Before carrying out rotation transformation, the coordinates of the vertices of the pre-image are;
A (3, -6)
B(1, 2)
C (7, -1).
What is the effect of clockwise rotation transformation?We are given the coordinates of the transformed image as:
A'(6, 3),
B'(–2, 1),
C'(1, 7).
We need to find the coordinates of the pre-image A, B and C.
The rule for rotation of 90° about the origin is (x,y) ---> (-y,x).
But we need to find the coordinates of the vertices of the pre-image.
So, we need to apply rule (-y,x) ---->(x,y).
Applying the 90 degrees clockwise rotation rule,
A'(6, 3) -----> A (3, -6)
B'(–2, 1) -----> B(1, 2)
C'(1,7) -----> C (7, -1).
Therefore, coordinates of the vertices of the pre-image are
A (3, -6)
B(1, 2)
C (7, -1).
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Complete question is;
After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?
Write this equation in standard form.
x^2+y^2-6x-6y+2=0
Show work.
The equation in standard form is mathematically given as
[tex](x-3)^2 +(y-3)^2 = 4^2[/tex]
This is further explained below.
What is a standard form.?Generally, A mathematical notion, such as an equation, number, or expression, maybe written down in a form called a standard form, which is a form that adheres to a predetermined set of guidelines.
The standard form is used if a condensed representation of a very big or very tiny number is required.
For instance, the number 4.5 billion years is represented by the numeral 4,500,000,000.
In conclusion,
[tex]x^2 + y^ 2- 6x-6y+2=0[/tex]
Therefore
[tex](x^2 - 6x) +(y^2-6y) +2 =0\\\\(x^2 - 2(3)x +3^2) -3^2 + (y^2 - 2(3)y +3^2) -3^2+2 = 0\\\\(x-3)^2 +(y-3)^2 = 4^2[/tex]
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If a and b are integers such that -6 ≤ a ≤ 3 and -4 ≤ b < 5, what is the least possible value of a times b?
SOLUTION
From the question, it means that
[tex]\begin{gathered} a=-6,-5,-4\text{ . . . . . .3} \\ b=-4,-3,-2\text{ .. .. . . . . .4} \end{gathered}[/tex]The least possible value of a and will be a ngative number, gotten by multiplying a negative value by a positive value. So this should be
the smallest value of a, that is the -6 multiplied by the biggest value of b = 4
[tex]-6\times4=-24[/tex]Hence the answer is -24
Why is square root of 15 to the nearest tenth 3.92
The reason why the square root of 15 to the nearest tenth is 3.9 is because the square root was rounded off to the tenth digit.
How to round off to tenth?When rounding off to the tenth digit, the decimal will need to be rounded off to number that comes immediately after the decimal.
This means that if the number that is two places after the decimal is 5 or more, the number in the tenth place (one digit after decimal) will be rounded up.
The square root of 15 is:
= √15
= 3.87298
The second number after the digit is 7 which is higher than 5 so the number 8 will need to be rounded up to 9 to get:
= 3.9
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which of the following is equivalent to the expression below?(attached is the question)
We know that
[tex]\begin{gathered} 36=6^2 \\ \text{and} \\ \sqrt[]{36x^3}=\sqrt[]{36}\cdot\sqrt[]{x^3} \end{gathered}[/tex]Square roots can be expressed as a fraction on the exponent:
[tex]\begin{gathered} \sqrt[]{36x^3}=(36x^3)^{\frac{1}{2}} \\ \sqrt[]{36}\cdot\sqrt[]{x^3}=\sqrt[]{6^2}\cdot\sqrt[]{x^3} \\ =6^{\frac{2}{2}}\cdot x^{\frac{3}{2}} \\ =6x^{\frac{3}{2}} \end{gathered}[/tex]Answer: CIs the list of no. 3,9,15,21 ........ From an Ap
The given list of numbers 3,9,15,21..form an Arithmetic Progression(AP).
What is Arithmetic Progression?A series in which the differences between each pair of following terms are the same is known as an arithmetic progression (AP). A fixed number is added to the term preceding it in the sequence to obtain each term, with the exception of the initial term.
Given list of numbers is 3,9,15,21 ...
To determine whether the series is an Arithmetic Progression, find the difference of the terms which should be constant in an AP.
9 - 3 = 6
15 - 9 = 6
21 - 15 = 6
Therefore, as each term of the given series differs from its preceding term by 6 it is an AP.
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Complete the following equation using <, >, or = 120%___1
The answer to the expression 120% (_____) 1 is:
120% > 1. See the explanation related to the percentage problem below.
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently indicated by the percent symbol, "%."
To overcome the above problem, we must transform the two numbers into the same form.
Because adding zeroes to the ending of a decimal does not modify the value, we know that 1 = 1.00.
To convert a decimal to a percentage, multiply it by 100 and add a percent sign.
1.00 * 100 = 100%
Hence, 1 = 100%
Because 120% is greater than 100%, it is right, therefore, to state that:
120% > 1
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Suppose the current cost of gasoline is $3.10 per gallon. Find the current price index number, using the 1975 price of 56.7 cents as the reference value.
The current price index is _____
(Round to one decimal place as needed.)
a box shaped as a cube has an edge of 13 inches. if a kickball with a diameter of 11 inches is placed inside of it how much of the space is not filled?(to the nearest cubic inch)
we get that the volume of each object is
[tex]\begin{gathered} V_{\text{box}}=13^3=2197 \\ V_{\text{ball}}=\frac{4}{3}\cdot\pi\cdot(5.5)^3\approx696.90997032\approx697 \end{gathered}[/tex]so the reamining space is:
[tex]2197-697=1500[/tex]WILL GIVE BRAINIEST TO THE FRIST ANSWER CORRECT!!!!!!
Five friends ate lunch and spent a total of $63.75. They each bought the same meal for $9.75, and they each bought the same dessert.
Write and solve an equation to determine the cost of the dessert, d.
(A) 5(9.75)d = 63.75; d = 1.31
(B)5(9.75 + d) = 63.75; d = 3.00
(C) 5d + 9.75 = 63.75; d = 10.80
(D)05(9.75) + d = 63.75; d = 15.00
The written and solved equation to determine the cost of the desserts, d is 5(9.75 + d) = 63.75; d = 3.00
How to solve an equations?Five friends ate lunch and spent a total of $63.75.
They each bought the same meal for $9.75, and they each bought the same dessert.
The equation to determine the cost of the dessert, d can be represented as follows:
Hence,
5 (9.75 + d) = 63.75
48.75 + 5d = 63.75
Therefore, let's use the equation to solve for d.
48.75 + 5d = 63.75
subtract 48.75 from both sides of the equation
63.75 - 48.75 = 5d
15 = 5d
divide both sides of the equation by 5
15 / 5 = 5d / 5
d = 3
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A certain star is 4.1 × 10² light years from the Earth. One light year is about 5.9 × 10¹² miles. How far from the earth (in miles) is the star?
Answer:
=24.19×10^14
Step-by-step explanation:
we will just all add to get the distance
=4.1×10²×5.9×10¹²
=4.1×5.9×10²×10¹²
=24.19×10^14
can yall help with this pls and ty
Answer:
4 1/3
Step-by-step explanation:
I believe it is 4 1/3 because all the other ones like 9=3 and 12=4 are divided by 3 so if you divide 14 by 3 you get 4 1/3 as your answer.
리 20 Use the figure below to determine the measures of the following angles. 21 X 42 35) m 21 - 36) m 22
I need help please!
Solving the Question
We're only given one angle: the angle that measures 35°.
This angle and ∠1 are supplementary angles, meaning they add up to 180°. To find ∠1, subtract 35 from 180:
180 - 35 = 145°
The angle and ∠2 are corresponding angles, meaning they are on the same sides of the diagonal line and the transversal.
Corresponding angles are always equal.
Therefore, ∠2 = 35°.
Answer∠1 = 145°
∠2 = 35°
Express the confidence interval (78.5,154.7) in the form of ¯x± ME (Error Bound).
The expression of the confidence interval (78.5, 154.7) in the form of x¯ ± ME is; CI = 116.6 ± 38.1
How to find the Confidence Interval?
We are given the confidence interval as;
CI = (78.5, 154.7)
Now, we want to express the given confidence interval in the error bound form which is; x¯ ± ME
where;
x¯ is sample mean
ME is margin of error
Now, the boundaries of the interval as two points is the midpoint between them which would be (78.5 + 154.7)/2 = 116.6.
This is right in the middle of 78.5 and 154.7.
This value of 116.6 is the sample mean represented by x¯, since x¯ is in the middle of the interval. This means that 78.5 and 154.7 are the same distance (the margin of error, ME) away from 116.6. .
116.6 - 78.5 = 38.1 and 154.7 - 116.6 = 38.1
Thus, the expression is;
CI = 116.6 ± 38.1
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1) A manufacturing unit produced 112, 336 and 1008 Easter baskets on days one,
two and three. If the unit continues to manufacture baskets at the same rate,
how many baskets will it produce on the 4th, 5th and 6th day respectively?
There are 3024, 9072 and 27216 baskets are produced in 4th, 5th and 6th days respectively.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A manufacturing unit produced 112, 336 and 1008 Easter baskets on days one, two and three.
Now,
On first day, there are 112 baskets.
And, On second day, there are 336 baskets.
So, Clearly 112 x 3 = 336
That's mean every day the number of produce baskets are three times the previous day.
So, On fourth day;
Number of Easter basket produce = 1008 x 3 = 3,024
On fifth day;
Number of Easter basket produce = 3,024 x 3 = 9,072
On sixth day;
Number of Easter basket produce = 9,072 x 3 = 27,216
Thus, There are 3024, 9072 and 27216 Easter baskets are produced in 4th, 5th and 6th days respectively.
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15. Choose the correct answer for this problem:
1/7 x ?
Thank you!
The required fraction is 1/14.
What is fraction?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.
For illustration: There are five kids in all.
Five in three are female. So, three-fifths of the population are girls.
Of the 5, two are boys. So, two-fifths of the population are boys.
As in this question 1 out of the 2 boxes are shaded.
Thus the required fraction is 1/2
Thus the required number is [tex]\frac{1}{7}[/tex]×[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{14}[/tex].
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How do I solve this problem?
To solve this question we will compute the magnitude of each vector.
Recall that the magnitude of a vector
[tex]a\hat{i}+b\hat{j}[/tex]is:
[tex]\parallel a\hat{i}+b\hat{j}\parallel=\sqrt[]{a^2+b^2}.[/tex]Therefore, the speed of the first car is:
[tex]\parallel26\hat{i}+31\hat{j}\parallel=\sqrt[]{26^2+31^2}\text{.}[/tex]Simplifying the above equation we get:
[tex]\parallel26\hat{i}+31\hat{j}\parallel=\sqrt[]{676^{}+961}=\sqrt[]{1637}\approx40.46.[/tex]The speed of the second car is:
[tex]\parallel40\hat{i}\parallel=\parallel40\hat{i}+0\hat{j}\parallel=\sqrt[]{40^2+0^2}\text{.}[/tex]Simplifying the above equation we get:
[tex]\parallel40\hat{i}\parallel=\sqrt[]{40^2}=40\text{.}[/tex]Answer:
The first car is the faster car.
Speed= 40.46.
1) A local company has a fixed cost of$45,507.00 each vear, and $34,614.00 foreachperson employed for the yearNext year, the company projects thatcosts will total $2.817,027.00. Whichequation below could be used todetermine how many people thecompany intends to employ next yearA. 2.817,027 = 34,644p + 45,507B. 2,817,027 = 45,507p +34 644C. 2,817,027 = 34,644p --- 45,507D. 2,817,027 = 34,644(p+ 45,507)
we have the following:
[tex]\begin{gathered} \text{total cost}=\text{variable cost + fixed cost } \\ $2817027=$34644\cdot p+45507 \end{gathered}[/tex]therefore, the answer is the first option
Josiah makes six 3-point baskets in his basket ball game. For questions 5a-5d choose yes or no tell if the equation shows a way to find the number of points Josiah scores
The only effective methods for determining the number of points are 5a and 5c.
What exactly are algebraic word issues?Solving algebraic word problems involves breaking down sentences into equations and then figuring out how to solve those equations.
To construct the equations we need, we will only need to employ one variable and basic arithmetic operations. The variable often represents an uncertain number in a real-world scenario.
Given that Josiah scores six three-pointers during his basketball game, 6*3 = 18, which is general multiplication; or adding three times six times, would be a workable choice for determining the number of points.
Therefore, the two viable alternatives for determining Josiah's point total are 5a and 5c.
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HELP! 100 POINTS!!!
1948 Olympics
Men's 100m Freestyle Swim Finals
Competitor Time
Wally Ris 57.3s
Alan Ford 57.8s
Géza Kádas 58.1s
Keith Carter 58.3s
Alex Jany 58.3s
Per-Olof Olsson 59.3s
Zoltán Szilárd 59.6s
Taha Youssef El-Gamal 1:00.5s
2012 Olympics
Men's 100m Freestyle Swim Finals
Competitor Time
Nathan Adrian 47.52s
James Magnussen 47.53s
Brent Hayden 47.80s
Yannick Agnel 47.84s
Sebastiaan Verschuren 47.88s
Cesar Cielo 47.92s
Hanser Garcia 48.04s
Nikita Lobintsev 48.44s
A. Calculate the mean and range for each set of data. Make sure to label each measurement in your answer.
B. Make two inferences based on your results from part A. Use complete sentences in your answer.
A. Mean and range for each set of data is given by:
Data 1:
Mean is equal to 58.59375
Range is equal to 3.2s
Data2:
Mean is equal to 47.87125
Range is equal to 0.92
B. Two inference based on results from part A is :
Mean of data1 is better than data2.
Range of data2 is less spread as compare to data1.
As given,
From the given values of data1 :
Note: 1:00.5s is 60.5s
57.3s, 57.8s, 58.1s , 58.3s, 58.3s, 59.3s, 59.6s, 60.5s
Mean = (Sum of all values)/ (Total number of values)
= (57.3+ 57.8+ 58.1+ 58.3+ 58.3+ 59.3+ 59.6+ 60.5)/8
= 468.75/8
= 58.59375
Range = Highest value -lowest value
=60.5 -57.3
= 3.2s
From the given values of data2 :
47.52s,47.53s, 47.80s, 47.84s, 47.88s, 47.92s, 48.04s, 48.44s
Mean =(47.52+47.53+ 47.80+ 47.84+ 47.88+ 47.92+ 48.04+ 48.44)/8
=382.97/8
= 47.87125
Range = 48.44 -47.52
= 0.92
Therefore,
A. Mean and range for each set of data is given by:
Data 1:
Mean is equal to 58.59375
Range is equal to 3.2s
Data2:
Mean is equal to 47.87125
Range is equal to 0.92
B. Two inference based on results from part A is :
Mean of data1 is better than data2.
Range of data2 is less spread as compare to data1.
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Eleanor owns a coffee shop.
She uses half a litre of mayonnaise each day.
Mayonnaise costs £2.45 for a 1 litre jar and £4.75 for a 2 litre jar.
Eleanor buys enough mayonnaise to last for 14 days.
What is the lowest price Eleanor can buy this mayonnaise for?
Show your working.
Mayonnaise cost of £4.75 for a 2 liter jar lowest price Eleanor can buy.
What is unitary method?This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.
How to Apply the Unitary Method
Let's first list the data that we currently have. The number of ice creams is 5. It costs $125 for 5 ice creams.
step 1:Let's start with finding the price of one ice cream. Divide the entire cost of ice cream by the total number of ice creams to get at that. A single ice cream will cost you 125 divided by the amount of ice creams, or 25 cents. Consequently, 1 ice cream costs $25.
Step 2: To calculate the price of three ice creams, multiply the price of one ice cream by the quantity. Cost of 1 ice cream x number of ice creams = 25 x 3 = $75 is the price of 3 ice creams. The final cost is $75, which is the price of three ice creams.
Given:
Cots of 1 liter jar of Mayonnaise (I) = 2.45
Cost of 2 liter jar of Mayonnaise (II)=4.75
Cots of 1 liter jar of Mayonnaise (II)= 4.75/2= 2.375
If she eats half liter Mayonnaise in a day
So, she eat in 14 days = 0.5 x 14 = 7 liter
Hence, Mayonnaise cost of £4.75 for a 2 liter jar lowest price Eleanor can buy.
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Liar, liar! From experience, we know that a certain lie detector will show a positive
reading (indicating a lie) 10% of the time when a person is telling the truth. Suppose that
a random sample of 5 suspects is subjected to a lie detector test. Find the probabil-ity of
observing no positive readings if all suspects are telling the truth.
Probability is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability of observing no positive reading if all the subjects are telling the truth is 9/10.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Positive reading when telling the truth = 10%
No positive reading when telling the truth = 90%
The probability of observing no positive reading if all the subjects are telling the truth
= 90%
= 90/100
= 9/10
Thus,
The probability of observing no positive reading if all the subject are telling the truth is 9/10.
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The figure shows JN and KM intersecting at pointL.What value of x proves JK || MN ?
If JK || MN, then angle JKM is equal 61;
Also, angle JLK = 39 degrees as it is opposite angle to MLN.
Thus;
[tex]\begin{gathered} 3x+5+39+61=180\ldots\ldots\ldots\ldots\text{.sum of angles in triangle JLK} \\ 3x+105=180 \\ 3x=180-105 \\ 3x=75 \\ x=\frac{75}{3} \\ x=25 \end{gathered}[/tex]Thus x= 25 proves that JK || MN
The surface of a city playground is being covered with rubber mulch, which is shredded rubber made from recycled tires. A city worker measures the dimensions of the playground as shown. The recommended depth of the mulch is 4 inches. A 1-ton bag of mulch contains about 3 cubic yards of mulch. How many bags of mulch are needed to cover the surface of the playground?
The width is 40.5 and the Length is 66.75
The number of bags of mulch that is needed to cover the playground is 3,605 bags.
How many bags of mulch is needed?The first step is to determine the volume of the surface of the city playground. The volume is the product of the length, width and height of the playground.
Volume = length x width x height
4 x 40.5 x 66.75 = 10,813.50 inches³
The second step is to determine the number of bags of mulch that is needed to cover the surface of the playground.
Number of bags of mulch = volume of the playground / volume one bag can cover
10,813.50 inches³ / 3 = 3,604.5 bags ≈ 3,605 bags
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2 hr 20 min, 5 hr 15 min
Answer:
7hrs 35mins
Step-by-step explanation:
addition 2hrs 15 mins +5hrs 20 mins
Kylie brought 5 pears to soccer practice to share with her teammates. She cuts each pear into thirds. Howmany slices of pears does she have to share with her teammates? Which equations can you use to solvethe problem?
Kylie has 5 pears and she divide each pear into 3.
So 1 pear will become 3 slices.
Then 5 pears will be 5 x 3 = 15 slices.
The answer is 15 slices
he equation you can use is :
umber of slices = 5 x 3
Answer:
The answer is 15
A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 58
5 52
7 48
10 42
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 62 through the point 1 comma 60
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 62 through the point 1 comma 59
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
The linear equation relating the given condition is y + 10x - 62 = 0 .
Each solution in the scenario with two variables can be understood as the Cartesian coordinate system of such a point on the Euclidean plane.
A line in the Euclidean space is formed by a linear equation's solutions, and every line may be thought of as the collection of all solutions to a linear equation with two variables. This is where the term "linear" for this class of equations came from. In the Euclidean space of dimension n, the equations of a linear equation with n variables generate a hyperplane (a subset of dimension n 1).Let the linear relation between the two variables be given by y=mx + c
Now we put the values to get the constants.
58 = 2m + c
52 = 5m + c
solving we get :
52 - 5m = 58 - 2m
or, -6 = 3m
or, m = -2
Now we put those values in the equations
52 = 5m + c
or, 52 = -10 + c
or, c = 62
The equation relating the sunglasses is y + 10x - 62 = 0 .
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Answer: it's A if ur on that question six flvs question counting that was so hardddddddddddddddddddddddddddd
Step-by-step explanation:
Answer this please please
Answer:
8
Step-by-step explanation:
Given: # of girls = 5+2x boys
GIRLS = 21
(21-5)/2
= 16/2
=8
x3 =x2 (?)
I dentify the missing factor!!!!!
The missing factor in the given expression x³ = x²(?) is; x
How to solve laws of exponents?
The laws of exponents are;
1) When multiplying like bases, keep the base the same and add the exponents.
2) When raising a base with a power to another power, keep the base the same and multiply the exponents.
3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.
Now, we are given the expression;
x³ = x²(?)
The question mark indicates a missing term. Thus, we will use division property of equality to divide both sides by x² to get;
x³/x² = x
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Find the volume and surface area of each prism one prism a 3 cm x 3 cm x 3 cm to prism beat 5 cm x 5 cm x 1 cm three compare the volume of the prisms and then there are surface areas does the prism with a greater volume also have the greatest surface area?
The volume of prism A and B are 27 cm³ and 25 cm³ respectively and the Surface area of prism A and B are 54 cm² and 70 cm² respectively.
No, the prism with a greater volume doesn't always have the greatest surface area.
What is the Volume and Surface Area of a Prism?The area that a prism takes up is referred to as its volume. A prism is a solid, three-dimensional structure with two identical faces and additional faces that resemble parallelograms. It is a polyhedron whose nomenclature is influenced by the various basic shapes. The total space filled by the flat faces of a prism is referred to as its surface area. Calculating the sum of the areas of all the faces (or surfaces) in a 3D plane, or the total space occupied by all the faces of the specific type of prism will yield the surface area of the prism.Given:
Prism B is a rectangular prism, whereas prism A is a cube.
The prism's volume is determined by
Volume = length × width × height
So, the Volume of prism A whose each side 3 cm is,
Volume of prism A = 3 × 3 × 3 = 27 cm³
Volume of prism B with sides 5 cm,5 cm, and 1 cm is
Volume of prism B = 5 × 5 × 1 = 25 cm³
The cube's surface area is 6a², where a is one of the cube's sides. So
Surface Area of prism A = 6 × (3)² = 6 × 9 = 54 cm²
Surface area of the rectangular prism is given by,
2(length × width + length × height + width × height)
Surface Area of prism B = 2(5×5 + 5×1 + 5×1)
= 2(25 + 5 + 5)
= 2 × 35 = 70 cm²
From the above calculations, it is clear that the prism with a greater volume doesn't always have the greatest surface area.
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Graph the function by first finding the relative extrema. f(x) = x + 4x2 - X-4 O 2 O I need help with this.
The equation is:
[tex]f(x)=x^3+4x^2-x-4[/tex]So to know that, we can find the intercept in the y axis by replacing x=0 so:
[tex]\begin{gathered} y=0^3+4(0)^2-0-4 \\ y=-4 \end{gathered}[/tex]So if you see the functions the only one that intercept the y axis in -4, then the solution is option (D)