A rectangle has a length of 32feet less than 8 times its width. If the area of the rectangle is 96 square feet, find the length of the rectangle.
Answers
L = 8w-32
w(8w-32) = 96
8x^2 - 32w - 96 = 0
w^2 - 4w - 12 = 0
(w - 6)(w + 2 ) = 0
w+2=0 results in negative measures
w-6=0 ---> w = 6
width is 6
length is 8(6) - 32 = 48-32 = 16
Related Questions
Referring to the figure, the two rectangles shown have
equal areas. Find the value of x.
Answers
Answer:
x = 2
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × breadth
given the rectangles have equal areas then equating the two areas gives
4x × 9 = 4(6x + 6) , that is
36x = 24x + 24 ( subtract 24x from both sides )
12x = 24 ( divide both sides by 12 )
x = 2
A biologist has two brine solutions, one containing 10% salt and another containing 25% salt. How many milliliters of each solution should she mix to obtain 1 L of a
solution that contains 23.5% salt?
a. 50 milliliters of the first brine solution, 950 milliliters of the second brine solution
b. 150 milliliters of the first brine solution, 850 milliliters of the second brine solution
Oc. 100 milliliters of the first brine solution, 900 milliliters of the second brine solution
O d. 200 milliliters of the first brine solution, 1,000 milliliters of the second brine solution
e. 900 milliliters of the first brine solution, 100 milliliters of the second brine solution
Answers
Using proportions, it is found that the correct option is:
c. 100 milliliters of the first brine solution, 900 milliliters of the second brine solution
The 1-liter solution, with 23.5% salt, is composed by:
x liters of the first brine solution, with 10% salt.1 - x liters of the second brine solution, with 25% salt.Hence, the combined equation is:
\(0.1x + 0.25(1 - x) = 0.235\)
\(0.1x + 0.25 - 0.25x = 0.235\)
\(0.15x = 0.015\)
\(x = \frac{0.015}{0.15}\)
\(x = 0.1\)
Hence, 0.1L = 100 mL of the first solution, 900 mL of the second, and option c is correct.
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Jacoby says that they
need to save $293.75
per week.
CARD 10:
The Hudson family is saving for a
family vacation to Disney World.
They determine that the trip will
cost $3,200. Mr. and Mrs.
Hudson have already set aside
$1,500 for the trip. If they leave
in 16 weeks, then how much
will they need to save
each week?
Janelle says that they
need to save $106.25
per week
Answers
help pls/////////////////
Answers
Answer:
It might be past the time, but I think the second one.
Step-by-step explanation:
I need help pleaseee
Answers
The result of the row 1 multiplication by 1/4 is determined as [¹/₂ 0 ].
What is the result of the row multiplication?The resultant of the row multiplication in the surd is calculated by applying the following method;
row 1 in the given surds = [2 0]
To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;
[2 0] x 1/4 = 1/4(2 0)
= [¹/₂ 0 ]
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that 2, and 0 by 1/4.
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Which statement about the function is true?
Answers
Answer:
the last one
number 4
A band expects to put 16 songs on their next CD. The band writes and records 50% more songs than they expect to put on the CD. During the editing process, 75% of the songs are removed. How many songs will there be on the final CD?
(I NEED HELP FAST:O)
Answers
Answer:
15 songs of 14 I am not sure
Find the value of x for which the function y = x5-x³ + x² - 1 has a local minimum.
Answers
The given function presents a local minimum in the coordinates (0,-1).
FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
For solving this question, the given equation should be rewritten from the factoring.
\(x^5-x^3+x^2-1=\left(x+1\right)^2\left(x-1\right)\left(x^2-x+1\right)=0\). Then, you have 3 equations.
From the Zero Factor Principle, you can write
Equation 1
(x+1)²=0
x+1=0
x= -1
Equation 2
x-1=0
x=1
Equation 3
x²-x+1=0
\(x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\ \\ x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{3}i}{2\cdot \:1}\)
From these points it is possible to plot a graph and you can see that the local minimum presents the coordinates (0,-1).
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16) How many more line segments will be needed to be added to Step 3 to create Step 4 of the
sequence?
Step 1
Step 2
Step 3
Answers
Harper is starting a printing business. She purchases plain t-shirts for $5 dollars each and spends $150 for printing equipment She decides to sell printed shirts for $10 each. How many t-shirts does Harper need to sell so that the amount of money she spends to start her business and the amount of money she earns are the same.
Answers
Answer:
30
Step-by-step explanation:
150/5 = 30
30+30+30+30+30 = 150
Please help i have an assignment due TODAY i need to get this done
rules:
NO LINKS not risking a virus
Answers
U is the radius
And the other line is the diameter
Calcular los 3/5 de los 2/3 de las 3/4 de 560
Answers
For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.
How to solve fractions?To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:
Step 1: Calculate 3/4 of 560:
3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420
Step 2: Calculate 2/3 of the result from Step 1:
2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280
Step 3: Calculate 3/5 of the result from Step 2:
3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168
Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.
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a sales manager analyzed the sales, in dollars, y, of snow shovels compared to the outside temperature, in degrees fahrenheit, x. the manager calculated the correlation coefficient of r
Answers
The correlation coefficient of r measures how closely the two variables, x and y, are related. If the coefficient is close to 1, it means that the two variables are strongly related, whereas if it is close to 0, it means that there is no relation between them.
The correlation coefficient of r is a measure of how closely related two variables are to each other. It is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations. The coefficient ranges from -1 to +1, with -1 indicating a perfectly negative linear relationship, 0 indicating no relationship, and +1 indicating a perfectly positive linear relationship. In the case of the sales manager analyzing the sales of snow shovels compared to the outside temperature, the correlation coefficient of r can be used to measure the strength of the relationship between the two variables. If the coefficient is close to 1, it indicates that the two variables are strongly related, while a coefficient close to 0 indicates that there is no relation between them.
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Least common multiple of 10,20 35
Answers
Answer: 140
Step-by-step explanation:
2log12 3 + 4log12 2 simplifying
Answers
Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.
The answer to this problem: 2
Simplify 4 – 8 × 2.
options:
A)
–10
B)
–4
C)
–12
D)
–8
Answers
Answer:
Is the answer -12 or something else?
Answer:
c) -12
Step-by-step explanation:
8 * 2 = 16
16 - 4 = 12
Numbers and operations
show work on paper if possible :)
Answers
Answer:
B. $5.99
Step-by-step explanation:
Let's start by finding the total cost of the sodas. We know that there were 5 sodas and each cost $0.75, so the total cost of the sodas is:
5 * $0.75 = $3.75
Next, we need to subtract the cost of the sodas from the total cost before tax to find the cost of the pizzas:
$33.70 - $3.75 = $29.95
Finally, we can divide the cost of the pizzas by the number of pizzas to find the cost of each pizza:
$29.95 ÷ 5 = $5.99
Therefore, the cost of each pizza pie was $5.99. Answer choice B is correct.
Solve for y. 7x-5y=-35
Answers
Answer:
y = 7(1 + x/5)
Step-by-step explanation:
7x - 5y = -35
-5y = -35 - 7x
5y = 35 + 7x
y = (35 + 7x) / 5
y = 7 + 7x/5
y = 7(1 + x/5)
O
X
y
X
y
X
y
X
y
0
2
0
0
-1
0
1
0
5
2
113
1
2
2
8
4
WIN
3
3
4
11
2.5 -2.5-7.5 -12.5
6
W/W
5
6
Select all table’s that represent proportional relationship between x and y
Answers
All tables that represent proportional relationship between x and y are:
B. table B.
E. table E.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)
Constant of proportionality, k = 1.
Therefore, the required linear equation is given by;
y = kx
y = x
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
please help!!! if i don’t get this test right then i fail and i really can’t ! i’ll mark brainlyist ! pleasee
anyone
Answers
Answer:
208 cubic units
Step-by-step explanation:
The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:
The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.
Now, let’s calculate the volume of the rectangular prism:
The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160
Now, add up the volumes of the rectangular and triangular prisms:
160 + 48 = 208 cubic units
1 Which set of ordered pairs does not represent a function?
1 {(1, 10), (3, 18), (5, 26), (7, 34), (9, 42)
2 {(2, 10), (3, 20), (4, 15), (5,5), (6,25)
3 {(0,8), (5,4), (10,0), (15, 4), (20,8)
4 {(9, 1), (6,2), (3, 3), (6,4), (9,5)}
Answers
7 and - 1 1/2 on the number line?
Answers
You can ignore the fraction and do
7-1
Which gives you 6.
Then add the fraction, and your final answer is
6 1/2
Change this radical to an algebraic expression with fractional exponents.
Answers
The required algebraic form of the given radical form ∛a is \(a^{1/3}\).
What is an algebraic expression?The algebraic expression consists of constant and variable. eg x, y, z, etc.
Here,
Given expression,
= ∛a
since we know that, \(a^{1/n} = \sqrt[n]{a}\)
So ∛a = \(a^{1/3}\).
Thus, the required algebraic form of the given radical form ∛a is \(a^{1/3}\).
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Condense each Logarithm
Answers
The equation of logarithm are solved and
a) A = 2 + 3 log x + 4 log b
b) B = ( 36 + x + y ) ( log 6 )
c) C = ( 1/2 )x log 5
d) D = ln ( x⁴ / y² )
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
a)
A = 2 log 10 + 3 log x + 4 log b
The base of the logarithm is 10 , so
A = 2 + 3 log x + 4 log b
b)
B = log 6³⁶ + log 6ˣ - log 6^ ( y )
From the properties of logarithm , we get
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
B = 36 log 6 + x log 6 + y log 6
On taking the common term , we get
B = ( 36 + x + y ) ( log 6 )
c)
C = ( 1/2 )log 5ˣ
From the properties of logarithm , we get
C = ( 1/2 )x log 5
d)
D = 4 ln x - 2 ln y
From the properties of logarithm , we get
D = ln x⁴ - ln y²
On further simplification , we get
D = ln ( x⁴ / y² )
Hence , the logarithmic equations are solved
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Malcolm is working full-time and wants to make sure he's saving strategically for four specific goals: an emergency fund ($5000), a flight home to see his parents for the holidays ($450), a downpayment on a new car ($3000), and his retirement (2% of his monthly take-home pay). What's his best strategy?
1
Answers
Answer: c. Set up 3 separate savings accounts for the first 3 goals and a retirement investment for the 4th
Step-by-step explanation:
The options are:
a. Put as much as he can every month into an investment, like shares of a company, so his money grows quickly
b. Keep all the money in his checking account so that he can spend it in the different categories as needed
c. Set up 3 separate savings accounts for the first 3 goals and a retirement investment for the 4th
d. Set up 4 separate savings accounts
Based on the information given in the question, the best startegy for Malcolm is to set up 3 separate savings accounts for the first 3 goals and a retirement investment for the 4th.
Since the first three goals include saving for an emergency fund ($5000), saving for a flight home to see his parents for the holidays ($450), and a downpayment on a new car ($3000), the best thing he should do is to set up 3 savings account for the first three goals.
The last goal relates to his retirement which is 2% of his monthly take-home pay, therefore he should set up a retirement investment for the 4th goal.
How to model 3 + x= 11 using algebra tiles
Answers
Answer:
A Beginner's Guide to Teaching with Algebra Tiles
explanation: hope it helps
study the visual fraction below. Is it A,B,C, or D?
Answers
Answer: B
Step-by-step explanation: the pic shows this
you can see it on the pic btw
can someone help me i will give brainlest
Answers
Answer:
(48, 3), (80, 5), (160, 10)
Find the quotient. 64 ÷ 32 =
Answers
Answer:
64÷32=2.
Step-by-step explanation:
if you add 32+32 it's 64, so that means 32x2=64 and yeahhh
The average distances between some objects in our solar system are described below.
• The average distance from Earth to the Moon is 3.844 × 105 kilometers (km).
• The average distance from Jupiter to the Sun is approximately 2 × 103 times the average distance from Earth to the Moon.
Based on this information, what is the average distance from Jupiter to the Sun
7.688 × 10, 2, km
7.688 × 10, 5, km
7.688 × 10, 8, km
7.688 × 10, 15, km, ,
Answers
Answer:
Jupiter to Sun = 7.688 * 10⁸km
Step-by-step explanation:
Given
Earth to Moon = 3.844 * 10⁵km
Jupiter to Sun = 2 * 10³ times Earth to Moon
Required
Determine the average distance from Earth to Moon
Jupiter to Sun = 2 * 10³ times Earth to Moon
Substitute 3.844 * 10⁵km for Earth to Moon
Jupiter to Sun = 2 * 10³ * 3.844 * 10⁵km
Collect Like Terms
Jupiter to Sun = 2 * 3.844 * 10³ * 10⁵km
Jupiter to Sun = 7.688 * 10³ * 10⁵km
Jupiter to Sun = 7.688 * 10⁸km
Hence, option C answers the question