The v-t and s- t graphs that describe the motion of the second stage for 0≤t≤60 are v(60)=1170, s(60)=29800.
The graph defines the acceleration and velocity of the rocket.
In graphs, 0-30 is the linear equation and 0-60 is constant acceleration.
First, we have to find the velocity, for velocity, there is the relationship of acceleration is the derivative of velocity with respect to time.
a=dv/dt ---> ∫dv=∫a dt
v=ds/dt-----> ∫ds=∫v dt
We have to find the first stage of the question which is 0≤t≤30.
a(t)=12t
By this we can find velocity:
∫dv=∫a dt
[tex]\int\limits^v_0 {dv} \, =\int\limits^t_0 {12t} \, dt\\ \\V(t)=\frac{12t^2}{2}\\\\V(t)=6t^2[/tex]
[tex]\int\limits{ds} \,= \int\limits {v} \, dt\\\\\int\limits^s_0 {ds} \, =\int\limits^t_0 6t^2 } \, dt\\\\s=\frac{12t^3}{6}[/tex]
S=2t³
Next to find the second stage:
for this, we have to find the limits and just plug the values
v(t)=6t²=450
s(t)=2t³=4500
30≤t≤60 second stage
a=24
∫dv=∫a dt
∫dv=∫24dt
[tex]v]^v_4_5_0=24]^t_3_0\\[/tex]
v-450=24t-720
v=24t-270
∫ds=∫v dt
∫ds=∫24t-270 dt
[tex]s]^s_4_5_0_0=12t^2-270t]^t_3_0[/tex]
s-4500=(12t²-270t)-(12(900)-270(30))
s-4500=(12t²-270t)-(10800-8100)
s-4500=(12t²-270t)-(2700)
s=(12t²-270t)-(2700)+4500
s=12t²-270t+2800
for the time 60s just plug the values in the v and s.
v(60)=24(60)-270
v(60)=1170
s(60)=12(3600)-270(60)+2800
43200-16200
s(t)=29800.
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A standard six-sided die is rolled 7 times. You are told that among the rolls, there was one 1, two 2's, and three 4's. How many possible sequences of rolls could there have been? (For example, 5, 1, 2, 2, 4, 4, 4 is one possible sequence. 4, 1, 4, 4, 2, 2, 4 is one possible sequence.)
The possible sequences of rolls are [tex]6^7[/tex].
What is sample space?It is the total number of possible outcomes from a given set.
We have,
Standard six-sided die:
The number of times the dice are rolled = 7 times.
Now,
Number of sides in a dice = 6
So,
The total possible outcomes.
= [tex]6^7[/tex]
Thus,
The possible sequences of rolls are [tex]6^7[/tex].
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Answer:
105
Step-by-step explanation:
First off, please don't simply copy this for your homework, as the only person that is harmed is you.
(7) (3)
(4) x (2) = 35 * 3 = 105
^
Is the ways to choose the positions of the 4
------------^
Is the way to choose the positions of the 1s and 2s.
consider an experiment that consists of determining the type of job - either blue-collar or white collar- and the political affiliation -republicans, democratic or independent - of the 15 members of an adult soccer team. how many outcomes are in the event that at least one of the team members is a blue-collow worker?
We rule up the team members, say by Social Security number. We now ask each in turn her/his job explanation and political affiliation and data the information.
For any person, the information can be recorded as an instruct pair (x ,y) where x is one of B or W, and y is one of R, D, or I. So, there are for any person 6 possible records. The team conclusion is a sequence of such records, of length 15. Thus, for our team there are 6^15 possible results.
How many of these results have at least one blue-collar worker? How many have no blue-collar worker? Then x=W, and y can still take on any of 3 values, for a total of 3^15 possibilities. Thus, the number of possible summaries with at least one B is 6^15−3^15.
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What is the value today of $5,100 per year, at a discount rate of 7.9%, if the first payment is received 6 years from today and the last payment is received 20 years from today?
The present value of the cash flows is $30,030.78.
What is the present value?In order to determine the value today of the series of payments, the present value has to be determined. Present value is the sum of the discounted cash flows.
Present value = 5,100 / (1.079)^6 + 5,100 / (1.079)^7 + 5,100 / (1.079)^8 + 5,100 / (1.079)^9 + 5,100 / (1.079)^10 + 5,100 / (1.079)^11 + 5,100 / (1.079)^12 + 5,100 / (1.079)^13 + 5,100 / (1.079)^14 + 5,100 / (1.079)^15 + 5,100 / (1.079)^16+ 5,100 / (1.079)^17 + 5,100 / (1.079)^18 + + 5,100 / (1.079)^19 + + 5,100 / (1.079)^20 = $30,030.78
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Please help me 10 points
Answer: Its 4(x+1)
Step-by-step explanation:
You combine all the x's, creating 4x+4.
In the last answer, it has 4(x+1) which by distributing you should get 4x+4!
2. the boom df of the jib crane and the column de has a uniform weight of 50lb/ft. if the hoist and load weight weigh 300lb, draw the fbd and establish the equilibrium equations to determine the resultant internal loadings in the crane on cross sections through points a, b, and c.
Load is when the collection of forces is applied on the beam or segment then it is called load and the unit of the load is the newton.
To solve these questions there are a few steps to follow:
first, as per the question we have to draw a free-body diagram by considering point A.
Resolve the force in the x-direction:
[tex]R_A_x=0[/tex]
Resolve the force in the y-direction:
[tex]R_A_y-150-300=0\\\\R_A_y=450lb[/tex]
Now take the moment about point A, we get
[tex]M_A+(150*1.5)+(300*3)=0\\\\M_A=-1125lb.ft[/tex]
Next, draw a free-body diagram by considering point B.
Resolve the force in the x-direction:
[tex]R_B_x=0[/tex]
Resolve the force in the y-direction:
[tex]R_B_y-550-300=0\\\\R_B_y=850lb.[/tex]
Now take the moment about point B, we get
[tex]M_B+(550+5.5)*(300*11)=0\\\\M_B=-6325lb.ft[/tex]
And the last one draws a free-body diagram by considering point C.
Resolve the force in the x-direction:
[tex]R_C_x=0[/tex]
Resolve the force in the y-direction:
[tex]R_C_y-250-650-300=0\\\\R_C_y=1200lb.[/tex]
Now take the moment about point B, we get
[tex]M_C+(650+6.5)*(300*13)=0\\\\M_B=-8125lb.ft[/tex]
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each student in a sample of 490 students at a state university was classified according to year in school (freshman, sophomore, junior, senior) and what types of body art the student had (body piercings only, tattoos only, both tattoos and body piercings, and no body art).
At a significance threshold of 0.10, p-value(0.0005)< [tex]\alpha[/tex] =0.10, therefore we reject [tex]H_{0}[/tex].
Under the assumption of independence, the expected frequencies for contingency tables are
[tex]e_{ij} = \frac{(Row_{i}Total)(Column_{j} total)}{SampleSize}[/tex]
Using the formula for the number of freshmen without body art: (247*168)/490=84.69.
State the null and alternative hypotheses:
[tex]\alpha = 0.10[/tex]
[tex]H_{0}[/tex]: There is a connection between body art and class standing
Ha: There is no connection between class standing and rejection from body art. [tex]H_{0}[/tex] if the probability is less than 0.10.
the test statistic for independence is
[tex]X^2= \sum\limits_i \sum\limits_j\frac{(f_{ij}-e_{ij} )^2 }{e_{ij} }[/tex]
where fij = observed frequency for the contingency table category in rows i and j
eij = expected frequency for the contingency table category in rows i and j based on the assumption of independence
We only need to add up the values as they have already been obtained and are listed in the table to obtain the chi-square value.
Therefore,
[tex]X^2= 2.56+ 4.33+1.1+0.02+0.69+0.02+1.2+0+0.49+0.51+0.33+0.25+4.99+4.31+8.41+0.27[/tex]
[tex]X^{2} = 29.48[/tex]
Consequently, the probability of p-value=0.0005
Given DF=9.
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when 2610 11.7 0.22 are added, the answer to the correct number of decimal places is . group of answer choices 2621.9 2600 2620 2621.92 2621
Answer: 2621.92
Step-by-step explanation:
The addition of the numbers 2610 and 11.7 and 0.22 is 2621.92.
Hence the correct option is given by (D).
Addition is a mathematical operation to sum up between two or more than two mathematical quantities or numbers specially.
Here given the numbers are 2610 and 11.7 and 0.22.
So the addition of the numbers 11.7 and 0.22 is given by,
= 11.7 + 0.22
= 11.92
So the sum of 2610, 11.7 and 0.22 is given by,
= 2610 + 11.7 + 0.22
= 2610 + 11.92
= 2621.92
Hence the correct option is given by (D).
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Please help me answer this :)
extra points
The values in the table do not represent the function.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
A data table.
The table does not represent the function.
Because the input value of -3 connected to two points 1 and 0.
Therefore, it is not a function.
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Blitzstein, 1.43) Let A and B be events. The symmetric difference AAB is defined to be the in A or B but not both. In logic and engineering, this event is also set of all elements that are called the XOR (exclusive or) of A and B. We will show P(AAB) P(A)+ P(B) 2P(An B) in two ways: words and a picture and (a) via an explanation of why this makes using your own sense (b) by using the definition and properties of probability.
The XOR (exclusive or) of two events A and B can be defined as the set of all elements that are in either A or B but not both.
The probability of this event, P(AAB), can be calculated by summing the probabilities of A and B and subtracting twice the probability of the intersection of A and B, as follows:
P(AAB) = P(A) + P(B) - 2P(AnB)
This can be illustrated with a Venn diagram, where A and B are represented by two overlapping circles. The intersection of A and B, AnB, is represented by the overlapping region, and the symmetric difference, AAB, is represented by the non-overlapping regions of A and B.
The probability of AAB can then be calculated by adding the area of the two non-overlapping regions and subtracting twice the area of the overlapping region.
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20 is to 28 as 3x-5 is to 3x-5+10
20 is 8 less than 28 as 3x-5 is 10 less than 3x-5+10.
What is comparison?Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.
Given that, 20 is to 28 as 3x-5 is to 3x-5+10
We see, 28-20 = 8
That mean, we need to add 8 to 20 or subtract 8 from 28 to make both equal,
Therefore, we can say, 20 is 8 less than 28, or 28 is 8 more than 20,
Similarly,
3x-5 and 3x-5+10
We see, 3x-5+10 - (3x-5)
= 3x+5-3x+5
= 10
That mean, we need to add 10 to 3x-5 or subtract 10 from 3x-5+10 to make both equal,
Therefore, 3x-5 is 10 less than 3x-5+10, or 3x-5+10 is 10 more than 3x-5,
Hence, 20 is 8 less than 28 as 3x-5 is 10 less than 3x-5+10.
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Amber is solving the inequality |x+6| - 12 < 13 by graphing. Which equations should Amber graph? a. y1 = |x+6|, y2 = 25 b. y1 = x+6, y2 = 25 c. y1 = |x+6|, y2 = 13 d. y1 = x+6, y2 = 13
Option(a) is the correct answer.
The inequality is:
|X+6|- 12 < 13
Here we can add 12 to both sides:
|X+6| <13 + 12
⇒|X+6| <25
⇒|X+6| < 25
We can separate it into two equations:
if x > -6, then |X+6| = x + 6
⇒ (x + 6) < 25
⇒x < 25 - 6
⇒ x < 19
if x < -6, then |X+6| = -(x + 6)
⇒-(x + 6) < 25
⇒ -x < 31
⇒ x > -31 (changing the sign)
And with those two equations, we get the:
-31 < x < 19
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Which of the following measures would create an infinite number of triangles?
three angles: 62°, 34°, and 84°
three sides: 3 cm, 5 cm, and 10 cm
two sides of 4 cm and 7 cm with an angle of 54° between them
three sides: 3 cm, 5 cm, and 7 cm
Answer:
(a) three angles: 62°, 34°, and 84°
Step-by-step explanation:
You want to know which specification can result in an infinite number of triangles.
Angles onlyIf only the angles are specified, the sides can have an infinite number of (related) lengths.
three angles: 62°, 34°, and 84° will create an infinite number of triangles
Sides onlyAssuming the side lengths can form a triangle, they will specify exactly one triangle.
Lengths 3 cm, 5 cm, and 10 cm cannot form a triangle.
Sides and angle betweenWhen two sides are specified along with the angle between them, exactly one triangle can be formed.
answer the question for me
Answer: 1, 2, and 4.
Step-by-step explanation: Each must be wider than the angle than a "L" has.
3. What is the value of the expression 6(10a + 2b)
Write an expression that shows the sum of exactly two terms
that is equivalent to 6(10a + 2b).
Answer:
60b + 12b
Step-by-step explanation:
I’m thinking of a number. When you multiply it by 5 and subtract 3 you will get a number less than 80. Form an inequality and solve it to describe the range of possible numbers
The range of possible numbers will be (-∞ , 16.6] as per the given conditions.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, I’m thinking of a number. When you multiply it by 5 and subtract 3 you will get a number less than 80.
Let "x" be the number
Thus from the given expression
=> 5*x - 3 < 80
add 3 on both sides
=> 5x -3 + 3 < 80 +3
=> 5x < 83divide by 5 into both sides
=> x < 83/5
=> x < 16.6
thus the range of x for the given Condition will be (-∞ , 16.6]
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Factor the expression using gcf of 42+24n
Answer: 6 (7+4n)
Step-by-step explanation: 6 is the gcf
Determine whether the function is continuous on the entire real number line. Explain your reasoning.
f(x) = (x2 − 9)3
O The function is not continuous because the function is not defined at x = 9.
O The function is not continuous because the function is not defined at x = ±3.
O The function is not continuous because the function is not a polynomial.
O The function is continuous because the function's domain is the entire real line.O The function is continuous because the function is a polynomial.
The function [tex]f(x) = (x^2 - 9)^3[/tex] is continuous on the entire real number line because its domain is the entire real line and it is a polynomial, which is a continuous function.
The function [tex]f(x) = (x^2 - 9)^3[/tex] is continuous on the entire real number line because its domain is the entire real line and it is a polynomial, which is a continuous function. A function is considered continuous at a point if the limit of the function as the input approaches the point exists and is equal to the function's value at that point. In this case, the function's domain is the entire real line, meaning that it is defined for all real values of x. The function is also a polynomial, which is a continuous function by definition. Thus, the function is continuous on the entire real number line.
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in each of problems 1 through 4: a. draw a direction field and sketch a few trajectories. b. express the general solution of the given system of equations
The general solution is an equation that describes all possible solutions of the system. Finally, we can use the general solution to find the specific solutions to the system.
1. [tex]\frac{dy}{dt} = t - y, \frac{dx}{dt} = y - t$a.[/tex]
b. [tex]$y^2 - 2ty + x = c$[/tex]
2.[tex]$\frac{dy}{dt} = y - t^2, \frac{dx}{dt} = t^2 - x$a.[/tex]
b. [tex]$y^2 - 2tx + x^2 - t^2 = c$[/tex]
3. [tex]$\frac{dy}{dt} = ty - x, \frac{dx}{dt} = y - tx$[/tex]
a.
b. [tex]$y^2 - 2tx + x^2 = c$[/tex]
4.[tex]$\frac{dy}{dt} = xy, \frac{dx}{dt} = x$[/tex]
a.
b. [tex]$y = cxe^{x^2/2}$[/tex]
In each of the four problems, we are given a system of equations. To solve the system, we first need to draw a direction field and sketch a few trajectories. This gives us a visual representation of the system, which helps us understand it better. Next, we need to find the general solution of the system. To do this, we need to solve the system of equations algebraically. The general solution is an equation that describes all possible solutions of the system. Finally, we can use the general solution to find the specific solutions to the system.
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what is x if 3x+4=19
3x + 4 = 19
3x = 19-4
3x = 15
[tex]x = \frac{15}{3} \\ [/tex]
x = 5
What is the product of 0.04 x 8?
Answer:
0.32
Step-by-step explanation:
which statement best describes a graph of paired points that form a proportional relationship? responses a straight line can be drawn through all the points, but the line does not pass through the origin. a straight line can be drawn through all the points, but the line does not pass through the origin. a straight line cannot be drawn through all of the the points, but the line passes through the origin. a straight line cannot be drawn through all of the the points, but the line passes through the origin. a straight line cannot be drawn through all of the the points, and the line does not pass through the origin. a straight line cannot be drawn through all of the the points, and the line does not pass through the origin. a straight line can be drawn through all the points, and the line passes through the origin.
A straight line can be drawn through all the points, and the line passes through the origin.
When two variables are proportional, the ratio of their values remains constant. A graph of paired points that form a proportional relationship will show a straight line when plotted on a graph. The position of the line on the graph will depend on the constant of proportionality, which determines the slope of the line. If the constant of proportionality is positive, then the line will slope upwards, and if the constant of proportionality is negative, the line will slope downwards. If the line passes through the origin, it means that when one variable is zero, the other variable is also zero. This is referred to as an "origin-centered proportional relationship." In this case, the line passes through the point (0, 0), which is the origin. If the line does not pass through the origin, it means that there is a non-zero intercept, and that the relationship between the variables is not centered on the origin. In this case, the line will have a non-zero y-intercept, which is the value of the second variable when the first variable is zero.
In conclusion, the statement "a straight line can be drawn through all the points, and the line passes through the origin" best describes a graph of paired points that form a proportional relationship centered on the origin.
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andre and priya are tracking the number of steps they walk. andre records that he can walk 6000 steps in 50 minutes. priya writes the equation y
Andre walks more steps than Priya
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
To solve this problem, we have to state the equation using the information of the problem:
Calculating Andre's steps we have:
y(Andre) = 6000 steps/50 minutes
y(Andre) = 120 steps/ minute
If the total of hours is 5 hours we convert hours to minutes and we have:
5 hours * (60 minutes/ 1 hours) = 300 minutes
Andre's steps in 300 minutes are:
y(Andre) = 120 steps/ minute * 300 minutes
y(Andre) = 36000 steps
Now we calculate the steps of Pria with the equation given:
y=118x
y(Pria) = 118*300
y(Pria) = 35400 steps
36000 steps > 35400 steps
y(Andre) > y(Pria)
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Correctly written question:
Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walk for a total of 5 hours. Who walks more steps?
Write an equation that would change the graph of y=(x-2)^3+5
A. Move it 2 spaces left
B. Flip it vertically
C. Vertically stretch it
Show work
We may multiply the y-values by -1 to flip the graph of y = (x - 2)^3 + 5 vertically. This will display the graph along the x-axis. The inverted graph's equation is y = -((x - 2)^3 + 5).
What is equation?An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
To flip the graph of y = (x - 2)^3 + 5 vertically, we can multiply the y-values by -1. This will reflect the graph across the x-axis. The equation for the flipped graph is: y = -((x - 2)^3 + 5).
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3. For a different shipment, cars are loaded first, and then trucks are loaded afterwards. a. Write an equation you could enter into a calculator or a spreadsheet tool to find the number of trucks that can be shipped if the number of cars is known. SEMI
b. Use vour equation and a calculator or a computer to find the number of trucks that can be shipped if the cargo already has 1,000 cars. What if the cargo already has 4,250 cars?
a) The solution to the equation is y = ( 21,600 - 3.6x ) / 7.5 , where y is the number of trucks and x is the number of cars
b) when x = 1,000 cars , y = 2,400 trucks and
when x = 4,250 cars , y = 840 trucks
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of cars be x
Let the number of trucks be y
The total cargo the ship can hold = 21,600 tons
The weight of one car = 3.6 ton
The weight of one truck = 7.5 tons
Now , the equation will be
3.6x + 7.5y = 21,600
On simplifying the equation , we get
Subtracting 3.6x on both sides of the equation , we get
7.5y = ( 21600 - 3.6x )
Divide by 7.5 on both sides of the equation , we get
y = ( 21,600 - 3.6x ) / 7.5
The number of trucks y = ( 21,600 - 3.6x ) / 7.5
b)
Now , when x = 1000 cars
Substitute the value of x in the equation , we get
y = ( 21,600 - 3.6 ( 1000 ) ) / 7.5
y = 2,400 trucks
And , when x = 4250 cars
Substitute the value of x in the equation , we get
y = ( 21,600 - 3.6 ( 4250 ) ) / 7.5
y = 840 trucks
Hence , the equation is y = ( 21,600 - 3.6x ) / 7.5
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Please help!!! I suck at algebra and this is middle school stuff:((
Answer:
77
Step-by-step explanation:
1. solve the first part by plugging in 7 for y.
14(7)+37/5
98+37/5
135/5
27
2. then solve the second part by plugging in 7 for y.
8(2(7)-1)
8(14-1)
104
3. then subtract 27 from 104
104-27=77
A square piece of cloth with an area of 324 square inches is folded in half twice to form the napkin shown. What is
the area of the folded napkin?
Answer:
I think it is 4.5 length
area= 20.25
Step-by-step explanation:
Step 1: I square rooted 324 to get 18
Step 2: I divided that number by 2 twice to get 4.5
18/2 = 9/2 = 4.5
multiply 4.5 by 4.5 to get 20.25!
Hope this is correct!
If a vehicle is going 60 mph, how many feet does it travel in one second?
The vehicle going at 60 mph travelled 88 feet in one second
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
Speed is the ratio of distance to time taken. It is given by:
Speed = distance / time
If a vehicle is going 60 mph.
1 second = 1/3600 hr
Therefore in one second:
Speed = distance / time
60 mph = distance / (1/3600)
distance= 60 * 1/3600 = 1/60 miles
1 mile = 5280 feet
1/60 miles = 1/60 miles * 5280 feet per mile = 88 feet
The vehicle travelled 88 feet
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Give the value of c in the interval [0,2] that satisfies the conclusion of the mean value theorem for g(x) = -3 root x + 2. a) 0 b) 2 c) 1/2 d) 3/2 e) 5/2
There exists a value of c in the interval [0,2] such that g(c) = 1, and that value is c = 1/2. (option c)
The mean value theorem states that for any continuous function over a closed interval, there exists a point at which the value of the function is equal to the average of the minimum and maximum values of the function. In this case, the interval is [0,2] and the function is g(x) = -3√x + 2.
To find the value of c, we need to find the average of the minimum and maximum values of g(x) in the interval [0,2]. The minimum value of g(x) in the interval is g(0) = 2, and the maximum value is g(2) = -3√2 + 2 = 0. The average of the minimum and maximum values is (0 + 2)/2 = 1. Hence, there exists a value of c in the interval [0,2] such that g(c) = 1, and that value is c = 1/2.
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PLEASE HELP 20 POINTS
Answer: 3 times 5 minus a number x
Step-by-step explanation:
(5x + 1) (12x - 8) =
The multiplication of the expression given is 60x² - 28x - 8.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is (5x + 1) (12x - 8).
We have to multiply the expressions and simplify.
For any numbers or algebraic expressions, a, b, c and d,
(a + b) (c + d) = ac + ad + bc + bd
(5x + 1) (12x - 8) = (5x × 12x) + (1 × 12x) + (5x × -8) + (1 × -8)
= 60x² + 12x - 40x - 8
= 60x² - 28x - 8
Hence the multiplication of the given expression gives 60x² - 28x - 8.
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