximately 25.12 cubic units.

Q # 17 , Find the slope

Answers

In order to find the slope we need to find two points on the line.

From the above graph we can see that the points (-4,-1) and (0, -3) lie on the line. So using these two points we can find the slope.

[tex]Slope=m= \frac{-3-(-1)}{0-(-4)} \\ \\ m= \frac{-3+1}{0+4} \\ \\ m= \frac{-2}{4} \\ \\ m= \frac{-1}{2} [/tex]

So, first option is the correct answer

The slope is given by:
m = (y2-y1) / (x2-x1)
Substituting values we have:
m = (- 4 - (- 3)) / (2-0)
Rewriting we have:
m = (- 4 + 3) / (2-0)
m = (- 1) / (2)
m = -1 / 2
Answer:
The slope is given by:
m = -1 / 2
option 1

when is periodic data useful? give examples to support your answer please

Answers

It's useful in following conditions:

(i) when you want to know the valency to male compounds
for example :
when H2 and O2 react in normal conditions they form H2O, amd here we needed crossmultiplication of their valencies.

(ii) To know masses while calculating mass number.
For example In case you wanna find mass of 100 molecules of H2O.

(iii) To find electronegativity (to determine type of bond formed).
For example: which kind of bond Hydrogen and Clorine will form.

PLEASE HELP!!! Find the equation , in the standard form of the line passing through the points (3,-4) and (5,1)

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 3 &,& -4~) % (c,d) &&(~ 5 &,& 1~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-4)}{5-3}\implies \cfrac{1+4}{5-3}\implies \cfrac{5}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-4)=\cfrac{5}{2}(x-3)\implies y+4=\cfrac{5}{2}x-\cfrac{15}{2}[/tex]

[tex]\bf y=\cfrac{5}{2}x-\cfrac{15}{2}-4\implies y=\cfrac{5}{2}x-\cfrac{23}{2}\impliedby \begin{array}{llll} \textit{now let's multiply both}\\ \textit{sides by }\stackrel{LCD}{2} \end{array} \\\\\\ 2(y)=2\left( \cfrac{5}{2}x-\cfrac{23}{2} \right)\implies 2y=5x-23\implies \stackrel{standard~form}{-5x+2y=-23} \\\\\\ \textit{and if we multiply both sides by -1}\qquad 5x-2y=23[/tex]

side note: multiplying by the LCD of both sides is just to get rid of the denominators

A father is giving his child a 30-inch long softball bat for her birthday.He has a rectangular box that has the dimensions of 5 inches by 6 inches by 25 inches. Will the bat fit in the box ? Explain

Answers

I think it will because 5 × 6 × 25 = 750 in.

The bat is 30 in.

So, I think it will fit.

Hope this helped☺☺

Answer:

No, the bat will not fit. Using the Pythagorean theorem, the length of a diagonal of a face of the box is about 24 inches, and the length of the diagonal of the cube is about 29.4 inches. This is less than the length of the bat.

Step-by-step explanation:

Edguenity

the slope of the line below is -3. which of the following is the point-slope form of the line? A.) y+2=3(x-2) B.) y+2=-3(x-2) C.) y-2=-3(x+2) D.) y-2=3(x+2)

Answers

The "point-slope" form of the equation of a straight line is:

[tex]y-y_1=m(x-x_1)\\\\(x_1;\ y_1)\ is\ a\ known\ point\\\\m\ is\ the\ slope\ of\ the\ line[/tex]

We have:

[tex]m=-3;\ (x_1;\ y_1)=(2;-2)[/tex]

Substitute

[tex]y-(-2)=-3(x-2)\\\\y+2=-3(x-2)[/tex]

Answer: B. y + 2 = -3(x - 2)

Answer:

B) y + 2 = -3(x - 2)

Step-by-step explanation:

it's what I got

draw 8 lines that are between 1inch and 3 inches long

Answers

This is not something we can really help you with, you'll have to do on your own paper. Just get a ruler and draw 8 different lines that measure 1-3 inches.

A batch of cookies requires 3/8 cup of butter. Butter can be purchased in boxes, each containing 4 sticks, with 1 stick equivalent to 1/2 cup of butter. If Monica is to bake 15 batches of cookies, which of the following is the best estimate for the total number of boxes of butter she needs to buy?

Answers

Firstly, we need to find how many cups of butter is needed to bake [tex]15[/tex] batches. We will need [tex]15 \cdot \frac{3}{8} = \frac{45}{8}[/tex] cups of butter. This is [tex]5.625[/tex] cups. Since we can only buy butter in boxes with 2 cups of butter in it, we will have to buy 3. This will give us 6 cups of butter, which will be enough. If we only buy 2, then we will only have 4 cups of butter, which won't be enough to bake 15 batches of cookies.
So, the answer is [tex]\boxed{3}.[/tex]

Choose the correct factorization for the polynomial 21xy+15x+35ry+25r

Answers

(21xy +15x )+ (35ry +25r)
3x(7y+5)+ 5r(7y+5)
(3x+5r)(7y+5)

Please rate

True or False? The shortest distance from the center of the circumscribed circle to the sides of the inscribed triangle is the circle's radius

Answers

Answer:

false

Step-by-step explanation:

The statement that the shortest distance from the center of the circumscribed circle to the side of the inscribed triangle is the circle's radius is false.

How to find the radius of the circumscribed circle around a triangle?

The intersection of the perpendicular bisectors of any two sides(or all three sides if you want) is the center of the circumscribed circle for that triangle.

The length of that intersection point from any of the vertices of the triangle is the radius of the circumscribed circle of that triangle.

When a triangle is placed in a circle such that the side of the circle touch the circumference of the circle, then the circle is a circumscribed circle.

The line drawn from the center of the circle to the side of the triangle is the shortest possible line.

However, it is certain that this line is the radius.

This is so because the side of the triangle lie on the circumference of the circle

Hence, the statement that the shortest distance from the center of the circle is false.

Read more about circumscribed circle at:

brainly.com/question/2699432

#SPJ5

Peter is working for an hourly wage of 12$ if he worked for 20 hours last week what is his gross pay

Answers

Hourly wage = $12
Number of hours Peter worked = 20 hours

Gross Pay = Hourly Wage x Number of Hours worked

Using the values, we get:

Gross Pay = 12 x 20 = $240

Thus, the gross pay of Peter was $240 for his work of last week

hey can you please help me posted picture of question

Answers

The correct answer is option B

(5 + 3i)(4+ 2i)

= 5(4+2i) + 3i(4+2i)

= 20 +10i + 12i +6i²

= 20 +22i +6(-1)

= 20 + 22i - 6

= 14 + 22i

Aisha wants to make two quilts, each with the same area. The first quilt will be square with sides s feet long. The second quilt will be a rectangle with a width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt. Which quadratic equation can be used to find s, the side length of the square quilt?
s^2 =(1/2s) (s + 6)
s^2 = (s)(s + 6)
s^2 =(1/2s) (6s)
s^2 = (s)(6s)

Answers

Sides of a square shape = S

Then, Area (A) = S^2

Width of rectangular shape = S/2
Length of rectangular shape = S+6

Then, Area (A) = (1/2S)(S+6)

The two area are equal. Therefore,
S^2 = (1/2S)(S+6)

The first option is the correct quadratic equation to solve for S.

Answer:

Option 1 - [tex]s^2=(\frac{1}{2}s)(s+6)[/tex]

Step-by-step explanation:

Given : Aisha wants to make two quilts, each with the same area. The first quilt will be square with sides s feet long. The second quilt will be a rectangle with a width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt.

To find : Which quadratic equation can be used to find s, the side length of the square quilt?

Solution :

The first quilt will be square,

Let the side of square be s

The area of the square is [tex]A=s\times s[/tex]

The second quilt will be a rectangle,

A width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt.

Width of the rectangle = [tex]\frac{1}{2}s[/tex]

Length of the rectangle = s+6

Area of the rectangle is [tex]A=(\frac{1}{2}s) \times (s+6)[/tex]

According to question,

Area of square and rectangle are equal,

So, [tex]s\times s=(\frac{1}{2}s) \times (s+6)[/tex]

[tex]s^2=(\frac{1}{2}s)(s+6)[/tex]

Therefore, Option 1 is correct.

The required equation is [tex]s^2=(\frac{1}{2}s)(s+6)[/tex]

a hiker walks 12 miles north. then she walks 9 miles west. What is the shortest distance the hiker can travel to return tonher starting point

Answers

If we were to draw the distance walked, it would be the "legs" of a right triangle. So, to determine the return distance we calculate the hypotenuse which equals:
hypotenuse^2 = 12^2 + 9^2 = 225 return distance = 15 miles.

At a school for performance art students
2/5

of the girls study music,
3/5

of the girls study dance and
1/6

of the girls study music and dance. What fraction of those who study music also study dance?

Answers

the to the girls studying music and dance the factions is 55

can someone help me x-7=2x-6

Answers

x=-1
x-7=2x-6
subtract x from both sides.
-7=x-6
add 6 on both sides.

x - 7 = 2x - 6 Add 6 to both sides
x - 1 = 2x Subtract x from both sides
-1 = x Flip it around so it's easier to read
x = -1

Check your answer by substituting -1 in for x.

(-1) - 7 = 2(-1) - 6 Simplify 2 times -1
(-1) - 7 = -2 - 6 Simplify both sides
-8 = -8

So, x = -1 .

hey can you please help me posted picture of question

Answers

Subtracting a number from value of x indicates a horizontal translation towards right.

F(x-5) indicates that F(x) is shifted 5 units to right. So G(x) can be obtained from F(x) by shifting it 5 units to the right.

Thus, the answer to this question is option C

which is an example x-intercept of the graph of the function y=tan(x-(5pi/6))

Answers

Answer: x = 5π/6

Explanation:

1) Given function:

[tex]y=tan(x- \frac{5 \pi }{6} )[/tex]

2) x-intercept are the roots of the function, i.e. the solution to y = 0

3) to find when y = 0, you can either solve the equation or look at the graph.

4) Solving the equation you get:

y = 0 ⇒ tan(x - 5π/6) = 0 ⇒ x - 5π/6 = arctan(0)

arctan(0) is the angle whose tangent is zero,so this is 0

⇒ x - 5π/6 = 0 ⇒ x = 5π/6.

Then, one example of an x-intercept is x = 5π/6, which means that when x = 5π/6, the value of the function is 0.

Since, the tangent function is a periodic function, there are infinite x-intecepts, that is why the questions asks for one example and not all the values.

You can verify by replacing the value x = 5π/6 in the given function:

y = tan (5π/6 - 5π/6) = tan(0) = 0.

Answer:

Step-by-step explanation:

To test upper h 0: muequals60 versus upper h 1: muless than60, a random sample of size nequals24 is obtained from a population that is known to be normally distributed. complete parts (a) through (d) below.

Answers

[tex]5 mu^2 x P =r[/tex]
random sample of size nequals24 is obtained from a population that is known to be normally distributed But we have equatoon

what is 103.468 rounded to the nearest liter

Answers

Rounded to the nearest liter: 103

Hope this helps!

This question is asking you to round a number, the number will be rounded up if 1 digit below them is a value of 5 or more and if the number below them is 4 or less. In this question you have to round to the nearest liter which means the nearest one. The number in this question is 103.368, one digit below one will be the 0.4. Since the value is 4, which is lower than 5, then the number is rounded down. So your answer would be 103.

Solve the system using the substituiton method
branliest offered
3x-7y=10
x-4y=5

Answers

Hi there!

To solve this problem using substitution, we need to set x equal to a value and substitute it into the other equation.

Since
x - 4y = 5,
x = 5 + 4y

3x - 7y = 10
3(5 + 4y) - 7y = 10
15 + 12y - 7y = 10
15 + 5y = 10
5y = -5
y = -1

Now that we know y is -1, we can substitute it back into the equation to find x:

y = -1
x - 4y = 5
x - 4(-1) = 5
x - (-4) = 5
x + 4 = 5
x = 1

So, your answers are x = 1 and y = -1.

Hope this helps!

the sum of a number and 7 is the same as double the number increased by 3

Answers

So, let’s represent the number as n:
n+7=2n+3
Subtract both sides by 3:
n+4=2n
Now by n:
2n=4
Divide:
n=2
The number is 2

The statement above is the same as the mathematical expression below...

x + 7 = 2x + 3

We want to solve for x in these types of problems. To do so, we must get all of the "x"s on one side of the equal sign and the constants on the other.

7 - 3 = 2x - x
4 = x

Our answer is x = 4.

circle the fraction in the set with the least value 4/3 5/5 4/4 1/2 1/1

Answers

when looking at fractions if the top number ( numerator) is larger then the bottom number ( denominator) the value of the fraction is greater than 1

if both the top and bottom numbers are the same, the fraction equals 1

if the top number is smaller than the bottom number then the fraction is less than 1
so with the fractions you have:

4/3 ( 4 is larger than 3 so this is greater than 1)
5/5 ( 5 = 5, so this = 1 )
4/4 ( 4=4, so this = 1)
1/2 ( 1 is smaller than 2 so this is less than 1)
1/1 ( 1 =1 so this = 1)

since 1/2 is less than 1, this is the fraction with the least value

which expression defines the given series for seven terms? -13 + (-16) + (-19) +...

Answers

[tex] - 13 + ( - 3) = - 16 \\ - 16 + ( - 3) = - 19 \\ - 19 + ( - 3) = - 22 \\ - 22 + ( - 3) = - 25[/tex]
you have to plus (-3) for each numbers

Answer:

[tex]a_n =-3n-10[/tex]

Step-by-step explanation:

-13 + (-16) + (-19) +...

Difference between two terms = -3

-16 -(-13)= -3

-19 -(-16)= -3

Common difference is a constant so it is arithmatic

[tex]a_n = a_1+(n-1)d[/tex]

where 'd' is the difference = -3

a1 is the first term that is -13

[tex]a_n = -13+(n-1)(-3)[/tex]

[tex]a_n = -13-3n+3[/tex]

Combine like terms

[tex]a_n =-3n-10[/tex]

lyzette's folder has a permeter of 38 inches.if the length of the paper is 11 inches what is the width of the folder

Answers

Perimeter = 2l + 2w

38 = 2(11) + 2w

2w = 38 - 22

2w = 16

w = 16 ÷ 2

w = 8

Answer: Width = 8 inches

Final answer:

To find the width of Jyzette's folder with a perimeter of 38 inches and a length of 11 inches, we use the perimeter formula for a rectangle, solve for width, and find that the width of the folder is 8 inches.

Explanation:

Finding the Width of a Folder

To determine the width of Jyzette's folder, we use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is perimeter, l is length, and w is width. Given that the perimeter is 38 inches and the length is 11 inches, we can set up the equation:

38 = 2(11) + 2w

Simplifying the equation: 38 = 22 + 2w. We then subtract 22 from both sides, resulting in 16 = 2w, and finally, dividing both sides by 2 gives us w = 8. Therefore, the width of the folder is 8 inches.

In general, the y-intercept of the function F(x)=a•b^x is the point what????

Answers

F(0) = a

The y-intercept is the point (0, a).

1. Assume you buy 100 shares of stock at a price of $63.75 per share and incur brokerage fees of $200. You own the stock for 5 years and receive dividends of 50 cents per share at the end of each quarter. Immediately after receiving the 20th quarterly dividend, you sell the stock at a price of $48.63 per share and incur brokerage fees of $200. Calculate your rate of return. (IRR)

2. You own a thriving restaurant but want to change careers. Your brother offers to buy the business with the following monthly payments: $2,750 at the end of each month for 4 years, followed by $3,000 at the end of each month for 3 years. Assuming that you can earn 9% compounded monthly, what is the equivalent cash price of your brother’s offer? (NPV)

Answers

1. Your cash flow is as follows.
initial outlay: $63.75*100 +200.00 = $6575
quarterly dividend: $0.50*100 = $50 . . . for 19 quarters
income from sale: $48.63*100 -200.00 +50.00 = $4713
A suitable financial calculator computes the IRR as -3.23% per year.

2. Your cash flow is as follows.
initial income/outlay: 0
monthly income: $2750 . . . for 48 months
monthly income: $3000 . . . for 36 months
applicable interest rate: .09/12 = 0.0075 . . . per month
A suitable financial calculator computes the NPV as $176,415.70.

hey can you please help me posted picture of question

Answers

The discriminant can be determined from the number of roots of the graph.

If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.

Since the given graph has no real root, i.e. it does not cross x-axis at any point, so we can say that the discriminant of the given function is negative.

So the answer to this question is option C

Solve triangle PQR is PQ 9, PR 7, and QR 8. POR is NOT a right triangle.

Answers

Given => PQ = 9 unit
PR = 7 unit
QR = 8 unit

To find => Area of triangle PQR

We can find area of triangle by Heron's Formula.

Where,

s = (9+7+8)/3

= 24/3

= 8

and,
a = 9
b = 7
c = 8

Heron's Formula = [tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]

= [tex] \sqrt{8(8 - 9)(8 - 7)(8 - 8)} [/tex]

= [tex] \sqrt{8( - 1)(1)} [/tex]

= [tex] \sqrt{ - 8} [/tex]

= [tex]2i \sqrt{2} [/tex]

Area of triangle = 2i√2 units

Hope this helps!

We will solve this using Heron's Formula for the area of a triangle.

[tex]\text {Formula = } \sqrt{p(p-a)(p-b)(p-c)} , \text { where p is half the perimeter}[/tex]

We will start off by find p:

[tex]\text {p = } \dfrac{9+7+8}{2} = \dfrac{24}{2}= 12 [/tex]

Now we know, p = 12, we plug in a = 9, b = 8 and c = 7 into the formula to find the area:

[tex]\text {area = } \sqrt{12(12-9)(12-8)(12-7)}[/tex]

[tex]\text {area = } \sqrt{12(3)(4)(5)}[/tex]

[tex]\text {area = } 26.83 \text{ units}^2[/tex]

a season ticket for bolton f.c. this season cost £410 it is to go up by 34% next season how.much will a season ticket cost next season?

Answers

This should be right if you're doing multipliers -

100 + 34 = 134
÷ 100 = 1.34
1.34 is your multiplier. So if you do 410 x 1.34 you'll have £549.40
I may be wrong, but I'm quite sure this is right!

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