Answer:
3a 2b ×2a 6b = 72a²b² = 72× (ab)²Step-by-step explanation:
3a 2b ×2a 6b = (3 × 2)×(a × b) × (2 × 6)×(a × b) [commutative property]
= (6×ab) × (12×ab) [associative property]
= (6×12) × (ab×ab) [commutative + associative]
= (72) × (ab)²
= 72× (ab)²
= 72a²b² [exponent property]
There are 9.5 ounces of juice in a container. An additional 1.75 ounces of juice are poured into the container each second. How many ounces of juice are in the container after 6 seconds? Enter your answer in the box
By concept of capacity and the assumption of constant flow rate, the amount of ounces of juice in the container after 6 seconds is 20 ounces.
How to determine the final capacity of a container
Given that the additional juice is added to the container at constant rate. Hence, the final capacity (C'), in ounces is equal to the sum of the initial capacity (C), in ounces, and the product of the flow rate (q), in ounces per second, and time (t), in seconds.
C' = C + q · t (1)
If we know that C = 9.5 oz, q = 1.75 oz/s and t = 6 s, then the final capacity of the container is:
C' = 9.5 oz + (1.75 oz/s) · (6 s)
C' = 20 oz
By concept of capacity and the assumption of constant flow rate, the amount of ounces of juice in the container after 6 seconds is 20 ounces.
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Simplify 5 + 20 - 4².
O 21
09
O 17
O 441
Answer:9
Step-by-step explanation:addition and subtraction done in order of appearance. 5+20-16
5 + 20 - 4²
Add 5 and 20 to get 25.
25 - 4²
Calculate 4 to the power of 2.
To calculate a power, multiply the base as indicated by its exponent.
4 is the basis2 is the exponentSo 4 is multiplied 2 times, so
4 x 4 = 1625 - 16
Subtract 16 from 25 to get 9.
9 ===> Answer[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Solve: −8(−3m−5)+2=5(−m−3)−1.
The enrollment at a local university increased from 14,000 students to 20,000 students over a six-year period. What was the approximate average percent increase per year in student enrollment at the university?
A. 5%
B. 30%
C. 7%
D. 43%
The approximate average percent increase per year in student enrollment at the university is = 5%. That is option A.
Calculation of average percent increaseInitial number of student = 14,000 students
Total number of students over 6 years = 20,000 students
The total additional students for 6 years,
= 20,000- 14,000
= 6,000 students.
Therefore every year additional 1000 students where admitted into the local university.
The average percent increase per year in student enrollment at the university,
= 1000/20000 × 100
= 100000/20000
=5%
Therefore, the approximate average percent increase per year in student enrollment at the university is = 5%.
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Which step is the same when constructing an inscribed square and an inscribed regular hexagon?
O Construct a circle first
O Construct a line first
O Set the compass to the radus
Set the compass to greater than half the diameter
Question 4 Multiple Choice Worth 1 points)
(01.03 MC)
After the construction of a circle, we have to "Set the compass to the radius of the circle" so, option C is correct.
What is a regular hexagon?A regular hexagon is defined as a closed shape consisting of six equal sides and six equal angles. The sum of the measure of angles of a regular hexagon is 120 degrees.
Steps to create an inscribed hexagon:
1: The structure needs to adjust the box thickness towards that radius.
2: Afterward moves around the outside of the circular path to just produce the 6 vertices of that similar hexagon.
"Set the compass to the radius of the circle" so, option C is correct.
Thus the above answer is correct.
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Answer:
Construct a circle first
Step-by-step explanation:
If you're going to inscribe any figure in a circle, the first construction you need to do is construct the circle.
__
Additional comment
The attached shows our construction of an inscribed square and an inscribed regular hexagon. Here are the steps we used. You will notice the first step is construct a circle. (It could be, construct line AB, then construct circle A with radius AB.)
We have used line AB in the construction of the hexagon, but the hexagon could have been constructed without it. That is why "construct a circle first" is likely a better choice for a common first step.
square
construct circle A and locate a point B on itconstruct line AB, and locate point C at the other intersection of AB and circle Aset the compass to greater than half the diameterusing B as a center, draw arc RSusing C as a center, draw arc RS using the same compass setting. Label the intersection points R and S.draw line RS. Label the points of intersection with the circle as T and U.draw inscribed square CTBUregular hexagon
construct circle A and locate a point B on itconstruct line AB, and locate point C at the other intersection of AB and circle Awithout changing the compass, using B as a center, draw arc KL. Label intersection points K and L.using C as a center, draw arc JM. Label intersection points J and M.draw inscribed hexagon CJKBLM__
Arguably, the first step to constructing a circle is set the compass to the radius. We chose to ignore this because one of the ways to construct an inscribed hexagon is to mark off successive arcs around a circle that have a radius equal to the radius of the circle. We did not use that method. (The use of diameter BC made drawing 5 arcs around the circle unnecessary. We drew 2 instead.)
Or, you could argue that construct a line first is needed before you set the compass to the radius. If this is the first step, then the next steps would be to mark the center of the circle on the line, and mark another point at a distance of the radius from that center point.
What you consider to be the first step depends on the level of detail you want to attend to.
Determine if the following angles are congruent. What theorem proves them to be congruent. Explain your reasoning.
Answer: AAS
Step-by-step explanation:
We know that [tex]\angle TSN \cong \angle HSU[/tex] because they are vertical angles, meaning the triangles are congruent by AAS.
Describe how you would find the missing numbers in the equation below. What is the missing numerator and denominator?
Answer:
3 and 5 is the correct answer in this question
Step-by-step explanation:
please makes me a brainlest
Compare 3.5 • 10^4 to standard form
Answer:
35,000
Step-by-step explanation:
^4 means 4 zeros
10^4 = 10,000
3.5 times 10,000 =
35,000
What is the slope of a line perpendicular to the line whose equation is 2x+3y=21. Fully simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]2x+3y=21\implies 3y=-2x+21\implies y=\cfrac{-2x+21}{3} \\\\\\ y=\cfrac{-2x}{3}+\cfrac{21}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+7\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
therefore then
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}[/tex]
Answer:
2x+3y=21.
the answer is [tex]\frac{3}{2}[/tex]
simplify the answer I think. x = 2 + y = 3 = 21
x = 2
x + 1 = 3
y = 3
y - 1
2 + 1 = 3
3 - 1 = 2
The answer will only be [tex]\frac{3}{2}[/tex] no y = [tex]\frac{3}{2}[/tex] just [tex]\frac{3}{2}[/tex]
Don't forget to look at the picture
Which polynomial is prime?
x2 + 7
x2 – 25
3x2 – 27
2x2 – 8
x² + 7 can not be factorized with rational numbers.
What is prime polynomial?A prime polynomial defined as a polynomial has only two factors 1 and itself. It is a polynomial with integer coefficients that cannot be factored into polynomials of lower degrees.
x² + 7 can not be factorized with rational numbers.
Therefore, it is a prime polynomial.
x² - 25 can be factored into (x+5)(x-5).
Therefore, it is not a prime polynomial.
3x² – 27 can be factored into 3(x+3)(x-3).
Therefore, it is not a prime polynomial.
2x² – 8 can be factored into 2(x+2)(x-2).
Therefore, it is not a prime polynomial.
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Deb started doing yard work at 9:52 A.M. After working for 1 hour and 48 minutes, she stopped to have lunch. It took her 36 minutes to eat lunch.
The time Deb finished eating lunch is 12:16 P.M. The correct option is the first option 12:16 P.M.
Calculating timeFrom the question, we are to determine when Deb finished eating lunch
From the given information,
Deb started doing yard work at 9:52 A.M and she stopped to have lunch after working for 1 hour and 48 minutes.
After working for 1 hour and 48 minutes, the time will be
9:52 A.M + 1 hour 48 minutes = 11:40 A.M
This means she stopped to have lunch at 11:40 A.M.
Then,
It took her 36 minutes to eat lunch
The time Deb finished eating lunch will be
11:40 A.M + 36 minutes = 12:16 P.M.
Hence, the time Deb finished eating lunch is 12:16 P.M. The correct option is the first option 12:16 P.M.
Here is the complete question:
Deb started doing yard work at 9:52 A.M. After working for 1 hour and 48 minutes, she stopped to have lunch. It took her 36 minutes to eat lunch.
When did Deb finish eating lunch?
12:16 P.M.
12:32 P.M.
1:16 P.M.
1:32 P.M.
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graph the function y=[x-3] on the set of axis below
Answer:
Step-by-step explanation:
To graph a function, you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point.
4(x-5)-(6x + 1)= 2x -19
Answer:
Step-by-step explanation:
Comment
I take it you want the value for x.
Solution
4(x-5)-(6x + 1)= 2x -19 Remove the Brackets.
4x - 20 - 6x - 1 = 2x - 19 Combine like terms
-2x - 21 = 2x - 19 Add 2x to both sides
-2x-21+2x = 2x + 2x - 19 Combine
-21 = 4x - 19 Add 19 to both sides
-21+19 = 4x -19 + 19 Combine like terms
-2 = 4x Divide by 4
-2/4 = x
x = - 1/2
Answer: x = - 1/2
or x = -0.5
Which best explains how to graph this location on the coordinate plane ? -
23.4571 to the nearest 10
23.4571 to the nearest 10
asnwer: 23.5
Why do test makers refer to the first term in a sequence as a sub zero sometimes as opposed to a sub 1?
The first term in a sequence is sometimes referred to as [tex]a_0[/tex] as opposed to [tex]a_1[/tex] because [tex]a_0[/tex] represents the initial value
How to explain the sequence statement?The question refers to the difference between the terms
[tex]a_o[/tex] and [tex]a_1[/tex]
The terms in a sequence are represented by a subscript number.
Take for instance a₂ or T₂ represents the second term.
However, when the first term is represented by a₀ instead of a₁.
It means that the sequence has an initial value, other than the first term.
Even though the words "first" and "initial" are synonyms, they do not entirely represent the same thing.
Take for instance, a₀ can be used instead of a₁ in the following scenario
The population of a country is 1000 in 1996 and The country experiences an increment of 250 people every year after 1996.
The above means that:
a₀ = 1000 --- the initial year
a₁ = 1000 + 250 = 1250 ---- the first year after 1996 (i.e. 1997)
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What happens when the function f(x)=cos(x) is transformed by the rule g(x)=f(1/2x)?
A: f(x) is stretched away from the y-axis by a factor of 2.
B: f(x) is compressed toward the y-axis by a factor of 1/2.
C: f(x) is compressed toward the x-axis by a factor of 1/2.
Answer:
A: f(x) is stretched away from the y-axis by a factor of 2
Step-by-step explanation:
Parent function:
[tex]f(x)=\cos(x)[/tex]
Given transformation:
[tex]g(x)=f\left(\dfrac{1}{2}x\right)=\cos \left(\dfrac{1}{2}x\right)[/tex]
Translation:
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis by a factor of} \: \dfrac{1}{a}[/tex]
Therefore, f(x) is stretched parallel to the x-axis (horizontally) by a factor of 2:
[tex]a=\dfrac{1}{2} \implies \dfrac{1}{a}=\dfrac{1}{\frac{1}{2}}=2[/tex]
If A(1,2), B(5,-4) and (-3,2) are the vertices of a triangle, which statement holds true?
A. Triangle ABC is scalene because all side lengths of the triangle are different.
B. Triangle ABC is isosceles because two sides of the triangle are equal in length.
C. Triangle ABC is equilateral because all sides of the triangle are equal in length.
D. Triangle ABC is acute because all angles of the triangle are acute angles.
Answer: A
Step-by-step explanation:
Using the distance formula,
[tex]AB=\sqrt{(5-1)^{2}+(-4-2)^{2}}=\sqrt{16+36}=2\sqrt{13}\\BC=\sqrt{(-3-5)^{2}+(-4-2)^{2}}=\sqrt{64+36}=10\\AC=\sqrt{(-3-1)^{2}+(2-2)^{2}}=4[/tex]
From this, we can conclude that ABC is scalene.
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is A.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The length of different sides are:
[tex]AB = \sqrt{(5-1)^2+(-4-2)^2} = \sqrt{16+36} = \sqrt{52}\rm\ units[/tex]
[tex]BC = \sqrt{(-3-5)^2+(2+4)^2} = \sqrt{64+36} = 10\rm\ units[/tex]
[tex]AC = \sqrt{(2-2)^2+(-3-1)^2} = \sqrt{16} = 4\rm\ units[/tex]
Since the length of all the sides of the triangle is not equal it is a scalene triangle.
Hence, the correct option is A.
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Based on the measures
provided in the diagram,
determine the measure of
the angle 0
(You may assume that point A is the
center of the circle and that DC is a
diameter.)
O 40°
O 50⁰
O 45⁰
1000
A circle is a curve sketched out by a point moving in a plane. The measure of the ∠ACB or θ is 50°.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
In order to solve the problem, we need to draw a line segment AB. Since A is the center of the circle AC and AC both will be the radius of the triangle ΔABC. Since two sides of the triangle are equal, the measure of ∠ABC and ∠ACB will be equal therefore, we can write,
∠ACB + ∠ABC + ∠BAC = 180°
2∠ACB + 80° = 180°
∠ACB = 50°
Hence, the measure of the ∠ACB or θ is 50°.
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Please help me and I need help with my 2 Ixls
if someone can please help me it will make me happy
Answer:
S = 40 square inches
Step-by-step explanation:
Surface area = area of base + area of lateral faces
Area of the base (square):
A = lw
A = 4(4)
A = 16
Area of lateral faces (triangle and there are 4 of them):
A = bh/2
A = 3(4)/2
A = 12/2
A = 6
Since there are 4 lateral faces, multiply the area by 4.
6 x 4 = 24
Surface area = 16 + 24
S = 40 square inches
Can someone help me with this pls.
Answer:
a. 1/20, 1 out of twenty, or 5%
b. three out of ten, 3/10, 30%
c. 3/20 = 3/20 yes.
Step-by-step explanation:
a. It is a fraction. out of the 20 divisions there is only one 20. so there is 1 out of twenty which as a fraction is 1/20. this is equal to 1 divided by 20 wich eqauls 0.05. You move the decimal to the right twice to get 5%.
b. 6 out of twenty, 6/20. They are both even so it can be simplified.
6 ÷ 2 = 3
20 ÷ 2 = 10
It becomes 3/10, 0.3 or 30%
c. I decided that 3, 17, 2, 15, 10, and 9 are the lower right region.
the odds are 6/20 wich we know is 3/10
I only see 20 hits, but out of the 20, 6 are in the lower right region.
the odds from this is 6/20 which we know is 3/10.
We can see that the odds are equal.
Write an explicit formula that represents the sequence defined by the following recursive formula
Gravano Engineering co has the following items appearing in its statement of financial position at the year end:
What is the total for:
1. Non-current assets?
2. Current assets?
Trade payables 39000
2) Cash at bank 14,000
3). Motor vans 25000 4)Inventories 7000
5) Bank overdraft 13,000 6)Property 96,000
7)Trade receivables 43,000
8)Plant and equipment 26,000
9)Trademarks 28,000 10. Fixtures and fittings 17,000 11. Mortgage on property 45,000
Based on the items appearing in Gravano Engineering's Statement of Financial Position at the year-end, the totals for the following are:
1. Non-current Assets = $192,000
2. Current Assets = $64,000
What is a Statement of Financial Position?A Statement of Financial Position is a financial statement that shows an entity's assets, liabilities, and equity.
Assets are items owned by an individual or entity that generate current, future, or potential economic benefits.
Liabilities are financial obligations that an individual or entity owes creditors.
Equity is the difference between assets and liabilities, which refers to the financial benefits accruing to the stockholders.
Data and Calculations:1. Trade payables $39,000
2. Cash at bank 14,000
3. Motor vans 25,000
4. Inventories 7,000
5. Bank overdraft 13,000
6. Property 96,000
7. Trade receivables 43,000
8. Plant and equipment 26,000
9. Trademarks 28,000
10. Fixtures and fittings 17,000
11. Mortgage on property 45,000
Current Assets:2. Cash at bank 14,000
4. Inventories 7,000
7. Trade receivables 43,000
Total current assets = $64,000
Non-Current Assets:3. Motor vans 25,000
6. Property 96,000
8. Plant and equipment 26,000
9. Trademarks 28,000
10. Fixtures and fittings 17,000
Total non-current assets = $192,000
Thus, the total non-current assets are $192,000 and the current assets total $64,000.
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8. Jia's Fashions recently paid a $2 annual dividend. The company is projecting that its dividends will grow by 20 percent next year, 12 percent annually for the two years after that, and then at 6 percent annually thereafter. Based on this information, how much should Jia's Fashions common stock sell for today if her required return is 10.5%?
Answer:
the stock will sell for $59.16
Step-by-step explanation:
P0 = 2 * (1+0.2) / (1+0.105) + 2 * (1+0.2) * (1+0.12) / (1+0.105)^2 +
2*(1+0.2)*(1+0.12)^2 / (1+0.105)^3 +
[(2 * (1+0.2) * (1+0.12)^2 * (1+0.06) / (0.105-0.06)) / (1+0.105)^3 ]
P0 = $59.16
A farmer has 13 cows.a bolt of lightening kill all but 5 of them.how many cows survived?
Answer:
8 cows survived
Step-by-step explanation:
13-x=5
-x=5-13
-x=-8
x=8
give brainliest please!
hope this helps :)
Answer:
all of them
Step-by-step explanation:
a litghing bolt isnt strong inof to kill a cow
find the equation of the function that is graphed.
The equivalent equation of the function that is graphed is g(x) = (x-1)² + 1
Graph of a quadratic functionThe quadratic function is a function that has a leading degree of 2. The parent graph of the given function is f(x) = x²
The vertex of the parabola of the parent function is at the origin. The given curve shows a translation of the function by 1 unit to the right and 1 unit up to have the function g(x) = (x-1)² + 1
Therefore the equivalent equation of the function that is graphed is g(x) = (x-1)² + 1
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The array shown has two numbers filled in: 2 and 7. What does the 2 mean in the
array? What does the 7 mean in the array?
An array data structure is a data structure that consists of a collection of items. In the array, 7 means that the sum of the number cube 1 and number cube 2 is equal to 7(3+4).
What is an array?An array data structure, often known as a simple array, is a data structure that consists of a collection of items, each of which is identifiable by at least one array index or key. A mathematical method is used to determine the location of each element from its index tuple in an array.
In the array, 2 means that the sum of the number cube 1 and number cube 2 is equal to 2(1+1).In the array, 7 means that the sum of the number cube 1 and number cube 2 is equal to 7(3+4).Hence, In the array, 7 means that the sum of the number cube 1 and number cube 2 is equal to 7(3+4).
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please help meeeee I really need it
0.00002165 in scientific notation.
Answer:
2.165 × 10⁻⁵
Step-by-step explanation:
Move the decimal -5 places to the right. For every scientific notation, 10 is the default number you are multiplying the decimal by. The exponent is the number of places you moved the decimal point. The exponent is positive when moving left, negative when moving right.
Hope it helps!
exponential decay functions
Exponential decay function is a form of an exponential function
What are exponential decay function?These are exponential functions that reduce in value as the input value increases.
This in other words, means that the rate of an exponential decay function is less than 1.
An exponential function is represented as:
[tex]y = ab^x[/tex]
Where b is the rate.
When b < 1, the function is an exponential decay function
For instance:
[tex]y = 3(0.9)^x[/tex] is an exponential decay function
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