7 m The side lengths of the base of a triangular prism are 7 meters, 5 meters, and 8 meters. The height of the prism is 12.5 meters. 12.5 m 6 m What is the lateral surface area of the prism in square meters? 5 m
Answers
Given a triangular prism with side lengths of the base as a, b, and c, and height h, then the lateral surface area, A is given by
[tex]A=(a+b+c)h[/tex]In our case,
[tex]a=5m,b=6m,c=7m,\text{ and }h=12.5m[/tex]Hence,
[tex]A=(5+6+7)12.5=18\times12.5=225m^2[/tex]Therefore, the lateral surface area in square meters is 225
Related Questions
How to graph it I know others one but not this one
Answers
Answer: (0, 2)
Explanation
The coordinates are a set of values that show the exact position of a point. In graphs, it is usually a pair of points in the form (x, y), where x represents the value in the horizontal axis and y represents the value of the vertical axis.
As we can see from the image above, in our point x = 0 (marked in red) while y = 2 (marked in purple). Rearranging the coordinate we get (0, 2).
Grocery store A is selling bananas for $9.75 for 1/2 pound .Grocery store B is selling 5 pounds of Bananas for $3.75 which store us offering the best unit rate
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Grocery Store B ($1.33 per pound of bananas)
1) With these data we can write the following, and ,
Grocery Store A:
$ pounds
9.75 1/2
x--------------- 1
1/2x=9.75 x 2
x =19.5
Cross multiplying it:
Grocery Store B
$ pounds
5 3.75
y 1
3.75y=5
y=5/3.75
y=1.33
2) The best unit rate is at Grocery Store B ($1.33 per pound of bananas)
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 277 people entered the park, and the admission fees collected totaled 828.00 dollars. How many children and how many adults were admitted?
Answers
Given:
Let x be the number of children.
Let y be the number of adults.
In total, there were 277 people.
So,
[tex]x+y=277\ldots\ldots\ldots(1)[/tex]According to the question, the fee of $1.50 for children and $4 for adults and the total fees collected is $828.
So,
[tex]1.5x+4y=828\ldots\ldots\ldots(2)[/tex]Multiply by 4 in equation (1),
[tex]4x+4y=1108\ldots\ldots\ldots(3)[/tex]Subtracting the equation (2) from (3), we get
[tex]\begin{gathered} 2.5x=280_{} \\ x=112 \end{gathered}[/tex]Substitute x=112 in equation (1), we get
[tex]\begin{gathered} 112+y=277 \\ y=165 \end{gathered}[/tex]Thus,
• The number of children is x = 112.
,• The number of adults is y = 165.
Darnell went to the movie theater with his friends. The movie theater started at 2:35 pm and lasted 1 hour 45 minutes. What time did the movie end?
Answers
If the movie started at 2:35 and lasted 1 hour
Answer: 4:20 pm
Step-by-step explanation:
We know that the movie started at 2:35 and lasted 1 hour and 45 minutes. We can split the time that it lasted into the hour and the 45 minutes to make things easier, since 1 hour after 2:35 is simply 3:35.
From here, we can add the extra 45 minutes. We can do this by first finding out how many minutes were left in that hour. There are 60 minutes in 1 hour, and 60 - 35 = 25 minutes
45 - 25 = 20
after adding the 25 minutes to complete the hour (4:00), we have 20 minutes left
4:00 + 0:20 = 4:20
Which function has the following characteristics? • A vertical asymptote at x = 3 • A horizontal asymptote at y = 2 Domain: {** +3] 2x - 8 X - 3 y=x2-9 2 9 x² - 4 4 OB. V C. 2x2 - 18 x² - 4 4 2x2 - 8 O D. ** - 9
Answers
SOLUTION
To get this, note that the vertical asymptote can be gotten by setting the denominator to be equal to 0.
If we do this, we will notice that the vertical asymptote of option A and option D is x = 3
That is
for option A
[tex]\begin{gathered} y=\frac{2x-8}{x-3} \\ x-3=0 \\ x=3 \end{gathered}[/tex]For option D
[tex]\begin{gathered} y=\frac{2x^2-8}{x^2-9} \\ x^2-9=0 \\ x^2=9 \\ x=3 \end{gathered}[/tex]So, the answer is either option A or D.
But to get the correct answer, let us look at the graphs for both functions
Graph of A
[tex]y=\frac{2x-8}{x-3}[/tex]From the graph, you can see that the domain is defined at x = 3. Notice that the green line cut across x = 3.
Now let's check Graph of option D
[tex]y=\frac{2x^2-8}{x^2-9}[/tex]From the graph, you can see that the domain is defined at x = -3 and x = 3. Notice that the purple and green line cut across x = -3 and x = 3. So, the domain here is
[tex]x=\pm3[/tex]Hence
You have the option of borrowing money from one source that charges simple interest or from another source that charges the same APR but compounds the interest monthly. Which would you choose, and why?
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I would choose the source that charges simple interest. This is because simple interest is based only on the principal (The amount borrowed), but compound interest is based on the principal and also the interest that has been generated from it.
Write down the domain of f-1 according to the following figure. A. {4, 5, 6, 7} B. {4, 3, 2, 7} C. {1, 2, 4, 5} D. {1, 2, 3, 4}
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given to find down the domain of f inverse of the function.
An inverse function is found interchanging the first and second coordinate of each ordered pair.
thus the answer is, option A. {4,5,6,7}
which description is correct for the polynomial[tex]4x {}^{2} + 3x - 2[/tex]a cubic trinomial b quartic trinomial c cubic trinomial d quadratic trinomial
Answers
4x² + 3x - 2
This is a quadratic trinomial
Explanation: A quadratic equation has 2 as its highest index power
Then a polynomial involving 3 terms is a trinomial equation.
Hence the expression
4x² + 3x - 2 has its highest index power as 2 (4x raised to the power of two) and it has three separate terms, and that makes it a quadratic trinomial.
A university student is selecting courses for his next semester. He can choose from 8 science courses and 4 humanities courses. In how many ways can he choose 4 courses if more than 2 must be science courses
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The number of ways which he can choose 4 courses if more than 2 must be science is; 224 ways.
Combination of outcomes;
He can choose from 4 humanities courses and 8 science courses.
If the condition requires that he chooses more than 2 science courses, it follows that;
He can only choose three science courses and only 1 humanities courses.
8C3 x 4C1 = 56x 4 = 224
On this note, the number of ways he can choose the required 4 courses is; 224 ways.
Learn more on combination here:
brainly.com/question/4658834
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2 STEP PROBLEM: QUADRATIC EQUATION 18x^2 = 21x
Answers
Explanation
[tex]18x^2=-21x[/tex]Step 1
to get the form
[tex]ax^2+bx+c=0[/tex]a) add 21 x in both sides
[tex]\begin{gathered} 18x^2=-21x \\ 18x^2+21x=-21x+21x \\ 18x^2+21x=0 \\ so\text{ a=18, b=21, c=0} \end{gathered}[/tex]Step 2
now, factorize the left hand side of the equation
[tex]\begin{gathered} 18x^2+21x=0 \\ (x)(18x+21)=0 \\ so\text{, the factors are x and (18x+21)} \end{gathered}[/tex]now, to get zero from those factors
[tex]\begin{gathered} (x)(18x+21)=0 \\ x=\text{ 0} \\ or \\ 18x+21=0 \\ \text{subtract 21 in both sides} \\ 18x+21-21=0-21 \\ 18x=-21 \\ \text{divide both sides by 18} \\ \frac{18x}{18}=\frac{-21}{18} \\ x=-\frac{21}{18}=-\frac{7}{6} \\ x=-\frac{7}{6} \end{gathered}[/tex]so, the answer is
[tex]x=\text{ 0 and x=-7/6}[/tex]I hope this helps you
Each angle of the equilateral triangle in the figure has measure (2x – 9)°. Determine the value of x.Question options:A) x = 69B) x = 34.5C) x = 25.5D) x = 60
Answers
On an equilateral triangle, each angle has a measure of 60º. Then:
[tex]2x-9=60[/tex]Solve for x. To do so, add 9 to both sides of the equation:
[tex]\begin{gathered} \Rightarrow2x-9+9=60+9 \\ \Rightarrow2x=69 \end{gathered}[/tex]Divide both sides of the equation by 2:
[tex]\begin{gathered} \Rightarrow\frac{2x}{2}=\frac{69}{2} \\ \Rightarrow x=34.5 \end{gathered}[/tex]Therefore, the value of x is:
[tex]34.5[/tex]Factor by grouping c^2-8c +16 -4d^2
Answers
INFORMATION:
We have the following expression
[tex]c^2-8c+16-4d^2[/tex]And we must factor it by grouping
STEP BY STEP EXPLANATION:
To factor it by grouping, we must:
1. group the first 3 terms of the expression
[tex](c^2-8c+16)-4d^2[/tex]2. factor the expression in the parenthesis
[tex](c-4)^2-4d^2[/tex]3. rewrite 4d^2 as unique exponential expression
[tex](c-4)^2-(2d)^2[/tex]4. factor by square difference
[tex]((c-4)+2d)((c-4)-2d)[/tex]5. simplify
[tex]=(c+2d-4)(c-2d-4)[/tex]ANSWER:
the factoring for c^2-8c +16 -4d^2 by grouping is
[tex](c+2d-4)(c-2d-4)[/tex]Use the pair of functions f and g to find the following values if they exist[tex] f(x) = \sqrt{x + 2} [/tex][tex]g(x) = 3x - 2[/tex]a. (f+g)(2)b.(f/g)(0)c.(f-g)(-1)
Answers
Two mechanics worked on a car. The first mechanic charged $105 per hour, and the second mechanic charged $120 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $2175. How long did each mechanic work?
Answers
Solution
The first mechanic charged $105 per hour.
The second mechanic charged $120 per hour.
The mechanics worked for a combined total of 20 hours
Let the first mechanic work for x hours
Then
[tex]\begin{gathered} 105x+(20-x)120\text{ =2175} \\ 105x+2400-120x=2175 \\ \text{collect like terms} \\ 105x-120x=2175-2400 \\ -15x=-225 \\ \\ \text{Divide both sides by -15} \\ \frac{\text{-15x}}{\text{-15}}=-\frac{225}{\text{-15}} \\ \\ x=15 \end{gathered}[/tex]The first mechanic work for x hours which 15hours
The second mechanic work for (20-x ) hours which is 20-15=5hours
.
What is the midpoint of the line segment graphed below?10-(5,9)-10-10-(2,-1)10
Answers
Step 1
The midpoint formula is given as;
[tex]\begin{gathered} \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \\ =\frac{5+2}{2},\frac{9-1}{2} \\ =3.5,4 \end{gathered}[/tex]Answer;
[tex](\frac{7}{2},4)[/tex]18#Suppose that 303 out of a random sample of 375 letters mailed in the United States were delivered the day after they were mailed. Based on this, compute a 90% confidence interval for the proportion of all letters mailed in the United States that were delivered the day after they were mailed. Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.)Lower limit:Upper limit:
Answers
ANSWER:
Lower limit: 0.77
Upper limit: 0.84
STEP-BY-STEP EXPLANATION:
Given:
x = 303
n = 375
We calculate the value of the proportion in the following way:
[tex]\begin{gathered} p=\frac{x}{n}=\frac{303}{375} \\ \\ p=0.808 \end{gathered}[/tex]For a 90% confidence interval we have the following:
[tex]\begin{gathered} \alpha=100\%-90\%=10\%=0.1 \\ \\ \alpha\text{/2}=0.1=0.05 \\ \\ \text{ For the normal table this corresponds to:} \\ \\ Z_{\alpha\text{/2}}=1.645 \end{gathered}[/tex]We calculate the limits of the 90% confidence interval using the following formula:
[tex]\begin{gathered} \text{ Lower limit: }p-Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}}=\:0.808-1.645\cdot\sqrt{\frac{0.808\cdot\left(1-0.808\right)}{375}}\:=0.77 \\ \\ \:\text{Upper limit: }p-Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot\left(1-p\right)}{n}}\:=0.808+1.645\cdot\sqrt{\frac{0.808\cdot\left(1-0.808\right)}{375}}=0.84 \end{gathered}[/tex]if I make 9.75 hour and work 30 hours a week. how much I make in a week? how much I make in a month? how much in a year?
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Since you make $9.75 per hour and you work 30 hours a week that means that you make:
[tex]9.75\cdot30=292.5[/tex]Therefore you make $292.5 in a week.
A month has 4 1/3 weeks, then per month you earn:
[tex]292.5\cdot4\frac{1}{3}=1267.5[/tex]Therefore you earn $1267.5 in a month.
Finally since each year has 12 month you earn:
[tex]1267.5\cdot12=15210[/tex]Therefore you earn $15210 in a year.
Which of the following are the xintercepts on the graph of the function shown below? f(x)=(x+2)(x-7)
Answers
Which of the following are the xintercepts on the graph of the function shown below? f(x)=(x+2)(x-7)
we have the function
f(x)=(x+2)(x-7)
This is a vertical parabola written in factored form
The zeros or x-intercepts of the function are
x=-2 and x=7
Remember that the x-intercepts are the values of x when the value of the function is equal to zero
therefore
the answer is
x=-2 and x=7Rewrite (4x4 + 8x2 + 3)/(4x2) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.
Answers
ANSWER
(x² + 2) + 3/4x²
EXPLANATION
Since the divisor is a single-term polynomial, to write the answer in the requested form, we can distribute the divisor into each of the terms of the dividend,
[tex]\frac{4x^4+8x^2+3}{4x^2}=\frac{4x^4}{4x^2}+\frac{8x^2}{4x^2}+\frac{3}{4x^2}[/tex]And simplify,
[tex]\frac{4x^4}{4x^2}+\frac{8x^2}{4x^2}+\frac{3}{4x^2}=(x^2^{}+2)^{}+\frac{3}{4x^2}[/tex]Hence, the answer is (x² + 2) + 3/4x².
What are the magnitude and direction of w = ❬–10, –12❭? Round your answer to the thousandths place.
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The direction of a vector is the orientation of the vector, that is, the angle it makes with the x-axis.
The magnitude of a vector is its length.
The formulas to find the magnitude and direction of a vector are:
[tex]\begin{gathered} u=❬x,y❭\Rightarrow\text{ Vector} \\ \mleft\Vert u|\mright|=\sqrt[]{x^2+y^2}\Rightarrow\text{ Magnitude} \\ \theta=\tan ^{-1}(\frac{y}{x})\Rightarrow\text{ Direction} \end{gathered}[/tex]In this case, we have:
• Magnitude
[tex]\begin{gathered} w=❬-10,-12❭ \\ \Vert w||=\sqrt[]{(-10)^2+(-12)^2} \\ \Vert w||=\sqrt[]{100+144} \\ \Vert w||=\sqrt[]{244} \\ \Vert w||\approx15.620\Rightarrow\text{ The symbol }\approx\text{ is read 'approximately'} \end{gathered}[/tex]• Direction
[tex]\begin{gathered} w=❬-10,-12❭ \\ \theta=\tan ^{-1}(\frac{-12}{-10}) \\ \theta=\tan ^{-1}(\frac{12}{10}) \\ \theta\approx50.194\text{\degree} \\ \text{ Add 180\degree} \\ \theta\approx50.194\text{\degree}+180\text{\degree} \\ \theta\approx230.194\text{\degree} \end{gathered}[/tex]Therefore, the magnitude and direction of the vector are:
[tex]\begin{gathered} \Vert w||\approx15.620 \\ \theta\approx230.194\text{\degree} \end{gathered}[/tex]I need quick answers please, is due soon. i need assistance finding 5 points. 2 to the left of vertex, i need the vertex, and 2 to the right of the vertex. the graph only goes up to 14. thank you!
Answers
We have to find 5 points of the parabola:
[tex]y=x^2+8x+11[/tex]and then graph it.
We can find the vertex by completing the square:
[tex]\begin{gathered} y=x^2+8x+11 \\ y=x^2+2\cdot4x+16-16+11 \\ y=(x+4)^2-5 \end{gathered}[/tex]As we now have the vertex form of the parabola, we can see that the vertex is at (x,y) = (-4,-5).
We can now calculate two points to the right of the parabola by giving values to x as x = 0 and x = -2:
[tex]y=0^2+8\cdot0+11=11[/tex][tex]\begin{gathered} y=(-2)^2+8\cdot(-2)+11 \\ y=4-16+11 \\ y=-1 \end{gathered}[/tex]We now know two points to the right of the parabola: (0, 11) and (-2, -1).
As the line x = -4 is the axis of symmetry, we will have the same value for y when the values of x are at the same distance from this line.
Then, we can write:
[tex]\begin{gathered} y(0)=y(-8)=11 \\ y(-2)=y(-6)=-1 \end{gathered}[/tex]Then, we have two points to the left: (-8, 11) and (-6, -1).
We can graph the parabola as:
In the figure, k//l, find the values of z and y.
Answers
Answer:
• z=113°
,• y=67°
Explanation:
In the diagram below, by the principles of vertical and corresponding angles:
[tex](6y-113)\degree=67\degree\text{ (Corresponding angles)}[/tex]We solve for y:
[tex]\begin{gathered} 6y=67+113 \\ 6y=180 \\ y=\frac{180}{6} \\ y=30 \end{gathered}[/tex]Next, angles z and (6y-113) are on a straight line. Therefore:
[tex]z+(6y-113)\degree=180\degree[/tex]However, recall we stated earlier that (6y-113)°=67°, therefore:
[tex]\begin{gathered} z+67\degree=180\degree \\ z=180\degree-67\degree \\ z=113\degree \end{gathered}[/tex]The values of z and y are 113° and 67° respectively.
Part A: Clancey and Ethan are starting new books. So far, Clancey has read 1/4 of his book, which has 240 total pages and Ethan has read 2/5 of his book, which has 170 total pages. Who has read more pages so far, Clancey or Ethan?Of the combined total number of pages in both books, what fraction have clancey and ethan read combined?
Answers
In order to find who has read more pages, let's find the number of pages read by each one.
The number of pages read by Clancey is:
[tex]\frac{1}{4}\cdot240=\frac{240}{4}=60[/tex]The number of pages read by Ethan is:
[tex]\frac{2}{5}\cdot170=\frac{340}{5}=68[/tex]So Ethan read more pages.
The combined number of pages in both books is 240 + 170 = 410.
The combined number of pages read is 60 + 68 = 128
So the fraction is:
[tex]\frac{128}{410}=\frac{64}{205}[/tex]kelly is knitting a scarf for her brother. it took her 1/3 hour to knit 3/8 foot of the scarf. How fast is Kelly's knitting speed, in feet per hour?A[tex]4 \frac{1}{2} [/tex]B[tex]3[/tex]C[tex]2\frac{1}{2} [/tex]D[tex]1 \frac{1}{8} [/tex]
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We need to divide the number of foot of scarf knitted by the number of time, in hours, taken.
[tex]\frac{\frac{3}{8}\text{ ft }}{\frac{1}{3}\text{ hour}}=\frac{3}{8}\cdot3\frac{\text{ ft}}{\text{ hour}}=\frac{9}{8}\frac{\text{ ft}}{\text{ hour}}=\frac{8+1}{8}\frac{\text{ ft}}{\text{ hour}}=1\frac{1}{8}\frac{\text{ ft}}{\text{ hour}}[/tex]( 14 + 2 ) 2 0 = 5 + 4 0 what type of property is this?
Answers
The question provides the relationship as shown below:
[tex](\frac{1}{4}+2)20=5+40[/tex]If we solve both sides individually, we have the left-hand side to give
[tex](\frac{1}{4}+2)20=45[/tex]and the right-hand side to give
[tex]5+40=45[/tex]Since both sides give the same result, we can attempt to manipulate the left-hand side of the equation with a common property we are familiar with: The Distributive Property.
The Distributive Property is written out as shown below:
[tex]a(b+c)=(a\cdot b)+(a\cdot c)[/tex]Applying this rule to the left-hand side, we get:
[tex]\begin{gathered} (\frac{1}{4}+2)20=\frac{1}{4}\cdot20+2\cdot20 \\ =5+40 \end{gathered}[/tex]This is the same expression present on the right-hand side of the equation.
Therefore, the property illustrated is the DISTRIBUTIVE PROPERTY.
Solve by completing the square. x2 - 8x + 5 = 0
Answers
Answer:
[tex]\begin{gathered} x_1=4+\sqrt[]{11} \\ x_2=4-\sqrt[]{11} \end{gathered}[/tex]Step-by-step explanation:
Solve the following quadratic completing the square:
[tex]x^2-8x+5=0[/tex]Keep x terms on the left and move the constant to the right side:
[tex]x^2-8x=-5[/tex]Then, take half of the x-term and square it.
[tex](-8\cdot\frac{1}{2})^2=16[/tex]Now, add this result to both sides of the equation:
[tex]x^2-8x+16=-5+16[/tex]Rewrite the perfect square on the left.
[tex]\begin{gathered} (x-4)^2=-5+16 \\ (x-4)^2=11 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{(x-4)^2}=\pm\sqrt[]{11} \\ x-4=\pm\sqrt[]{11} \\ x=\pm\sqrt[]{11}+4 \end{gathered}[/tex]Hence, the two solutions of the equation are:
[tex]\begin{gathered} x_1=4+\sqrt[]{11} \\ x_2=4-\sqrt[]{11} \end{gathered}[/tex]sin38° = ? (Write the Trigonometic ratio as a fraction)
Answers
Solution
The trigonometric ratio of sin 38 =
[tex]\begin{gathered} \sin \text{ 38 =}\frac{opposite}{hypothenus} \\ \text{opposite = a} \\ hypothenuse\text{ = c} \\ Sin\text{ 38 =}\frac{a}{c} \\ \end{gathered}[/tex][tex]Sin38^o\text{ = 0.6157= }\frac{6157}{10000}[/tex]2. FR has a midpoint M. Use the given information to find the missing endpoint. F(-2,3) and M(3,0)
Answers
ANSWER:
R(8, -3)
STEP-BY-STEP EXPLANATION:
We have that the midpoint formula is the following:
[tex]M(m_1,m_2)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]In this case, we know the midpoint M, that is, m1 and m2 and the startpoint F, that is, we know, x1 andy1, we replace to calculate the values of R, the endpoint:
[tex]\begin{gathered} 3=\frac{-2+x_2}{2} \\ 6=-2+x_2 \\ x_2=6+2=8 \\ \\ 0=\frac{3+y_2}{2} \\ 0=3+y_2 \\ y_2=-3 \\ \\ \text{Therefore, the missing endpoint is: (8,-3)} \end{gathered}[/tex]Question 1: Identify the vertex. *A. (-2, -1)B. (-2, 1)C. (2, -1)D. (2, 1)
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The standard equation of parabola with vertex (h,k) is :
(x - h)² = 4a(y - k)
The given eqation is : (x + 2)² = 4(y - 1)
On comparing the given equation with the standard equation we get
h = -2, a = 1 and k = 1
Vertex is ( h,k)
So, the vertex of the given equation of parabola is (-2, 1)
Answer : B (-2, 1)
f(x) = 9x² + 5x +4
g(x) = - 8x² - 3x - 4
Find (f + g)(x).
Answers
Answer:
1x^2+2x
Step-by-step explanation:
Put into Equation
(9x^2 +5x+4)+(-8x^2-3x-4)
Distribute
9x^2+5x+4-8x^2-3x-4
Combine like terms
1x^2+2x
Hope this helped!