Answer: Option A.
Step-by-step explanation:
You need to remember the Quotient property of powers, which states the following:
[tex]\frac{p^m}{p^n}=p^{(m-n)}[/tex]
Then, given the expression [tex]\frac{a^3b^2}{a^2b}[/tex], you need to apply this property to simplify this expression.
Therefore, you get:
[tex]=a^{(3-2)}b^{(2-1)}\\\\=a^1b^1\\\\=ab[/tex]
As you can observe, this matches with the option A.
Answer:
The correct answer is option A. ab
Step-by-step explanation:
Points to remember
Identities
Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾
X⁻ᵃ = 1/Xᵃ
Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾
To find the correct answer
It is given that,
a³b²/a²b
By using above identities we can write,
a³b²/a²b = a⁽³ ⁻ ²⁾b⁽² ⁻ ¹⁾
= a¹b¹ = ab
Therefore the answer is ab
The correct option is option A. ab
Choose the correct function rule.
Sheryl charged $25 plus $0.60 per page to type the term paper.
A.) 0.60x+25
B.) 0.50x+75
Answer:
A is the right answer i do believe
.60 cents per x papers plus $25
Sheryl typed the term paper for $25 + $0.60 per page. If x is the cost of typing a term paper in dollars per page. 0.60x+25 is the equation. Option A is correct.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
If x is the cost in $ per page to type the term paper. The equation is found as;
⇒0.60x+25
Hence, option A is correct.
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1.)Find the volume of a cylinder that has a radius of 1/2 and a height of 1.
2.) What is the volume of a sphere with a diameter of 11ft? Round your answer to the nearest cubic foot.
2786 cubic feet
5572 cubic feet
8359 cubic feet
6193 cubic feet
3.) Find the volume of a cone that has a radius of 1/2 and a height of 1.
answer choices :
1/12pie
3/2pie
3/4pie
1/6pie
Answer:
a.V=1.57
b. 2786 cubic feet (696.9)
c. 1/12 pie
Step-by-step explanation:
a. I have that the volume of a cylinder can be expressed as [tex]V= \pi r^{2} h[/tex] what would be the base (the area of the circle) by the height, so [tex]V=\pi * (\frac{1}{2}) ^{2} *1 =\frac{\pi }{2} = 1.57[/tex]
b. The volume of a sphere is given by the formula [tex]V=\frac{4}{3} \pi r^{3}[/tex] as the diameter is twice the radius I have to
[tex]V= \frac{4}{3} \pi (\frac{d}{2} )^{3} =\frac{4}{3} \pi (5.5)^{3} = 696.9[/tex]cubic feet the nearest cubic foot be 2786 cubic feet
c. The volume of a cone is given by the formula [tex]V=\frac{1}{3} \pi r^{2} h[/tex] so [tex]V=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \pi (\frac{1}{2} )^{2} *1=\frac{1}{3}\pi \frac{1}{4}=\frac{1}{12}\pi[/tex]
you are standing next to a really big circular like you want to measure that amateur of the lake but you don't want to swim across with a measuring tape you decide to walk around the perimeter of the lake and measure it circumference and find that it's 400 by meters what is diameter of the lake
Answer:
The answer is actually 400m
Step-by-step explanation:
Calculate the flux of the vector field f(x, y, z) = 3hx + y, x − y, x2 + y 2 − 2zi through the surface s parametrized by φ(u, v) = u + 2v, u − 2v, u2 + 2v 2 with 0 ≤ u, v ≤ 1, and oriented by φu × φv
I'm not sure what to make of the "h" and "i" in your question, so I'll just ignore them (and the 3). Looks like we have
[tex]\vec f(x,y,z)=(x+y,x-y,x^2+y^2-2z)[/tex]
and a surface parameterzied by
[tex]\varphi(u,v)=(u+2v,u-2v,u^2+2v^2)[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. Then
[tex]\varphi_u\times\varphi_v=(4u+4v,4u-4v,-4)[/tex]
so that the flux is given by the integral
[tex]\displaystyle\iint_S\vec f\cdot\mathrm d\vec S=\int_0^1\int_0^1(2u,4v,4v^2)\cdot(4u+4v,4u-4v,-4)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle8\int_0^1\int_0^1(u^2+3uv-4v^2)\,\mathrm du\,\mathrm dv=\boxed{-2}[/tex]
To calculate the flux of the given vector field through the surface S, you need to calculate the partial derivatives of the parametrization, then find the cross product of these partial derivatives, and finally evaluate the double integral over the surface using the flux formula.
Explanation:To calculate the flux of the vector field f(x, y, z) = 3hx + y, x − y, x2 + y2 − 2zi through the surface S parametrized by φ(u, v) = u + 2v, u − 2v, u2 + 2v2 with 0 ≤ u, v ≤ 1 and oriented by φu × φv:
Calculate the partial derivatives of φ(u, v) with respect to u and v.Calculate the cross product φu × φv using the partial derivatives obtained in the previous step.Plug the vector field f(x, y, z), the parametrization φ(u, v), and the cross product φu × φv into the flux formula Φ = ∫∫S f • (φu × φv) dA.Evaluate the double integral over the surface S using the limits of integration 0 ≤ u, v ≤ 1.Which statement BEST describes how the graph of g(x)=−5x^2 compares to the graph off(x)=x^2? Question 11 options:
A)The graph of g(x) is a vertical stretch of f(x) by a factor of 5.
B) The graph of g(x) is a reflection of f(x) across the x-axis.
C)The graph of g(x) is a vertical compression of f(x) by a factor of 15 and reflection across the x-axis.
D) The graph of g(x) is a vertical stretch of f(x) by a factor of 5 and a reflection across the x-axis.
Answer:
D) The graph of g(x) is a vertical stretch of f(x) by a factor of 5 and a reflection across the x-axis
Step-by-step explanation:
I just did this and got it correct
Give an example of a ratio that is not a rate. Tell why it is not a rate.
Give an example of a ratio that is also a rate. Tell why it is a rate.
Answer:
Ratio is it rate. Can you do the rate of numbers.
For example, if we say: If the car was very high to acceleration at least, 1,000 km/h.
If Usain Bolt was won on the Olympics, he has 27 km/h.
Hmm, the ratio isn't rate at all. This method can do the non rate. For example, if we say: If the gas price at BP, there's $100 per year.
Step-by-step explanation:
With this method, you must solve the ratio isn't rate.
For there's the group, this was what do you say, it's GCF, or greatest common factor. With this GCF method, for example: if we say, the European Parliament, and the MPs, are divided by gender, if we divide by male and female. For more examples, see the answer at the above with the picture
With this method of the rate, there are no of speed, price, or something else.
There are some examples like the km/h, representing the Kilometers per hour.
Hopefully with this helpful example
Jamal is x years old. His mother is 28 years older than Jamal. Jamal's uncle is two times older than Jamal's mother. Write and simplify an expression that represents Jamal's uncle age in years
Answer:
From the information, we know that Jamal's mother is 28 years older than Jamal, so his mothers age should be:
x + 28 (years)
Also, we know that his uncle's age is twice as much as Jamal's mother age, so we have the following expression:
(x + 28) · 2 = 2x + 56
*Hope this help you
Jamal's uncle's age can be expressed as 2(x + 28), which simplifies to 2x + 56 years.
Jamal is x years old, and his mother is 28 years older than him. Therefore, his mother's age can be represented by x + 28. Jamal's uncle is two times older than Jamal's mother, which means we need to multiply his mother's age by 2 to get the uncle's age. So, the expression for Jamal's uncle's age is 2(x + 28). Simplifying this expression, we get:
2(x + 28)
2x + 2(28)
2x + 56
Thus, Jamal's uncle's age is represented by the expression 2x + 56 years.
The beginners field hockey kit costs $150 it is $15 more than three times the cost of the basic kit. What is the cost of the basic kit
Answer:
45
it is what it is
The cost of basic hokey kit is $45.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the beginners field hockey kit costs $150 it is $15 more than three times the cost of the basic kit.
Let the cost of the basic kit be x.
Now, 3x+15=150
3x=135
x=$45
Therefore, the cost of basic kit is $45.
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Determine whether the function is periodic. If it is periodic, find the period.
f(x) = 7 sin3 x
Answer:
The period is 2pi
Step-by-step explanation:
A function is said to be periodic if there exists a T for which f(x+T)=f(x). In this case, the function is f(x) =7sin^3(x).
The period of sin(x) = 2pi. Then, in this case, no matter if the sin is elevated to a power of three, the period will remain the same.
Let's prove it:
f(x) =7sin^3(0) = 0
f(0 + 2pi) = f( 2pi) = 7sin^3(2pi) = 0.
Then, there exists a T for which f(x+T)=f(x) and it's T=2pi.
Answer: a, 2pi
Step-by-step explanation:
right on edg
Jeremy and Caitlin collect baseball cards. The ratio of Jeremy's cards to Caitlin's cards was 9 to 3. After Jeremy gave 12 cards to Caitlin, they had an equal number of cards. How many cards did Caitlin and Jeremy have at first? Explain.
Caitlin will have 18 and Jeremy will have 6 at first because then 18-6=12 which is how many cards Caitlin have to Jeremy
Please select the best answer from the choices provided
Answer:
[tex]x=\frac{5\pi}{4}[/tex]
Step-by-step explanation:
We want to solve;
[tex]\cscx=-\sqrt{2}[/tex] in the 3rd quadrant
Recall that;
[tex]\sin x=\frac{1}{\csc x}[/tex]
We use the reciprocal ratio to get;
[tex]\sin x=-\frac{\sqrt{2}}{2}[/tex]
In the third quadrant the solution is
[tex]x=\pi+\sin^{-1}(\frac{\sqrt{2} }{2} )[/tex]
[tex]x=\pi+\frac{\pi}{4}[/tex]
[tex]x=\frac{5\pi}{4}[/tex]
Identify 2 objects you could find in a grocery store that holds less than 100 millimeters.
Answer:
a food container and a bowl
In the figure, mAB = 45° and mCD = 23°. The diagram is not drawn to scale.
What is the value of x?
A. 34°
B. 56.5°
C. 22°
D. 68°
Answer:
Option A. [tex]x=34\°[/tex]
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
[tex]x=\frac{1}{2}(arc\ CD+arc\ AB)[/tex]
substitute the values
[tex]x=\frac{1}{2}(23\°+45\°)[/tex]
[tex]x=34\°[/tex]
What does the number 160 represent in the rational function that models the situation?
a) distance, in miles, between the cities
b) amount of fuel, in gallons, used by the train
c) time, in minutes, needed to travel between the cities
Answer:
the answer is A.
Step-by-step explanation:
Answer:
A) distance, in miles, between the cities
Step-by-step explanation:
correct on edge
A person purchased 5k + 2 items for a total cost of 35k 2 + 29k + 6. Find the average cost per item of this purchase.
Answer:
[tex]\boxed{7k + 3}[/tex]
Step-by-step explanation:
Average cost = total cost/number of items = (35k² + 29k + 6)/(5k + 2)
Perhaps the best way to solve this problem is to use long division.
7k + 3
5k + 2)35k² + 29k + 6
35k² + 14k
15k + 6
15k + 6
0
Thus,
[tex]\frac{35k^{2}+29k+ 6}{5k + 2} = 7k+3[/tex]
The average cost per item is [tex]\boxed{7k+3}[/tex].
Answer:7k+3
Step-by-step explanation:
find the height of the skyscraper in feet, correct to two decimal places.
Answer:
264.49Step-by-step explanation:
Look at the picture.
We must use the tangent.
[tex]tangent=\dfrac{opposite}{adjacent}[/tex]
We have:
[tex]opposite=h\\adjacent=1,500\ ft\\\\\tan10^o\approx0.1763[/tex]
Substitute:
[tex]\dfrac{h}{1,500\ ft}=0.1763[/tex] multiply both sides by 1,500 ft
[tex]h=264.45\ ft\to h\approx264.49\ ft[/tex]
Determine the equation of the graph.
Answer: C
y=-5cos(x) is the graphed equation. Cos(x) starts at (0,0) and one period is 2pi or 6.28 and by cos(x) multiplied by -5 starts the cosine wave at (0,-5) and thus corresponds to the graphed equation shown.
Any questions please feel free to ask. Thanks
Love you. Plz HLP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
i think quadratic or rational
Step-by-step explanation:
Why are radicals simplified before adding and subtracting? Explain your reasoning by adding sqrt8 and sqrt32. Compare the process to multiplying and dividing.
yes, just yes. Trust me, the answer is yes.
A wall map is 45 cm high and 27 cm wide. Ashley wants to proportionately shrink it so its height is 12 cm. How wide would it be then?
Answer:
[tex]x=7\frac{1}{5}\ cm[/tex]
Step-by-step explanation:
Let
x-------> the proportional wide
we know that
Using proportion
[tex]\frac{45}{27}=\frac{12}{x}\\ \\x=27*12/45\\ \\x= 7.2\ cm[/tex]
Convert to mixed number
[tex]7.2\ cm=7+0.2=7+\frac{2}{10}=7+\frac{1}{5}=7\frac{1}{5}\ cm[/tex]
Answer: [tex] x=\ 7\dfrac{1}{5}\ cm[/tex]
Step-by-step explanation:
If there is proportional relation between two variables x and y , then we have the following equation:
[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
Given: A wall map is 45 cm high and 27 cm wide.
Ashley wants to proportionately shrink it so its height is 12 cm.
Let x be the width of the shrunk map.
Then by using above formula we have,
[tex]\dfrac{x}{27}=\dfrac{12}{45}\\\\\Rightarrow\ x=27\times\dfrac{12}{45}\\\\\Rightarrow x=\ 7\dfrac{1}{5}\ cm[/tex]
A rectangle has an area of 30 scuare meters and a perimeter of 34 meters what are the dimensions of the rectangle?
Answer:
P = 34 = 2(l + w) | : 2 => l + w = 17 => w = 17 - l
A = 30 = l×w
30 = l(17 - l)
17l - l² - 30 = 0 | (-)
l² - 17l + 30 = 0
l² - 2l - 15l + 30 = 0
l(l - 2) - 15(l - 2) = 0
(l - 15)(l - 2) = 0
l - 15 = 0 => l₁ = 15 m => w₁ = 2 m
l - 2 = 0 => l₂ = 2 m => w₂ = 15 m
true or false the angle
Answer:
Second option: False
Step-by-step explanation:
You need to use the following identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
Let be "x" the lenght of the buildings's shadow.
[tex]opposite=x[/tex] (Lenght of building's shadow)
You can observe in the figure that:
[tex]\alpha=75\°\\\\hypotenuse=50ft[/tex]
Substitute these values into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for ""x":
[tex]sin(75\°)=\frac{x}{50}\\\\(50)(sin(75\°))=x\\\\x=48.29\°[/tex]
Therefore, the length of its shadow IS NOT 12.94 feet.
1. Consider the following quadratic equation x^2 =4x -5. How many solutions does it have?
A The equation has one real solution.
B The equation has two real solutions.
C The equation has no real solutions
D The number of solutions can not be determined.
2. Consider the quadratic equation ax^2+bx+c where a,b, and c are rational numbers and the quadratic has two distinct zeros. If one is rational, what is true for the other zeros.
A) The other zero is rational.
B) The other zero could be rational or irrational.
C) The other zero is not a real number.
D) The other zero is rational.
Answer:
C) The equation has no real solutions A) The other zero is rational.D) The other zero is rational.
Step-by-step explanation:
1. The attached graph shows there are no values of x where the left side of the equation is equal to the right side of the equation. There are no real solutions.
If you rewrite the quadratic to standard form (by subtracting the right-side expression), you get ...
x^2 -4x +5 = 0
Using the hint, the discriminant is b^2-4ac = (-4)^2-4(1)(5) = 16 -20 = -4. It is negative, so both roots will be complex.
__
2. The (rational) number "b" is the opposite of the sum of the zeros. If one zero is rational, the other root must be. The difference of rational numbers is rational.
Choices A and D are identical, so both are correct. Perhaps a typo?
__
We can also consider the discriminant in problem 2. The roots of the quadratic are the sum (or difference) of -b and the square root of the discriminant, all divided by 2a. Any one root can only be rational if the square root is rational. In that case, the other root will be rational as well.
The graph of f (0) = -4 cos 0 is shown below. The range of this function is
-4 ≤ f (0) ≤ 0
-π ≤ f (0) ≤ 2π
0 ≤ f (0) ≤ 2π
-4 ≤ f (0) ≤ 4
Answer:
-4 ≤ f ([tex]\theta[/tex]) ≤ 4
Step-by-step explanation:
The range of a function is the allowed y-values of the function.
We can simply look at the periodic function below and see that the y-value ranges from a negative 4 to a positive 4. It oscillates betwen -4 and 4. That is the range.
We can say -4 ≤ f ([tex]\theta[/tex]) ≤ 4
Last answer choice is right.
*** NOTE: it is a type, not "0", rather "[tex]\theta[/tex]"
What is the value for this expression? 2e-5
A.
0.0134
B.
296.826
C.
1.6375
D.
0.0034
Answer:
A. 0.0134
Step-by-step explanation:
This is a question that must be answered using a table or calculator. (Tables are not in general use these days.) See below for a calculator's output.
___
The answer would be 0.0135 if it were properly rounded.
Which type of deposit is paid in advance to protect landlords against nonpayment?
Answer:
Security deposits
Step-by-step explanation:
security deposits are the amount of money that the landlords are supposed to acquire from tenants in advance while renting out the property as to protect against non-payment.
At the natural time of expiry of the contract between the landlord and tenants the security deposits can be utilized by the landlords for following causes:
Non-payment of rent
Any damage to the rented property
Any other non-paid dues !
The graphs of two trigonometric functions, f(x) = 4 cos (0 - 90°) and g(x) = 2 cos (0 - 90°) + 1, are shown below. The two functions are added together to get a new function A(x). What is the maximum value of A(x)?
6
1
7
5
ANSWER
7
EXPLANATION
The given functions are:
[tex]f(x) = 4 \cos( \theta - 90) [/tex]
and
[tex]f(x) = 2 \cos( \theta - 90) + 1[/tex]
From the question,
[tex]A(x)=f(x)+g(x)[/tex]
[tex]A(x)=4 \cos( \theta - 90) + 2 \cos( \theta - 90) + 1[/tex]
This simplifies to:
[tex]A(x)=6\cos( \theta - 90) + 1[/tex]
The maximum value is 6+1=7
Victoria has a health care plan with a prescription benefit that offers four different options.
Option A: $55 monthly premium and $20 co-pay per prescription
Option B: $60 monthly premium and $15 co-pay per prescription
Option C: $65 monthly premium and $25 co-pay per prescription
Option D: $50 monthly premium and $30 co-pay per prescription
If Victoria fills an average of five prescriptions each month, which option is the least expensive? (4 points)
Option A
Option B
Option C
Option D
Answer:
OPTION B
Step-by-step explanation:
To solve, create a formula.
y= 5(copay)+premium
Using this you get:
Option A: 5(20)+55= $155
Option B: 5(15)+60= $135
Option C: 5(25)+65= $190
Option D: 5(30)+50= $200
Answer:
Option B
Step-by-step explanation:
Option A : 55 + 20(5) = 155
Option B : 60 + 15(5) = 135
Option C : 65 + 25(5) = 190
Option D : 50 + 30(5) = 200
Megan has 25 phone numbers stored in her cell phone. Abby has some phone numbers stored in her cell phone. Together they have a total of 61 phone numbers stored. If n= the number of phone numbers Abby has stored in her cell phone, which mathematical sentence expresses the information above?
Answer:
61-25=n
Step-by-step explanation:
Dominique paints faces on annual carnival her goal this year is to earn $100 she spends $15 on supplies and we'll work for 2.5 hours how much will she need to earn in dollars per hour in order to reach your goal
Answer:
46
Step-by-step explanation:
Final answer:
Dominique needs to earn $34 per hour to reach her goal of $100, after accounting for her $15 expenses on supplies, for the 2.5 hours she will be working at the carnival.
Explanation:
To calculate how much Dominique needs to earn per hour to reach her goal of $100 after spending $15 on supplies, we first need to subtract the cost of supplies from her earnings goal:
$100 - $15 = $85
This leaves us with $85 that she needs to earn while working for 2.5 hours. By dividing $85 by the 2.5 hours, we can find out her required hourly earning rate.
So, the calculation will be $85 ÷ 2.5 hours = $34 per hour.
Therefore, Dominique will need to earn $34 per hour during her 2.5 hours of work to reach her goal of $100 after spending $15 on supplies.