ANSWER FOR BRAINLIST AND HEARTS DUE TODAY
Solve m^2 − 6m = 3. Use the Quadratic Formula. Leave your answers as simplified radicals.
Show ALL your work.
Answer:
m = 3 + 2√3 or m = 3 - 2√3
Step-by-step explanation:
The given equation is:
m^2 - 6m = 3
We can rewrite the equation in standard quadratic form as:
m^2 - 6m - 3 = 0
We can use the quadratic formula to solve for m:
m = [-b ± √(b^2 - 4ac)] / 2a
where a = 1, b = -6, and c = -3.
Substituting these values, we get:
m = [-(-6) ± √((-6)^2 - 4(1)(-3))] / 2(1)
m = [6 ± √(36 + 12)] / 2
m = [6 ± √48] / 2
m = [6 ± 4√3] / 2
Simplifying the expression, we get:
m = 3 ± 2√3
Therefore, the solutions to the equation are:
m = 3 + 2√3 or m = 3 - 2√3
If this helps, please mark my answer as brainliest so i can help you more!:)
Answer:
[tex]x=3+2\sqrt{3}\\\\ x=3-2\sqrt{3}[/tex]
Step-by-step explanation:
The quadratic formula is:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore, to solve the given equation using the quadratic formula, first subtract 3 from both sides of the equation so that it is in the required form.
[tex]m^2-6m-3=3-3[/tex]
[tex]m^2-6m-3=0[/tex]
Comparing the coefficients:
a = 1b = -6c = -3Substitute the values of a, b and c into the formula and solve for x:
[tex]\implies x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(-3)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{6 \pm \sqrt{36-4(-3)}}{2}[/tex]
[tex]\implies x=\dfrac{6 \pm \sqrt{36+12}}{2}[/tex]
[tex]\implies x=\dfrac{6 \pm \sqrt{48}}{2}[/tex]
Rewrite 48 as a 4² · 3:
[tex]\implies x=\dfrac{6 \pm \sqrt{4^2 \cdot 3}}{2}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
[tex]\implies x=\dfrac{6 \pm \sqrt{4^2} \sqrt{3}}{2}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies x=\dfrac{6 \pm 4 \sqrt{3}}{2}[/tex]
Simplify:
[tex]\implies x=\dfrac{6}{2}\pm\dfrac{4 \sqrt{3}}{2}[/tex]
[tex]\implies x=3\pm2 \sqrt{3}[/tex]
Therefore, the values of x are:
[tex]x=3+2\sqrt{3}\\\\ x=3-2\sqrt{3}[/tex]
Let v be the vector from initial point P₁ to terminal point P2. Write v in terms of i and j.
P₁ = (-5,3), P₂ = (-2,6)
V=
(Type your answer in terms of i and j.)
The value of v in terms of i and j is v = 3i + 3j
We are given that;
P₁ = (-5,3), P₂ = (-2,6)
Now,
To find the component form of a vector, we need to subtract the coordinates of the initial point from the coordinates of the terminal point3.
We have P₁ = (-5,3) and P₂ = (-2,6).
v = P₂ - P₁ = (-2 - (-5), 6 - 3) = (3, 3). We can write v in terms of i and j as v = 3i + 3j.
Therefore, by vectors the answer will be v = 3i + 3j.
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(c) log, 12-( log, 9+ log 1 3 log, 8), write a single form equation
What is the answer to this question
The maximum profit that can be made is $1737.82
What is an equation?An equation is an expression showing the relationship between numbers and variables using mathematical operators.
The profit function is the difference between the revenue and cost of a commodity. Given that:
Revenue, R(x) = 700x - 11.3x²
Cost, C(x) = 8068 - 34.25x
Profit, P(x) = Revenue - Cost
P(x) = (700x - 11.3x²) - (8068 - 34.25x)
P(x) = 665.75x - 11.3x² - 8068
The maximum profit is at P'(x) = 0; hence:
P'(x) = 665.75 - 22.6x
665.75 - 22.6x = 0
22.6x = 665.75
x = 29.45
P(29.45) = 665.75(29.45) - 11.3(29.45)² - 8068
P(29.45) = 1737.82
The profit to be made is $1737.82
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The graph shown corresponds to someone who makes
Total earnings
80
60
40
20
1
2
Hours worked
OA. $40 a day
B. $40 an hour
C. $20 an hour
D. $20 a day
The graph shown corresponds to someone who makes: C. $20 an hour.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the total earnings in dollars.x represents the hours worked.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 20/1 = 40/2 = 60/3 = 80/4
Constant of proportionality, k = 20.
Therefore, the required linear equation or function is given by;
y = kx
y = 20x
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Fwam and Eva are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Fwam is gar miles away from the stadium and Eva is 396 miles away from the stadium. Fwam is driving along the highway at a speed of 42 miles per hour and Eva is driving at speed of 65 miles per hour. Let F represent Fwam's distance, in miles, away from the stadium t hours after noon. Let E represent Eva's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine how far both Fwam and Eva are from the stadium at the moment they are an equal distance from the stadium.
Fwam and Eva are an equal distance of 69 miles away from the stadium when the time t = 3 hours
Given data ,
The formula for the distance (F) of Fwam from the stadium is:
F(t) = 327 - 42t
Since Fwam is travelling at a 42 mph pace, his distance from the stadium is reducing at a 42 mph rate.
The formula for Eva's separation from the stadium is:
E(t) = 396 - 65t
Eva's distance from the stadium also shrinks at a pace of 65 miles per hour as she drives at a speed of 65 mph.
Set F(t) = E(t) and solve for t to get the time at which Fwam and Eva are equally far from the stadium
On simplifying the equations , we get
327 - 42t = 396 - 65t
Adding 65t to both sides:
65t + 327 - 42t = 396
23t + 327 = 396
Subtracting 327 from both sides:
23t = 396 - 327
23t = 69
Dividing both sides by 23:
t = 69 / 23
t = 3 hours
Hence , at t = 3 hours after noon, both Fwam and Eva are an equal distance of 69 miles away from the stadium.
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The complete question is attached below :
Fwam and Eva are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Fwam is gar miles away from the stadium and Eva is 396 miles away from the stadium. Fwam is driving along the highway at a speed of 42 miles per hour and Eva is driving at speed of 65 miles per hour. Let F represent Fwam's distance, in miles, away from the stadium t hours after noon. Let E represent Eva's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine how far both Fwam and Eva are from the stadium at the moment they are an equal distance from the stadium.
50 POINTS ANSWER FOR BRAINLIST SHOW YOUR WORK
Answer:
a) Two real solutions.
b) Solutions: y = -6, y = 12
Step-by-step explanation:
The discriminant is defined as the expression b² - 4ac, which appears under the square root sign in the quadratic formula.
The value of the discriminant determines the nature of the solutions to the quadratic equation:
[tex]\boxed{\begin{minipage}{12 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real solutions.\\when $b^2-4ac=0 \implies$ one real solution.\\when $b^2-4ac < 0 \implies$ no real solutions (two complex conjugate solutions).\\\end{minipage}}[/tex]
To find the number and type of solutions of the given quadratic equation, first rewrite the equation in the form ax² + bx + c = 0.
[tex]\begin{aligned}(y-3)^2-10&=71\\y^2-6y+9-10&=71\\y^2-6y-1&=71\\y^2-6y-72&=0\end{aligned}[/tex]
Compare the coefficients:
a = 1b = -6c = -72Substitute the values of a, b and c into the discriminant formula:
[tex]\begin{aligned}b^2-4ac&=(-6)^2-4(1)(-72)\\&=36-4(-72)\\&=36+288\\&=324\end{aligned}[/tex]
As the discriminant of the given equation is greater than zero, there are 2 real solutions.
To solve the equation, we can use the quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when}\;\;ax^2+bx+c=0[/tex]
As we have already calculated that the discriminant is 324, we can substitute this, along with the values of a and b, into the formula:
[tex]\implies y=\dfrac{-(-6) \pm \sqrt{324}}{2(1)}[/tex]
[tex]\implies y=\dfrac{6 \pm \sqrt{324}}{2}[/tex]
Solve for y:
[tex]\implies y=\dfrac{6 \pm 18}{2}[/tex]
[tex]\implies y=3 \pm 9[/tex]
[tex]\implies y=-6, 12[/tex]
Therefore, the solutions of the given equation are:
y = -6y = 12Help. Confused. Pic below
Answer:
Step-by-step explanation:
I agree it's convenience and biased.
It's the easiest way to convey a survey so it is convenient.
it is biased because not everyone has accessible to modern technology, or that particular social media app. Not all park users use social media. It is biased because it is targeting a younger demographic, but excludes the youngest demographic as well, that are not allowed ot have social media.
Answer:
I agree it's convenience and biased.
It's the easiest way to convey a survey so it is convenient.
it is biased because not everyone has accessible to modern technology, or that particular social media app. Not all park users use social media. It is biased because it is targeting a younger demographic, but excludes the youngest demographic as well, that are not allowed ot have social media.
Step-by-step explanation:
U={31,32,33……,50}
A={35,38,41,44,46,50}
B={32,36,40,44,48}
C= {31,32,41,42,48,50}
Find AorB
Find BandC
In the given sets, the values of A or B and B and C are:
A or B = {32, 35,36, 38, 40, 41, 44, 46, 48, 50}
B and C = {32, 48}
Set theory: Determining the intersect and union of A and BFrom the question, we are to determine the values of A or B and B and C in the given set.
From the question,
The universal set is
U = {31,32,33……,50}
and
A={35,38,41,44,46,50}
B={32,36,40,44,48}
C= {31,32,41,42,48,50}
A or B means we should find the union of A and B. That is, the elements present in A or B or both
A or B = {32, 35,36, 38, 40, 41, 44, 46, 48, 50}
B and C means we should find the intersect of B and C. That is, the elements that present both in B and C
B and C = {32, 48}
Hence,
A or B = {32, 35,36, 38, 40, 41, 44, 46, 48, 50}
B and C = {32, 48}
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what is the value of x? right triangles and trigonometry.
Answer:
The value of x is 10√2, so A is correct.
Step-by-step explanation:
In an isosceles right triangle, the length of the hypotenuse is √2 times the length of a leg. Since each leg has length 10, the hypotenuse has length 10√2. A is correct.
A virus takes 5 days to grow from 90 to 200. How many days will it take to grow from 90 to 410? Round to the nearest whole number.
The number of days it will take the virus to grow from 90 to 410 is 15 days.
What is the growth rate of the virus?The growth rate of the virus is calculated as follows;
growth rate = (200 - 90) / 5
growth rate = 22 per day
The number of days it will take the virus to grow from 90 to 410 is calculated as follows;
growth = 410 - 90
growth = 320
Number of days = 320 / 22/day = 14.55 ≈ 15 days
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this question!
thank you!
Answer:
7
Step-by-step explanation:
solve for x by using the quadratic formula 20x^2-33x+10=0
The number is less than 6,000.
The number is odd.
2/4 of the digits are even.
The digit in the thousand's place is the number
of days in a typical school week.
The digit in the ten's place is twice the value of the
digit in the hundred's place.
The digit in the one's place is the number of sides on a nonagon.
The digital root of the number is the number of sides on a stop sign.
The number is 4,175.
How do we explain?points to note:
The number is less than 6,000.The number is odd.2/4 of the digits are even means that even digits can only be 4 and 6.The digit in the thousand's place is the number of days in a typical school week and we have 7 days in a typical school week.The digit in the ten's place is twice the value of the digit in the hundred's place and we have the only even digit left as 6, to be the hundreds place. The ten's place digit is 2 * 6 = 12, hence the ten's digit is 2.The digit in the one's place is the number of sides on a nonagon which is equal to 9.The digital root of the number is the number of sides on a stop sign means that the sum of the digits in the number is 4 + 1 + 7 + 5 = 17, which reduces to a digital root of 1 + 7 = 8. A stop sign has 8 sides, so the digital root matches.Learn more about digital root at: https://brainly.com/question/24487815
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What is the area of this figure?
17 m
15 m
4 m
6 m
5 m
Write your answer using decimals, if necessary.
5 m
7m
9 m
The calculated value of the area of the figure is 230.5 sq meters
What is the area of this figure?From the question, we have the following parameters that can be used in our computation:
The composite figure
The area is the sum of the individual areas
Using the above and the area formulas as a guide, we have the following:
Area = 5 * 5 + (6 + 5) * 4 + 1/2 * 17 * (15 + 4)
Evaluate
Area = 230.5
Hence, the area is 230.5 sq meters
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what is the average rate of change for the following intervals?
[-5,-4]
[-4,-3]
[-4,-1]
[-3,-1]
The average rate of change for the given intervals are:
(-5, -5) and (-4, 0): 0(-4, 0) and (-3, 3): 3(-4, 0) and (-1, 3): 1(-3, 0) and (-1, 0): 0How to find the average rate of changeTo compute the average rate of change for any given interval, determine the change between the function values at the endpoints and divide this value by the difference in independent variable values. it can be expressed as follows:
Average Rate of Change = (f(b) - f(a)) / (b - a)
The average rate of change for each point in the interval is determined form the graphs and used to solve for the average rate of change
(-5, -5) and (-4, 0):
Average Rate of Change = (0 - 0) / (-4 - (-5)) = 0 / 1 = 0
(-4, 0) and (-3, 3):
Average Rate of Change = (3 - 0) / (-3 - (-4)) = 3 / 1 = 3
(-4, 0) and (-1, 3):
Average Rate of Change = (3 - 0) / (-1 - (-4)) = 3 / 3 = 1
(-3, 0) and (-1, 0):
Average Rate of Change = (0 - 0) / (-1 - (-3)) = 0 / 2 = 0
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o
You select a marble without looking and then put it back. If you do this 12 times, what is the best prediction possible for the number of times you will pick an orange marble?
If we assume that the marbles are equally likely to be picked, then the probability of picking an orange marble is 1/3.
The number of times an orange marble is picked in 12 trials follows a binomial distribution with parameters n = 12 and p = 1/3.
The expected value of the number of orange marbles picked is given by:
E(X) = np = 12 * (1/3) = 4
Therefore, the best prediction possible for the number of times an orange marble will be picked is 4.
Answer:
The probability of selecting either a purple or a blue marble for the 6 marbles is 0.3333 or 33.33%
Step-by-step explanation:
please mark brainliest
Find the volume for each figure. Use 3.14 for Pi
2.
V=
r = 6 in
Round your answer 2 decimal places if possible.
1
2 3
4
10
5
6
7 8
9
Answer:
V = (4/3)π(6^3) = 288π square inches
= 904.78 square inches
Using 3.14 for π, V = 904.32 square inches.
4 identical glasses and 4 identical jugs hold a total of 11.12 ℓ of water.
Each glass holds 0.33 ℓ of water.
How much water does each jug hold ?
Answer:
2.45ℓ
Step-by-step explanation:
0.33ℓ x 4 = 1.32ℓ (1ℓ 320 ml)
11.12ℓ - 1.32ℓ = 9.8ℓ (total in 4 jugs)
9.8ℓ ÷ 4 = 2.45ℓ (each jug)
hope this helped :)
Let v = - 8i+2j, and w=-i-5j. Find 6w + 9v.
6w +9v = (Type your answer in terms of i and j.)
..
The value of the given expression in terms of i and j is -78i-12j.
Given that, v = - 8i+2j and w = -i-5j.
We need to find the value of 6w+9v.
Substitute v = - 8i+2j and w = -i-5j in 6w+9v, we get
6(-i-5j)+9(-8i+2j)
= -6i-30j-72i+18j
= -78i-12j
Therefore, the value of the given expression in terms of i and j is -78i-12j.
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Construct a sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8)
The sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8) is y = 5 sin(π/2(x - 3)) + 3
We are given that;
Minimum point= (3,-2)
Maximum point= (7, 8)
Now,
To construct a sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8), we can use the following steps:
Find the amplitude A. The amplitude is the distance from the midline of the function to the maximum or minimum point. The midline is the average of the maximum and minimum values, which is (8 + (-2))/2 = 3. The distance from 3 to 8 or -2 is 5, so A = 5.
Find the period P. The period is the length of one cycle of the function, or the horizontal distance between two consecutive maximum or minimum points. In this case, the period is 7 - 3 = 4. The constant B is related to the period by the formula B = 2π/P, so B = 2π/4 = π/2.
Find the horizontal shift C. The horizontal shift is the amount that the function is shifted left or right from its standard position. In this case, we want the function to have a minimum point at x = 3, so we need to shift it right by 3 units. This means that C = 3.
Find the vertical shift D. The vertical shift is the amount that the function is shifted up or down from its standard position. In this case, we want the function to have a midline at y = 3, so we need to shift it up by 3 units. This means that D = 3.
Putting it all together, we get:
y = 5 sin(π/2(x - 3)) + 3
Therefore, by the function the answer will be y = 5 sin(π/2(x - 3)) + 3.
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Is 18 three more than nine true or false
Answer: False
Step-by-step explanation:
Counting up from 9, you get 10, 11, and 12. To get to 18 from 9 you would need to add 9.
If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage e for a child of age a, pharmacists use the equation c = 0.0417D(a + 1).
Suppose the dosage for an adult is 150 mg.
(a) Find the slope of the graph of e. (Round your answer to two decimal places.)
P
What does it represent?
The slope represents the Select of the dosage for a child for each change of 1 year in age.
(b) What is the dosage for a newborn? (Round your answer to two decimal places.)
ma
a) The slope shows that the appropriate dose c for an older child increases by 6.225 mg if the child is one year older.
b) The dose for newborn baby is: 6.225 mg
How to interpret the slope?The equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
(a) Let a be an age of an child in years. Then:
c = 0.0417Da + 0.0417D
Where D is a constant
Since D = 150 mg, then we have:
The slope of the graph = 0.0417(150)
= 6.225 mg/year
The slope shows that the appropriate dose c for an older child increases by 6.225 mg if the child is one year older.
(b) Newborn baby: a=0
Thus:
c(0) = 0 + 6.225
= 6.225 mg
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if u are given the midpoint of a segment and one endpoint find the other endpoint (6,2) (1,3)
The other endpoint is (11, 1).
We have,
Midpoint = (6, 2) and endpoint = (1, 3).
and, ratio of m: n = 1 :1
Using section formula
6 = ( 1 + a) / (1+1)
6 = (1+a)/2
1 + a = 12
a = 11
and, 2 = (3 + b) / (1+1)
2 = (b + 3) /2
b +3 = 4
b = 1
Thus. the other endpoint is (11, 1).
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6. Error Analysis Dakota said the third term of the expansion of (2g + 3h) is 36g2h². Explain Dakota's error. Then correct the error.
The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression
Given data ,
Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.
So , on simplifying the equation , we get
= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²
= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²
= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²
Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.
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Diego buys water bottles for his softball team, he buys 7 cases, each with t bottles. Diego buys a total of 168 bottles. Create an equation that models this situation, where t represents the number of bottles per case purchased
An electrician has 42.3 meters of wire to use on a job. On the first day, she uses 14.742 meters of the wire. How many meters of wire does she have remaining after the first day?
There are 27.558 meters of wire does she have remaining after the first day.
We have to given that;
An electrician has 42.3 meters of wire to use on a job.
And, On the first day, she uses 14.742 meters of the wire.
Hence, We get;
The remaining wire does she have remaining after the first day is,
⇒ 42.3 - 14.742
⇒ 27.558 meters
Thus, There are 27.558 meters of wire does she have remaining after the first day.
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According to a National Center for Health Statistics, the lifetime odds in favor of dying from heart disease are 1 to 5, so the probability of dying from heart disease is
Answer:
The probability of dying from heart disease based on the given information is 1/6 or approximately 0.1667. This is because the odds in favor of dying from heart disease are 1 to 5, which means there is 1 chance of dying from heart disease for every 5 chances of not dying from heart disease. To convert odds to probability, we divide the number of chances of the event occurring by the total number of chances. So, the probability of dying from heart disease is 1/(1+5) = 1/6 or approximately 0.1667.
Can you help me with this question?
Kyla finds a pair of roller blades that she would like to purchase. They are originally priced at $110 but are marked 30% off. What is the final price Kyla will pay for the roller blades if the tax rate is 5%?
To find the final price Kyla will pay for the roller blades, we first need to calculate the amount of the discount.
Discount = 30% of $110Discount = 0.30 x $110Discount = $33So Kyla will get a discount of $33 off the original price of $110.
Next, we need to calculate the pre-tax price of the roller blades after the discount.
Pre-tax price = Original price - DiscountPre-tax price = $110 - $33Pre-tax price = $77So the pre-tax price of the roller blades after the discount is $77.
Finally, we need to calculate the final price Kyla will pay, including the 5% tax.
Tax amount = 5% of $77Tax amount = 0.05 x $77Tax amount = $3.85Final price = Pre-tax price + Tax amountFinal price = $77 + $3.85Final price = $80.85Therefore, the final price Kyla will pay for the roller blades, including tax, is $80.85.The figure below is a right rectangular prism with
rectangle ABCD as its base.
What is the area of the base of the rectangular prism? 2, 9, 18 sq centimeters
What is the height of the rectangular prism? 2, 6, 9 centimeters
What is the volume of the rectangular prism? 17, 54, 108 cubic centimeter
Area of rectangular base is 18 square centimeters.
The height (given) is 6 centimeters.
The volume of the rectangular prism is 108 cubic centimeters.
For the area of the base, multiply the length of AD times length of CD
9cm × 2cm = 18cm² remember that is square unit measure:
cm² means square centimeters.
The height is the distance between the two bases. Given as AW = 6
To get Volume, multiply the area of one base by the height
18cm² × 6cm = 108cm³
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