Answer:
[tex]\large\boxed{16a^6x^4y^2}[/tex]
Step-by-step explanation:
[tex]\text{Use}\\\\(ab)^n=a^nb^n\\\\(a^n)^m=a^{nm}\\=====================\\\\\left(-4x^2ya^3\right)^2=\\\\=(-4)^2(x^2)^2(y)^2(a^3)^2\\\\=(-4)(-4)x^{2\cdot2}y^2a^{3\cdot2}\\\\=16x^4y^2a^6[/tex]
The expression (−4x^2ya^3)^2 written as a monomial in standard form is 16x^4y^2a^6.
Explanation:To write the given expression, (−4x2ya3)2, as a monomial in standard form, we first need to calculate square ofeach part of the term inside the parentheses. The square of -4 is 16. The rule of exponents states that when raising a power to a power, you multiply the exponents. Therefore, the square of x2 is x4 (since 2*2=4), the square of y is y2, and the square of a3 is a6 (since 3*2=6). Combining these, we find that the expression in standard form is 16x4y2a6.
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Please help asap!! Explain too!
Answer:
x = 31°
Step-by-step explanation:
Since, CB ║ FG and AB is a transverse, so ∠ BAG = ∠ ABC = 28° {Alternate angles}
Now, ∠ CAG = 90° = ∠ CAD + ∠ BAG
⇒ ∠ CAD = 90° - 28° = 62°
From, Δ ADE, ∠ ADE + ∠ DEA + ∠ EAD = 180°
⇒ ∠ ADE = 180° - 62° - 3x = 118° - 3x.
Now, ADB being a straight line, so ∠ ADE + ∠ EDC + ∠ CDB = 180°
⇒ 118 - 3x + x + 4x = 180
⇒ 2x = 62
⇒ x = 31° (Answer)
complete the equation of the lines whose slope is 5 and y-intercept is (0,4)
y = ?
Answer:
y = 5x + 4
Step-by-step explanation:
y - 4 = 5(x - 0)
That is point-slope form. I'm not sure if you want it in slope intercept form, but slope intercept form of the equation is -
y = 5x + 4
Answer:
Step-by-step explanation:
thx i needed this
4 friends evenly divided up an
n slice pizza. One of the friends, Harris, ate
1 fewer slice than he received.
Complete Question:
4 friends evenly divided up a n-slice pizza. One of the friends,Harris, ate 1 fewer slice than he received. How many slices of pizza did Harrison eat?
Answer:
Harrison ate [tex]\frac{n}{4}-1[/tex] slices of pizza.
Step-by-step explanation:
Given data, 4 friends evenly divided up a ‘n’ slice pizza.
Thereby, the number of slices that each friend get = [tex]\frac{n}{4}[/tex]
Now, given Harrison ate 1 fewer slice than he received. As he received [tex]\frac{n}{4}[/tex] slices, so 1 fewer than [tex]\frac{n}{4}[/tex] means [tex]\frac{n}{4}-1[/tex]
Thus, Harrison ate [tex]\frac{n}{4}-1[/tex] slices of pizza.
Answer:
n/4 - 1
Step-by-step explanation:
Hope this helps!
What is the solution to the system of equations
below?
y=2x+8
3(-2x + y) = 12
1) no solution
2) infinite solutions
3) (-1,6)
4) (1/2,9)
Answer:
No solution
Step-by-step explanation:
There is no way we can find the value of y, if x eliminates itself. Therefore, there is no solution.
Zahra runs an 800 meter race at a constant speed. Which graph shows her distance from the finish line during the race?
Answer:
The graph is attached below.
Step-by-step explanation:
Given:
Zahra runs a 800-meter race at a constant speed.
Race starts from the finish line.
Finish line is at a distance of 800 m from the starting point.
Time is plotted on the x axis and Distance is plotted on the y axis.
So, the graph must start from the [tex]800^{th}[/tex] mark on the y axis when time is 0.
Now, the speed is constant which means that the slope of the line of distance versus time is a straight line because,
Speed [tex]=\frac{Distance}{TIme}[/tex].
Now, the graph should have the following properties:
1. Starting point of the graph should be (0, 800).
2. Final point of the graph should be (t, 0).
3. Slope should be constant everywhere. So, the graph must be a straight line.
Thus, the graph is a line joining the points (0, 800) and (t, 0) as shown below.
Answer:
bottom left
Step-by-step explanation:
o a map, the distance from Los Angeles to San Diego is 6.35 cm. the scale is 1 cm - 20 miles. What is the actual distance?
The actual distance from Los Angeles to San Diego is 130 miles.
Step-by-step explanation:
Given,
Distance from Los Angeles to San Diego on map = 6.35 cm
The given scale is;
1 cm = 20 miles
For measuring the actual distance we will multiply the distance on map with 20.
Actual distance = 6.5*20 = 130 miles
The actual distance from Los Angeles to San Diego is 130 miles.
Keywords: distance, multiplication
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Final answer:
To find the actual distance from Los Angeles to San Diego, multiply the map distance (6.35 cm) by the scale conversion factor (20 miles per cm), resulting in an actual distance of 127 miles.
Explanation:
The question deals with calculating the actual distance between Los Angeles and San Diego, given the scale on the map and the measured distance. To find the actual distance, you multiply the distance on the map by the conversion factor provided by the scale. In this case, the scale is 1 cm for every 20 miles. The measured distance on the map is 6.35 cm.
Therefore, the actual distance between Los Angeles and San Diego is calculated as follows:
Actual distance = Map distance × Scale conversion factor
Actual distance = 6.35 cm × 20 miles/cm
Actual distance = 127 miles
The actual distance from Los Angeles to San Diego is 127 miles.
If Q is half way between 0 and -1 what is Q
Answer:
it's -1/2
Step-by-step explanation:
you need to go half way between 0 and -1 and that's -1/2
Answer:
-0.5 or -1/2
Step-by-step explanation:
You can solve using operations or with a number line.
To find the value halfway between two numbers, add the two numbers and divide the sum by 2.
Q = (0 + -1)/2
Q = (0 - 1)/2
Q = -1/2
Q = -0.5
Number line:
<- (-1) --------- (-0.5) ---------- 0 ----------- (0.5) --------- (1) ->
Find halfway between 0 and 1.
Q = -0.5
3. If f(x)= 3x+ 2 , what is the equation for f^-1(x)
Answer:
option 3 ⇒ f⁻¹(x) = [tex]\frac{x^{2} -2 }{3} [/tex]
Step-by-step explanation:
Given F(x) = [tex]\sqrt{3x+2}[/tex]
let y = f(x)
y = [tex]\sqrt{3x+2}[/tex] ⇒ squaring the both sides
y² = 3x + 2 ⇒ subtract 2 from both sides
y² - 2 = 3x ⇒ divide both sides by 3
[tex]\frac{y^{2} -2 }{3} = x[/tex]
replace the location of x and y
∴ y = [tex]\frac{x^{2} -2 }{3} [/tex]
So, y will be f⁻¹(x)
∴ f⁻¹(x) = [tex]\frac{x^{2} -2 }{3} [/tex]
If x/a = 4, a/y = 6, a2 = 9 and ab2 = −8 then x + 2y = ?
Select one:
A. −10
B. −15
C. −5
D. −13
Answer:
-13
Step-by-step explanation:
We are given:
[tex]\frac{x}{a}=4[/tex]
[tex]\frac{a}{y}=6[/tex]
[tex]a^2=9[/tex]
[tex]ab^2=-8[/tex]
Since [tex]ab^2=-8[/tex] then [tex]a[/tex] has to be negative.
Solving [tex]a^2=9[/tex] therefore gives [tex]a=-3[/tex].
(Note: [tex](-3)^2=(-3)(-3)=9[/tex].)
[tex]\frac{x}{a}=4[/tex] and [tex]a=-3[/tex] gives us:
[tex]\frac{x}{-3}=4[/tex].
Multiplying both sides by -3 gives: [tex]x=-12[/tex].
[tex]\frac{a}{y}=6[/tex] and [tex]a=-3[/tex] gives us:
[tex]\frac{-3}{y}=6[/tex].
Multiplying both sides by [tex]y[/tex] gives: [tex]-3=6y[/tex].
Divide both sides by 6 gives: [tex]\frac{-3}{6}=y[/tex].
Simplifying this gives us [tex]\frac{-1}{2}=y[/tex].
Now we are asked to find the numerical value for [tex]x+2y[/tex].
[tex]-12+2(\frac{-1}{2})[/tex]
[tex]-12+-1[/tex]
[tex]-13[/tex]
D.
If u (x) = negative 2 x squared and v (x) = StartFraction 1 Over x EndFraction, what is the range of (u circle v) (x)?
A(one-third, 0)
B(3, infinity)
C(negative infinity, 3)
D(negative infinity, positive infinity)
Answer:
Option B is the required answer.Step-by-step explanation:
As per the given question, [tex]u(x) = -2x^{2}[/tex] and [tex]v(x) = \frac{1}{x}[/tex].
Hence, (u circle v) (x) = u{v(x)} = [tex]\frac{-2}{x^{2} }[/tex]
The range of the function, (u circle v) (x) means the set of the values of x so that we will be able to get a proper finite, countable and exact value of the function.
For the above function, (u circle v) (x) we can not get a proper value of the function for x = 0.
Hence, the options A, C, D can not be the range of the function, since it contains 0.
The range of the given function will be the option B, since it does not contain the value 0.
Answer: C (pictured below)
This is the answer I selected on e2020 and got it correct.
Need answers ASAPP,please show work
This is the remainder when 64 oz is divided by 6 oz,
64 = 6 × 10 + 4
That's a remainder of 4.
Answer: 4 ounces
Answer:
Step-by-step explanation:
64 = 60 + 4 = 6*10 +4
Left over =4 ounce
Sharon will drink 4 ounces of juice
Please can someone help I try it hard but I don’t understand it
He could have scored 7, 14, 21, 28, 35, or 42 points (all multiples of 7 less than 45).
answer: B
What is D and R? Please answer I need help.
Answer:
31. D: {8, 4, 0, -4}; R: {2, -1}; yes
32. D: {-1, 2, 7}; R: {-4, -3, -2, 0}; no
33. D: {-4, -3, -1, 2, 3, 5}; R: {-3, -2, 0, 3, 5}; yes
34. D: (-∞, ∞); R: (-∞, 4]; yes
35. D: [0, 5]; R: [-2, 3]; no
Step-by-step explanation:
In this context, D means "domain" and R means "range." The domain of a function is the list of input values for which the function is defined. For ordered pairs, it is the first number of the pair. For an x-y table, it is the list of x-values. For a graph, it is the possible values of x.
A relation is a function only if there are no repeated values in the domain (2 or more outputs for the same input.)
The range of a function is the list of output values produced by the function. For ordered pairs, it is the second number of the pair. For an x-y table, it is the list of y-values. For a graph, it is the possible values of y.
__
31. D: {8, 4, 0, -4}
R: {2, -1}
Function: yes
Domain and range values don't need to be repeated. Often, they're listed in order from lowest to highest. Here, we have listed them in order of occurrence in the function definition.
__
32. D: {-1, 2, 7}
R: {-4, -3, -2, 0}
Function: no
__
33. D: {-4, -3, -1, 2, 3, 5}
R: {-3, -2, 0, 3, 5}
Function: yes
__
34. D: (-∞, ∞)
R: (-∞, 4]
Function: yes
__
35. D: [0, 5]
R: [-2, 3]
Function: no . . . . . . there are 2 y-values for most x-values
What is the equation of a line that passes through the point (3,2) and has a slope of 1/3
Answer:
y-2=1/3(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-2=1/3(x-3)
Eric and his wife are each starting a saving plan. Eric will initially set aside $50 and then add $30.65 every week to the savings. The amount A (in dollars) saved this way is given by the function A=50+30.65N, where N is the number of weeks he has been saving.
His wife will not set an initial amount aside but will add $55.85 to the savings every week. The amount B (in dollars) saved using this plan is given by the function B= 55.85N.
Let T be the total amount in dollars saved using both plans combined. Write and equation relation T to N. Simplify your answer as much as possible
Answer:
T=50+86.49N
Step-by-step explanation:
you just have to combine A and B.
Total (T)=A(50+30.65N)+B(55.85N) thank just open the prentices and add 30.65N and 55.85N=86.49N. so total is initial savings+ weekly savings by both.
The bake stars need to arrange 718 pup ales on trays for a pooch party. If each tray can hold 9 pupcakes, about how many trays will the bakery need? choose the best estimate.
Answer: the bakery will need about 70 trays
Step-by-step explanation:
718 can be rounded to 700
9 can be rounded to 10
700/10 = 70
Answer:
80 trays
Step-by-step explanation:
718
÷ 9
_________
79.78 ≈ 80 trays
what is the value of sin0 given that (-6,-8) is a point on the terminal side of 0
Answer:
[tex]sin \theta =\frac{-8}{10} =-\frac{4}{5}[/tex]
Step-by-step explanation:
For this case we have a point given (-6,-8) and we know that this point is terminal side of 0
We can assume that the length of th opposite side is given by:
b=-8 and the length for the adjacent side would be a=-6
And we can find the hypothenuse on this way:
[tex] c= \sqrt{a^2 +b^2}=\sqrt{(-6)^2 +(-8)^2}=10[/tex]
From the definition of sin we know this:
[tex]sin O =\frac{opposite}{hypothenuse}[/tex]
And if we replace we got this:
[tex]sin \theta =\frac{-8}{10} =-\frac{4}{5}[/tex]
We can aslo find the cos with the following identity:
[tex]cos^2 \theta + sin^2 \theta = 1[/tex]
And then:
[tex]cos \theta = \pm \sqrt{1-sin^2 \theta}=\pm \sqrt{1- (-4/5)^2}=\pm \frac{3}{5}[/tex]
But since both corrdinates are negative we are on the 3 quadrant and then [tex]cos \theta= -\frac{3}{5}[/tex]
Amanda has a shipping box in the shape of a triangular prism. It is 9 inches tall with a triangular base that is 3 inches by 2 inches. What is the volume of this shipping box?
Answer:
The volume of the shipping box is [tex]V=27\ in^3[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
The volume of the triangular prism is equal to
[tex]V=BH[/tex]
where
B is the area of the triangular base
H is the height of the prism
In this problem we have
[tex]H=9\ in[/tex]
Find the area of the triangular base B
[tex]B=\frac{1}{2}bh[/tex]
we have
[tex]b=3\ in\\h=2\ in[/tex]
substitute
[tex]B=\frac{1}{2}(3)(2)=3\ in^2[/tex]
Find the volume of the triangular prism
[tex]V=BH[/tex]
we have
[tex]B=3\ in^2[/tex]
[tex]H=9\ in[/tex]
substitute
[tex]V=(3)(9)=27\ in^3[/tex]
Please help me with this and can you show me how to do it??
Answer:
8 ft²
Step-by-step explanation:
Since ΔEFG ~ ΔABC, they are proportionately related. Each of the corresponding sides differ by the scale factor, which shows how much bigger or smaller the new triangle is from the original triangle.
Purple = original triangle, triangle 1
Pink = new triangle, triangle 2
Find the scale factor, "k". It will be a fraction because the triangle gets smaller.
k = FG/BC = 2/3
The scale factor can be used to find a side, the height or the area of the new triangle.
Use the scale factor squared to find the area.
A₂ = (A₁)(k²)
= (18 ft²)(2/3)²
= 7.999...ft²
= 8 ft²
team tool Bella canoed 15 3/4 miles in 5 1/4 hours
Answer:
Step-by-step explanation:
What's the question?
Solve for the value of z: 14/5 = z/25
Answer: z = 70
Explanation: To solve this proportion for z, we can use cross products.
*Image provided.*
When we get the equation 5z = 350, we can get z by itself on the left side of the equation by dividing both sides of the equation by 5. On the left, the 5's cancel each other out and we have z. On the right, 350 divided by 5 simplifies to 70 so we have z = 70.
Answer:
z = 75
Step-by-step explanation:
For the open-ended question below, be sure to show your work and/or explain your reasoning.
Scott has $15.00, and he earns $6.00 an hour babysitting.
a) Write an equation for the amount of money (m) Scott has after a number of hours babysitting (h).
b) After how many hours of babysitting will Scott have $51.00?
(a) m=6h+15 can be used to find the total amount of money for h hours of babysitting.
(b) After 6 hours of babysitting, Scott will have $51.00
Step-by-step explanation:
Given,
Amount Scott has = $15.00
Per hour amount of babysitting = $6.00
a) Write an equation for the amount of money (m) Scott has after a number of hours babysitting (h).
Total amount of money = m
Number of hours babysitting = h
Total amount of money = Per hour earning from babysitting*Number of hours + Amount Scott has
[tex]m=6h+15[/tex]
m=6h+15 can be used to find the total amount of money for h hours of babysitting.
b) After how many hours of babysitting will Scott have $51.00?
Putting m = 51
[tex]51=6h+15\\51-15=6h\\36=6h\\6h=36[/tex]
Dividing both sides by 6
[tex]\frac{6h}{6}=\frac{36}{6}\\h=6[/tex]
After 6 hours of babysitting, Scott will have $51.00
Keywords: linear equation, division
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To the nearest degree, what us the angle measure if the angle formed with the positive x-axis and the equation given below
Y=5/4 (x)
The measure of the angle formed with the positive x-axis and the equation of the given line is 51° to the nearest degree
Step-by-step explanation:
The formula to find the angle between the positive part of x-axis and a line y = m x + b is tan(Ф) = m, where
Ф is the angle between the line and the positive part of x-axism is the slope of the line∵ The equation of the line is [tex]y=\frac{5}{4}x[/tex]
∵ The form of the equation of a line is y = m x + b
∴ m = [tex]\frac{5}{4}[/tex] and b = 0
∵ Ф is the angle between the line and the positive part of x-axis
∵ tan(Ф) = m
∴ tan(Ф) = [tex]\frac{5}{4}[/tex]
- To find Ф use the inverse function of tan ( [tex]tan^{-1}[/tex]
∵ Ф = [tex]tan^{-1}(\frac{5}{4})[/tex]
∴ Ф = 51.34°
- Round it to the nearest degree
∴ Ф = 51°
The measure of the angle formed with the positive x-axis and the equation of the given line is 51° to the nearest degree
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if the number of square centimetire on the surface of a sphear is equal to the number of cubic centimetres in its volume what is the diameter of the sphere
Answer:
The diameter of the sphere is 6 centimeters
Step-by-step explanation:
we know that
The surface area of a sphere is
[tex]SA=4\pi r^{2}[/tex]
The volume of the sphere is
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
Equate both formulas
[tex]\frac{4}{3}\pi r^{3}=4\pi r^{2}[/tex]
Simplify
[tex]\frac{1}{3}r^{3}=r^{2}[/tex]
[tex]\frac{r^3}{r^2}=3[/tex]
[tex]r=3\ cm[/tex]
Remember that the diameter is two times the radius
so
[tex]D=2r=2(3)=6\ cm[/tex]
therefore
The diameter of the sphere is 6 centimeters
Final answer:
The diameter of a sphere where the surface area equals the volume is 1.5 cm.
Explanation:
To find the diameter of a sphere where the surface area in square centimeters is equal to the volume in cubic centimeters, we use the formulae for the surface area and volume of a sphere:
Surface Area (SA) = 4πr²Volume (V) = 4/3πr³Since the surface area is equal to the volume (SA = V), we can set the equations equal to each other and solve for the radius (r):
4πr² = 4/3πr³r³/r² = 3/4r = 3/4Now that we have the radius, we can find the diameter, which is twice the radius:
Diameter (d) = 2r = 2 × (3/4) = 3/2 cm or 1.5 cm
Simplify this expression:
16 + 28 ÷ 2 – 6
______________
10 – 4 x 2
-2.4
-4.8
8
12
20
Answer:
12
Step-by-step explanation:
28/2=14
16+14=30
30-6=24
-----------------
4*2=8
10-8=2
---------------
24/2=12
t rectangular prism has a length of 2 1/2 feet, a width of 3 feet, and a height of
1 1/2 feet. Unit cubes with side lengths of 1/2 foot are added to completely
fill the prism with no space remaining. What is the volume, in cubic feet, of the right rectangular
prism?
Show your work.
Answer:
Volume of the rectangular prism is [tex]11\frac{1}{4}[/tex] cubic feet.
The number of small cubes required is 90.
Step-by-step explanation:
The rectangular prism has a length of [tex]2\frac{1}{2}[/tex] feet, a width of 3 feet, and a height of [tex]1\frac{1}{2}[/tex] feet.
Now, the volume of the rectangular prism will be [tex](2\frac{1}{2} \times 3 \times 1\frac{1}{2}) = (\frac{5}{2} \times 3 \times \frac{3}{2}) = \frac{45}{4}[/tex] cubic feet i.e. [tex]11\frac{1}{4}[/tex] cubic feet. (Answer)
Now, the volume of the small unit cubes of side lengths of [tex]\frac{1}{2}[/tex] feet will be [tex](\frac{1}{2})^{3} = \frac{1}{8}[/tex] cubic feet.
So, the number of small cubes required to fill the large cube will be [tex](\frac{45}{4} \div \frac{1}{8}) = 90[/tex]. (Answer)
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18. Point p is chosen at random on EH. Find the probability that p is on FG.
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
The total length of this line is 15 units. FG is 6 units long.
This means that the probability of p being on FG would be [tex]\frac{6}{15}[/tex] which can be simplified to [tex]\frac{2}{5}[/tex]
Answer:
2/5
Step-by-step explanation:
Line EH has three line segments:
EF which measure 4
FG which measures 6
GH which measures 5
The total measure of the line (EH) = 4 + 6 + 5 = 15
So if we are calculating the probability of landing on FG,
6 / 15
Reduce the fraction to make,
2 / 5
You put 1200 in an account that earns 3% simple interest. What is the total amount in the account after four years?
Answer: A = 1350.61
Step-by-step explanation:
Using the formula for calculating amount, which is given as
A = P [tex](1 + r)^{n}[/tex]
A = amount
P = Principal
r = rate
n = number of years
substituting the values given into the formula , we have
A = 1200 ([tex](1 + 0.03)^{4}[/tex]
A = 1200 ([tex](1.03)^{4}[/tex]
A = 1350.61
Therefore , the amount after four years is 1350.61
A baseball team played 154 regular season games. The ratio of the number of games they won to the number of games they lost was 5/2. How many games did they win?
Answer:
Number of games won = 110
Step-by-step explanation:
Given:
Total games played = 154
The ratio of number of games won to number of games lost = [tex]\frac{5}{2}[/tex]
Solution:
Let the number of games won be = [tex]5x[/tex]
Thus, number of games lost = [tex]2x[/tex]
The total games played can be given as = [tex]5x+2x=7x[/tex]
Thus, we have:
[tex]7x=154[/tex]
Dividing both sides by 7.
[tex]\frac{7x}{7}=\frac{154}{7}[/tex]
∴ [tex]x=22[/tex]
So, number of games won = [tex]5\times 22 = 110[/tex]
Explain how to simplify this complex fraction. Interpret the meaning of the result.
Answer:
330 pages in 45 minutes
Step-by-step explanation:
All the work I did is at the top.So first we want to know how many minutes is 3/4 of an hour. We already know an hour is 60 minutes. Since it is out of 4 we are going to divide 60 by 4.
Hopefully you can read the work I put up there, but anyways it equals 15. Now we have to do 15 times 3 to get our answer
This equals 45. This means the person read 330 pages in 45 minutes!