The area of a rug is 36 square feet. the length of the rug is 5 feet longer than the width. what is the width of the rug?
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Related Questions
Is g(x)= 5 + 6/x a linear function
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Tom and Rob are brothers who like to make bets about the outcomes of different contests between them. Before the last bet, the ratio of the amount of toms money to the amount of robs money was 4:7. Rob lost the latest competition, and now the ratio of the amount of robs money is 8:3. If rob had $280 before the last competition, how much rob have now that he lost the bet?
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before the bet Rob had 7 out of 11 ( 4+7)
280/7 = 40
after bet Rob had 3
3*40 = 120
he has $120
If the federal reserve decreases the reserve rate from 7% to 5%, how does this affect the amount of money that would result because of fraction-reserve rbanking from an initial deposit into a bank of $30,000
Answers
30,000÷0.07=428,571
If the federal reserve rate was 5%, the money supply would be
30,000÷0.05=600,000
If the federal reserve decreases the reserve rate from 7% to 5%
600,000−428,571=171,429
The money supply increases by 171429
Hope it helps!
When the Federal Reserve decreases the reserve rate from 7% to 5%, the amount of money resulting from fraction-reserve banking increases. In this case, an initial deposit of $30,000 would result in $28,500 due to the change in reserve rate.
Explanation:When the Federal Reserve decreases the reserve rate from 7% to 5%, it means that banks are required to hold a smaller percentage of deposits as reserves. This change allows banks to lend out a larger portion of the initial deposit. In this case, if the initial deposit into a bank is $30,000, the amount that would result from fraction-reserve banking would increase because the bank can now lend out a greater percentage of the deposit.
To calculate the new amount that would result from fraction-reserve banking, we need to calculate the reserve amount and the loan amount.
Reserve amount = $30,000 * 0.05 = $1,500
Calculate the loan amount by subtracting the reserve amount from the initial deposit:
Loan amount = $30,000 - $1,500 = $28,500
Therefore, the amount that would result from fraction-reserve banking from an initial deposit of $30,000 would be $28,500.
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let f(x)=4x-7 and g(x)-5+9x. what are f+g and f-g? what are their domains?
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The product of (a − b)(a − b) is a2 − b2.
Sometimes
Always
Never
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Final answer:
The statement that the product of (a − b)(a − b) equals [tex]a^2 - b^2[/tex] is never true; the correct product is always [tex]a^2 - 2ab + b^2[/tex], representing the square of a difference formula.
Explanation:
The statement "The product of (a − b)(a − b) is [tex]a^2 - b^2[/tex]." is never true. Instead, using the distributive property to expand the expression (a − b)(a − b) yields a different result, as each term in the first binomial must be multiplied by each term in the second binomial.
The correct expansion is:
(a − b)(a − b) = a(a − b) - b(a − b)= aa - ab - ba + bb= [tex]a^2 - 2ab + b^2[/tex](since ab and ba are equivalent)Thus, the product of (a − b)(a − b) is always [tex]a^2 - 2ab + b^2[/tex], which is the square of a difference formula, not [tex]a^2 - b^2[/tex] which is the difference of squares formula. The latter is applicable to the product (a + b)(a - b).
Which equation is equivalent to
X/ +11 = 15
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√x= 15-11 x=16
Make a table for a function whose graph has a y-intercept of 4 and a slope of 2/3.
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y = mx + b
where
m is the slope
b is the y-intercept
Substituting the given values, the equation of the line is:
y = 2/3*x + 4
To make a table, substitute arbitrary values of x, so that you would get the corresponding values of y using the equation. The table is shown in the attached picture.
Six identically shaped place mats, marked a, b, c, d, e and f, are piled neatly in a stack. how many arrangements are possible if a and b must touch each other?
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1. A, b, c
2. A, b, d
3. A, b, e
4. C, a, b
5. D, a, b
6. E, a, b
Hope I helped!
Standard form of 5y=35+10x
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Answer:
[tex]5y - 10x - 35 = 0[/tex]
Step-by-step explanation:
The standard way to write a linear relationship between the x and y variables is through a homogeneous equation as a combination of the x and y variables with real coefficients. The form is given by the expression:
[tex]ax + by + c = 0[/tex]
The equation [tex]5y = 35 + 10x[/tex] can be written in standard form if terms are transposed, obtaining [tex]5y - 10x - 35 = 0[/tex]
A quota is when one country
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This is done in order to give prominence to domestic suppliers and producers. If you limit the amount of foreign goods, then its price will rise, which will make consumers buy more domestic goods and thus help develop domestic trade.
Could -2 be used as a base to rewrite 32? 64? Why or why not?
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Jen bought 5 cds for 57.50. What was the unit price
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$11.50
Hope this helps!
assume f(x)=4x+8 and g(x)=5. what is the value of (golf)(-1)
idk what is it, show work plz?
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what hourly rate does the repair shop charge for labor?
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The mechanic's hourly rate is $55.
Understanding Labor Costs in a Repair Shop
To determine the hourly rate a repair shop charges for labor, we must analyze the information given and apply simple arithmetic operations. According to the examples provided, an auto mechanic charges a flat fee and an hourly rate for labor. For instance, a mechanic charging a flat fee of $75 per car, plus an hourly rate of $55 can be represented by the linear equation y = 75 + 55x, where 'y' is the total labor charge, and 'x' is the number of hours worked.
Example Calculation
Using the equation above, if the job takes 3.5 hours, the labor charge (y) would be calculated as $75 + ($55 imes 3.5) = $75 + $192.50 = $267.50. Hence, we can infer that the mechanic's hourly rate is $55.
In 2003, the population of an african country was about 12 million people, which is 3 million more than 2 times the population in 1950. enter and solve an equation to find the approximate population p (in millions) in 1950. an equation is . the approximate population in 1950 was million people.
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12 - 3 = 2p
9 = 2p
9/2 = p
4.5 = p......so the population in 1950 was approximately 4.5 million people
Answer:
3 million
Step-by-step explanation:
24% of 1321 is how much? round the answer to the nearest hundredth
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How to find mass when given density and volume?
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Round 156, 782 to nearest thousand and the nearest ten thousand.
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156, 782 rounded to the nearest ten thousand is 160,000.
The answer is 167,000 because if you round to the 6,782 up it is 7,000. If you round 57,782 up it is 60,000. so then just add those 2 together and plug the 100,000 into it.
The equation 14m = 400.40 can be used to find the cost per yard m, in dollars, of mulch. what is the value of m? m = $
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14m ÷14 = 400.40 ÷ 14
m = 28.60
The population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 7 years, how long will it take to triple? (round your answer to one decimal place.)
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To determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(rt) for t. Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.
Explanation:To solve this problem, we can use the equation P = P0e^(rt), where P is the population at a given time, P0 is the initial population, e is the base of the natural logarithm (approximately 2.71828), r is the growth rate, and t is the time in years.
In this case, the population has doubled in 7 years, so we can write the equation as 2P0 = P0e^(r*7). We need to solve for r.
Dividing both sides of the equation by P0 gives us 2 = e^(7r). Taking the natural logarithm of both sides gives us ln(2) = 7r. Solving for r, we find that r ≈ ln(2)/7.
Now, to determine how long it will take for the population to triple, we need to solve the equation 3P0 = P0e^(r*t) for t. Substituting the value of r we found, we get 3 = e^((ln(2)/7)*t). Taking the natural logarithm of both sides to solve for t, we have ln(3) = (ln(2)/7)*t. Solving for t, we find that t ≈ 7 * ln(3)/ln(2). Rounding the answer to one decimal place, it will take approximately 10.1 years for the population to triple.
It takes approximately 11.1 years for the population to triple.
The population growth can be modeled by the exponential function [tex]P(t)=P_0 \times e^{k t}[/tex], where [tex]P_0[/tex] is the initial population, k is the growth rate, and t is time.
In this case, since the population doubles in 7 years, we have the relationship P(7) = 2 x [tex]P_0[/tex].
[tex]P(7)=P_0 \times e^{7 k}[/tex]
[tex]2 \times P_0=P_0 \times e^{7 k}[/tex]
Divide both sides by [tex]P_0[/tex].
[tex]2=e^{7 k}[/tex]
Take the natural logarithm (ln) of both sides to solve for k:
ln(2) = 7k
[tex]k=\frac{\ln (2)}{7}[/tex]
Now that we have the growth rate k, we can use it to find the time it takes for the population to triple.
[tex]P(t)=P_0 \times e^{k t}[/tex]
For tripling, [tex]P(t)=3 \times P_0[/tex].
[tex]3 \times P_0=P_0 \times e^{k t}[/tex]
[tex]3=e^{k t}[/tex]
Take the natural logarithm again:
ln(3) = kt
[tex]t=\frac{\ln (3)}{k}[/tex]
Substitute the value of k we found earlier:
[tex]t=\frac{\ln (3)}{\frac{\ln (2)}{7}}[/tex]
Using natural logarithm values:
[tex]t \approx \frac{1.0986}{\frac{0.6931}{7}}[/tex]
[tex]t \approx \frac{1.0986}{0.0990}[/tex]
t ≈ 11.09
Identify where the given information is sufficient for graphing a linear equation. Check all that apply.
A.one point and the slope of the line
B.one point
C.one of the intercepts and the slope of the line
D.both the intercepts
E.two points
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To graph a linear equation, you need at least two pieces of information: the slope and a point, both intercepts, or two points. One point and the slope, or one intercept and the slope, are also sufficient to graph a linear equation.
Explanation:For graphing a linear equation, there are several options that provide sufficient information:
A. One point and the slope of the lineC. One of the intercepts and the slope of the lineD. Both the interceptsE. Two pointsTo graph a linear equation, you need at least two pieces of information, such as the slope and a point or both intercepts. Having two points is also sufficient since it helps determine the slope. Having just one point or one intercept along with the slope is also enough to graph the line.
Prove that composition of injective functions is injective. prove that composition of surjective functions is surjective.
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f(x) is injective
f(a) = f(b) <--> a = b
g(x) is injective
g(a) = g(b) <--> a = b
prove f(g(x)) is injective
f(g(a)) = f(g(b))
f(a) = f(b) ... since g(x) is injective
a = b
So that proves if f(g(a)) = f(g(b)), then a = b
Now go the other direction
a = b
g(a) = g(b)
f(g(a)) = f(g(b))
So that wraps up the sub-proof of "f(g(a)) = f(g(b)) iff a = b"
-------------------------
proving g(f(x)) is injective is going to follow a similar path of steps
------------------------------------------
------------------------------------------
Proof 2: Proving the composition of surjective functions is itself a surjective function.
f(x) is surjective
The range of f(x) is the set of all real numbers
g(x) is surjective
The range of g(x) is the set of all real numbers
f(g(x)) is also surjective because of property 1 listed above. The range of f(x) is the set of all real numbers. The fact that g(x) represents all reals as well means that we touch all of the inputs needed to generate all the outputs for f(x).
-------------------------
Proving g(f(x)) to be surjective follows a similar path.
It is found that the composition of injective functions is injective.
What is an injective function?An injective function is not a surjective function. This means that we want a function that has a unique output for each input, that doesn't cover the natural numbers.
Proof 1: Proving the composition of injective functions is injective.
f(x) is injective
f(a) = f(b)
a = b
Thus g(x) is injective
g(a) = g(b)
a = b
To prove; f(g(x)) is injective
f(g(a)) = f(g(b))
f(a) = f(b)
Since, g(x) is injective
a = b
Therefore, if f(g(a)) = f(g(b)), then a = b
That proving g(f(x)) is injective is going to follow a similar path of steps.
Proof 2: Proving the composition of surjective functions is surjective.
f(x) is surjective
The range of the function of x is the set of all real numbers
g(x) is surjective
The range of the function of x is the set of all real numbers
f(g(x)) is also surjective. The range of f(x) is the set of all real numbers. where g(x) represents all reals as well means that we touch all of the inputs needed to generate all the outputs for f(x).
Proving g(f(x)) to be surjective follows a similar path.
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90 points correct answer
If the parent function f(x) = x2 is modified to g(x) = 2x2 + 1, which statement is true about g(x)?
It is an even function.
It is an odd function.
It is both an even and an odd function.
It is neither an even nor an odd function.
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hope it helps
275 mm = _____ cm
954 g = _____ kg
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1mm = 0.1cm
275 * 0.1 = 27.5 cm
1 g = 0.001 kg
954 x 0.001 = 0.954 kg
954g=0.945kg
Hope this helped
A line passes through the point (–2, 7) and has a slope of –5. What is the value of a if the point (a, 2) is also on the line?
A.–7
B.–1
C.1
D.7
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Answer:
The correct option is B.
Step-by-step explanation:
The slope of a line is constant.
If a line passes through two points then the slope of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
It is given that the line passes through (-2,7) and (a,2).
Using the above formula the slope of the line is
[tex]m=\frac{2-7}{a-(-2)}[/tex]
[tex]m=\frac{-5}{a+2}[/tex]
It is given that the slope of the line is -5. Substitute m=-5 in the above equation.
[tex]-5=\frac{-5}{a+2}[/tex]
On cross multiplication we get
[tex]-5(a+2)=-5[/tex]
Divide both sides by -5.
[tex]a+2=1[/tex]
Subtract 2 from both the sides.
[tex]a=1-2[/tex]
[tex]a=-1[/tex]
The value of a is -1. Therefore the correct option is B.
Answer:
The answer is B.
Step-by-step explanation:
Sue has 18 sweets. tony has 18 sweets.sue gives tony x sweets. Sue then eats 5 sweets. Tony then eats half of his sweets. Write expressions for the number of sweets sue and tony have now
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The expressions for the number of sweet Sue and Tony have are 13 - x and
18 + x / 2 respectively
Sue has 18 sweet.
Tony has 18 sweet.
Sue gives Tony x sweet . Sue sweet will be
18 - xSue then eats 5 sweets then his sweet will be
18 - 5 - x = 13 - xTony collected x sweet from Sue. His sweet will be
18 + xTony ate half of his sweets . His remaining sweet will be
18 + x / 2The expression for Sue sweets is : 13 - x
The expression for Tony sweets is : 18 + x / 2
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Expressions for the number of sweets sue and tony have now :
Sue: 13 - x sweets
Tony: (3/2)x + 18 sweets
Here are the expressions for the number of sweets Sue and Tony have now:
Sue: 18 - x - 5 = 13 - x
Tony: 18 + x - (1/2)x = (3/2)x + 18
Here's a breakdown of the calculations:
Sue's sweets:
Sue starts with 18 sweets.
She gives Tony x sweets.
She then eats 5 of her sweets.
Therefore, Sue now has 18 - x - 5 sweets, which can be simplified to 13 - x.
Tony's sweets:
Tony starts with 18 sweets.
Sue gives him x sweets.
He then eats half of his sweets.
Since Tony eats half of his sweets, he is left with (1/2) of his sweets. Therefore, Tony now has 18 + x - (1/2)x sweets, which can be simplified to (3/2)x + 18.
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Find the quotient.
110/10=
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the / means divide
110 divided by 10 is 11.
The quotient is 11.
Hope this helps.
The sum of -4 and 8 times a number is multiplied by 3. The result is 15 less that 25 times the number. What is the number?
A) -12
B) 6/7
C) 0
D) 3
E) none of the above
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-12 + 24x = 25x - 15
25x - 24x = -12 + 15
x = 3
answer is
D) 3
If f(x)=3/x+2-root x-3 complete the following statement (round answer to the nearest hundredth) f(7)=
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f(x) = 3 /(x+2) - √(x-3)
f(7 ) = 3/(7+2) - √(7-3)
f(7) = 1/3 - √2 = 0.33 - 1.41 = - 1.1
Which graph represents the system of inequalities?
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sorry if i'm wrong
try (0,0), if it's true then the answer is C
it's false, not C
try (-4,5), if it's true, it's D
it's false, it's not D
try (1,4), if it's true, it's A
it's true
answer is A