In a paint factory, an old conveyer line has filled 40 barrels of paint, and is filling more at a rate of 1 barrel per minute. A worker just switched on a newer line that can fill 3 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How many barrels will each line have filled?
Write a system of equations, graph them, and type the solution.
Answer:
5 minutes
Step-by-step explanation:
let the time after which two lines will have filled an equal number of barrels is 'X' minutes.
so, according to the question after 'X' minutes;
⇒ number of barrels in old conveyer line = number of barrels in new conveyer line
⇒ 40x + 2X = 10X
⇒ X = 5
Burt's grandparents started a savings account for him when he was born. They invested
$1250 in an account that pays 7.5% interest every year. How much money is in the
account on Burt's 18th birthday?
Answer:
4594.76 USD will be in the account on Burt's 18th birthday.
Step-by-step explanation:
Since interest rate is constant in time, we can use the definition of composite interest to determine how much money will be on Burt's 18th birthday, that is:
[tex]C = C_{o}\cdot \left(1+\frac{r}{100} \right)^{t}[/tex] (1)
Where:
[tex]C_{o}[/tex] - Initial amount, measured in US dollars.
[tex]C[/tex] - Current amount, measured in US dollars.
[tex]r[/tex] - Annual interest rate, measured in percentage.
[tex]t[/tex] - Time, measured in years.
If we know that [tex]C_{o} = 1250\,USD[/tex], [tex]r = 7.5[/tex] and [tex]t = 18[/tex], then the money in the savings account on Burt's 18th birthday is:
[tex]C = (1250\,USD)\cdot \left(1+\frac{7.5}{100} \right)^{18}[/tex]
[tex]C = 4594.76\,USD[/tex]
4594.76 USD will be in the account on Burt's 18th birthday.
If 3x−y=12, what is the value of
8x.2y? Explain.
A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.
Answer:
A
Step-by-step explanation:
use the equation x=4+y/3 to find out.
8x + 2y = 24
2y = -8x + 24
y = -4x + 12.....so the slope is -4, and the y int is 12 or (0,12)
to find the x int, sub in 0 for y and solve for x....in either the original equation or the slope intercept equation
8x + 2y = 24
8x + 2(0) = 24
8x = 24
x = 24/8
x = 3.....so the x int is 3 or (3,0)
now plot ur intercepts (3,0) and (0,12)......now start at ur y int (0,12)...and since ur slope is -4, u come down 4 spaces, then to the right 1 space, then down 4, and to the right 1...keep doing this and u should cross the x axis at (3,0)
Answer:
Step-by-step explanation:
A)212
Simplify the expression.
–9 – 6(w + 5)
A. –15w + 5
B. –15w + 30
C. –6w – 39
D. –6w + 21
Answer:
C. -6w-39
Step-by-step explanation:
Answer:
the correct solution is C.-6w-39
Find "x" so that a line drawn through the given points has the given slope. (Sketching the
problem may be helpful.)_
Given: A(x,6) B(2,4)
m=1/3
Answer:
x = 8Step-by-step explanation:
Slope is expressed as shown;
m = y2-y1/x2-x1
Given
m = 1/3
Coordinates A(x,6) B(2,4)
Substitute and get x
1/3 = 4-6/2-x
1/3 = -2/2-x
Cross multiply
2-x = 3(-2)
2-x = -6
-x = -6-2
-x = -8
x = 8
Hence the value of x is 8
The area of a rectangle is represented by the expression 16m - 24. Which expression shows a factored version of the Area, one that shows the length and the width.
A | 8(2m+3)
B | 8(2+3m)
C | 8(2-3m)
D | 8(2m-3)
Answer:
The espression 8(2m - 3) shows the length and the width of the rectangle ⇒ D
Step-by-step explanation:
Let us find the greatest common factor of 16 and 24
∵ 16 = 1 × 16, 2 × 8, 4 × 4
∴ The factors of 16 are 1, 2, 4, 8, 16
∵ 24 = 1 × 24, 2 × 12, 3 × 8, 4 × 6
∴ The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
→ Find the common factors of 16 and 24
∵ The common factor of 16 and 24 are 1, 2, 4, 8
∵ The greatest one is 8
∴ The greatest common factor of 16 and 24 is 8
→ Take 8 as a common factor from 16m and 24
∵ 16m ÷ 8 = 2m
∵ 24 ÷ 8 = 3
∴ 16m - 24 = 8(2m - 3)
∴ The espression 8(2m - 3) shows the length and the width of
the rectangle
—5 + 3x + 2 = 12
Solve for x
Answer:
x=5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
B) Use the table of values to determine if this
relationship is linear or non-linear
Answer:
Step-by-step explanation:
Tamara walked 5/8 mile in 2 ½ hours. Which of the following represents the unit rate that Tamara walked?
POSSIBLE POINTS 100
A video rental store charges a $20 membership fee and $2.50 for each video rented. Write a linear equation (y=mx++) to model this situation
y = 20x + 25
y = 2.5x + 20
y = 2.5x + 20
y = -20x + 25
y = 20 + 2.5x
have to write more or I cant post this
f(x) = 2\3x -6 identifiy 0
A system of two linear equations is graphed. The lines have the same slope, but different intercepts. How many solutions does the system have?. A. 0. B. 1. C. 2. D. infinite
Answer:
D
Step-by-step explanation:
I hope this is correct and have a great day
Given angle FGH - angle LMN, which must be true?
Answer:
A, B, C and E are true. Only D is false.
Step-by-step explanation:
Della went to the market to buy 4.5 pounds of sliced fruit in a container. She paid with a $20 bill and a $5 and received $4.67 as change. She paid $1.62 in taxes and for the fruit. What was the cost for one pound of sliced fruit before taxes
Answer:
the cost for one pound before taxes is $4.52
Step-by-step explanation:
The computation of the cost for one pound before taxes is shown below:
= Paid a bill + amount - change amount
= $20 + 5 - $4.67
= $20.33
Now the cost of one pound would be
= Total amount ÷ number of pounds purchased
= $20.33 ÷ 4.5 pounds
= $4.52
Hence, the cost for one pound before taxes is $4.52
hello! I need help on these questions, I’ll give brainlist! :)
Answer:
1] the original perimeter will be multiplied by three.
2} the original area will be multiplied by 9
Step-by-step explanation:
Rick is taking a 1-mile ride on his bicycle. For each rotation of his tire, he travels 72 inches. How many rotations will his tire make during the 1-mile trip?
Answer:
880 rotations
Step-by-step explanation:
Answer:
880 rotations
Step-by-step explanation:
Guided Practice #3:
A group of adults plus one child attend a movie at the movie theater. Tickets cost $9 for adults and $6
for children. The total cost for the movie is $78. Write an equation using a to find the number of adults
in the group
Use your equation to solve for a (adults).
Click to add speaker notes
Answer:
8 adults
Step-by-step explanation:
78-6 for the child is 72 and tben since each adult is $9 so $72 divide by $9
Jason can travel 23 3/4 miles in 2/3 of an hour. what is his speed in mph
Answer:
I agree buster. I can't even run that far.
Step-by-step explanation:
I’m giving 20 points and will give brainliest.
Answer:
Express 5 72 in simplest radical form:
Factorize the 72 in your expression:
5√72 = 5√(2*2*2*3*3)
take a pair of two's and a pair of three's out of the radical sign:
5√72 = 5*2*3√2 = 30√2
this is the simplest radical form
Step-by-step explanation:
Answer: Express 5 72 in simplest radical form:
Factorize the 72 in your expression:
5√72 = 5√(2*2*2*3*3)
take a pair of two's and a pair of three's out of the radical sign:
5√72 = 5*2*3√2 = 30√2
this is the simplest radical form
Step-by-step explanation:
HOPE I HELPED
Find the unit rate: 6 children from 2 families.
2 children per family
1/2 children per family
3 children per family
1/6 children per family
Answer:
The answer is 3 children per family.
Step-by-step explanation:
This is a fraction equal to
6 children ÷ 2 familys =3 children per family.
Just took the quiz.
Reason abstractly, Evaluate each expression: |13 - 6| = ____
Answer:
7
Step-by-step explanation:
13-6=7 the other line doesn't affect the answer because it isn't negative
Answer:
7
Step-by-step explanation:
»Solve inside the absolute value sign | |
|13 - 6| = |7|
The absolute value of 7 is just 7:
|7| = 7
Answer: 7
PLEASE HELP...
A car is bought at the price of $20,000. The value decreases at the rate of .20 every year (t). The exponential expression 20,000(0.80)t describes this situation. Find the price of the car after 3 years.
Question 2 options:
A)
$10,240
B)
$11,874
C)
$5,892
D)
$9,399
Answer:
$10,240
Step-by-step explanation:
y = 20,000 (.80)^t
y = 20,000 (0.80)^3
0.8^3 = 0.512
0.512 x 20,000 = 10240
Your answer would be A. $10,240.
Question 2 What is the length of segment BC? a:4 b:5 c:6 d:7
Answer:
a
Step-by-step explanation:
which of the following shows the length of the third side, in inches, of the triangle below?
Answer:
20 inches
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Trigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²Step-by-step explanation:
Step 1: Identify Variables
Leg a = x
Leg b = 15
Hypotenuse c = 25
Step 2: Solve for x
Substitute [PT]: x² + 15² = 25²Isolate x term: x² = 25² - 15²Exponents: x² = 625 - 225Subtract: x² = 400Isolate x: x = 20Answer:
20 inches
Step-by-step explanation:
Step 1: Understanding Pythagorean Theorem
The Pythagorean Theorem is [tex]a^{2} +b^{2}+c^{2}[/tex]. It is used to find the side lengths of a right triangle.
Step 2: Using the Theorem
We can see that the triangle shown is a right triangle and we know two sides so we can solve for the last side.
We can denote -
a - 15
b - unknown
c - 25
(note, c is always the hypotenuse or the longest side of the triangle)
We can plug in the numbers -
[tex]15^{2} +b^{2} =c^{2}[/tex]
[tex]225 +b^{2}=625[/tex]
[tex]b^{2} =625-225[/tex]
[tex]b^{2} =400[/tex]
[tex]b=20[/tex]
Please help me out!
Answer:
4/3
Step-by-step explanation:
interest 600$ invested at6% compounded annually for 7 years
Answer:
The interest earned is $302.18
Step-by-step explanation:
Compound Interest
It occurs when the interest is reinvested rather than paying it out. Interest in the next compound period is earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
The investment described in the question is of P=$600 at a rate of r=6%=0.06 for t=7 years compounded annually. The compounding period coincides with the time of interest rate, thus n=1.
Applying the formula:
[tex]{\displaystyle A=600\left(1+{\frac {0.06}{1}}\right)^{1*7}}[/tex]
[tex]{\displaystyle A=600\left(1.06}\right)^{7}}[/tex]
A = $902.18
The interest is:
I = A - P = $902.18 - $600 = $302.18
The interest earned is $302.18
a company that makes hair care products had people try a new shampoo of the 200 people 20 had a mild allergic reaction. what percent of the people had mild allergic reaction?
Answer:
4%
Step-by-step explanation:
8 divided by 200 equals 0.04
0.04 times 100 equals 4
Therefore 4 percent of the people had a mild allgergic reaction.
The Great Pyramids of Giza are named the Pyramid of Menkaure, the Pyramid of Khafre and the Pyramid of Khufu. The height and base of each of these pyramids are: 65.5 m by 103.4 m2, 136.4 m by 215.25 m2, 138.8 m by 230.4 m2 respectively. What is the volume of each of the Great Pyramids of Giza?
Step-by-step explanation:
The volume of a pyramid is equal to one third the product of the area of the base and the height.
Pyramid of Menkaure
Area of Base, B = 103.4 m2
Height, H = 65.5 m
Volume = 1/3 * BH
Volume = 1/3 * 103.4 * 65.5 = 2257.56 m3
Pyramid of Khafre
Area of Base, B = 215.25 m2
Height, H = 136.4 m
Volume = 1/3 * BH
Volume = 1/3 * 215.25 * 136.4 = 9786.7 m3
Pyramid of Khufu
Area of Base, B = 230.4 m2
Height, H = 138.8 m
Volume = 1/3 * BH
Volume = 1/3 * 230.4 * 138.8 = 10598.4 m3
Simplify 2 root 1/2 - 6 root 1/8 - 10 root 4/5
Answer:
0.70710678 is 2 root 1/2 simplified
Step-by-step explanation:
a worker can complete the assembly of 15 chairs in 6 hours. At the rate,how many can the worker complete in a 40-hour work week?
Answer:
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Step-by-step explanation:
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