Mathematics High School

Which expression forms an equation with the given expression?

24 - 5 * 2 = ______


A. (5 + 3) * 2

B. 2(6 + 1)

C. 5 * 8 - 2

D. 4 * 9 + 2

Answers

Answer 1
First, using PEDMAS, find the answer is 14 (24-10) 

Check which of the options also give you 14. 

A) (8)*2 => 16 
B) 2(7) => 14 (CORRECT) 
C) 40-2 => 38 
D) 36+2 => 38 

Hope I helped :) 
Answer 2
24 - 5 * 2 = 14 since 5 * 2 = 10 and 24 - 10 = 14.

A) is not the right answer because the answer for that is 16

B) is the correct answer because it equals 14 since 6 + 1 is 7 and 2 * 7 is 14

C) is not the right answer because the answer for that is 38

D) is not the right answer because the answer for that is 44.

Related Questions

How much in Federal taxes does Curtis annually pay?

Answers

he pays 29.59 a week

 multiply that by 52 weeks in a year

29.59 * 52 = 1538.68 a year

 Answer is A

Use the graph of f to estimate the local maximum and local minimum. (explain)

Answers

check the picture below.

Answer:

The graph has local maximum at (0,0) and minimum at  (-2,-4) and (2,-4).

Step-by-step explanation:

Consider the provided graph.

it is not always possible to find maximum or minimum for the whole function, but locally it is.

To find the local maximum and minimum we need to choose an interval first.

Local maximum: f(c) ≥ f(x) for all x in the interval

Local minimum: f(c) ≤ f(x) for all x in the interval

For better understanding refer the figure 1

Now consider the provided graph:

The graph of the function at (-2,-4) and (2,-4) shows the minimum value that is -4.

Because at x = -2 and 2 the value of function f(x)≥f(c) for every x in the domain.

Also the graph of the function has local maximum at (0,0) as at x = 0

The value of function f(x)≤f(c) for every x in the domain.

Hence, the graph has local maximum at (0,0) and minimum at  (-2,-4) and (2,-4).

Find the distance from point A(−1, 7) to the line y= 3x. Round your answer to the nearest tenth.

Answers

the line joining A to y = 3x will be perpendicular to the latter so its slope will be -1/3.

its equation will be y - 7  = -1/3(x  + 1)

= y = -1/3x + 20/3

where the lines intersect:-

3x = -1/3x + 20/3
10/3 x  = 20/3

x =  2   and y =   3*2 = 6

so we need to find distance between (-1,7) and (2,6)  


this is  sqrt[((7-6)^2 + (-1-2)^2)]  =  sqrt 10   =  3.2 to nearest tenth.

I assume that we want to find the minimum distance between the point A(-1, 7) and the line y = 3x.

We will get that the distance is 3.22

So first, let's see how to get the distance between two points (x₁, y₁) and (x₂, y₂). We just use the general formula:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Now we want to find the distance between (-1, 7) and a point on the line y = 3*x, that can be written as (x, 3x)

That distance is:

[tex]d = \sqrt{(-1 - x)^2 + (7 - 3x)^2}[/tex]

Now we want to minimize this, which is equivalent to minimize d^2, then we can define:

D = d^2

and write:

[tex]D = (-1 - x)^2 + (7 - 3x)^2\\\\D = 1 - 2x + x^2 + 49 - 42x + 9x^2\\\\D = 10x^2 - 44x + 50[/tex]

Now we need to minimize this, which is a parabola, so the minimum will be at the vertex of the parabola (we know this because the leading coefficient is positive, thus the parabola opens upwards).

Remember that for a parabola like:

a*x^2 + b*x + c

The vertex is at:

x = -b/2a

Then for our parabola, the vertex will be at:

x = -(-44)/(2*10) = 44/20 = 2.2

Thus the minimum distance is given by:

[tex]d = \sqrt{(-1 - 2.2)^2 + (7 - 3*2.2)^2} = 3.22[/tex]

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Let r1 and r2 be relations on a set a represented by the matrices mr1 = ⎡ ⎣ 0 1 0 1 1 1 1 0 0 ⎤ ⎦ and mr2 = ⎡ ⎣ 0 1 0 0 1 1 1 1 1 ⎤ ⎦. find the matrices that represent
a.r1 ∪ r2.
b.r1 ∩ r2.
c.r2 ◦r1.
d.r1 ◦r1.
e.r1 ⊕ r2.

Answers

Given:
[tex]r1 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] \,\, and \,\, r2= \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&1&1\end{array}\right] [/tex]

Part a. r1 ∪ r2
This assembles matrix elements from either r1 and/or r2.
[tex]r1 \cup r2 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&1&1\end{array}\right] [/tex]

Part b. r1 ∩ r2
This assembles matrix elements common to both r1 and r2.
[tex]r1 \cap r2 = \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&0&0\end{array}\right] [/tex]

Part c. r2 . r1
[tex]r2 \circ r1 = \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&1&1\end{array}\right] \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] = \left[\begin{array}{ccc}1&1&1\\2&1&1\\2&2&1\end{array}\right] [/tex]

Part d. r1 . r1
[tex]r1 \circ r1 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] = \left[\begin{array}{ccc}1&1&1\\2&2&1\\0&1&0\end{array}\right] [/tex]

Part e. r1 ⊕ r2 (Direct sum)
[tex]r1 \oplus r2 = \begin{bmatrix} r1&0\\0&r2\end{bmatrix} = \begin{bmatrix} 0&1&0 &0&0&0\\ 1&1&1 &0&0&0\\ 1&0&0 &0&0&0\\ 0&0&0 &0&1&0\\0&0&0 &0&1&1\\ 0&0&0 &1&1&1\end{bmatrix}[/tex]



Final answer:

The operation results on the matrices representing relations r1 and r2 are beautiful illustrations of how relations are manipulated in set theory. Given the limitations imposed by the data available, only three of the five stipulated operations can be carried out.

Explanation:

In the given question, the student needs to perform different operations on the matrices that represent relations r1 and r2. Here is the solution:

r1 ∪ r2 (Union of r1 and r2): It's obtained by taking the union of the corresponding elements in the two matrices. If either or both of the matrices have a 1 in a position, then put a 1, else 0. So the matrix for r1 ∪ r2 is ⎡ ⎣ 0 1 0 1 1 1 1 1 1 ⎤ ⎦ r1 ∩ r2 (Intersection of r1 and r2): It's obtained by taking the intersection of the corresponding elements in the two matrices. If both of the matrices have a 1 in a position, then put a 1, else 0. So the matrix for r1 ∩ r2 is ⎡ ⎣ 0 1 0 0 1 1 1 0 0 ⎤ ⎦ r2 ◦r1 (Composition of r2 and r1): If there exists an element in the set such that (a, b) is in r1 and (b, c) is in r2, then put a 1 in A[ac] else put a 0. Due to this, the matrix comprehension is studied in higher mathematics, and it can't be calculated from the given matrices. r1 ◦r1 (Composition of r1 and r1): Same as the previous operation but with both relations being r1. It also requires the full set of elements to calculate and can't be derived from the given matrices. r1 ⊕ r2 (Symmetric difference of r1 and r2): It is obtained by taking the XOR of each element in the matrices. So if the two elements are the same, put a 0, else put a 1. So the matrix for r1 ⊕ r2 is ⎡ ⎣ 0 0 0 1 0 0 0 1 1 ⎤ ⎦

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The height of a triangle is 7 ft more than its base. if the area of the triangle is 30 ft^ what is the lentgh of the base

Answers

since the area of a triangle is in the form
area=0.5(base)(height)
height=base+7
let base=x
area=0.5(x)(7+x)
30=3.5x+0.5x^2
multiply the equation by 2
60=7x+x^2
subtract 60 from both sides
x^2+7x-60=0
(x-5)(x+12)=0
thus  x=5 or x=-12 since we are only considering positive answers
x=-12 is rejected
so base=5 and height=5+7=12

Write the equation of the line that passes through (–1, 5) and has a slope of 3 in point-slope form.

Answers

Hello,

The equation for point-slope form is y-y1 = m (x-x1).

Let's plug in the numbers for the equation: y-5 = 3 (x+1). This is the equation for point-slope form with the given slope and pair.

Hope this helps!

May

Final answer:

The equation of the line that passes through the point (-1,5) and has a slope of 3 in point-slope form is y = 3x + 8.

Explanation:

The subject of this question relates to Mathematics, specifically algebra and line equations. The line equation in point-slope form is given by y - y1 = m(x - x1). In this equation, (x1, y1) represents the point that the line passes through and m represents the slope of the line. In our case, we know that the line passes through the point (-1,5) and has a slope of 3.

By substituting these values into the point-slope formula, we get the following:y - 5 = 3(x - (-1)), or, after simplifying, y - 5 = 3x + 3. So, the equation of the line that passes through (-1,5) and has a slope of 3 is y = 3x + 8.

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Answer for 6-9 please asap

Answers

6. False
7.True
8. False
9. False
#6 is false
Weight can change, but mass is constant
#7 is true
Sodium and Chlorine make table salt
#8 is true
this one is both true and false, like adding kool-aid to water changes the color, but so does fireworks, which explodes into colors.
#9 is false
it goes Reactants>Products

hope this helps!

Find the equation of the line that is parallel to the given line and passes through the given point y= -x +5; (2,7)

Answers

y=3x + 13 ( you should use Quilt ) 

Given the expression,y = 2x^2/ x + 4, choose the correct vertical asymptote.

Answers

There is a vertical asymptote when the denominator x + 4 = 0 That is when x = -4
It is x = -4.

In the diagram ABC = WRS. What is the perimeter of WRS?

Answers

AB = 3, BC = 4, AC = 5 because of a 3-4-5 right triangle.
Perimeter = 12 for both triangles.
The correct answer is 12 units ( on edgenuity )

Um cone reto tem 24cm de altura e o raio da base é igual a 18cm. Calcule
A) a medida de sua geratriz
B) a área total lateral (aproximadamente)
C) a área total (aproximadamente)
+volume

Answers

A)
A geratriz pode ser encontrada através dum teorema de Pitágoras. Tendo a altura e o raio, podemos chegar à medida da geratriz. Soma-se o quadrado da altura com o quadrado do raio para se obter o quadrado da geratriz. depois basta fazer a raíz quadrada do quadrado da geratriz para encontrar a medida da geratriz. 
[tex]\sqrt{24^{2}+ 18^{2} } = g [/tex] ⇔ 30 = g
A medida da geratriz é 30cm

B)
A área total lateral é obtida multiplicando o raio pela geratriz e pelo π.
Área total lateral = r×g×π ⇔ Atl = 18cm×30cm×π ⇔ Atl ≈ 1696,5cm²

C)
A área total é calculada somando a área da base e a área lateral. A área da base é calculada multiplicando o quadrado do raio pelo π.
Área total ≈ 1696,5cm²+(18²cm×π) ≈ 1696,5cm²+1017,9cm² ≈ 2714,4cm²

O volume do cone é dado pela área da base vezes a altura a dividir por três.
Volume do cone = (área da base×altura do cone)÷3 ≈ (1017,9cm²×24cm)÷3 ≈ 24429,6cm³÷3 ≈ 8143,2cm³

9 minutes less than Frances time as an expression

Answers

Let Frances time = F

9 minutes less than frances time = F - 9

F - 9 is your expression

hope this helps

What is the greatest common factor of 125,50 and 275

Answers

To start, look at the factors of the smallest number: in this case, 50. The factors of 50 are: 1,2,5,10,25,50. Moving to the next smallest number, 125, the factors are: 1,5,25,125. The final number, 275, has factors of: 1,5,11,25,55,275. Looking at all three of these numbers, the common factors are: 1,5,25. The greatest common factor, then, is 25.

a store manager orders t-shirts so that 15 out of every 35 are medium. how many medium t-shirts would you expect to find when there are 105 t-shirts on the rack. explain how to get

Answers

I'm pretty sure you do 15/35 (fifteen over thirty-five) times x/105 (x over one hundred and five) and cross multiply. If you get a calculator and multiply, you'll find that 15x105 is 1,575, and 35 times x is 35x. Your equation is then 35x=1,575. If you divide 1,575 by 35 you get 45. Another way to check this is by putting 15/35= in a calculator. It'll tell you 3/7. The same thing will happen with 45/105. Also, 105 divided by 35 is three, so you can multiply 15 by three. Either way, the answer is 45 medium per every 105 a rack.

A map has a scale of 1 cm : 11.5 km. Two cities are 5.5 cm apart on the map. To the nearest tenth of a kilometer, what is the actual distance corresponding to the map distance?

Answers

multiply 5.5 cm by 11.5 km

5.5 * 11.5 = 63.25

 rounded to nearest tenth = 63.3 km

Please help me with this!!!!

Answers

Let's get a feel for what the question is asking here, and what tools we can use to approach it. A quick list of information we're given:

- Small bottles can hold 2/5 L of vinegar
- Containers hold 5 L of vinegar

The question asks us specifically about the case where we have 3 containers; together, their volume totals to 3 x 5 = 15 L of vinegar.

We're asked to find the number of 2/5 L bottles we can make from those 15 L, or in other words, we're being asked to divide the 15 L up into 2/5 L portions. The math question at the core of this is really 15 ÷ 2/5.

If you have much familiarity with division by fractions, you might know that dividing by a fraction is the same as multiplying by its reciprocal. In this case, the reciprocal of 2/5 is 5/2, so 15 ÷ 2/5 is the same as 15 x 5/2. Solving that out, we get:

[tex]15\times \frac{5}{2} = \frac{15\times5}{2}= \frac{75}{2}[/tex]

75/2 as a mixed number is 37 1/2; if we were going for an exact answer, we could stop there and say that the containers fill exactly 37 1/2 bottles, but the question specifically asks how many containers can be completely filled, so we'll have to throw away the fractional part, leaving us with an answer of 37 bottles.

1. In ΔPQR, PQ = PR and M is the midpoint of QR . Prove that PM bisects ∠QPR.

ANSWER FORMAT: ΔPQM = Δ (?) because... (reason)



2. In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets
AC
at point H and the angle bisector of ∠C meets
AB
at point K. Prove that BH = CK.


ANSWER FORMAT: ΔBCK = Δ (?) because... (reason)


3. In ∆ABC the median
AM
is extended to ray
AM
and point P on
AM
is taken so that
PM = AM. What is the distance from point P to vertices C and B if AB = c and AC = b?

Answers

This is my answer. Hope this help :))))

Find the combined volume of the two rectangular prisms.

A.1,800
B.1,926
C.2,016
D.2,176

Answers

V = L * W * H
[tex] V_{1} [/tex] = 15 * 12 * 10
[tex] V_{1} [/tex] = 1800
[tex] V_{2} [/tex] = 12 * 6 * 3
[tex] V_{2} [/tex] = 216
[tex] V_{1+2} [/tex] = 1800 + 216
[tex] V_{1+2} [/tex] = 2016

Hope that helps and you can remember the formula and steps for future use!

Sharon needs 64 credits to graduate from her community college. So far she has earned 24 credits. What percent of the required credits does she​ have?

Answers

She has 37.5 % of her answers because 64/124 is 37.5

A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. Hence, Sharon has [tex]12.5[/tex]% of the credits required.

What is the percentage?

A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. It is often denoted using the percent sign, "%".

Here given information:-

Sharon needs [tex]64[/tex] credits and he earned [tex]24[/tex] credits.

So,

[tex](\frac{24}{64})[/tex]×[tex]100[/tex][tex]=\frac{1}{8}[/tex]×[tex]100[/tex]

[tex]=0.125[/tex]×[tex]100[/tex]

[tex]=12.5[/tex]%

Hence, Sharon has [tex]12.5[/tex]% of the credits required.

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Complete the square: x2 – 6x + ____ = –13 +  ____
Help Please!!!

Answers

to complete the square, you add (b/2)^2  on both side. in this case, b is -6, half of -6 is -3, -3 squared is 9, so:
x^2-6x+9=-13+9
(x-3)^2=-4
This quadratic equation have unreal solutions

The complete expression for the given equation is x^2 - 6x + 9= -13 +9

Complete the square

Given the quadratic expression x^2 - 6x = -13

In order to complete the square, we will follow the steps

Coefficient of x is -6

Half of the coefficient. = (-6/2) = -3

Square of the result = (-3)^2 = 9

Add 9 to both sides of the equation

x^2 - 6x + 9= -13 +9

Hence the complete expression for the given equation is x^2 - 6x + 9= -13 +9

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Théo Has $5 more than Denise and denise has $11 more than Rudy. Together they have $45. How much money does each have?

Answers

let theo have x dollars, then denise has x-5 dollars, rudy has x-5-11 dollars

x+(x-5)+(x-5-11)=45
x+x-5+x-16=45
         3x-21=45
              3x=66
                x=22
x-5=17
x-5-11=6

theo has 22 dollars, denise has 17 dollars, rudy has 6 dollars.

hey i need help solving these and not just the answer i really would like to know how

Answers

Hello,

1)
Let's put some name of vertex:
A with angle A=45°
B with angle B=90°
C The 3 vertex of the triangle of left.
AC=9 , y=AB=BC
With Pythagore, we can say: y²+y²=9²==>2y²=81===>y=9/√2=9√2/2

The other triangle is BDC: cos(60°)=x/y==>x=y*1/2=9√2/4

2)
Let's give some names:

A with angle A=60°
B with angle B=90
C the 3th vertex of the  left triangle.
AB=10, BC=y
tan 60°=y/10=sin(60°)/cos(60°)=(√3/2)/(1/2)=√3==>y=10√3

D is the 3 th vertex of the  right  triangle.
We use Pythagore: y²+y²=x²
x²=2*(10√3)²===>x=10*√6

Which graph models the equation 2x + 3y = 6?

Answers

:  you have to solve for y. So if you do that you get y= -2/3x + 6

graph according to y=mx + b

b is y intercept, so the graph crosses the point (0, 6)

m is the slope and slope is rise over run. So go down 2 and right 3 from (0,6) as many times as you need to fill up the graph.

Then go up 2 and left 3 from (0,6) as many times as you need to fill the graph.

Put arrows at each end of your line to show that it's a line.

Answer: i did the test and i got B and i was right so its B

Step-by-step explanation:

the scatter plot shows how many desks and computers were found in 12 different offices

how many offices had 11 computers

1
2
3
4

Answers

Answer:

It's three. Look at 11 on the Y axis (computers) and count how many dots are at  11. There's a total of three computers based on the dots at 11.

Step-by-step explanation:

A scatter plot is a set of points plotted on horizontal and vertical axes.

It shows the relationship between two sets of data.

The number of offices that have 11 computers is 3.

What is a scattered plot?

A scatter plot is a set of points plotted on horizontal and vertical axes.

It shows the relationship between two sets of data.

We have,

Horizontal axes =  number of desks

Vertical axes = number of computers

Each dot in the scatter plot indicates offices.

Number of offices = 12 dots = 12

We need to find the number of dots that is with 11 computers.

We see that there are 3 dots with 11 computes so there are 3 offices that have 11 computers.

Thus the number of offices that have 11 computers is 3.

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Help please!!! Q: A manufacturing company finds that 0.0019 of the light bulbs it makes are defective. Write this as a percent.

Answers

The answer is 0.19%.

(:
0.0019 as a percent is 0.19%

A train traveling 50 mph left a station 30 minutes before a second train running at 55 mph. How soon did the second train overtake the firstIf 50x represents the distance the slower train travels, then the faster train travels?

Answers

Train A : 50 mph
Train B : 55 mph

After 30 mins  train A has travelled 25 miles
Relative speed of trains is 5 mph

Consider train A at rest and train B at 5 mph

t = 25 / 5 h

t = 5 h

Second train overtakes after 5 h

For two trains with speeds given as 50 mph and 55 mph and a 30-minute head start for the first, the second train overtakes the first after 5 hours, based on their relative speed.

Here's how to solve a similar problem based on the given examples:

Let the first train's speed be 50 mph and the second train's speed be 55 mph.

The first train has a 30-minute head start, which at 50 mph means it has traveled 25 miles before the second train departs (since 50 miles/hour * 0.5 hours = 25 miles).

The second train travels 5 mph faster than the first, so the relative speed is 55 mph - 50 mph = 5 mph.

Now calculate the time it takes for the second train to catch up by dividing the head start distance by the relative speed: Time = Distance / Relative Speed, which is Time = 25 miles / 5 mph = 5 hours.

So, the second train will overtake the first train after 5 hours.

Find the quotient. Show all work for full credit. 4+2i/6-i

Answers

Multiply top and bottom of the fraction by the conjugate of 6 - i:-

(4 + 2i)(6 + i)         24 + 16i - 2            22 + 16i 
-----------------  =     ----------------  =       -----------
(6 - i)(6 + i)             36 - (-1)                    37

The quotient of  4+2i/6-i is (11/4-4i)/*1/5.

What is quotient?

Quotient is a result obtained by dividing one quantity by another.

explanation;

(4-2i)/(6-i)

Multiply and divide by the denominator = (6+i)

=>(4-2i)/(6-i)/(6+i)(6+i)

=> (4*6 + 4i - 12i - 2i^2)/[6^2 - (2i)^2]

=>  (24 - 8i -2)/ [36 + 4]                            [since i^2 = -1]

=> (22-8i) /40

=> 22/40 - 8i/40

=> 11/20 - i/5

Hence, the quotient of 4+2i/6-i is (11/4-4i)/*1/5.

A ratio is an ordered pair of numbers a and b, written a / b in which b does no longer identical zero. A proportion is an equation wherein ratios are set equal to each other. The share components is used to depict if two ratios or fractions are same. we can find the lacking fee by dividing the given values. the proportion formula can be given as a: b::c : d = a/b = c/d wherein a and d are the acute terms and b and c are the mean phrases.

The quantitative relation among two quantities showing the number of times one cost consists of or is contained inside the other. The indicated quotient of two mathematical expressions. b : the connection in quantity, quantity, or size among  or more matters.

A ratio can be defined as the connection or assessment among two numbers of the same unit to check how larger is one variety than the alternative one. as an instance, if the quantity of marks scored in a take a look at is 2 out of 5, then the ratio of marks received to the total range of marks is written as 2:5.

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A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. What is the rate of the current?

3 mph
4 mph
5 mph

Answers

With the current 40 miles per hour
Against the current 30 miles per hour
bv means boat velocity with NO current
cv means current velocity
A) bv + cv = 40 mph
B) bv - cv = 30 mph
Adding both equations:
2bv = 70
boat velocity with NO CURRENT = 35 miles per hour

Using equationA
bv + cv = 40
35 + cv = 40

current velocity = 5 miles per hour


Answer:

Speed of current = 5 mph

Step-by-step explanation:

Let u be the speed of boat and v be the speed of current.

A boat makes a 120-mile trip downstream in 3 hours.

120 = 3(u+v)

u + v = 40

It makes the return trip in 4 hours.

120 = 4(u-v)

u - v= 30

Adding both equations

u + v + u - v = 40+30

2u = 70

u = 35 mph

35 + v = 40

v = 5 mph

Speed of current = 5 mph

number we give to rate how strongly two variables are related to one another

Answers

I believe that the correct word here is correlation. Correlation is the term that we use when we want to say that something is strong related to the other. Correlation must be however differentiated from causality. Correlation is when two things occur at the same time. Causality is when one results in the occurrence of the other.

Correlation coefficient has a maximum value of 1 which indicates strong relationship.

Rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x)+r(x)/b(x).

Answers

I have attached an image of a long division method that can be used to find the quotient and remainder.

Hope I helped :)

Answer:

[tex]x^2+x-1-\frac{6}{x+4}[/tex]

Step-by-step explanation:

Rational expression form : [tex]\frac{a(x)}{b(x)}=q(x)+\frac{r(x)}{b(x)}[/tex]

a(x) = dividend

b(x) = divisor

q(x) = quotient

r(x) = remainder

Given expression : [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex]

We know that [tex]Dividend = Divisor \times Quotient+Remainder[/tex]

So, [tex]x^3+5x^2+3x-10 =x+4 \times (x^2+x-1)-6[/tex]

Thus a(x) = dividend =  [tex]x^3+5x^2+3x-10 [/tex]

b(x) = divisor= [tex]x+4[/tex]

q(x) = quotient=[tex]x^2+x-1[/tex]

r(x) = remainder=-6

Substitute the value in the rational form.

[tex]\frac{x^3+5x^2+3x-10}{x+4}=x^2+x-1-\frac{6}{x+4}[/tex]

Hence the rational expression [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex] in the form of [tex]q(x)+\frac{r(x)}{b(x)}[/tex] is  [tex]x^2+x-1-\frac{6}{x+4}[/tex]

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