The expression that is equivalent to the given expression, (ab⁷)⁴, is a⁴b²⁸. The correct option is the last option a4b28
Writing an equivalent expressionFrom the given information, we are to determine the expression that is equivalent to the given expression
The given expression is
(ab⁷)⁴
To determine the expression that is equivalent to this expression, we will expand the given expression
Expanding the expression
(ab⁷)⁴
Applying the distributive exponent law of indices,
(a)⁴ × (b⁷)⁴
Simplifying
a⁴ × b²⁸
= a⁴b²⁸
Hence, the equivalent expression is a⁴b²⁸
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Answer:
I think it's a4b28
Step-by-step explanation:
1. The population of a town was 7420 in 2010. The population grows at a rate of 2.3% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010. (b) Estimate the population of the town in 2022. Show your work.
Hello,
I hope you and your family are doing well!
(a) The exponential growth model is given by the equation P(t) = P0 * r^t, where P(t) is the population t years after 2010, P0 is the population in 2010 (7420), and r is the annual growth rate (2.3%).
Substituting the given values into the equation gives us:
P(t) = 7420 * 1.023^t
This is the equation that estimates the population t years after 2010.
(b) To estimate the population of the town in 2022, we can substitute t = 12 into the equation:
P(12) = 7420 * 1.023^12
Calculating this gives us:
P(12) = 7420 * 1.023^12 = 7420 * 1.291891 = 9593.45
So the estimated population of the town in 2022 is approximately 9593
Happy to help!
Look at HIJ. Which of the triangles below can be proven similar to HIJ based only on the given information? Select all that apply.
The tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.
What is the similarity of the triangles?
When it comes to Euclidean geometry, two things are said to be comparable if they have the same shape or the same shape as each other's mirror image. One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.
We have,
In ΔHIJ
∠HIJ = 64°
∠JHI = 96°
and the side are
HI = 2 unit
IJ = 5.5 unit
HJ = 5 unit
So, the third angle will according to the sum of the angles of a triangle:
∠IJH = 20°
the triangles similar to ΔHIJ are:
A) It is similar to ΔHIJ cause,
∠HIJ ≅ ∠KLM
∠IJH ≅ ∠LMK
so, the third also will be equal:
∠JHI ≅ ∠LKM
D) It is similar to ΔHIJ cause,
∠IJH ≅ ∠XZY
HI/YX = 2/4 = 1/2
HJ/YZ = 5/10 = 1/2
C) It is similar to ΔHIJ cause,
HI/UV = 2/4 = 1/2
HJ/UW = 5/10 = 1/2
IJ/VW = 5.5/11 = 1/2
Hence, the tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.
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Round to the nearest degree
The measure of angle A of the triangle is 50°.
How to find angles of the triangle?
Eight angles are created when a transversal intersects two parallel lines. The pair of non-adjacent interior angles that are on the same side of the transversal are known as the same side internal angles.Two angles that are inside (between) the two lines, more especially on the same side of the transversal, are referred to as same side inside angles.Similar side interior angles therefore:
have unique vertices or no shared verticesstraddle two lineswas developed on the same transverse side of theCo-interior angles are another name for "same side interior angles."So, ∠C = ∠A
∠A = 50°
Hence, the measure of angle A of the triangle is 50°.
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Find the perimeter of the following polygon. Be sure to include the correct unit in your answer.
7m
16 m
9cm
15 m
The perimeter of the polygon is 57 meters.
What is polygon?A polygon is an enclosed two-dimensional shape with three or more straight sides that are connected together. It can be regular or irregular and can be made up of triangles, squares, rectangles, and other shapes. Polygons are classified by the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and hexagons (6 sides). Polygons can also be classified by their internal angles, such as acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees), and reflex (greater than 180 degrees). Polygons are used in many mathematical problems and can be used to represent a variety of real-world objects, such as buildings, mountains, and stars.
The perimeter of the polygon is 57 meters.
The perimeter is calculated by adding up the lengths of each side. 7m + 16m + 9cm + 15m = 57m.
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- Roll a die twice and consider the events A = {first roll gives at
least 4}, B = {second roll gives at most 4} and C = {the sum of the
rolls is 10}.
(a) Find P(A), P(B),P(C), and P(A ∩ B ∩ C).
(b) Are A, B, and C independent?
Part a: P(A) = 1/2; P(B) = 2/3; P(C) = 1/12; P(A ∩ B ∩ C) = 1/36.
Part b: Part b: A, B, and C independent events.
What is meant by the term sample space?All potential results make up the sample space of the a random experiment. A subset of a sample space is an event connected to a random experiment. Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.Rolling a dice twice has 36 possible results, hence the following is the sample space:
S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
For the stated question-
A = {first roll gives at least 4}, B = {second roll gives at most 4} and C = {the sum of the rolls is 10}.Part a: P(A), P(B),P(C), and P(A ∩ B ∩ C).
P(A) = 18/36 = 1/2
P(B) = 24/36 = 2/3
P(C) = 3/36 = 1/12
P(A ∩ B ∩ C) = 1/36
Part b: A, B, and C independent or not.
For the events to be independent,
P(A ∩ B ∩ C) = P(A).P(B).P(C)
P(A).P(B).P(C) = 1/2*2/3*1/12 = 1/36
As, P(A ∩ B ∩ C) = P(A).P(B).P(C).
Thus, the events are independent.
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Ann made $35.000 in taxable income last year. Suppose the income tax rate is 10% for the first $8000 plus 16% for the amount over $8000. How much must Ann pay in income tax for last year?
Answer:
Ann must pay $800 in income tax for the first $8,000 of her taxable income because 8000 * .1 = 800
Ann must pay $4,600 in income tax for the amount of her taxable income over $8,000 because (35000 - 8000) * .16 = 4600
Therefore, Ann must pay a total of $800 + $4,600 = $<<800+4600=5400>>5,400 in income tax for last year.
Answer:
$5,120 in taxes, total
Step-by-step explanation:
Ann made $35,000 in taxable income last year. Suppose the income tax rate is 10% for the first $8,000 plus 16% for the amount over $8,000. How much must Ann pay in income tax for last year?
8,000 * 10% = 800 in taxes for first $8,000
remaining: 35,000 - 8,000 = $27,000 to be taxed at 16%
27,000 * 16% = $4,320
$800 + $4,320 = $5,120 in taxes, total
Which lines are perpendicular to 3x – y = 10? Select all that apply.
A. y = 3x + 5
B. y = –13x + 17
C. x + 3y = 27
D. y – 2 = 13(3x + 36)
C. x + 3y = 27 lines are perpendicular to 3x – y = 10
What is the lines?A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. In a two-dimensional plane, it is specified by two points. The term "collinear points" refers to two points that are on the same line.
As we know,
When two lines are perpendicular then the product of their slope is -1.
The slope is given by: y = mx+c
where, m is the slope.
Thus, the given equation:
3x – y = 10
y = 3x - 10
Comparing this equation with y = mx+c, we get
m₁ = 3
So, the slope of the given equation (m₁) = 3
Now find slope of others lines:
A) y = 3x + 5, Comparing this equation with y = mx+c, we get -
m₂ = 3
When two lines are perpendicular then the product of their slope is -1.
Here, product of the slope is:
= m₁ × m₂
= 3×3 (putting the values we get)
= 9 ≠ -1
So, this line is not perpendicular to given line.
B) y = –13x + 17, Comparing this equation with y = mx+c, we get -
m₃ = -13
When two lines are perpendicular then the product of their slope is -1.
Here, product of the slope is:
= m₁ × m₃
= 3× (-13) (putting the values we get)
= -39 ≠ -1
So, this line is not perpendicular to given line.
C) x + 3y = 27
3y = 27 - x
y = 9 - x/3, Comparing this equation with y = mx+c, we get -
m₄ = -1/3
When two lines are perpendicular then the product of their slope is -1.
Here, product of the slope is:
= m₁ × m₄
= 3× (-1/3) (putting the values we get)
= - 1
So, this line is perpendicular to given line.
D) y – 2 = 13(3x + 36)
y = 39x +470, Comparing this equation with y = mx+c, we get -
So, m₅ = 39
When two lines are perpendicular then the product of their slope is -1.
Here, product of the slope is:
= m₁ × m₅
= 3× (39) (putting the values we get)
= 117 ≠ -1
So, this line is not perpendicular to given line.
Therefore, option C is correct.
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Graph the inequality on the axes below.
-x + 2y > 4
Answer:
Check out the image shown above/below
If $300 is invested at an interest rate of 2.5% per year, find the amount of the investment at the end of 10 years for the
following compounding methods. (Round your answers to the nearest cent.)
(a) Annually
$
(b) Semiannually
$
(c) Quarterly
$
(d) Continuously
The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x2 – 2
y ≥ –x2 + 5
Change the equations to inequalities to modify the graph and the solutions are (-1.871, 1.5) and (1.871, 1.5)
How to modify the graphsThe graph is the given parameter
From the graph, we have the following equations
f(x) = x² - 2
g(x) = -x² + 5
To modify the graph, we simply change the equations to inequalities
How to identify the solution setAfter the modifications in (a), we have:
f(x) > x² - 2
g(x) ≥ -x² + 5
From the graph of the inequalities, the curves of the inequalities intersect at (-1.871, 1.5) and (1.871, 1.5)
Hence, the solutions are (-1.871, 1.5) and (1.871, 1.5)
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Using the matrix solve the following simultaneous equations
2x+5y=18
x-3y=-2
2x+5y=18 equ(1)
x-3y=-2 equ(2)
from equ (2) make x the subject of the formula
x=-2+3y
substitute x=2+3y in equ (1)
2+(-2+3y)+5y=18
-4+6y+5y=18
6y+5y=18+4
11y/11=22/11
y=2
substitute y=2 in equ(2)
x+3(2)=-2
x-6=-2
x=-2+6
x=4
x=4 and y=2
t a student government fundraiser, a notebook costs $7 and a t-shirt costs $12. If the total received for 60 items was $540, how many notebooks were sold?
The number of notebook is 36.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the notebook be n.
Let the t shirt be t.
The equation will be:
n + t = 60 ..... i
7n + 12t = 540 ..... ii
From I n = 60 - t ..... iii
Put equation III into ii
7n + + 12t = 540 .
7(60 - t) + 12t = 540
420 - 7t + 12t = 540
5t = 540 - 420
5t = 120
Divide
t = 120 / 5
t = 24
Notebook will be:
= 60 - 24
= 36
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Tristan has $1.40 worth of nickels and dimes. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Tristan has. Define the variables that you use to write the system.
The system of equations that Tristan needs to solve is:
x*0.05 + y*0.10 = 1.40
x = 2*y
How to write the system of equations?
Let's define the variables:
x = number of nickels.
y = number of dimes.
Knowing that the net is $1.40 and that he has twice as many nickels as dimes, we can write:
x*0.05 + y*0.10 = 1.40
x = 2*y
That is our system of equations that Tristan can use to find the numbers of nickels and dimes.
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Hurry please I will give brainly need this in about 15 mins help me help meee
Answer:
x = -2
Step-by-step explanation:
The first thing we can notice about this figure is that the two small outer triangles are congruent because of the given side congruence markings as well as the fact that the large triangle ABC is isosceles, thus angle A is congruent to angle C.
Using the above information, we can construct the equation:
3x + 2 = 2x
and solve it for x.
x = -2
The equation we constructed simply equates the corresponding sides of the two small outer triangles, as they are congruent by the CPCTC theorem.
Geometry Support 4. Given: 6x-4 = 3x + 8. Prove: x = 4
Answer:
6(4)-4=3(4)+8
24-4=12+8
20=20
Step-by-step explanation:
To prove x=4, substitute four into the equation
6(4)-4=3(4)+8
24-4=12+8
20=20
Therefore x=4 is proved
Answer:
(Answer in Image)
Step-by-step explanation:
6x-4=3x+8
6x-4-3x=3x+8-3x subtract -3x on both sides
3x-4=8
3x-4+4=8+4 add four on both sides
3x=12 simplify
3/3x=12/3 divide both sides by 3
x=4
5. My sister and I wanted to go to the circus. A ticket was 10% less on a Tuesday than it was on a Saturday. We paid $27 each to attend Tuesday's show. What would our total cost have been had we attended the circus on Saturday?
Hello,
I hope you and your family are doing well!
If a ticket to the circus was 10% less on a Tuesday than it was on a Saturday, then it was 90% of the Saturday ticket price. If you paid $27 each to attend Tuesday's show, then the Saturday ticket price was $27 / 0.9 = $30.
Since you bought two tickets, the total cost of attending the circus on Saturday would have been 2 * $30 =60
Therefore, your total cost would have been $60 had you attended the circus on Saturday.
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Happy Holidays and New Year!
find the total surface area of this triangular prism
The total surface area of this triangular prism = 976
What is surface area?Surface area is the amount of space covering the outside of a three-dimensional shape.
A triangle would be divided in half, but since there are two, the ratio would remain the same.
14 x 24 = 336
10 x 25 = 250[ because there are two of them, multiply by 2.]
10 x 14 = 140
The total surface area of this triangular prism = 336 + 250 + 140
= 976
Therefore, the total surface area of this triangular prism = 976
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Quel est le plus grand nombre que l' on puisse obtenir avec les chiffres 2,3 et 5?
4.4 times 2.727 the answer with explanation
Answer:
11.9988
Step-by-step explanation:
Use a calculator.
Which compound inequality has no solution? x ≤ –2 and 2x ≥ 6 x ≤ –1 and 5x ≤ 5 x ≤ –1 and 3x ≥ –3 x ≤ –2 and 4x ≤ –8
The correct inequality which has no solution will be;
⇒ x ≤ –2 and 2x ≥ 6
⇒ x ≤ –1 and 5x ≤ 5
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
There are some inequality is shown.
Now,
Find the inequality which has no solution as;
a) x ≤ –2 and 2x ≥ 6
⇒ x ≤ - 2
⇒ 2x ≥ 6 = x ≥ 6/2 = x ≥ 3
We get;
⇒ x ≤ - 2 and x ≥ 3
Which is not possible.
Hence, it has no solution.
b) x ≤ –1 and 5x ≤ 5
⇒ x ≤ - 1
⇒ 5x ≤ 5 = x ≤ 1
We get;
⇒ x ≤ - 1 and x ≤ 1
Which is not possible.
Hence, it has no solution.
c) x ≤ –1 and 3x ≥ –3
⇒ x ≤ - 1
⇒ 3x ≥ - 3 = x ≥ - 1
We get;
⇒ x ≤ - 1 and x ≥ - 1 ⇒ x = - 1
Thus, It has solution.
d) x ≤ –2 and 4x ≤ –8
⇒ x ≤ –2 and
⇒ 4x ≤ - 8 = x ≤ - 2
Thus, It has solution.
Therefore, The correct inequality which has no solution will be;
⇒ x ≤ –2 and 2x ≥ 6
⇒ x ≤ –1 and 5x ≤ 5
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I need help please!!
Answer:
it is 3/5
Step-by-step explanation:
cos is the adjuacent devided by hypotenuse so it is 27/45 and that is 3/5
Graph the line with y-intercept -5 and slope -1/3
can you mark the points on the graph pleases
Answer:
(0,-5) , (3, -6) , (6, -7) ,(9, -8)
Step-by-step explanation:
I apologize for being unable to graph, but here are some of the points.
(0,-5) <-- The "y intercept"
slope is y2-y1/x2-x1, so "-1" is added to the "y" of the coordinate, and 3 is added to the "x"
(3,-6)
(6,-7)
(9,-8)
Hope this helps :)
help meeeeeeeeeee pleaseee
The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.
What is an algebraic expression?An algebraic expression is formed by variables, constants, and arithmetic operations.An algebraic expression provides the relation between the input and output variables i.e., x and f(x) respectively.Calculation:It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,
C(x) = 270 ln(x+1) + 1900
The average intake of calories consumed per day is given by C(x) = 2200
Here x is the number of acres of land. Then, the required number of acres of land is
C(x) = 270 ln(x+1) + 1900
⇒ 2200 = 270 ln(x+1) + 1900
⇒ 270 ln(x+1) = 2200 - 1900
⇒ 270 ln(x+1) = 300
⇒ ln(x+1) = 300/270 = 10/9
Applying base 'e' on both sides, we get
⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]
⇒ x+1 = 3.0377
⇒ x = 3.0377 - 1 = 2.0377
When rounding the final answer to the nearest tenths, we get x = 2 acres.
When rounding the final answer to the nearest thousand, we get x = 2.038 acres.
Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.
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Find tanθ + sinθ for the angle θ shown in the right triangle?
12.6
Step-by-step explanation:
We need to find the hypotenuse
hyp² = opp² + adj²
hyp²= 2² + 3²
hyp²= 4 + 9
hyp²= 13
hyp=√13
hyp=3.6
sinθ=opp/hyp
sinθ=2/3.6
sinθ=5.6
cosθ=adj/hyp
cosθ=3/3.6
cosθ= 0.8
tan θ=sinθ/cosθ
tanθ= 5.6/0.8
tanθ=7
tan θ+sinθ
=7+5.6
=12.6
Look at this graph:
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
4/3
Step-by-step explanation:
you use the slope formula y^1 - y^2 over x^1 over x^2, substitute the said values and are left with the slope of 4/3 in its improper form.
Hope this helps!!! :3
(2) Solve the system of linear equations by elimination. CH
8x - 5y = 11
4x
3y = 5
By solving the system of linear equations by elimination we get the value of x= 2 and y = 1.
What is the system of linear equations?
A grouping of one or more linear equation containing the same variables is known as a system of linear equations.
Here, we have
Given: 8x - 5y = 11....(1), 4x - 3y = 5...(2)
We solve equation(2) and find the value of x
4x = 5+ 3y
x = 5/4 + 3y/4
Now, we put the value of x in equation (1) and we get
8(5/4 + 3y/4) - 5y = 11
5×2 + 2×3y - 5y = 11
10 + y = 11
y = 1
Now, we put the value of y in equation(2) and we get
4x = 5+ 3(1)
4x = 8
x = 2
Hence, by solving the system of linear equations by elimination we get the value of x= 2 and y = 1.
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A graph is shown
For which line does y decrease as x increases
A.line 1
B.line 2
C.line 3
D.line 4
Answer:
Line 2
Step-by-step explanation:
This would represent a negative slope. A negative slope goes down if you start on the left side and go down.
It takes Martin 1 hour to drive 65 miles, 2 hours to drive 130 miles and 3 hours to drive 195 miles. Is this a proportional relationship? Define variables and write an equation to represent the relationship.
Yes, it is a proportional relationship. The relationship is distance (d) is directly proportional to time(t). The equation of the relationship is d= 65t
What is direct variation?Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If d( distance) is directly proportional to t( time) the equation is of the form d= kt (where k is a constant).
When d =65miles and t= 1hour, k =d/t
k= 65/1= 65
for other values of d and t, k = 65
Therefore the relationship between the distance and time is a proportional relationship. And the equation of the relationship is d= 65t
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Solve for all values of x by factoring x2-53=-4
The values of x in the given equation, x² - 5x = -4, are x = 4 and x = 1
Solving Quadratic equations: Determining the values of xFrom the question, we are to solve the given equation by factoring
The given equation is
x² - 5x = -4
To solve the equation by factoring, transfer the constant to the other side of the equation
x² - 5x + 4 = 0
Factorize the left hand side expression
x² -x -4x + 4 = 0
x(x - 1) -4(x -1) = 0
(x - 4)(x - 1) = 0
x - 4 = 0 OR x - 1 = 0
x = 4 OR x = 1
Hence, the values of x are 4 and 1
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You are playing a game that involves tossing a single die. If you roll a one, you win $50. If you roll a 2, you win $25. If you roll anything else, you lose $15. What are you expected winnings?
Step-by-step explanation:
chances of rolling 1= 1/6
chances of rolling 2=1/6
chances of rolling anything else=2/3