The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.
The given polynomial expression is 3x² + 3bx - 6x - 6b.
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The factors of given polynomial can be find using grouping method, that is
(3x² + 3bx) - 6x - 6b
=3x(x+b)-6(x+b)
=(x+b)(3x-6)
=3(x-2)(x+b)
The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.
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Assume a triangle ABC has standard labeling. Determine whether SAA, ASA, SSA, SAS, or SSS is given. Then decide whether the law of sines or the law of cosines should be used to begin solving the triangle.B, C and bOption 1: SSA; law of sinesOption 2: SSA; law of cosinesOption 3: SAA; law of cosinesOption 4: SAA; law of sines
Answer:
Explanation:
cos(θ)= 1/6Trig: use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function.a. Sin (θ)b. Tan (θ)c. Sec (θ)d. Csc (90° -θ)
a. Sin (θ) = √35 / 6
b. Tan (θ) = Tan θ = √35
c. Sec (θ) = 6
d. Csc (90° -θ) = 6
Explanations:Note that according to trigonometric identities:
cos θ = Adjacent / Hypotenuse
From the question:
cos θ = 1/6
Comparing this with the given trigonometric identity:
Adjacent, A = 1
Hypotenuse, H = 6
Let us look for the opposite, O
Using the pythagora's theorem
H² = A² + O²
6² = 1² + O²
36 = 1 + O²
36 - 1 = O²
O² = 35
O = √35
Therefore, Opposite = √35
a) Sin θ = Opposite / Hypotenuse
Sin θ = √35 / 6
b) Tan θ = Opposite / Adjacent
Tan θ = √35 / 1
Tan θ = √35
c) Sec θ = 1 / cos θ
Sec θ = 1 ÷ 1/6
Sec θ = 1 x 6
Sec θ = 6
d) Csc ( 90 - θ) = Sec θ
Since Sec θ = 6
Csc ( 90 - θ) = 6
The number of cookies in a shipment of bags are normally distributed with a mean of 58 and a standard deviation of 5. There are normally 800 bags of cookies in a a shipment. How many bags of cookies will contain between 48 and 68 cookies?
The percent of bags of cookies will contain between 48 and 68 cookies is 68.29%.
What is mean?The average of the specified collection of numbers is what is referred to as mean. It indicates that values in a particular data set are distributed equally.
μ = 58, σ = 5,
Z₁ = X₁ - (μ/ σ)
= 48 - (58/5)
= 36.4
again,
Z₂= X₂ - (μ/ σ)
= 68 - (58/5)
= 56.4
Thus, we know P( 48 < X < 68)
= p(-1 < Z < 1)
= 0.6829
= 68.29%
68.29% bags of cookies will contain between 48 and 68 cookies.
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Simplify the following expressions by using the properties of exponents. Assume none of the denominators is zero.
a^3 (2a^2 + 4bc^4)^ 0
The total value of the exponential expression is a³
What is Exponentiation ?
Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.
Now, The given expression is :
a^3 (2a^2 + 4bc^4)^ 0
From the properties of exponents we know that:
a⁰ = 1
Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1
Hence, The total value of the exponential expression is a³
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What is the position vector of the midpoint of the line PQ if P has coordinates(-13,-4,6) and Q has coordinates (0,4,11)?OA. ( 130 - 17)B.(-13,0,1)c. (2.0.1D. (-2,0. - 1)
The general formula to find the midpoint of a line in a 3D space is given by
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2})[/tex]In this case, we have
[tex]M=(\frac{-13+0}{2},\frac{-4+4}{2},\frac{6+11}{2})=(\frac{-13}{2},0,\frac{17}{2})[/tex]So the position vector of the midpoint of the line PQ is
[tex]M=(-\frac{13}{2},0,\frac{17}{2})[/tex]which is option B.
Write the following numbers in order of size.
Start with the smallest number.
0.4
0.38
0.02
0.2
0.113
Answer:
0.02, 0.113, 0.2 0.38 0.4
Step-by-step explanation:
Jackson is packing a moving truck with cube-shaped boxes that each have a side length of 1.5 square feet. The moving truck is 8 feet long, 6.5 feet wide, and 6.25 feet tall. What is the greatest number of boxes that Jackson can fit in the moving truck?
Answer:
96 boxesStep-by-step explanation:
the volume of the box: (cubes have all equal sides)
"cube-shaped boxes that each have a side length of 1.5 square feet."
V = lwh
V = 1.5 * 1.5 * 1.5
V = 3.375 cubic feet
the space inside the truck:
"The moving truck is 8 feet long, 6.5 feet wide, and 6.25 feet tall."
V = lwh
V = 8 * 6.5 * 6.25
V = 325 cubic feet
Now we see how many boxes we can fit, by dividing the size of the truck, by the boxes:
325 ÷ 3.375 = 96.2962963
96.2962963 boxes BUT you can't have .2962963 (part) of a box so you can only fit...
96 boxesExpress the interval using inequality notation.
(-4, -1)
Expression of the given interval (-4,-1) in inequality notation is -4< x <-1.
As given,
Given interval:
( -4 , -1 )
Let us consider x variable belongs to given interval x ∈ ( -4 , -1 ).
Given interval ( -4 , -1 ) is open interval.
In open interval when we plot it on the real number line , we are not including upper limit and the lower limit of the given interval.
-4 and -1 are exclusive values for the given variable.
Symbol representing open interval is sign of < or >.
Interval (-4,-1) in inequality notation is given by -4 < x < -1.
All values are included between -4 and -1 except -4 and -1.
Therefore, the expression of the given interval (-4,-1) in inequality notation is -4 < x < -1.
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The economy's real GDP was $100 billion in 2019 and $240 billion in 2020. Its
population was 15 million in 2019 and 15 million in 2020.
What is the growth rate of real GDP per capital from 2019 to 2020?
The growth of the real GDP per capita from 2019 to 2020 is 1.4.
How To calculate the growth rate of real GDP?It also calculates the amount of money spent on finished goods and services or the income generated from that production.GDP = private consumption + gross private investment + government investment + government spending + (exports – imports).GDP can be assessed in a variety of methods. The most popular techniques include Nominal GDP, Real GDP, Actual GDP, and Potential GDP.One of the key metrics used to assess the general health of a nation's economy and standard of life is its gross domestic product (GDP), which reflects economic growth and productivity. GDP growth rate is one approach to assess how well a nation's economy is doing. This rate indicates changes in the proportion of economic output over the course of a month, a quarter, or a whole year.Therefore, the formula to compute real GDP per capita = Real GDP / Population.
The real GDP in 2019 is $100B.
And the real GDP in 2020 is $240B.
Real GDP per capita of 2019 = 100B/15M. = 6666.6Real GDP per capita of 2020 = 240B/15M = 16000The growth rate of real GDP = current value - previous value / previous value
The growth rate of real GD P= 1.4Therefore, the growth of the real GDP per capita from 2019 to 2020 is 1.4.
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Find the perimeter and area of the shaded figure below.
The perimeter of the shaded figure is 12 units
The area of the shaded figure is 8 square units
Given,
Length of the shaded figure = 4 units
Width of the shaded figure = 2 units.
The shaded figure resembles a rectangle
So,
Perimeter of the shaded figure = 2( length + width)
Perimeter, P = 2 ( 4 + 2)
P = 2 × 6
P = 12 units
Now,
Area of the shaded figure = length × width
Area, A = 4 × 2
A = 6 square units
Therefore,
The perimeter of the shaded figure is 12 units
The area of the shaded figure is 8 square units
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A real estate company balances the books for its business on the first day of each month. It hopes to sell houses every other day of the month. The average number of houses, S, the company sells each day, t, is represented by the inverse of the function Inverse of S is equal to the quantity t squared plus 3 times t minus 4 end quantity over the quantity t squared minus 6 times t plus 6 end quantity
Which equation represents the average sales each day for the real estate company?
An inverse function which represents the average sales each day for the real estate company is: D. S⁻¹ = (t + 4)/(t - 5).
How to determine equation?In order to determine equation which represents the average sales each day for the real estate company, we would factorize the numerator and denominator of the given inverse function as follows:
Numerator = t² + 3t - 4
Next, we would solve the quadratic equation by using the factorization method:
t² + 3t - 4 = t² + 4t - t - 4
t² + 4t - t - 4 = t(t + 4) - 1(t + 4)
t² + 4t - t - 4 = (t - 1)(t + 4)
Numerator = (t - 1)(t + 4)
For the denominator, we have:
t² - 6t + 5 = t² - 5t - t + 5
t² - 5t - t + 5 = t(t - 5) - 1(t - 5)
t² - 5t - t + 5 = (t - 1)(t - 5)
Denominator = (t - 1)(t - 5)
Now, we would rewrite the inverse function as follows:
S⁻¹ = Numerator/Denominator
S⁻¹ = (t - 1)(t + 4)/(t - 1)(t - 5)
S⁻¹ = (t + 4)/(t - 5)
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If x is 5 more than y, and y is 3 less than z, what is the value of x when z=3
Answer: X=5
Step-by-step explanation: If x is 5 more than y, and y is 3 less than z. Well we already know z=3 so z=3 - 3 less than Y=0. Making Y=0, and if x is five more than Y, 5+0=5. Making x=5
what is the 6th term in the sequence? f(1) = 10 f(n) = f(n-1) + 3
We will investigate the evaluation of recursive sequences.
A iterative sequences are categorized by two values i.e one value preceding and the current value. The current value is evaluated on the basis of the previous value. In other words the current value is a function of preceeding value or depends on it.
All iterative relations of a sequence are expressed mathematically by two values as follows:
[tex]\begin{gathered} f\text{ ( n ): Current nth term value} \\ f\text{ ( n - 1 ): preceeding/ previous value} \end{gathered}[/tex]A iterative relation is a unique mathematical relationship between the current term f ( n ) and the previous value given as follows:
[tex]\textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( n ) = f ( n - 1 ) + 3}}[/tex]For this particular relationship the first term value is given as follows:
[tex]\textcolor{#FF7968}{n}\text{\textcolor{#FF7968}{ = 1, f ( 1 ) = 10}}[/tex]We will now start determining the terms in the sequence by plugging the respective term numbers ( n ) and use the mathematical relationship for the sequence as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 2,}} \\ f\text{ ( 2 ) = f ( 1 ) + 3} \\ f\text{ ( 2 ) = 10 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 2 ) = 13}} \end{gathered}[/tex]We have evaluated the 2nd term in the sequence as 13. We will repeat the above steps for all term numbers ( n = 3 , 4 , 5 , 6 ).
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 3,}} \\ f\text{ ( 3 ) = f ( 2 ) + 3} \\ f\text{ ( 3 ) = 13 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 3 ) = 16}} \\ \\ \text{\textcolor{#FF7968}{For n = 4,}} \\ f\text{ ( 4 ) = f ( 3 ) + 3} \\ \text{f ( 4 ) = 16 + 3} \\ \text{\textcolor{#FF7968}{f ( 4 ) = 19 }} \\ \\ \text{\textcolor{#FF7968}{For n = 5,}} \\ f\text{ ( 5 ) = f ( 4 ) + 3} \\ f\text{ ( 5 ) = 19 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 5 ) = 22}} \end{gathered}[/tex]And them lastly for the 6th term in the sequence as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 6,}} \\ f\text{ ( 6 ) = f ( 5 ) + 3} \\ f\text{ ( 6 ) = 22 + 3} \\ \text{\textcolor{#FF7968}{f ( 6 ) = 25}} \end{gathered}[/tex]Hence, the answer to the 6th term number is:
[tex]\textcolor{#FF7968}{25}[/tex]
775,710 teenagers voted for their favorite singer on a TV show. Each singer received the exact same number of votes. How many singers could there have been?a) 5b) 2c) 6d) 9
There could have been 2,5,6, and 9 singers
1) Regarding 775,710 as an even number then for sure there could have been 2 singers on this TV Show
[tex]775710\colon2=387,855[/tex]2) On the other hand, 775710 is also divisible by 5, for its last number is 0. So there could also have been 5 singers.
[tex]775710\colon5=155,142[/tex]3) This number of teenagers can also be divided by 6 (for it is divisible by 2 and by 3) and by 9 as well ( the sum of the digits of 775710, 7+7+5+7+1+0=27 is also divisible by 9).
Hence, there could have been 2,5,6, and 9 singers since 775,710 can be divided exactly by 2,5,6, and 9.
Answer the image here
Answer:
1/100 or -1/100
Step-by-step explanation:
the two solutions are
0.01 = 1/100
-0.01 = -1/100
Express the interval in using inequality notation
(-4,-1)
Expression of the given interval (-4,-1) in inequality notation is -4< x <-1.
As given,
Given interval:
( -4 , -1 )
Let us consider x variable belongs to given interval x ∈ ( -4 , -1 ).
Given interval ( -4 , -1 ) is open interval.In open interval when we plot it on the real number line , we are not including upper limit and the lower limit of the given interval.-4 and -1 are exclusive values for the given variable.Symbol representing open interval is sign of < or >.Interval (-4,-1) in inequality notation is given by -4 < x < -1.All values are included between -4 and -1 except -4 and -1.Therefore, the expression of the given interval (-4,-1) in inequality notation is -4 < x < -1.
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Determine whether the graph represents a function.
The given graph representing function is a relation.
What is meant by relation and function?A function is a relation that states that there must be only one output for every input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be related with only one y-value.The Cartesian product is a subset of it. Alternatively, a slew of points (ordered pairs). In other words, the connection between the two sets is described as a collection of a ordered pair, where the ordered pair is formed by an object from each set.(INPUT, OUTPUT): An ordered pair is depicted as (INPUT, OUTPUT):For the given question,
For every singles value of 'x' there is value on y. Thus, no domain element is repeating for the graph.
Thus, the graph shows the relation of the function.
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A recycling plant processes an average of \frac{{7}}{{8}}
8
7
ton of cardboard each minute. At this rate, how many tons of cardboard does this plant process per day? (1 day = 24 hours)
By taking some products, we will see that the average amount processed per day is 1,260 tons.
How many tons of cardboard the plant process per day?We know that the recycling plant processes an average of 7/8 tons of cardboard each minute.
In one hour we have 60 minutes, so the amount processed per hour is given by the product:
60*7/8 tons = 52.5 tons.
And in one day we have 24 hours, so the total amount processed in one day is 24 times what we got above, which is:
24*52.5 tons = 1,260 tons.
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I rlly need help on this problem-
Two factors are multiplied and their product is 34.44. One factor is a whole number. What is the least number of decimal places in the other factor?
The least number of decimal places in the other factor is 2
What is a factor?A factor simply means the number that can b multiplied with another number to get the original number.
Based on the question asked, lat the whole number be represented as 2. In this case the multiplication will be:
= 2 × 17.22
=34.44
In this case, one can see that 17.22 has 2 decimal places.
Therefore, the correct option is 2.
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Use the following cell phone airport data speeds (Mbps) from a particular network. Find P70
Note that the data is in ascendinhg order.
We shall find the position of the pth percentile as follows;
[tex]\begin{gathered} i=\frac{p}{100}\times n \\ \text{Where } \\ p=70,n=50\text{ (number of data)} \end{gathered}[/tex]We now have;
[tex]\begin{gathered} i=\frac{70}{100}\times50 \\ i=35 \end{gathered}[/tex]In the 34th and 35th position we have;
[tex]\begin{gathered} \text{The 35th percentile is;} \\ (\frac{5.4+5.7}{2}) \\ =(\frac{11.1}{2}) \\ =5.55 \end{gathered}[/tex]ANSWER:
[tex]P_{70}=5.55\text{Mbps}[/tex]i need help :). it sure how to do synethetic división so it would help if u showed me how
The dividend is
and the divisor is
x+2
We begin by arranging them as follows:
now, we divide the leading term in the dividend by the leading term in the divisor to get the first term of the quotient: 4x^2 / x = 4x.
Then we multiply the divisor by 4x and subtract
the result from the dividend. That is:
We repeat the same procedure: using the last line -3x - 6 as the dividend:
So, the leading term of -3x-6 is -3x, so we have -3x/x = -3. Then we multiply the divisor by -3 and subtract the result from the dividend. That is:
Because the remainder is 0, we have finished the division. So the correct answer will be 4x-3
What is the surface area of the cube below?
A. 96 units²
B. 120 units²
C. 64 units²
D. 80 units²
Answer:
A. 96 U2
Step-by-step explanation:
The cube has 6 faces
Multiply by 6 the area of one face
Surface area = 6 (4)(4) = 96 units2
Hope this helps
Use the formula for nCr to evaluate the expression. 10c3/6c4
SOLUTION
The given expression is
[tex]\frac{^{10}C_3}{^6C_4}[/tex]Recall the formula for combination
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]Solving the given expresssion
[tex]\frac{^{10}C_3}{^6C_4}=\frac{10!}{(10-3)!3!}\div\frac{6!}{(6-4)!4!}[/tex]This further gives
[tex]\begin{gathered} \frac{10!}{(10-3)!3!}\div\frac{6!}{(6-4)!4!} \\ =\frac{10!}{7!3!}\div\frac{6!}{2!4!} \\ =\frac{10!}{7!3!}\times\frac{2!4!}{6!} \end{gathered}[/tex]This further gives
[tex]\begin{gathered} =\frac{10\times9\times8\times7!}{7!\times3\times2!}\times\frac{2!4!}{6\times5\times4!} \\ =\frac{10\times9\times8}{6\times5\times3} \\ =8 \end{gathered}[/tex]Therefore the solution is 8
5. Noah orders an extra-large pizza. It costs $12.49 for the pizza plus $1.50for each topping. He orders an extra-large pizza with t toppings that costsa total of d dollars. Select ALL of the equations that represent therelationship between the number of toppings t and total cost d of the pizzawith t toppings."12.49 + t = 012.49 + 1.501 - 012.49 +1.500 t12.49 = d + 1.500t = (d. 12.49) / 1.5t=d12.49/1.5
The cost of 12.49 is fixed, while the extra cost for toppings is 1.5 per topping.
If we have a total of t topping, the cost of the toppings will by 1.50t, adding the fixed cost, we will have the total cost, which should be equal to d. so we have the equation:
[tex]d=12.49+1.50t[/tex]Now, we can manipulate the equation to check which ones are equivalent to it.
As we can see, the first one is missing the 1.50, so it is not equivalent.
The second have the 1.50, it is just inverted:
[tex]12.49+1.50t=d[/tex]So, it is equivalent.
The third had the t and d switched, so it is not equivalent.
The fourth get the 1.50t to the other side, but don't change the sign accordingly, so it is not equivalent.
The fifth solved for t let's do that:
[tex]\begin{gathered} 12.49+1.50t=d \\ 1.5t=d-12.49 \\ t=\frac{(d-12.49)}{1.5} \end{gathered}[/tex]So, it is equivalent.
The sixth don;t distribute the denominator correctly, so it is not equivalent.
So, the alternatives that are equivalent are:
[tex]\begin{gathered} 12.49+1.50t=d \\ t=(d-12.49)/1.5 \end{gathered}[/tex]The second and fifth.
Which of the folowing expressions is equivalent to 8^3?A 4^3× 4^3B 4^3× 2^3C 8^2× 1^1 D 4^2× 2^1
5. When purchasing a new video game system, thestore charges 9% on tax. What decimal isequivalent to 9%?
The decimal that is equivalent to 9% is:
[tex]\frac{9}{100}=0.09[/tex]Then, the decimal which is equivalent to 9% is 0.09.
Practice
Solve each equation. Check your solution (Example 1-3)
1. -2a-9=6a+15
2. 14+3n = 5n-6
3. 1/2 x -5=10 - 3/4 x
4. 7/3 y+1=1/6 y+8
Answer:
a = -3n = 10x = 12y = 42/13Step-by-step explanation:
You want to solve the equations and check the solutions for ...
1. -2a-9=6a+15
2. 14+3n = 5n-6
3. 1/2 x -5=10 - 3/4 x
4. 7/3 y+1=1/6 y+8
Three-step linear equationEach of these equations has both a variable term and a constant term on each side of the equal sign. The usual 3-step solution is ...
Subtract one of the variable terms from both sidesIdentify the constant term on the side with 2 terms and subtract that from both sidesDivide by the coefficient of the variableThis can be made less error-prone by choosing the variable term in Step 1 that has the smallest (least) coefficient. Then the constant in Step 2 will be the constant on the side of the equation that has the variable term with the largest coefficient.
We can do the subtractions of Step 1 and Step 2 both at the same time, reducing the work slightly. Of course, subtraction is the same as adding the opposite. Then what remains is dividing by the coefficient of the variable (or multiplying by its inverse).
1. -2a-9=6a+15Add 2a -15 to both sides:
-24 = 8a
-3 = a . . . . . . divide by 8
check: -2(-3)-9 = 6(-3) +15 ⇒ -3 = -3 . . . checks OK
2. 14+3n = 5n-6Add -3n+6 to both sides:
20 = 2n
10 = n . . . . . . divide by 2
check: 14 +3(10) = 5(10) -6 ⇒ 44 = 44 . . . checks OK
3. 1/2 x -5=10 - 3/4 xAdd 3/4x +5 to both sides:
5/4x = 15
x = 12 . . . . . . multiply by 4/5
check: 1/2(12) -5 = 10 -3/4(12) ⇒ 1 = 1 . . . checks OK
4. 7/3 y+1=1/6 y+8Add -1/6y -1 to both sides:
13/6y = 7
y = 42/13 . . . . . multiply by 6/13
check: (7/3)(42/13) +1 = (1/6)(42/13) +8 ⇒ 98/13 +1 = 7/13 +8
⇒ 8 7/13 = 8 7/13 . . . checks OK
f(x) = x2 − 5.) Multiply by 3, then subtract 2.
The required expression is f(x) = (3x - 2).
A linear expression is an algebraic equation of highest degree 1 and it contains only one variable. A quadratic expression is an algebraic expression in which the variable has highest degree of 2. In a quadratic equation the two values of variable which satisfies the equation ax² + bx + c = 0 is called the roots of the given equation. According to the given question Square then subtract 5 is expressed as the function f(x) = x² - 5
∴ The function Multiply by 3, then subtract 2 will be expressed as
f(x) = (3x - 2).
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Complete question:
Express the rule in function notation. (For example, the rule "square, then subtract 5" is expressed as the function f(x) = (x2 − 5.)Multiply by 3, then subtract 2.
6 less than the number x
find the volume of the following rectangular prism Round to the nearest tenth if necessary.
Consider that the volume of a rectangular prism is given by the following formula:
V = l·h·w
l: length = 4 cm
w: width = 5.1 cm
h: height = 9 cm
replace the previous values of the parameters into the formula for V:
V = (4 cm)(5.1 cm)(9 cm)
V = 183.6 cm³
Hence, the volume of the rectangular prism is 183.6 cm³