Answer:
(x+2)(x-2)=32(x+2)(x-2)=32x^2+2x-2x-4=32(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0x^2-36=0(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0x^2-36=0(x+6)(x-6)=0(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0x^2-36=0(x+6)(x-6)=0x-6=0x=6 the length of the original side of the square.(6+2)(6-2)=32(6+2)(6-2)=328*4=32(6+2)(6-2)=328*4=3232=32How much should you invest at 2.4 simple interest in Oder to earn $50 interest in 9 months?
By using the method of interest, principle is 2777.7.
What is interest?An expense associated with borrowing money or other assets is interest. The principal is the amount borrowed, and the interest is calculated as a percentage of the principal for a specific period of time. The expense of borrowing money is interest. It equates to a fee or additional charge the borrower pays the lender for the loaned amount, and is sometimes stated as a percentage. When you make a payment on a loan with simple interest, the money first goes toward the interest for that month and the rest is applied to the principal. S.I. = P R T, where P = Principal, R = Rate of Interest in% per annum, and T = Time, typically calculated as the number of years, is the formula used to compute simple interest.
Given that,
S.I= PTR
Simple interest= 50
Time= 9/12= 0.75
Rate of interest= 2.4
Principle amount=?
S.I= PTR
50= P x 0.75 x 2.4
50= P x 1.8
P = 50X1.8
P= 2777.7
Therefore, principle is 2777.7
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A family of six consisting of a mother, father, and four children line up (shoulder-to-shoulder) for a family portrait in a random order. Find the probability mass function of the random variable X, the number of children located between the father and mother in the photograph.
The probability mass function for this is given by the table that is attached below.
Probability is defined as the proper fraction which signifies the likelihood of an event to occur.
Total number of possible arrangements of 6 people are 6! = 720
Here X can take value 0, 1, 2, 3, or4.
For the probability function : When X= 0 , it means there is no child between mother and father. Taking mother and father as one , number of possible arrangements of 5 people are 5!.
And mother and father can arranged themselves is 2! ways. So for X=0, possible ways are 5! *2 = 240.
Therefore the require probability at X=0 is given by:
P(X=0) = 240 /720 = 0.3333
For the probability function : When X = 1 , then there is one child between mother and father. Number of ways of selecting one child is C(4,1) = 4.
Mother and father can be arrange themselves in 2 ways so possible number of arrangements are 4 * 2 * 4! = 192
Therefore the require probability at X=1 is given by:
P(X=1) = 192 /720 = 0.2667
For the probability function :When X=2 , then there are two children between mother and father. Number of ways of selecting two children is C(4,2) = 6.
Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 2 ways so possible number of arrangements are 6 * 2 * 2* 3! = 144
Therefore the require probability at X=2 is given by:
P(X=2) = 144 /720 = 0.2
For the probability function : When X=3 , then there are three children between mother and father. Number of ways of selecting three children is C(4,3) = 4.
Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 3! ways so possible number of arrangements are 4 * 2 * 3!* 2! = 96
Therefore the require probability at X=3 is given by:
P(X=3) = 96 /720 = 0.1333
For the probability function: When X=4 , then there are 4 children between mother and father. Number of ways of selecting 4 children is C(4,4) = 1.
Mother and father can arranged themselves in 2 ways, children between mother and father can arranged themselves in 4! ways so possible number of arrangements are 1 * 2 * 4! = 48
Therefore the require probability at X=0 is given by:
P(X=4) = 48 /720 = 0.0667
Hence the probability mass function can be represented by a table below.
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a table costs five times as much as a chair a trader bought six more chairs than tables and spent $18594. if a chair costs$ 1033 how many chairs and tables did he buy?
An athlete completes a marathon(42.2 km) at a pace of 3 min per km what was her speed in km/hrs? if the world record for marathon is 2 hrs 3 mins 23 sec what pace must an athlete achieve in order to break the world record
Answer:800
Step-by-step explanation:
x + 4x = 1000
5x = 1000
x = 1000/5 = 200 dollars.
please, help me
Select the interval where g(x)>0
When f(x) > 0, it means that on a graph, the line is above the x-axis.
Solving the Question
Out of all the options, only in -2 < x < -1 is the graph above the x-axis.
For the other two intervals, the graph is below the x-axis.
Answer-2 < x < -1
PLEASE HELP I MISSED OUT ON CLASS BECAUSE I WAS SICK AND I DONT UNDERSTAND
Answer:
A)Linear angles
B) they have a sum of 180
C)25x+5+4+32x=180
57x+9=180
57x=171
x=3
D)25(9)+5=
75+5=80
32(3)+4=
96+4=100
Step-by-step explanation:
Find a polynomial f(x) of degree 4 that has the following zeros.
1, -4, 0, 6
Leave your answer in factored form.
ƒ(x) = 0
X
A polynomial of degree 4 in factored form with zeros 1, -4, 0, and 6 is
f(x) = x(x - 1)(x + 4)(x - 6).
What are polynomials?An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.Any polynomial must have variable exponents that are non-negative integers. The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial.Given:
x₁ = 1
x₂ = -4
x₃ = 0
x₄ = 6
Utilize the fact that x - b is a factor of the polynomial if b is a root.
Simply take each zero, modify its sign, and add an x in front of it to obtain the four factors.
The polynomial is,
f(x) = (x - x₁)(x - x₂)(x - x₃)(x - x₄)
f(x) = (x - 1)(x - (-4))(x - 0)(x - 6)
= (x - 1)(x + 4(x)(x - 6)
Therefore,a 4 degree polynomial in factored form with zeros 1, -4, 0,and 6 is x(x - 1)(x + 4)(x - 6).
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_______1.afraction whose denominator is 3 more than it's numerator x
_______A.if x=6, what is the value of the fraction?
_______B. what is the fraction if the denominator is 8?
_______2 the length of a rectangular garden with an area of 32 square meters and has width w meters
_______A. what is the length of the garden if the width 4 meters?
_______B. find the width of the garden if the length is 16 meters?
________3. the rate of a car traveled 240 kilometers in t hours?
_________A. Find the rate of the car if t= 2.5 hour?
_________B. what is the rate of the car if the time is doubled?
1. A fraction whose denominator is 3 more than it's numerator x: x/(x+3)
A. If x =6, then the value of the fraction is 2/3.
B. If the denominator is 8, then the fraction is 5/8.
2. The length of a rectangular garden with an area of 32 square meters and has width w meters: 32/w.
A. The length of the garden if the width 4 meters = 8 meters
B. The width of the garden if the length is 16 meters = 2 meters
3. The rate of a car traveled 240 kilometers in t hours = 240/t km per hour
A. The rate of the car if t= 2.5 hour is 96 km/hour.
B. The rate of the car if the time is doubled is 120/t.
1. Let 'x' be the numerator. Then the denominator is 3 more than its numerator. So the denominator = x +3.
Hence the fraction whose denominator is 3 more than it's numerator x: x/(x+3).
A. If x = 6, then x+3 = 6+3 = 9.
So x/x+3 = 6/9 = 2/3
So the fraction is 2/3
B. Denominator = 8
⇒ x+3 = 8
⇒ x = 8-3 = 5
So the fraction is x/x+3 = 5/8.
2. Area of the rectangular garden = 32 square meters
⇒ length x width = 32
⇒ length x w = 32
⇒ length = 32/w
So the length of a rectangular garden with an area of 32 square meters and has width w meters is 32/w.
A. Width, w = 4 meters
Then, length = 32/w = 32/4 = 8 meters
B. Length = 16 meters
⇒ 32/w = 16
⇒ w = 32/16
⇒ width, w = 2 meters
3. Distance travelled by the car = 240 kilometers
Let 't' be the time taken in hours.
Then, Rate of the car = Distance / Time taken
⇒ Rate of the car in t hours = 240/t kilometers per hour
A. If t = 2.5 hour, then,
Rate of the car = 240/2.5 = 96 kilometers/ hour
B. If the time is doubled, then time = 2t
Rate of the car = 240/2t = 120/t
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What is the distance between -112 and -80 on a number line?
Answer: 32
Step-by-step explanation:
You need to take -112 and subtract it by -80 to get 32
Hope this helped! :)
The stock market report says that 6 stocks went up for every 7 stocks that went down. If 721 stocks went down yesterday, how many went up? Set up and solve a proportion for the problem.
The number of stocks that went up yesterday given the stocks that went down yesterday is 618.
How many stocks went up yesterday?
Ratio is used compare two or values together. It shows the number of times that one value is contained in another value or values. According to the information provided in the question, the ratio of stocks that go up and the stock that goes down is 6 : 7.
The number of stocks that went up yesterday = (ratio of stocks that went up x number of stocks that went down yesterday) / ratio of stocks that went down yesterday
The number of stocks that went up yesterday =(6 x 721) / 7 = 618
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HELPPPP!!!!!!!!!!!!!!!
Answer: see answers below
Step-by-step explanation:
F(x) is bascially the y
the absolute value means any numbers that you use for x when substituted into x-2 will always be a positive number even if x-2 is negative as with any number 3 or greater, or any number -3 or less.
for the values that are 0, 1, 2, 3, 4 or 0, -1, -2 the answer for f(x) will be a negative number. All other numbers positive or negative for x will result in a positive answer.
So you need to graph your line with an arrow on each end to show it goes to infinity. in your chart you choose a number for x, and the f(x) number (which is equivalent to the y number for purposes of graphing.
I cannot draw on her a graph for you because I don't have that ability without an app for that.
here are some sample points for your chart. THe first number in each parenthesis is x and the second is f(x)
(-1, -2), (-2, -1), (0, -3), (-3, 0), (1, -4), (2, -5), (3-4), (4,-3), (5-2), (6, -1) All other numbers positive or negative for x will result in f(x) being positive.
You only need two sets of points to put on the graph to draw the line through.
So negative values for f(x) can only be -1, -2, -3, -4, -5. x can include all negative numbers through infinity.
Positive will include all positive numbers through infinity for x and f(x).
F(x) cannot decrease beyond -5. x can decrease all numbers through infinity.
A ski gondola carries skiers to the top of a mountain. Assume that the total weights of adult skiers (including their equipment) are normally distributed with a mean of 200 lb and a standard deviation of 40 lb. Further assume that the gondola can carry a maximum of 25 skiers and has a maximum load limit of 5,000 lb. If the gondola is full, it will be overloaded if the mean total weight of the skiers exceeds 5,000 lb / 25 skiers = 200 lb/skier. If the gondola is filled with 25 randomly selected skiers, what is the probability that it will be overloaded? (Round your answer to three decimal places; add trailing zeros as needed.)
If the gondola is filled with 25 randomly selected skiers, the probability that it will be overloaded is; 50%
How to find the mean weight from normal distribution?The formula to find the maximum mean weight of passengers is;
Maximum mean weight = Load limit ÷ number of passengers
We are given;
Load limit = 5000 lb
Maximum number of passengers = 25
Thus;
Maximum mean weight of passengers = 5000 ÷ 25 = 200lb
Let us find the z-score:
z = (max value - mean) / st. dev
z = (200 - 200)/40
z = 0
From online p-value from z-score calculator, the p-value = 0.5 and so that is the probability that it will be overloaded.
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URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
This diagram is used to prove the Pythagorean theorem, and to show that the purple square- the green square= the red square
A. True
B. False
Answer:
true
Step-by-step explanation:
the answer of both the smaller squares added is the same as the andwer of the bigger square
I will give brainliest, like and rating if u solve this right
If ƒ(x) = x³+ 3x² + 4x + 5 and g(x) = 5, then g (ƒ (x)) =_
A) (5x² +15x + 25
B) 5x³+15x²+ 20x + 255
C) 5
D) 225
E) 1125
14. Find the common difference of the arithmetic sequence.
25, 18, 11, 4,...
A 18/25
B 1 7/18
C -7
D 43
Answer:
C -7
Step-by-step explanation:
the numbers keep on decreasing by 7
Your sister is planning her wedding reception. She can have round tables that sit 8 people and rectangular tables that sit 10 people. She plans on having 200 people at the reception altogether. Write an equation that represents the possible tables that may be used to seat 200 people at the wedding.
What are two possible combinations of table types that your sister can use at
her wedding reception? Show your calculations to prove that your amounts are
viable answers to the question.
The equation that represents the possible tables that may be used to seat 200 people at the wedding is 8x + 10y = 200.
The combination will be 10 round tables and 12 rectangular tables; 15 round tables and 8 rectangular tables.
How to illustrate the information?Based on the information, there can be round tables that sit 8 people and rectangular tables that sit 10 people and the total number will be 200.
Therefore, the equation that represents the possible tables is 8x + 10y = 200
where x = number of round table
y = number of rectangular tables
The possible combinations of table types that your sister can use at her wedding reception will be 10 round tables and 12 rectangular tables. This will be:
8x + 10y = 8(10) + 10(12) = 200
Another combination will be 15 round tables and 8 rectangular tables
8x + 10y = 8(15) + 10(8) = 200
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write the equation of a line perpendicular to 12y=2x+10 and passing though the point (-2,-1)
The equation of the line perpendicular to 12y = 2x + 10 and passing though the point (-2,-1) is y = -6x -7.
Writing the equation 12y = 2x + 10 in slope intercept form, we get,
y = (1/6)x + 5/6
The slope of the line is 1/6.
We know that,
Product of slope of two lines perpendicular to each other = -1.
Let the slope of the line perpendicular to the given line be m.
Hence, we can write,
m*(1/6) = -1
m = -6
Let the line perpendicular to the given line be y = mx + c.
It is given that the line perpendicular to the given line goes through (-2,-1).
Hence, we can write,
-1 = -6.(-1) + c
-1 = 6 + c
c = -7
Hence, the slope-intercept form of the line perpendicular to the given line is y = -6x -7.
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What is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%?
Review Later
9.00%
8.75%
11.94%
12.13%
[tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.
In the given question we have to find the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.
Firstly we learn about terms used in this question,
The return needed by either a business or an individual to justify an investment in equity is known as the cost of equity.
The relationship between systemic risk, or the general dangers of investing, and expected return for assets, particularly equities, is described by the Capital Asset Pricing Model.
Since we have to find the cost of equity using the capital asset pricing model. So the formula is
Cost of equity = Risk free rate + Beta * Equity Risk Premium
Risk free rate = 4.5%
Beta = 1.75
Equity Risk Premium = 4.25%
Now putting the value in the formula
Cost of equity [tex]=4.5\%+1.75\times4.25\%[/tex]
Simplifying
Cost of equity [tex]=4.5\%+7.4375\%[/tex]
Cost of equity [tex]=11.9375\%[/tex]
Hence, [tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.
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I will give brainliest, like and rating if u solve this right
TRUE OR FALSE?
Please I need help with this
a. 5x + 3x b. 9s - 3s + 4s
Answer:
Step-by-step explanation:
A) 5x+3x
5x+3x
= 8x
B) 9s-3s+4s
9s-3s+4s
6s+4s
=10s
Tripping the radius of a cylinder! Someone help me please I'm so confused :(
Before change
Dimensions: r= 2 ; h=7
Lateral Surface area= 2πrh= 28π sqyd
Total Surface area= 2πr(h+r)=4π(9)= 36π sqyd
After change(trippling radius)
Dimensions: r= 6 (3*2); h=7
Lateral Surface area= 2πrh= 84π sqyd
Total Surface area= 2πr(h+r)=12π(13)= 156π sqyd
What is surface area of a cylinder?
The total area that is occupied by the cylinder's curved surface, flat base surfaces, and flat surface is known as the surface area of a cylinder. Two separate components, a curved surface area and two flat surface areas make up the cylinder's overall surface area as the area that is covered by the curved surface of the cylinder and the flat surface of its bases.To learn more about surface area of cylinder, refer:
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1. A tool rental company charges $25 for the first hour of a tractor rental. Each additional hour costs $20 per hour. Which statement describes the relationship between total cost and hours?
A It is proportional; each ratio for related pairs is equivalent.
B It is proportional; each x-term is a multiple of the previous term.
C It is not proportional; each ratio y/x for related pairs is not equivalent.
D It is not proportional; each x-term is not a multiple of the previous term.
Answer:
C. It is not proportional. y/x ratios are not equivalent
Step-by-step explanation:
Given a rental charge of $25 for the first hour and $20 for each additional hour, you want to know if the charges are proportional to the time.
ProportionalityIn this situation, if the relationship were proportional, the charge per hour (constant of proportionality) would be the same for every hour. Here, the first hour costs more, so the hourly charge is not constant.
Here, we have, for x=hours, y=dollars, ...
(1, 25) ⇒ y/x = 25
(2, 45) ⇒ y/x = 22.5
(3, 65) ⇒ y/x ≈ 21.67
The y/x values are not constant (because the charge per hour is not constant). The relationship is not proportional.
<95141404393>
Trigonometry Functions of Any Angle CAA point on the terminal side of angle O is given. Find the exact value of the indicated trigonometric function of e.1) (12, 16) Find csc 0.I need help with #2
1) I'll calculate the hypotenuse
hyp = squared root [(16)^2 + (12)^2]
= squared root [ 256 + 144]
2) the answer is letter C. 5/7
3) calculate the hypotenuse
hyp = squared root [(2^2 + (-3)^2]
= squared root [ 4 + 9]
= squared root [13]
sin 0 = -3/squared root 13
= -3squared root (13) / 13
The answer for number three = letter B
While traveling to his grandmother's for Christmas, George fell asleep a quarter of the way through the journey. When
he awoke, he still had to travel half the distance that he had traveled while sleeping. For what part of the entire
journey had he been asleep?
George had been asleep for of the entire journey
(Type an integer or a simplified fraction.)
While traveling to his grandmothers for Christmas, George had been asleep for 50% of the entire journey and this distance is found by reviewing the information given to us.
What is distance travelled?The length of the entire journey taken to get from one point to another is the distance travelled. Travel distance is not a vector. It has no orientation.
In this question,
Let us take that George had been asleep for x distance.
Then according to question, we can form the equation
3/4 = 1/2x + x
3/4 = 3x/2
x = 1/2
so, the total distance travelled is 50% of the entire journey.
What are its displacement and travel distance?Displacement is the straight path between the initial and final points, whereas distance travelled is the actual length the body covers.
What is the travelled distance measured in?The International System of Units defines a meter as the distance unit.
How can velocity be used to calculate distance travelled?
Finding the area under the velocity, in particular when velocity is positive on an interval, allows us to determine the total distance travelled.
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4-5g>39 what is the set for the inequality
Answer:
g
<
−
7
Step-by-step explanation:
What is the sum of all the numbers less than 496 that divide evenly into 496?
Answer:
Step-by-step explanation : devise ----> divide496 = 2*2*2*2*31The 2's can be used in 5 ways, that is, not take anytake 1take 2take 3take all 4the 31 can be used in 2 ways, either take or not take itnumber of factors = 5*2 = 10but that includes taking all or noneif we correspond to none as the factor 1 and if we take all we would get 496the factors would be1, 2, 4, 8, 16, 31, 62, 124, 248, and 496
Which of the following systems linear inequalities does the graph represent? Select all that apply.
To answer this question, first of all, we need to find the equation for each of the lines on the graph. To do so, we have to identify two points for each line, and then use the two-point form equation (of the line) to find the equation of each line.
Then, we have:
Equation of the solid lineWe identify two points: (1, 1) and (2, 2).
Then we have:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Then if we label both points above:
• (1, 1) ---> x1 = 1, y1 = 1
,• (2, 2) ---> x2 = 2, y2 = 2
Therefore:
[tex]\begin{gathered} y-1=\frac{2-1}{2-1}(x-1) \\ y-1=1(x-1)=(x-1) \\ y-1=x-1\Rightarrow y=x-1+1\Rightarrow y=x \end{gathered}[/tex]Therefore, the equation of the line for the solid line is y = x.
Equation of the dotted lineWe can proceed similarly as we did before. Then we have:
The two points are (2, 4) and (4, 8).
Then we can label them as follows:
• (2, 4) ---> x1 = 2, y1 = 4
,• (4, 8) ---> x2 = 4, y2 = 8
[tex]\begin{gathered} y-4_{}=\frac{8-4_{}}{4_{}-2_{}}(x-2) \\ y-4=\frac{4}{2}(x-2) \\ y-4=2(x-2)\Rightarrow y-4=2x-4 \\ y=2x-4+4 \\ y=2x \end{gathered}[/tex]Therefore, the equation for the dotted line is y = 2x.
We need to remember that when we have the symbols < or > the inequality is represented by a dotted line. Conversely, when it appears additionally an equal sign in the inequality symbol, ≥ or ≤ the line is represented as a solid line.
If we see the graph, we can say that the graph is represented by the following inequalities:
[tex]\begin{gathered} y>2x\Rightarrow Dotted\text{ line} \\ y\ge x\Rightarrow Solid\text{ line} \end{gathered}[/tex]Since if we represent them graphically, we have - using a graphing calculator:
We can observe that the shaded area is the same as the one represented in the graph given in the question.
We can prove that if we take a point in the solution region as follows:
1. For example, we can test the point (-2, 2). Then we have:
[tex]\begin{gathered} 2>2(-2)\Rightarrow2>-4\Rightarrow True \\ 2\ge-2\Rightarrow2>-2\Rightarrow True \end{gathered}[/tex]Now, using this we can check if the other system of inequalities is equivalent to this:
We can check the following inequalities:
[tex]\begin{gathered} -2x+y>0\Rightarrow y>2x \\ -x+y\ge0\Rightarrow y\ge x \end{gathered}[/tex]Which is equivalent to the previous one.
In summary, we have that the systems of linear inequalities are the following:
[tex]\begin{cases}-2x+y>0 \\ -x+y\ge0\end{cases}[/tex][Third option]
And
[tex]\begin{cases}y>2x \\ y\ge x\end{cases}[/tex][Fourth option]
[The second and the third options are not answers since both have the symbol, ≥, - and it means that we have two solid lines representing the inequality system.]
[In the first option we have that the first inequality represents a solid line, and this is not the case. The dotted line is represented by y > 2x.]
Slope is -1/2 and (-9,3) is on the line.
the equation of the line will be:
[tex](y-3)=-\frac{1}{2}(x-(-9))[/tex]then
[tex](y-3)=-\frac{1}{2}(x+3)[/tex]and we obtain
[tex]y=-\frac{1}{2}x-\frac{3}{2}+3[/tex]and making the subtraction, we have
[tex]y=-\frac{1}{2}x+\frac{3}{2}[/tex]which is the same as
[tex]y=-\frac{1}{2}(x-3)[/tex]Make h the subject of the formula A = 2nrh + 2nr.2
Given:
The formula is
[tex]A=2nrh+2nr^2[/tex]Required:
Make h the subject of the formula.
Explanation:
We will put formula in terms of h as:
[tex]\begin{gathered} A=2nrh+2nr^2 \\ A-2nr^2=2nrh \\ h=\frac{A-2nr^2}{2nr} \end{gathered}[/tex]Answer:
Hence, above is the answer.
27
X 10
I need to estimate but I don’t understand
Answer: 270
Step-by-step explanation: A tip for multiplying a number with any power of 10 is to just "add" a 0 to the end of the number depending on how many 0's there are in the power of 10.
For example, there is one 0 in 10. So I would just add a 0 to the end of 27 to get 270. If I were to multiply 27 by 100, there are two 0's in 100 so it would be 2700. 27 x 1000 would be 27000.
Hope this helped