Kuta Software - Infinite Algebra 2 Factoring By Grouping Factor ench completely. 1) 12a-9a? +40 - 3 Name Sarn on the ears Date : 120, 37443 4ac3a ²+1)-3(3u341) ta 2373 (403) 2) 2p'+ 5p² +6p+ 15 apstept sport 2plpa
Answers
Factor the expression.
[tex]\begin{gathered} 90au-36av-150yu+60yv=90au-150yu+60yv-36av \\ =30u(3a-5y)-12v(3a-5y) \\ =(3a-5y)(30u-12v) \\ =(3a-5y)(6\cdot5u-6\cdot2v) \\ =6(3a-5y)(5u-2v) \end{gathered}[/tex]So answer is,
[tex]6(3a-5y)(5u-2v)[/tex]Related Questions
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
Answers
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
Express the interval using inequality notation.
(-4, -1)
Answers
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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Find the perimeter and area of the shaded figure below.
Answers
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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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
Answers
Answer:
Explanation:
what is the 6th term in the sequence? f(1) = 10 f(n) = f(n-1) + 3
Answers
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]
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)
Answers
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
5. When purchasing a new video game system, thestore charges 9% on tax. What decimal isequivalent to 9%?
Answers
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.
find the volume of the following rectangular prism Round to the nearest tenth if necessary.
Answers
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
Write the following numbers in order of size.
Start with the smallest number.
0.4
0.38
0.02
0.2
0.113
Answers
Answer:
0.02, 0.113, 0.2 0.38 0.4
Step-by-step explanation:
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
Answers
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?
Answers
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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Please help me I beg you I love you!
Answers
1) [tex]\overline{AB} \cong \overline{CD}[/tex] (given)
2) [tex]\angle BAC \cong \angle ACD[/tex] (given)
3) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)
[tex]\triangle ABC \cong \triangle CDA[/tex] (SAS)
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)
Answers
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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If x is 5 more than y, and y is 3 less than z, what is the value of x when z=3
Answers
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
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
Answers
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.
i need help :). it sure how to do synethetic división so it would help if u showed me how
Answers
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
May I please get help with this. For I am confused as to how i can get the correct answers as I’ve tried may times
Answers
The new coordinates are (-1, 7), (-3, 3) and (-8, 5)
Explanation:To get the new coordinates after the translation, we will first find the initial coordinates of the three vertices
The three vertices: (3, 3), (1, -1) and (-4, 1)
A translation of 4 units to the left:
[tex]\begin{gathered} \text{suntract 4 units form the x coordinates:} \\ (3,\text{ 3): (3-4, 3) = (-1, 3)} \\ (1,\text{ -1): (1-4},\text{ -1) = (-3, -1)} \\ (-4,\text{ 1): (-4 -4, 1) = (-8, 1)} \end{gathered}[/tex]A translation of 4 units up:
[tex]\begin{gathered} \text{Add 4 units to y coordinates} \\ (-1,\text{ 3): (-}1,\text{ 3 + 4) = (-1, 7)} \\ (-3,\text{ -1): (-3, -1+4) = (-3, 3)} \\ (-8,\text{ 1): }(-8,\text{ 1+ 4) = (-8, 5)} \end{gathered}[/tex]Plotting the points:
the left coordinate is (-8,5)
the right coordinate is (-1,7)
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?
Answers
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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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)
Answers
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.
What is the surface area of the cube below?
A. 96 units²
B. 120 units²
C. 64 units²
D. 80 units²
Answers
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
Determine an equation of the line that is perpendicular to the tangent to the graph y=1/x at x=2 and intersects at the point of tangency.
Answers
ANSWER
[tex]y=4x-\frac{15}{2}[/tex]EXPLANATION
Two lines are perpendicular if they have opposite reciprocal slopes. So, to find the line, first, we have to find the slope of the line tangent to the graph of y = 1/x at x = 2. To do so, we have to find the derivative of the function and evaluate it at x = 2. That is the slope of the tangent line at that point.
The derivative of the function is,
[tex]y^{\prime}=\left(\frac{1}{x}\right)^{\prime}=(x^{-1})^{\prime}=-1\cdot x^{-1-1}=-1x^{-2}=-\frac{1}{x^2}[/tex]So, the slope of the tangent line at x = 2 is,
[tex]y^{\prime}(2)=-\frac{1}{2^2}=-\frac{1}{4}[/tex]Therefore, the slope of the perpendicular line is the opposite reciprocal,
[tex]m=-\frac{1}{y^{\prime}(2)}=-\frac{1}{-\frac{1}{4}}=4[/tex]So we have that the perpendicular line we are looking for is,
[tex]y=4x+b[/tex]We have to find the y-intercept, b. We know that this perpendicular line intersects the graph at the tangency point, so with that point, we will find b.
The x-coordinate of the tangency point is x = 2, and the y-coordinate is,
[tex]y(2)=\frac{1}{2}[/tex]Substitute (x, y) with (2, 1/2) in the equation of the line to find b,
[tex]\begin{gathered} \frac{1}{2}=4\cdot2+b \\ \\ \frac{1}{2}=8+b \end{gathered}[/tex]Subtract 8 from both sides,
[tex]b=\frac{1}{2}-8=\frac{1-8\cdot2}{2}=\frac{1-16}{2}=-\frac{15}{2}[/tex]Hence, the equation of the line perpendicular to the tangent of the graph at x = 2 passing through the tangency point is,
[tex]y=4x-\frac{15}{2}[/tex]Express the interval in using inequality notation
(-4,-1)
Answers
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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find the value of the misssing variables im pretty sure the answer is either a or c
Answers
the sum of the internal angles of the 4-sided polygon is 360, therefore
[tex]\begin{gathered} m\angle D+m\angle G+m\angle F+m\angle E=360 \\ m\angle D+m\angle G+64+119=360 \\ m\angle D+m\angle G+183=360 \\ m\angle D+m\angle G+183-183=360-183 \\ m\angle D+m\angle G=177 \end{gathered}[/tex]then
[tex]m\angle D=y=116[/tex][tex]m\angle G=z=61[/tex]answer: a. y = 116° and z = 61°
Use the following cell phone airport data speeds (Mbps) from a particular network. Find P70
Answers
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]f(x) = x2 − 5.) Multiply by 3, then subtract 2.
Answers
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.
Answer the image here
Answers
Answer:
1/100 or -1/100
Step-by-step explanation:
the two solutions are
0.01 = 1/100
-0.01 = -1/100
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?
Answers
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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Consider the following sequence: 7,14,28,56,... find a19
Answers
We have the sequence:
[tex]\begin{gathered} a_1=7, \\ a_2=14, \\ a_3=28, \\ a_4=56, \\ \ldots \end{gathered}[/tex]We rewrite the sequence as:
[tex]\begin{gathered} a_1=7\cdot1=7\cdot2^0=7\cdot2^{1-1}, \\ a_2=7\cdot2=7\cdot2^1=7\cdot2^{2-1}, \\ a_3=7\cdot4=7\cdot2^2=7\cdot2^{3-1}, \\ a_4=7\cdot8=7\cdot2^3=7\cdot2^{4-1}, \\ \ldots \end{gathered}[/tex]From the previous equations, we see that the general term is given by:
[tex]a_n=7\cdot2^{n-1}.[/tex]Replacing n = 19, we get:
[tex]a_{19}=7\cdot2^{19-1}=7\cdot2^{18}=7\cdot262144=1835008.[/tex]Answer
[tex]a_{19}=7\cdot2^{18}=1835008[/tex]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?
Answers
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 boxes5. 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
Answers
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.