Answer:
A.) 55/8
Step-by-step explanation:
To make 6 7/8 an improper fraction, multiply the whole number by the denominator and add the result to the numerator.
That’s
6 x 8 = 48
48 + 7 = 55
Also, the denominator of the mixed number still remains the denominator of the improper fraction.
That’s
55/8
The mixed number 6 7/8 is equal to the improper fraction 55/8, making option A correct.
Explanation:To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction and then add the numerator of the fraction. The mixed number 6 7/8 can be converted to an improper fraction by following this method: Multiply 6 (the whole number) by 8 (the denominator) to get 48, and then add 7 (the numerator) to get 55. Therefore, 6 7/8 as an improper fraction is 55/8, which makes option A correct.
A woman earns $ 1,350 in interest from two accounts in one year. If she has three times as much invested at 7% as she does at 6%, how much does she have in each account?
Answer:
The woman invested $15,000 at 7% interest rate and $5,000 at 6% interest rate.
Step-by-step explanation:
We are given the following in the question:
Let x be the interest earned from 7% interest rate and y be the interest earned from 6% interest rate.
The woman invested has three times as much invested at 7% as she does at 6%.
Thus, we can write the equation:
[tex]x = 3y[/tex]
The total interest is $1,350.
Thus, we can write the equation:
[tex]1350 = \dfrac{7x}{100} + \dfrac{6y}{100}\\\\7x + 6y = 135000[/tex]
Solving the two equations by substitution method:
[tex]7(3y) + 6y = 135000\\27y = 135000\\y = 5000\\x = 3(5000) = 15000[/tex]
Thus, she invested $15,000 at 7% interest rate and $5,000 at 6% interest rate.
What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12
The solution of the system of equations is [tex]x=-2[/tex] and [tex]y=3[/tex]
Explanation:
The system of equations are [tex]4 x+5 y=7[/tex] and [tex]3 x-2 y=-12[/tex]
To determine the solution of the equation, let us solve the equations by elimination method.
Thus, multiplying the equation [tex]4 x+5 y=7[/tex] by 2, we get, [tex]8x+10y=14[/tex]
Multiplying the equation [tex]3 x-2 y=-12[/tex] by 5, we get, [tex]15x-10y=-60[/tex]
Adding these two equations, we have,
[tex]\ \ 8x+10y=14\\15x-10y=-60\\---------\\23x=-46[/tex]
Dividing both sides by 23, we have,
[tex]\frac{23x}{23} =\frac{46}{23}[/tex]
[tex]x=-2[/tex]
Thus, the value of x is [tex]x=-2[/tex]
Substituting [tex]x=-2[/tex] in the equation [tex]4 x+5 y=7[/tex], we get,
[tex]4 (-2)+5 y=7[/tex]
[tex]-8+5 y=7[/tex]
[tex]5y=15[/tex]
[tex]y=3[/tex]
Thus, the value of y is [tex]y=3[/tex]
Hence, the solution of the system of equations is [tex]x=-2[/tex] and [tex]y=3[/tex]
The solution to the system of equations, is: (-2, 3).
Solution to System of EquationsTo find the solution, you can use the elimination method by first making both equations equivalent. Then add or subtract to eliminate a variable.
Given:
4x + 5y = 7 --> Eqn. 13x – 2y = –12 --> Eqn. 2Multiply eqn. 1 by 3 and eqn. 2 by 4:
12x + 15y = 21 --> Eqn. 1
12x – 8y = –48 --> Eqn. 2
Subtract:23y = 69
Divide both sides by 23y = 3
Substitute y = 3 into eqn. 1.
4x + 5(3) = 7
4x + 15 = 7
4x = 7 - 15
4x = -8
x = -2
Therefore, the solution to the system of equations, is: (-2, 3).
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(I NEED THIS ANSWERED QUICKLY! I WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER!)
Rectangle ABCD is reflected about the x-axis.
What are the coordinates of vertex D’?
A. (-6, -8)
B. (6, -8)
C. (6, 8)
D. (-6, 8)
Answer:
Option D, (-6, 8)
Step-by-step explanation:
Since it is reflected across the x-axis, that means the y values flip their signs.
Since D was (-6, -8) flip the y value you get (-6, 8)
Answer: Option D, (-6, 8)
Answer:
D. (-6, 8)
Step-by-step explanation:
correct on EDGE
John answered 80% of the questions correctly. There were 30 questions on the test. How many questions did John answer correctly?
Answer:
he got 24 right
Step-by-step explanation:
30 time 80% is 24
John answered 24 questions correctly out of 30 by answering 80% of the questions correctly.
To determine how many questions John answered correctly, we can use the information that he answered 80% of the 30 questions correctly. We can follow these steps to find the answer:
First, convert the percentage to a decimal. 80% becomes 0.80.Next, multiply the total number of questions (30) by the decimal (0.80):0.80 * 30 = 24
Therefore, John answered 24 questions correctly out of the 30 questions on the test.
Sandra budgets $580 each month for living expenses. She nets $1640 semimonthly.
What percent of her net monthly income does she budget for living expenses?
35%
24%
18%
16%
Answer:18%
Step-by-step explanation:
Sandra's Monthly budget on expenses for living expenses = $580
Sandra's semimonthly net = $1640
Sandra's monthly net = $1640 x 2 = $3280
The percent of her net monthly income that she budget on living expenses is:
= (Budget on living expenses / Monthly net) x 100
= (580 / 3280) x 100
= (0.176829) x 100
= 17.68% = 18% (approximately)
Answer:
18%
Step-by-step explanation:
Multiply.
(5x - 2)2
A. 25x + 20x + 4
B. 25x2 - 4
C. 25x2 - 20x+ 4
D. 25x2 - 10x + 4
Answer:
Step-by-step explanation:
Factor using the perfect square rule.(5x−2)2
answer using factor
Answer: 25x2+40x+16
Step-by-step explanation:
line Q passes through points (3,9) and ( 10,5) line R is perpendicular to Q what is the slope of
line R
Answer:
7/4
Step-by-step explanation:
The slope of Q is (9-5)/(3-10) = -4/7
Perpendicular lines' slopes are opposite reciprocals of eachother (so the +/- changes and then x/y becomes y/x).
This means the slope of R is 7/4
The required slope of line R will be 7/4.
What are the perpendicular lines?Perpendicular lines are two lines that cross one other and create a 90-degree angle.
Two lines are perpendicular if the product of their slopes is -1.
The line Q is given which passes through points (3,9) and ( 10,5)
Let
x₁ = 3, y₁ = 9
x₂ = 10, y₂ = 5
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in the formula
The slope of line Q will be:
m = (9-5)/(3-10)
m = -4/7
Since line R is perpendicular to Q, so the slope of line R will be
⇒ -1/m
⇒ -1/(-4/7)
Reciprocal the term in the denominator,
⇒ -1 × -7/4
Apply the multiplication operation, and we get
⇒ 7/4
Therefore, the required slope of line R will be 7/4.
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Six times a certain number is 12 more than four times the number. Find the number.
Answer:
6
Step-by-step explanation:
Let the number be A
Given 6 times A is 12+ (4 xA)
That’s
6 x A = 12 + 4A
6A = 12 + 4A
Subtract 4A from both sides
6A - 4A = 12 - 4A - 4A
2A = 12
Divide both sides by 2
A = 12/2
A = 6
The number is 6
a. At the beginning of the year, Addison Company’s assets are $300,000 and its equity is $100,000. During the year, assets increase $80,000 and liabilities increase $50,000. What is the equity at year-end?
Equity at the end of the year = $130,000
Step-by-step explanation:
Step 1:
Given ,
Asset of the company at beginning of year = $300,000
Equity of the company at beginning of year = $100,000
Increase of the assets during the year = $80,000
Increase of the liabilities during the year = $50,000
We need to find the equity at the year end.
Step 2 :
The equity at any point can be obtained by using the formula
equity = assets - liability
At the beginning of the year ,
100,000 = 300,000 - liability
So liability = 300,000 - 100,000 = 200,000
Step 3 :
During the year, assets increase $80,000 and liabilities increase $50,000
So assets at the year end = 300,000 + 80,000 = $380,000
liabilities at the year end = 200,000 + 50,000 = $250,000
Therefore
Equity at the year end = 380,000 - 250,000 = $130,000
Step 4 :
Answer :
Equity at the year end = $130,000
On the Price Is Right game show, to get into the showcase at the end, contestants spin a wheel with 20 equally sized spaces, numbering 5 cents, 10 cents, 15 cents,and so on, up to $1.00. If the contestant spins once, find the probability of getting a $1
Find
196
O A) 14
OB) 13
OC) 17
OD 15
What is -2(w-5)+4w+3 simplified
Answer:
2w + 13
Step-by-step explanation:
Step 1: Distribute
-2(w - 5) + 4w + 3
-2w + 10 + 4w + 3
Step 2: Combine like terms
-2w + 10 + 4w + 3
2w + 13
Answer: 2w + 13
Noah starts with 0 and then adds the number 5 four times. Diego starts with 1 and then multiplies by the number 5 four times. For each expression, decide whether it is equal to Noah’s result, Diego’s result, or neither.
4 ⋅ 5
4 + 5
4^5
5^4
Answer:
4•5 is Noah's result, 4+5 is Neithers, 4^5 is Noah's result, and 5^4 is Diego's result
Step-by-step explanation:
I am just trying to help. I hope it works!
Diego's result is the same as Noah's result and that is 4 ⋅ 5, For each expression.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
Noah starts with 0 and then adds the number 5 four times.
i.e. we get,
Noah: 5+5+5+5=20
again, we have,
Diego starts with 1 and then multiplies by the number 5 four times.
i.e. we get,
Diego: (1x5) + (1x5)+(1x5)+(1x5)= 20
so, we have,
that, For each expression, we get 20
we know,
20 = 4*5
i.e. 4 multiplied by 5.
Hence, Diego's result is the same as Noah's result and that is 4 ⋅ 5, For each expression.
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I really need help but I keep getting my question taken down. Please help.
2. Draw a right triangle with side lengths of 3, 4, and 5 units (cm or inches – your choice). Make sure to label all parts including side lengths, vertices, and the right angle. You may insert an actual picture of your drawing below or upload the picture in the Unit 2 TGA submission area.
Answer:
See the figure attached.Explanation:
In a right triangle the longest side is the hypotenuse. In this case the length is 5 units.
The hypotenuse is opposite to the right angle.
You must draw a small square inside the right angle. In the figure the right angle is labeled C.
The other two sides are the legs: in this case their lengths are 3units and 4 units.
The side with the shortest length is opposite to the smallest angle; the side with the intermediate length is opposite to the angle with the intermediate measure.
The vertices are marked with capital letters. I used A, B, and C.
With this explanation you can understand the figure attached and build one on your own.
Answer:
My options of triangles
Round to the nearest percent
Answer:
79%
Step-by-step explanation:
Area of the square:
1 + 1 = 2
2 × 2 = 4
Square = 4 units^2
Area of the circle:
pi × 1^2
pi × 1
1pi
Square = 3.14 units^2
Let's find probability:
3.14 ÷ 4 = 0.785
0.785 × 100 = 78.5
There is a 78.5% chance of landing in the circle. This percentage can be rounded to 79%
X² – 4x – 12=0
solve by completing the square
Answer:
x = -2 0r x = 6
Step-by-step explanation:
from the question
X² – 4x – 12=0
solve by completing the square method
we have;
X² – 4x – 12=0
X² – 4x = 12
to make the left hand side a perfect square we add 4 to both sides.
X² -4x + 4 = 12 + 4
X² -4x + 4 = 16
from left hand side X² -4x + 4
= (x -2) × ( x -2)
it can be simply expressed as
( x-2)²
so since X² -4x + 4 has been simplified to be ( x-2)²
then,
( x-2)² = 16
x - 2 = √ 16
since square root has two values it can either be positive or negative
so we have
x = 2 + √16
or
x = 2 - √16
therefore
x = 2 + √16
x = 2 + 4
x = 6
0r
x = 2 - 4
x = -2
Answer:
-2,6
Step-by-step explanation:
Savings Account You deposit $1800 into a savings account that
earns 2% interest compounded annually. Find the balance after
2 years.
The balance after 2 years will be $1872.72.
To find the balance after 2 years when you deposit $1800 into a savings account that earns 2% interest compounded annually, we can use the compound interest formula:
[tex]\[ A = P(1 + r)^n \][/tex]
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (expressed as a decimal).
- n is the number of years the money is deposited for.
Given:
[tex]- \( P = $1800 \)[/tex]
[tex]- \( r = 2\% = 0.02 \)[/tex] (expressed as a decimal)
[tex]- \( n = 2 \)[/tex] years
Plug these values into the formula and solve for A :
[tex]\[ A = 1800(1 + 0.02)^2 \][/tex]
[tex]\[ A = 1800(1.02)^2 \][/tex]
[tex]\[ A = 1800(1.0404) \][/tex]
[tex]\[ A = 1872.72 \][/tex]
Simplify this algebraic expression completely 9x-6(x+4)
Step-by-step explanation:
9x-6(x+4)
9x-6x-24
3x-24
Answer: 3x-24
Step-by-step explanation:
Please help with this question ¯\(°_o)/¯
|-1| < |-2|
third answer
When a negative number is in a pair of | |, it turns into a positive. Positive numbers stay the same.
Peter left his home in Chicago and drove to a town a few hours away. On the way there, he drove 40 mph due to traffic, but on the way back home, he drove 60 mph. What was his average speed?
Answer:
50 mph
Step-by-step explanation:
To calculate averages you add up all the items and divide by the total number of items there is.In this problem were 2 items so you divide it by 2
Add the two numbers
40+60=100
now just divide by 2 because there was 2 drives giving you 50 mph
Hope this helps!
:)
Solve the following equation.
c/4 = 12
Answer:
48
Step-by-step explanation:
c÷4=12
4×c÷4=4×12
c=48
Teds car is now worth 9000 which is 60% of what he paid for it . What did he pay for his car
Answer:? 5,400.
Step-by-step explanation:
A cubic centimeter is the space taken by a square whose sides are 1
centimeter long.
O
A. True
SE3
B. False
SUBMIT
Answer:
False
Step-by-step explanation:
A cubic centimeter refers to a cube because it would be LWH (Lengeth * Width * Height) and if they were all one centimeter the volume would be 1 cubic centimeter. If it was a centimeter squared then it would be a square with 1 cm long sides.
Helpppp How do y’all do this
8^(x+2)÷2^(x+2)=4⁶
4^(x+2)=4⁶
x+2=6
x=4
Answer:
x=4
Step-by-step explanation:
8^(x+2)÷2^(x+2)=4⁶
4^(x+2)=4⁶
x+2=6
x=4
Lashonda bought a suit on sale for $603. This price was 33% less than the original price.
Answer:
$404.01 dollars
Step-by-step explanation:
603*33%=198.99
600-198.99=$404.01
MARK BRAINLIEST
Answer:
The suit costs $401.01
Step-by-step explanation:
$603.00 x .33 = $198.99
600.00 - 198.99 = 401.01
How do i write the decimal of 214.013 in words?
two hundred fourteen and thirteen thousandths
Answer: two hundred fourteen and thirteen thousandths
Step-by-step explanation: If you wanted to do this with 214.013, I start with the whole number, which in this case is 214. To write 214 in words, that would be two hundred fourteen. Now, if you add the decimal, you know the first decimal spot is tenths, second is hundredths, and third is thousandths. The decimal would be thirteen thousandths. To add that up, you get two hundred fourteen and thirteen thousandths.
what is the focus of the parabola
[tex]y = - \frac{1}{4} {x}^{2} - 2x - 2[/tex]
enter your answer in the Box
I've seen so many wrong answers and I got it wrong on my quiz
answer: (-4,1)
Answer:
(-4,1)
Step-by-step explanation:
The given parabola is
[tex]y = - \frac{1}{4} {x}^{2} - 2x - 2[/tex]
When we rewrite in vertex form, we get;
[tex]y = - \frac{1}{4} {(x + 4)}^{2} + 2[/tex]
Or
[tex]{(x + 4)}^{2} = - 4( y - 2)[/tex]
When we compare to:
[tex]{(x - h)}^{2} = 4p( y - k)[/tex]
We have 4p=-4
This means p=-1
But the vertex is at:
(-4,2)
Since it is a vertical parabola that opens down, the focus is one unit(|p|=1) below the vertex.
Hence the focus is (-4,1)
28913 To the nearest thousand
Answer:
29000
Step-by-step explanation:
Nearest thousand means the thousand at which the digit is nearest to. Now in approximation, we round up numbers from 1 to 4, to Zero while numbers from 5 to 9 are rounded up to 1.
28913 is between thousand 28,000 and 29000.
And then to be rounded up to the nearest thousand, the digit 9, before the thousand digit 8, in the number 28913 will therefore will rounded up to 1 and added to the thousand digit 28.
We therefore have 29,000
Write in simplest terms3.2x-5+4t(-7)
Answer:
-7(6 x t) *2
Step-by-step explanation:
1. Juan paid $2.52 for 12 ounces of peanuts
What is the unit rate?
P.S I’m in 6th grade and I need to know if I got this right please!!
Answer:
$0.21
Step-by-step explanation:
2.52/12