Answer:
[tex]y=25[/tex]
Step-by-step explanation:
We have been given that y varies inversely as x and [tex]y=50[/tex], when [tex]x=10[/tex].
We know that when y varies inversely with x, then the equation is: [tex]y=\frac{k}{x}[/tex], where, k represents constant of variation.
First of all, we will find constant of variation using point [tex]y=50[/tex], and [tex]x=10[/tex] as shown below:
[tex]50=\frac{k}{10}[/tex]
[tex]50*10=\frac{k}{10}*10[/tex]
[tex]500=k[/tex]
Upon substituting [tex]k=500[/tex] in inversely proportion we will get:
[tex]y=\frac{500}{x}[/tex]
To find the value of y, we will substitute [tex]x=20[/tex] in above equation as:
[tex]y=\frac{500}{20}[/tex]
[tex]y=\frac{50}{2}[/tex]
[tex]y=25[/tex]
Therefore, the value of y is 25.
When is it necessary to use three points to name an angle? If CP bisects and DPB , what is the measure of angle CPB?
In geometry, three points are used to name an angle when there are multiple angles that share the same vertex. If CP bisects angle DPB, angle CPB is divided into two equal angles, and the measure of angle CPB is half of the measure of angle DPB.
Explanation:In geometry, it is necessary to use three points to name an angle when there are multiple angles that share the same vertex. By using three points, we can clearly identify which angle we are referring to. In this case, if CP bisects angle DPB, it means that angle CPB is divided into two equal angles, and CP is one of the dividing lines. Therefore, the measure of angle CPB is half of the measure of angle DPB.
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Jen bought 5 cds for 57.50. What was the unit price
The perimeter of a square garden is to be at least 20 ft but no more than 32 ft. find all possible values for the lengths of its sides using a compound inequality
Answer:
Answer in pic
Step-by-step explanation:
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 = $
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
Including a 8 %8% sales tax, an inn charges $ 135$135 per night. Find the inn's nightly cost before the tax is added.
Find the value of x for which l is parallel to m. The diagram is not to scale.
a. 31
b. 62
c. 93
d. 149
If f(x)=3/x+2-root x-3 complete the following statement (round answer to the nearest hundredth) f(7)=
Is g(x)= 5 + 6/x a linear function
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?
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
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
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:
Summer paints a room that has 400 square feet of wall space in 2.5 hours. at this rate, how long will it take her to paint a room with 720 square feet of wall space?
How to find mass when given density and volume?
Could -2 be used as a base to rewrite 32? 64? Why or why not?
Find the amount (future value) of the ordinary annuity. (round your answer to the nearest cent.) $1500/semiannual period for 8 years at 2.5%/year compounded semiannually
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.
Kwamee bought kona beans that cost 11.00 and bought fuji beans that cost 7.50.he bought a total of 23 pounds of coffee and it cost 197.00 write a system of equations to solve how many pounds of kona and fuji beans kwamee bought
Find the quotient.
110/10=
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.)
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
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
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.
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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The product of (a − b)(a − b) is a2 − b2.
Sometimes
Always
Never
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).
6=x+2/3
Please help ASAP!!! 10 Points!!! :)
How to solve equations
Which graph represents the system of inequalities?
What's the parabola in vertex for for (-5,0) and has a vertex (-2,1)
hello :
the parabola's equation is : f(x) = a(x+2)²+1
but ; f(-5) = 0
0 = a(- 5+2)²+1
9a+1=0.....a= -1/9
f(x) = (-1/9)(x+2)²+1
what hourly rate does the repair shop charge for labor?
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.
A quota is when one country
24% of 1321 is how much? round the answer to the nearest hundredth
If a(x)=3x+1 and b(x)=
The answer is C. [1, ∞] on edge
Find the value of x in the equation 2√ x
a. –5
b. 1
c. 16
d. 25 11. simplify the expression .
a.
b.
c.
d. + 20 = 15 + 3√ x