Which is the value of this expression when a = 5 and k=-2?
*
32a-2
75
9
* 25
25
9
75
Answers
Answer: it’s A
Step-by-step explanation: I got it right, hope it helps ✨
The value of the expression [tex](\frac{3^{2}a^{-2} }{3a^{-1} } )^{k}[/tex] when a = 5 and k = -2 is [tex]\frac{25}{9}[/tex]
How to substitute and get the value of an expression?The expression is as follows:
[tex](\frac{3^{2}a^{-2} }{3a^{-1} } )^{k}[/tex]
using law of indices
Hence,
when a = 5, k = -2
[tex](\frac{3^{2}a^{-2} }{3a^{-1} } )^{k} = (\frac{9(5^{-2} )}{3(5^{-1} )})^{-2}[/tex]
Then,
[tex](\frac{9(5^{-2} )}{3(5^{-1} )})^{-2}=(\frac{\frac{9}{25} }{\frac{3}{5} } )^{-2}[/tex]
[tex](\frac{\frac{9}{25} }{\frac{3}{5} } )^{-2}=(\frac{9}{25} (\frac{5}{3}))^{-2}[/tex]
[tex](\frac{9}{25} (\frac{5}{3}))^{-2}=(\frac{3}{5})^{-2}[/tex]
[tex](\frac{3}{5})^{-2}=\frac{25}{9}[/tex]
Therefore, the value of the expression is 25 / 9
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Related Questions
Find the total surface area of the following
cone. Leave your answer in terms of m.
12 cm
5 cm
Hint: Surface Area of a Cone = url + B
Where l = slant height, and B = area of the base
S.A. = [? ]n cm?
Answers
Answer:
[tex]S.A.=90\pi~cm^2[/tex]
Step-by-step explanation:
Surface Area of a Cone
Given a cone of base area B and slant height L, the surface area can be calculated with the formula:
[tex]S.A.=\pi rL +B[/tex]
The cone presented in the image has a circular base of radius r=5 cm, thus its base area is:
[tex]B=\pi r^2[/tex]
[tex]B=\pi 5^2[/tex]
[tex]B=25\pi~cm^2[/tex]
The slant height can be calculated as the hypotenuse of a right triangle with legs 5 cm and 12 cm by using Pythatgora's Theorem:
[tex]L^2=5^2+12^2[/tex]
[tex]L^2=25+144=169[/tex]
Taking square roots
[tex]L = \sqrt{169}[/tex]
L = 13 cm
The surface area is:
[tex]S.A.=\pi (5~cm)*13~cm +25\pi~cm^2[/tex]
Operating:
[tex]S.A.=65\pi~cm^2 +25\pi~cm^2[/tex]
[tex]\mathbf{S.A.=90\pi~cm^2}[/tex]
Answer:
90
Step-by-step explanation:
Need some help here please.
Answers
Answer:
C
Step-by-step explanation:
Begin by isolating y
-6y = - x - 1
Divide everything by -6
y = -x/-6 - 1/-6
y = x/6 + 1/6
Now you want the perpendicular
m1 * m2 = - 1
m1 = 1/6
1/6 * m2 = -1
multiply by 6
m2 = - 6
That's C
The number tine shows four points. Which point represents the approximate tocation of Vo??
A)
point
.
point
point
point D
Answers
Answer: It is point B
Step-by-step explanation:
Answer: point b
Step-by-step explanation:
Please help!!!!!!!!!!
Answers
Answer:
x=81
Step-by-step explanation:
I am 100% sure you can go with it
The area of the triangle is 22.4cm^2.
Calculate the length, b, of the longest side of the triangle.
Please help, I will mark first correct answer brainliest.
Answers
Answer:
The longest side length b is approximately 13.172 cm
Step-by-step explanation:
The given parameters are;
The area of the triangle = 22.4 cm²
The given angles of the triangle = ∠97°
The given side of the triangle = 3.7 cm
The formula for the area of a triangle, A = 1/2 × a × b × sin(C)
Where;
a, and b are the side legs forming the angle C
Therefore, we have;
A = 22.4 = 1/2 × 3.7 × a × sin(97°)
a = 22.4/(1/2 × 3.7 × sin(97°)) ≈ 12.199
a ≈ 12.199 cm
Therefore, by cosine rule, we have;
b² = a² + c² - 2 × a × c × Cos(B)
Substituting the values, gives;
b² = 12.199² + 3.7² - 2 × 12.199 × 3.7 × Cos(97°)
b² ≈ 173.507
∴ b ≈ √173.507 ≈ 13.172
b ≈ 13.172 cm
What prime is 4 greater than a perfect square and 7 less than the next perfect square?
Answers
Answer:
29
Step-by-step explanation:
The squares cannot be very big. For example the difference between 10^ and 11^2 = 100 to 121 which is a difference of 21.
What you are talking about is x + 4 prime + 7 next square.
Write the squares
1
4
9
16
25
36
add 4 to get to the prime, add 7 to get to the next square. That's 12
1 and 4 have a difference of 3 too small
4 and 9 have a difference of 5 too small
9 and 16 have a difference of 7 which is too small
16 and 25 have a difference of 9 which just a little too small.
25 and 36 has a difference of 11. Just right
25 + 4 = 29
29 + 7 = 36
Just right.
Can someone find the slope to number 4
Answers
Answer:
-7/1
Step-by-step explanation:
Slope = ((-26)-2) / (2-(-2))
Slope = (-28) / (4)
Slope = -7
1. Find the slope of a line that passes through (-2,-3) and (1,1).
2. For the equation-4=8x, what is the constant of variation
3. Suppose y varies directly with x, and y=24 when x=8. What is the value of y when x=10
Answers
Answer:
1:
m=4/3
2:
-2
3:
First, you want to set up a proportion.
8/24 = 10/y
Cross multiply to get
240 = 8y, then divide 8 from both sides to get y = 30.
Sophie buys x packages of graph paper for $2.55 each (tax included). She pays with a $20 bill.
Write an algebraic expression to represent the amount of change the cashier should give back to Sophie.
Answers
Answer:
x=$20/$2.55.
Step-by-step explanation:
if each package is $2.55 then and it cost $20 then you will have to divide the numbers wich will give u x
Answer:
20 - 2.55x
Step-by-step explanation:
20 is the dollar bill Sophie bought the packages with, x represents the number of packages bought and 2.55 is the price for each, so by subtracting 20 by the cost of the total packages results in the amount of change the cashier should give back to Sophie.
For example, if Sophie bought 3 packages of graph paper with a $20 bill the cashier should give back to Sophie $12.35.
20 - 2.55 (3)
20 - 7.65
12.35
hope this helps!
What is the equation for line D?
a. y = 2.5x
b. y = x + 10
c. y = -x + 10
d. y = -x + 60
Answers
Answer:
D
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP ASAP
Write an equation in slope-intercept form of a line with a y-intercept of 11 and slope the same as the line whose equation is y = -3x + 9
Answers
answer:
y=11x+11?
Step-by-step explanation:
from what i got from the equation it sounds like this might be the answer doory ^^'
-3x+2y=-39 and 5x+4y=21
Answers
Answer:
X= 9
Y = -6
Step-by-step explanation:
first of all setting up the equation and solve it like a system of linear equations
5x+4y=21
-3x+2y=-39
then multiply -2 on the entire second equation
5x+4y = 21
6x-4y= 78
then eliminate the 4ys and you get
11x = 99
x = 9
lastly subsititue the 9 back into one of the original equations
5(9) + 4y =21
45 + 4y = 21
4y = -24
y = -6
Answer:
-3x+2y=-39
2y=-39+3x
y=-39+3x÷2 equation 1
5x+4y=21 equation 2
5x+4(-39+3x)÷2=21
5x+2(-39+3x)=21
5x+(-78)+6x=21
5x-78+6x=21
5x+6x-78=21
11x-78=21
11x=21+78
11x=99
x=99÷11
x=9
putting value of equation 2 in equation 1
y=-39+3x÷2
y=-39+3×9÷2
y=-39+27÷2
y=-12÷2
y=-6
x=9 and y=-6 answer
hope this may help you !!!!
How would I create a graph for this equation? The equation is c=4.95+3.99b
Answers
Answer:
C is your y intercept 3.99b is your slope
Step-by-step explanation:
simplify 3^(5)*3^(4)
Answers
A triangle has an area of
2x2 + 4x – 16 square meters. If the base
is x – 2 meters, find the height
Answers
Answer:
The expression for the area of the given triangle is 5x^4+4x^3units
Step-by-step explanation:
Mr.Turner invested $8,000 in an account for his daughter’s college education. The account pays 5% interest, compounded yearly. How much will Mr.Turner have in the account after 4 years to the nearest dollar?
Answers
Answer:
$9,724.05
Step-by-step explanation:
8000(1+.05)^4= 9724.05
sry if im wrong :)
The amount after 4 years will be equal to $9,724.05
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.
Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-
Given that Mr.Turner invested $8,000 in an account for his daughter’s college education. The account pays 5% interest, compounded yearly.
The amount after 4 years will be calculated as:-
[tex]A = P ( 1 + \dfrac{r}{100})^{nt}[/tex]
[tex]A = 8000 ( 1 + \dfrac{5}{100})^{4}[/tex]
A = 9724.05
Therefore, the amount after 4 years will be equal to $9,724.05.
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Can anyone help me with this plzz?
Answers
===========================================================
Explanation:
Check out figure 1 in the attached images below. In this figure, I've plotted the function y = 6/(2x-3) on a 2D grid system. The function curve is in blue. Then I've plotted (2,0) and (3,0) on the x axis. Point A is somewhere between those endpoints. Point A is also on the x axis. Directly above A is point B such that B is on the blue function curve.
The distance from A to B is found by subtracting the y values of each point.
The y coordinate of A is y = 0. The y coordinate of B is y = 6/(2x-3)
Therefore, the distance from A to B is 6/(2x-3) units. This will form the radius of each cylindrical slice as figure 2 shows. Note the color coding to help see how the 2D view corresponds to the 3D view. The xy plane has been laid flat on the floor. So we're viewing the function curve at a downward angle now. Each of those gray cylinders combine to form an approximate 3D volume. The more cylinders we have, and the finer the cuts, the more accurate the total volume.
So it comes down to finding the volume of each cylindrical slice and adding up the volumes. This is effectively what integral calculus is all about.
------------------------------------
Since the radius of each cylinder is y = 6/(2x-3), this means r = 6/(2x-3) is plugged into the formula
V = pi*r^2*h
which is the volume of a cylinder formula
The height of each cylinder is delta x, which we'll use dx for short. So this is where the dx comes from in integrals.
This is what the integral will look like
[tex]\displaystyle V = \int_{2}^{3} \pi*\left(\frac{6}{2x-3}\right)^2dx[/tex]
which turns into
[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx[/tex]
after a bit of algebra. We're able to factor the 36pi out because it's a constant
From here we use u-substitution. Let u = 2x-3
This leads to du/dx = 2 which can be solved to dx = du/2
Since u = 2x-3, the lower endpoint x = 2 leads to
u = 2x-3 = 2*2-3 = 1
and x = 3 leads to
u = 2x-3 = 2*3-3 = 3
So the interval 2 < x < 3 turns into 1 < u < 3
After using u-sub, making the proper replacements, and integrating, we get
[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx\\\\\\\displaystyle V = 36\pi\int_{1}^{3}\frac{1}{u^2}\frac{du}{2}\\\\\\\displaystyle V = 36\pi*\frac{1}{2}\int_{1}^{3}\frac{1}{u^2}du\\\\\\\displaystyle V = 18\pi\int_{1}^{3}u^{-2}du\\\\\\\displaystyle V = 18\pi\left[-u^{-1}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\[/tex]
Let's evaluate that to get the following
[tex]\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[\left(-\frac{1}{3}+C\right)-\left(-\frac{1}{1}+C\right)\right]\\\\\\\displaystyle V = 18\pi\left(-\frac{1}{3}+1\right)\\\\\\\displaystyle V = 18\pi\left(\frac{2}{3}\right)\\\\\\\displaystyle V = 12\pi\\\\\\[/tex]
So the 3D volume formed by rotating that region (under the curve from x = 2 to x = 3) is exactly 12pi cubic units
Find two numbers whose sum is 45 and whose difference is 19.
Answers
Answer: 32 and 13
Step-by-step explanation:
32+13=45
32-13=19
Answer:
32 and 13
Step-by-step explanation:
What is the slope of the line?
a. 3
b. 1/3
c. -1/3
d. -3
Answers
Answer:
B. 1/3
Step-by-step explanation:
If you look at points (-3,0) and point (0,1). Then you would see the it would take one unit up and 3 units right this would make the slope be 1/3.
Which of these tables represents a function?
Answers
apparently brainly needs 20+ characters so ejsorjxlhelehIwbekzheknf
please help and thank you!
Answers
Answer:
Its d i took the class
Step-by-step explanation:
Which division problem does the diagram below best illustrate?
A). 30 divided 5 = 6
B). 35 divided 7 = 5
C). 21 divided 7 = 3
D). 40 divided 5 = 8
Plz hurry !!!
Answers
Answer:
B) 35 divided by 7 = 5
Step-by-step explanation:
You have 35 blocks, you are devideding them in groups of 7, how many groups do you have?
For questions 3 - 5, use the FOIL method to find the product of the binomials.
3. (2x+3)(x + 1)
4. (x - 5)(3x + 2)
5. (x2 + 2)(5x + 1)
Please make it a easy way to understand.
Answers
Answer:
Step-by-step explanation:
Which choice below shows the value of 2.16? Choose all that apply.
Group of answer choices
two and six hundredths
2 + 0.1 + 0.06
2 + 0.01 + 0.06
two and sixteen
2 + 0.16
two and sixteen hundredths
Answers
Answer:
2 + 0.1 + 0.06
2 + 0.16
two and sixteen hundredths
i'll give brainliest!!! what is the width of a rectangle that has an area of 96 square inches and a length of 12 inches?
Answers
Answer:
it's 8 inches luvvvv
Step-by-step explanation:
hope this helps
Carrie earns $8.50 per hour for tutoring her little brother. How many hours must Carrie tutor to earn $408?
Answers
Answer:
48 hours
Step-by-step explanation:
The number of hours that Carrie must tutor to earn $408 will be 48 hours.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Carrie earns $8.50 per hour for tutoring her little brother.
Let x be the number of hours. Then the equation is given as,
8.50x = 408
Simplify the equation, then we have
x = 408 / 8.50
x = 48 hours
The number of hours that Carrie must tutor to earn $408 will be 48 hours.
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20. Given f(x) = 2x + 9, if f(x) = 15, find x.
Answers
Answer:
the answer is located in the screenshot that is attached.
Step-by-step explanation:
The work is also in the screenshot attached. Hoped this helped!
The value of x if f(x) = 15 in the given function is 3
From the question,
We were given the function f(x) = 2x + 9
To determine the value of x if f(x) = 15, we will put f(x) to be equals to 15 and then solve for x in the equation
That is,
f(x) = 2x + 9
Since f(x) = 15
∴ 15 = 2x + 9
Now, to solve the above equation,
First, subtract 9 from both sides
That is,
15 - 9 = 2x +9 -9
6 = 2x
Then, we can write that
2x = 6
∴ x = 6 ÷ 2
x = 3
Hence, the value of x if f(x) = 15 in the given function is 3
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A 40-degree angle is translated 5 inches along a vector
Answers
Answer :need the options you choose frome
Step-by-step explanation:
What is the equivalent fraction for 2/3??
Answers
c. 4/6
This is the answer
Answer:
C. 4/6
Step-by-step explanation:
2*2=4
3*2=6
4/6
Please help !!!!!!!!!
Answers
Answer:
4,5
Step-by-step explanation:
I think it is 4,5. It says reflection of it across the line, and it is in the 4th quadrent, so that -5 will become a positive 5, and the 4 will stay the same.