⇒In this case I will use the law of exponents that states:
[tex](x^{m} )^{n} \\=x^{m*n}[/tex]
⇒[tex]=(-3x)^{2y*4} \\=(-3x)^{8y}[/tex]
Answer: 81x^8y^4
Step-by-step explanation:
1. DISTRIBUTE EXPONENT by using the power rule: (ab)^n = (a^n)(b^n)
> Apply PRODUCT RULE: -3x^2y = (-3x^2)^4y^4
>Apply PRODUCT RULE: -3x^2 = (-3)^4 (x^2)^4y^4
2. RAISE -3 to the power of 4 = 81(x^2)^4y^4
3. MULTIPLY THE EXPONENTS in (x^2)^4
> Apply POWER RULE and MULTIPLY EXPONENTS, (a^m)^n = a^mn
(81x^2*4)(y^4)
> MULTIPLY 2 by 4 = 81x^8y^4
And that is your answer, 81x^8y^4
Laura jogs at an average rate of 5.6 miles per hour for 2 hours. Priya
jogs the same distance but takes 13 hours. Write an expression you can use
to find Priya's average rate, using a decimal value or an operation symbol
(+,-, x, ) to fill in each box.
5.6 x 2.6
The expression to represent the average rate of Priya is (5.6×2)÷13 and the average rate is approximately 0.86 miles per hour .
Laura jogs for 2 hours at the rate of 5.6 miles per hour.
Distance travelled = speed × time
= 5.6 × 2
= 11.2 miles
Priya jogs the same distance in 13 hours.
Now to calculate the average rate of Priya we haver to divide the total distance travelled by the total time taken to complete the journey.
Average rate of Priya:
= 11.2 / 13
= 0.86153
≈ 0.86 miles per hour
You will be better able to appreciate the pace of a journey if you are aware of average speed. The speed may occasionally fluctuate while travelling. The need of determining the average speed then increases in order to estimate how quickly the trip will be completed.
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akis bicycle designs has determined that when x hindered bicycles are built the average cost
The bicycles which the shop should build to minimize the average cost per bicycle is 25 bicycles
How to find number of bicycles that will minimize average cost?Average cost function:
C(x) = 0.2x² - 0.1x + 3.799This is a quadratic function, So
a = 0.2b = -0.1c = 3.799Average cost is minimum when
x = - b / 2a
= -(-0.1) / 2(0.2)
= 0.1 / 0.4
x = 1/4
Number of bicycles which should to minimize average cost per bicycle = minimum average cost × total cost
= 1/4 × 100
= 25 bicycles
Therefore, the number of bicycles which will minimize the average cost function is ,25 bicycles.
Complete question:
Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.2x^2-0.1x+3.799, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
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The area of a parallelogram is 780sq cm if the length of one side is 26cm find the corresponding height.
20 points
Step-by-step explanation:
area of parallelogram = length × height
780 = 26 × height
height = 780/26 = 30cm
hi guys please answer that question I should show the teacher
please answer the question that is under the graph
Answer:
with 12 students 3 fear spiders and other while 1 fear of snake and one of dogs. Some fear of all four
Step-by-step explanation:
hey hon, you were not very specific with what you teacher wanted but this is what i got hope it helps!!!!
Kadeesha is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $4.75. Kadeesha spent $48.75 altogether at the carnival and the number of games she played is twice the number of rides she went on. Write a system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on. Define the variables that you use to write the system.
Using system of equation, we can determine that Kadeesha played 10 games and went on 5 rides.
System of EquationSystem of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
Let;
x = gamesy = rides2.50x + 4.75y = 48.75 ...eq(i)
x = 2y ...eq(ii)
Solving equation (i) and (ii)
x = 10, y = 5
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IXL Please Help Fast!
Answer:
Step-by-step explanation:
so we need slope intercept form, which is y=mx+b ... just memorize this, you'll need it many many times
next we are told to find a line perpendicular to y= [tex]\frac{1}{8}[/tex]x+10
recall that the reciprocal of the slope will give us a perpendicular line with a sign change also.
then the slope m is:
m = -8
and we are given the point P(x1,y1) = ( -1,1)
now use the point-slope formula to find the equation to the line in the slope intercept form.
y-y1 = m(x-x1)
plug in our given info.
y-1 = (-8)(x-(-1))
y-1 = -8(x+1)
y-1= -8x -8
y = -8x -8+1
y=-8x-7
there is your slope intercept form of the equation :)
Tyshawn took a taxi from his house to the airport. The taxi company charged a pick-
up fee of $2.50 plus $3.50 per mile. The total fare was $79.50, not including the tip.
Which equation could be used to determine m, the number of miles in the taxi ride?
3.5m + 2.5 = 79.5 is the equation that could be used to determine m, the number of miles in the taxi ride.
Given in question,
Pick-up fee = $2.50
Fee per mile = $3.50
Total fare = $79.50
Let the no. of miles = m
Fee for m miles = 3.50m
Equation, 3.50m + 2.50 = 79.50.
Hence, the equation is 3.50m + 2.50 = 79.50.
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Use the marginal tax rate chart to answer the question.
Marginal Tax Rate Chart
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Determine the effective tax rate for a taxable income of $75,400. Round the final answer to the nearest hundredth.
10.05%
16.27%
22.00%
24.90%
The effective tax rate is 24% for a taxable income of $75,400
What is the Marginal tax rate?The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate.
the"marginal" income is what is taxed at the next highest tax bracket as moves up in tax brackets, this tax rate is known as the marginal tax rate.
Given that;
Marginal Tax Rate Chart Tax Bracket
$0 –$10,275 10%
$10,276 –$41,175 12%
$41,176 –$89,075 22%
$89,076 –$170,050 24%
$170,051 –$215,950 32%
$215,951 –$539,900 35%
> $539,901 37%
Thus, the effective tax rate for income of $95, 600 lies in the range of a marginal tax rate of 24%.
So, the effective tax rate;
= 72,026/ 95600
= 24 %
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Answer:
16.27%
Step-by-step explanation:
Hello,
10275 × 10% = 1027.5
41175 - 10276 = 30899
30899 × 12% = 3707.88
Then we would input 75400 since it fits in to ($41176–$89075)
75400 - 41176 = 34224
34224 × 22% = 7529.28
Then we would add it all up
1027.5 + 3707.88 + 7529.28 = 12264.66
Then to determine the effective tax rate for 75400 we would
[tex]\frac{12264.66}{75400}[/tex] × 100 = 16.27%
So, the effective tax rate for the taxable income of 75400 is 16.27%.
Need done soon pls! Super easy
Answer:
choose 3rd option
Step-by-step explanation:
Can you help with these vocabulary word
Answer:
is more than 90 degrees right angles are 90 degrees
You have \$20$20dollar sign, 20 to spend on taxi fare. The ride costs $5 per kilometer.
Write an inequality to determine the distance in kilometers, ddd, you can ride for sign, 20.
What is the maximum distance, in kilometers, you can ride for $20?
Answer:
5d≤20
4 kilometers
Step-by-step explanation:
pls mark
What was the difference between the population of Prince George's county (908,670) and Charles county (159,428) show your work on an open number line
The difference between Prince George's County's population (908,670) and Charles county (159,428) is 749,242.
What is the difference between the two values?To find the difference between two values, we use the mathematical operation of subtraction.
Subtraction operation involves the use of the minuend, subtrahend, difference, and equation sign.
The subtrahend is the number deducted from the minuend, to get the difference.
908,670 ... minuend
- 159,428 ... subtrahend
= 749,242 ... difference
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What is/are the x-intercept(s) and y intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The point where the gradient line intercepts (touches) the y-axis is called y intercept.
The point where the gradient line intercepts (touches) the x-axis is called x intercept.
check the sketch attached.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The inequality - 3(2x - 5) < 5(2 - x) is x > 5 represents a line with an open circle at x = 5 and going indefinity to positive infinity.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, inequality is - 3(2x - 5) < 5(2 - x).
∴ - 6x + 15 < 10 - 5x.
- 6x + 5x < 10 - 15.
- x < - 5.
x > 5 (think of moving x to the other side to make it positive.
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A line of best fit was drawn to the plotted points in a data set below. Based on the line of best fit, for what y-value does x=16x=16?
Answer:yes its 15
Step-by-step explanation:
what is x/-4<16 need help??
Answer: 2.3x is the answer
Find the equation of the line with slope -1 and y-intercept (0,-3)
NO LINKS!! Use the diagram below, describe the relationship as parallel, intersection, or skew
Answer:
a) Intersecting lines.
b) Parallel lines.
c) Skew lines.
d) Intersecting planes.
e) Parallel planes.
Step-by-step explanation:
A prism is a polyhedron that has:
Two bases that are congruent and parallel to each other.Lateral sides that are parallelograms and link the two bases.Height that is the distance between the two bases.From inspection of the give diagram, the figure appears to be a triangular prism with triangular bases ADE and BCF.
Lines
Parallel lines are lines on a plane that never meet and are the same distance apart.Intersecting lines cross each other in a plane and share a common point called the point of intersection.Skew lines are a pair of non-coplanar lines that do not intersect, and are not parallel to each other.Planes
A plane is a flat, two-dimensional surface that extends into infinity.
A plane can be named by the letters naming three non-collinear points in the plane.
Parallel planes are planes that never intersect. Intersecting planes are not parallel and always intersect along a line.a) AB and BC are intersecting lines as they share the common point B.
b) AE and BF are parallel lines because they both lie on the plane ABF, do not intersect and are the same distance apart.
c) EF and AD are skew lines because the do not lie on the same plane, they do not intersect and they are not parallel.
d) Plane ABC and plane ABF are intersecting planes as they intersect along line AB.
e) Plane AED and plane BFC are parallel planes as they are the bases of the prism and never intersect.
Ballentine Company expects sales for June, July, and August of $56,000, $62,000, and $52,000, respectively. Experience suggests that 45% of sales are for cash and 55% are on credit. The company collects 60% of its credit sales in the month following sale, 35% in the second month following sale, and 5% are not collected. What are the company's expected cash receipts for August from its current and past sales?
The company's expected cash receipts for August from its current and past sales is $126220.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the sales for June, July, and August are $56000, $62000, and $52000 respectively.
The company collects 45% of sales in cash, therefore, for June month the cash collected by the company is,
June = 56000×45%
June =56000×45/100
June =25200
Therefore, the credit amount for June is,
56000 - 25200
=30800
The cash collected by the company for July is,
= 62000×45%
= 62000×45/100
= 27900
The company will also collect 60% of its credit from June sales in July, therefore, the total collected cash in July is,
July = 27900 + 60% of 30800
July = 27900 + 60×30800/100
July = 46380
The remaining credit after July is,
62000-27900
= 34100
The cash collected for August is,
52000×45%
= 52000×45/100
= 23400
The company also collects cash credits in June and July. Therefore, The net cash collected by the company is,
August = 23400 + 30800×35% + 34100×60%
August = 23400 + 30800×35/100 + 34100×60/100
August = 23400 + 10780 + 20460
= 54640
Therefore, the total cash collected by the company for august from its current and past sales is,
June + July + August
= 25200 + 46380 + 54640
= 126220
Hence, the company's expected cash receipts for August from its current and past sales is $126220.
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Six car batteries weigh 46.2 pounds. Fourteen car batteries weigh 107.8 pounds. Does this represent a proportional relationship? If so, state the constant of proportionality.
The relationship of the battery represent a proportional relationship and the constant is 7.7 pounds.
How to calculate the constant of proportionality?From the information, 6 car batteries weigh 46.2 pounds. The weight per battery will be:
= 46.2 / 6
= 7.7 pounds
Also, rourteen car batteries weigh 107.8 pounds, the weight per battery will be:
= 107.8 / 14
= 7.7 pounds
The constant of proportionality is 7.7.
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X
-5
0
The table of ordered pairs shows the coordinates of the two points on the graph of a line. Which equation
describes the line?
y
2
7
a. y=x+7
b. y=x-7
A
C
Please select the best answer from the choices provided
c.
d.
Mark this and return
y = -5x +2
y = 5x + 2
Save and Exit
Next
Submit
The equation of the line that best describes the given table of ordered pair is y = x + 7
Equation of the line:
By using the slope and y intercept of the point, we can calculate the equation of the line as
y = mx + c
here m refers the slope and c refers the intercept.
Given,
Here we have the table of ordered pairs shows the coordinates of the two points on the graph of a line.
Now, we need to find the equation of the line that best suits this one.
In order to find the equation of the table, first we have to calculate the slope and the y intercept of the given table.
But in order to calculate the slope we need the points.
So, the point take has been taken by the table are
=> (-5, 2) and (0,7)
Now, the slope of the line is,
=> m = (0 - (-5))/ (7-2)
=> m = 5/5
=> m = 1
By looking into the point we have identified that the y intercept is 7,
Therefore, the equation of the line is
=> y = 1x + 7
=> y = x + 7
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Kala the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 3 clients who did Plan A and 5 who did Plan B. On Thursday there were 9 clients who did Plan A and 7 who did Plan B. Kala trained her Wednesday clients for a total of 6 hours and her Thursday clients for a total of 12 hours. How long does each of the workout plans last?
Kala the trainer lasted 0.75 hours for each of the work out.
How to find out how long each of the work out lastedLet A represent plan A and B for plan B
On Wednesday there were 3 clients who did Plan A and 5 who did Plan B for a total of 6 hours. this is represented mathematically as
3A + 5B = 6 hours
On Thursday there were 9 clients who did Plan A and 7 who did Plan B for a total of 12 hours. this is represented mathematically as
9A + 7B = 12 hours
hence we have two system of equations with two unknown
9A + 7B = 12 hours
3A + 5B = 6 hours
solving the equation gives that A = B = 0.75 hours = 45 minutes
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What is the area of a triangle whose vertices are J(-2, 1), K(0, 3), and L(3,-4)?
The area of the given triangle is 10 square units.
We have a triangle. The vertices of the triangle are J (-2, 1), K (0, 3), and L (3,-4). We need to find the area of the triangle. We will use the determinant method to calculate the area of a triangle if the coordinates of the vertices are given. If the vertices of a triangle are (x1, y1), (x2, y2), and (x3, y3), then the formula for the area of the triangle is given below.
A = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
A = (1/2)|-2(3 - (-4)) + 0(-4 - 1) + 3(1 - 3)|
A = (1/2)|-2(3 + 4) + 0(-5) + 3(-2)|
A = (1/2)|-14 + 0 + -6|
A = (1/2)|-20|
A = 10
Hence, the area of the triangle is 10.
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Does this table represent a function? Why or why not? X 2 3 4 5 5 A y 1 4 4 2 5 A. No, because two of the y-values are the same. OB. Yes, because there is the same number of x-values as y-values. OC. No, because one x-value corresponds to two different y-values. D. Yes, because every x-value corresponds to exactly one y-value.
Answer:no
Step-by-step explanation:
No because 2 5's in x
Complete the equation of the line through (3, -8) and (6, -4).
Use exact numbers.
y =
By the Factor Theorem, what can be said about the polynomial function s(x) if s(−5)=−4 ?
a) x+5 is not a factor of s(x)
b) s(x) has no real zeros
c) x+5 is a factor of s(x)
d) s(x) has 5real zeros
The polynomial function s(x) if s(−5) = −4 is a) x+5 is not a factor of s(x) is the correct option.
Given:
polynomial function s(x) if s(−5)=−4 .
x = -5 when substitute in s(x) the output is -4 which is not equal to zero so
x+5 is not a factor of s(x) is correct.
The factor theorem tells you that a polynomial f(x) has a factor (x - k) only when f(k)=0 . So if s(-5) is not 0, we can draw the conclusion that (x+5) is not a factor of s(x).
Therefore the polynomial function s(x) if s(−5) = −4 is a) x+5 is not a factor of s(x) is the correct option.
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Which equation is the slope-intercept form of the line that passes through (12, 9) and is perpendicular to the graph of y = -3/4x+1
The equation of a line perpendicular to y = -3/4x +1 and passes through (12, 9) is y = 4 /3 x - 7
How to represent equation of a line?A linear graph can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptThe line passes through the points (12, 9) and its perpendicular to the graph y = -3/4x +1.
The products of the slope of perpendicular lines is equals to negative one.
Therefore,
m₁ m₂ = -1
Hence,
- 3 / 4 m₂ = - 1
cross multiply
-3m₂ = -4
m₂ = 4 / 3
Therefore, let's find the y-intercept of the line using (12, 9)
y = 4 / 3 x + b
9 = 4 /3(12) + b
9 = 16 + b
b = 9 - 16
b = - 7
Therefore, the equation of the line is y = 4 /3 x - 7
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For f(x) = 9x + 8 and g(x) = 7x, find the following composite functions and state the domain of each.
(a) fog
(b) gof
(c) fof
(d) gog
For the given composite function, then values of
(a) 63x + 8
(b) 63x + 56
(c) 81x + 80
(d) 49x
Composite functions:
An operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)) is known as composite functions.
Given,
Here we have the functions f(x) = 9x + 8 and g(x) = 7x
Now, we have to find the composite function of each.
(a) The composite function is written as,
=> f(g(x)) =f(7x)
=> f(7x) = 9(7x) + 8
=> f(g(x)) = 63x+ 8
(b) The composite function is written as,
=> g(f(x))
=> g(f(x)) =g(9x + 8)
=> g(9x + 8) = 7(9x + 8)
=> g(9x + 8) = 63x + 56
(c) The composite function is written as,
=> f(f(x))
=> f(9x +8) = 9(9x + 8) + 8
=> f(9x + 8) = 81x + 72 +8
=> f(9x + 8) = 81x + 80
(d) The composite function is written as,
=> g(g(x))
=> g(7x) = 7(7x)
=> g(7x) = 49x
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The functions and are defined as follows.
Find the value of .
The expression we get from the given functions r and s defined for all real numbers x.
r( s(-3))= -38
Given that,
All real numbers x are defined by the functions r and s.
r(x) =2x+1
s(x) =-2x²-2
We have to find the expression
r( s(-3))
Take the functions,
r(x) =2x+1
s(x) =-2x²-2
Now, Take
r( s(-3))
Substitute s function first
r(-2(-3)²-2)
r(-2(9)-2)
r(-18-2)
r(-20)
Now substitute r function
2(-20)+2
-40+2
-38
Therefore, The expression we get from the given functions r and s defined for all real numbers x.
r( s(-3))=-38=
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Today only, a table is being sold for $333. This is 74% of its regular price. What was the price yesterday?