Answers
The equations of the transformed graphs are [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex] and [tex]y = -\frac34\sin(2x)[/tex]
How to transform the functions?The tangent function
The parent function is:
y = Atan(Bx) + k
It has a period of 4.
So, we have:
[tex]\frac{\pi}{B} = 4[/tex]
Make B the subject
[tex]B = \frac{\pi}{4}[/tex]
It is shifted vertically up by 3 units.
So, we have:
k = 3
Substitute these values in y = Atan(Bx) + k and remove A
[tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]
Hence, the equation of the transformed graph is [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]
The sine function
The parent function is:
y = Asin(Bx) + k
It has a period of [tex]\pi[/tex]
So, we have:
[tex]\frac{2\pi}{B} = \pi[/tex]
Make B the subject
B = 2
It has an amplitude of 3/4
So, we have:
A = 3/4
It is flipped across the x-axis
So, we have:
A = -3/4
Substitute these values in y = Asin(Bx) + k and remove k
[tex]y = -\frac34\sin(2x)[/tex]
Hence, the equation of the transformed graph is [tex]y = -\frac34\sin(2x)[/tex]
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Related Questions
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answers
Answer: [tex]\triangle RQP \sim \triangle VPW[/tex]
Step-by-step explanation:
By the corresponding angles theorem, [tex]\angle RPQ \cong \angle VWP[/tex] and [tex]\angle RQP \cong \angle VPW[/tex].
Therefore, [tex]\triangle RQP \sim \triangle VPW[/tex] by AA.
Kindly solve this please!
Diagram for both the questions are given.
Answers
Answer:
Q9 - B) 8Q10 - D) 4.5========================
Question 9We have a diagram and need to find the number of routes without repeat paths:
[tex]ABCA[/tex] or [tex]ACBA[/tex]We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.
This gives us the number of routes:
[tex]ABCA = 1*2*2 = 4[/tex][tex]ACBA = 2*2*1 = 4[/tex]Total number is:
[tex]4 + 4 = 8[/tex]The matching answer choice is B
---------------------------------------------------------------------------
Question 10From the given we can observe that:
ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.
From similarity we get same ratio of corresponding sides:
[tex]AE/DE = AB/CD = 3/9 = 1/3[/tex]We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:
[tex]S_{ACD} - S_{ECD} = S_{AEC}[/tex]As per ratio of corresponding sides:
[tex]AE/DE = 1/3[/tex]As per segment addition:
[tex]AE + DE = AD = 4[/tex]From the two equations above we get:
[tex]DE = 3/4*AD = 3/4*4 = 3[/tex]Now, the required area is:
[tex]S_{ACD} - S_{ECD} = 1/2(4*9) - 1/2(3*9) = 4.5[/tex]This is matching the answer choice D
Answer:
9) B. 8
10) D. 4.5
Step-by-step explanation:
Question 9
For ease of visualization, label the different legs of the journey on the diagram (see attachment).
The journey needs to start and end at point A, go through points B and C (in any order), and not travel any road twice.
The different routes are:
AB (u), BC (x), CA (w)AB (u), BC (y), CA (w)AB (u), BC (x), CA (z)AB (u), BC (y), CA (z)AC (w), CB (x), BA (u)AC (z), CB (x), BA (u)AC (w), CB (y), BA (u)AC (z), CB (y), BA (u)Therefore, there are 8 different routes.
Question 10
Triangles EDC and EAB are similar since they have congruent angles:
∠EDC ≅ ∠EAB (both right angles)∠DEC ≅ ∠AEB (vertical angle theorem)Therefore, their corresponding sides are in proportion.
⇒ CD : BA = ED : EA
⇒ 9 : 3 = ED : EA
⇒ 3 : 1 = ED : EA
Since we know that AD = 4:
⇒ ED = 3
⇒ EA = 1
Area of a triangle
[tex]\sf Area = \dfrac{1}{2} \times base \times height[/tex]
To find the area of triangle AEC, subtract the area of triangle EDC from the area of triangle ADC.
[tex]\begin{aligned}\textsf{Area of triangle AEC} & = \sf Area\:of\:\triangle ADC - Area\:of\:\triangle EDC\\& = \sf \dfrac{1}{2} \cdot CD \cdot AD-\dfrac{1}{2} \cdot CD \cdot ED\\& = \sf \dfrac{1}{2}(9)(4)-\dfrac{1}{2}(9)(3)\\& = \sf 18-13.4\\& = \sf 4.5\:\:units\:squared\end{aligned}[/tex]
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You are investigating having business cards printed for your new game store. A local printing company charges $250 for the cardboard used and an hourly rate for labour of $40.
a. If h is the number of hours of labour required to print the cards, construct an equation for the cost
of the cards, C.
b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give
your answer to the nearest minute.
c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you
get printed with your current budget?
d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?
Answers
Answer:
See below.
Step-by-step explanation:
a. If h is the number of hours of labour required to print the cards, construct an equation for the cost of the cards, C.
C = $250 + ($40/hr)*h
b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give your answer to the nearest minute.
$1000 = $250 + ($40/hr)*h
($40/hr)*h = $750
h = 18.75 hours
(18.75 hours)(60 min/hr) = 1125 minutes
c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you get printed with your current budget?
(18.75 hr)*(1000 cards/hr) = 18,750 cards
d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?
Photocopy Cost for the first 1000 single-sided cards is:
(1000 cards)*($0.15) = $150
Photocopy Cost for the final 17,750 single-sided cards is:
(17,750)*($0.10) = $1,775
Totoal photocopy cost for 18,750 single-sided cards is $1,925. [1775+150]
The cheapest option for 18,750 cards is printing: $1,000
Printing is (1,925 - 1000) $925 cheaper than photocopying.
3. You recently bought a rolled up poster at a convention and need to fit it in
your luggage. In order to pack it efficiently, we need to know the surface
area of the tube. If the radius measures out to be 0.4 inches and the height
is 25 inches, what is the full surface area? Use 3.14 for .
63.8 in²
1in²
62.8 in²
63.8 in3
Answers
Answer:
A. 63.8 in^2
Step-by-step explanation:
The surface area of a cylinder is given by:
A=2πrh+2πr^2
2πr^2 gives the area of the 2 ends, each with area πr^2.
2πrh gives the suface area of the outside of the cylinder.
r = 0.4 inches
h = 25 inches
Area = 63.8 in^2
Which statement is true regarding the graphed functions?
I need help and can’t find the answers anywhere
Answers
Answer:
f(0)=g(0)
Step-by-step explanation:
The problem is asking for where the output (y value) of one function, f(x), matches the output of another function, g(x), otherwise called an intersection. You can see that the two lines intersect at 0 on the x axis in the graph, therefore f(0)=g(0) meaning the outputs of f(x) are the same as g(x) at x value 0.
How do I do C?Someone please help asap.
Answers
You have to find the slope of the line. It will give you the conversion rate from inches to centimetres or the other way around.
Looking closely at the graph, or using a ruler as reference, you can estimate that 30 cm ≈ 12 in. In terms of the graph, the line very nearly passes through the point (12, 30). It also passes through the origin, (0, 0), since 0 cm = 0 in exactly.
The slope of the line is then
[tex]\dfrac{30\,\mathrm{cm}-0\,\mathrm{cm}}{12\,\mathrm{in}-0\,\mathrm{in}} = \dfrac{30\,\rm cm}{12\,\rm in} = \dfrac{5\,\rm cm}{2\,\rm in} = 2.5\dfrac{\rm cm}{\rm in}[/tex]
which means that 1 in ≈ 2.5 cm.
So, if Sarah's height is 64 in, we convert this to cm and find her height is (approximately)
[tex]64\,\mathrm{in} \times 2.5\dfrac{\rm cm}{\rm in} = \boxed{160\,\rm cm}[/tex]
a set of data has the values 11,14,23 and 16
Answers
The number to add to the set of data is 26
How to determine the new number?The set of data is given as:
11,14,23 and 16
Let the new number be x
So that
Mean = 18
Mean is calculated as:
Mean = Sum/Count
So, we have:
(11 + 14 + 23 + 16 + x)/5 = 18
Multiply by 5
11 + 14 + 23 + 16 + x = 90
Evaluate the like terms
x = 26
Hence, the number to add is 26
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Complete question
A set of data already has the values 11, 14, 23, and 16. What value would have to be added to the set for the mean of the five numbers to be 18?
Chemotherapy in adult highgrade glioma: a systematic review and metaanalysis of individual patient data from 12 randomized trials
Answers
Systemic chemotherapy's impact on survival and recurrence in people with high-grade glioma has not been conclusively studied.
What is Systemic chemotherapy?Patients undergoing systemic chemotherapy can get their chemotherapy drugs intravenously or orally. The medication may be injected into the body intravenously, or through an IV, or intramuscular, into a muscle (IM).
Some Key features of systemic chemotherapy are-
Background: In order to evaluate the effects of such treatment on survival and recurrence, we conducted a systematic review and meta-analysis.Methods: From 12 randomised controlled studies, information on 3004 patients was incorporated (11 published and one unpublished).Findings: Overall, the findings indicated a significant survival extension associated with chemotherapy, with a hazard ratio of 0.85 (95 percent confidence interval [CI] 0.78–0.91, p0.0001) or a relative reduction in mortality risk of 15%. There was no proof that a patient's age, gender, histology, performance status, or degree of resection affected how chemotherapy worked in any particular way.Interpretation: Further research into pharmacological treatment for malignant tumors is encouraged by this modest but noticeable improvement in survival from chemotherapy.To know more about Chemotherapy, here
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In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor. Is there a significant difference between the proportions of urban and suburban residents who favor constructing nuclear plants
Answers
The p value for the difference is 0.005.
According to the statement
we have given that the 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor.
And we have to find the difference between them in proportions.
So,
X1 = 74 represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant
X2 = 70 represent the number of people suburban residents are in favor
N1 = 100 sample 1 selected
N2 = 125 sample 2 selected
AND
P1 = 0.74 represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant
And P2 = 0.56 represent the proportion of suburban residents are in favor And z would represent the statistic (variable of interest)
Pv represent the value for the test (variable of interest)
Here we apply the Z test to find the difference then
Z = (0.74 - 0.56) / (0.64(1-0.64)(1/100+1/125) )^1/2
Now after solving
Z = 2.795.
Now The significance level provided is ,and we can calculate the p value for this test.
Since is a two tailed test the p value would be:
P = (z>2,795)
P = 0.005.
So, The p value for the difference is 0.005.
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The equation represents an ellipse. which points are the vertices of the ellipse? (7, 1) and (7, −5) (7, −10) and (7, 6) (10, −2) and (4, −2) (15, −2) and (−1, −2)
Answers
The points which represents the vertices of the given equation are; (15, −2) and (−1, −2).
Which points among the answer choices represents the vertices of the ellipse whose equation is given?The complete question gives the equation of the ellipse as; (x-7)²/64+(y+2)²/9=1.
Since, It follows from convention that general equation of ellipse with centre as (h, k) takes the form;
(x-h)²/a² +(y-k)²/b² = 1.
Consequently, it follows from observation that the value of a and b in the given equation in the task content is; √64 = 8 and √9 = 3 respectively.
Since, 8 > 3, The vertices of the ellipse are given by; (h±a, k).
The vertices in this scenario are therefore;
(7+8, -2) and (7-8, -2).
= (15, -2) and (-1, -2).
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Jeri finds a pile of money with at least $\$200$. If she puts $\$80$ of the pile in her left pocket, gives away $\frac{1}{3}$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $\$200$ of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
Answers
Solving an inequality, we will see that there is less than $280 in the pile of money.
How much money is originally in the pile?Let's say that the amount of money is defined by the variable.
First, we know that Jeri keeps $80, so now in the pile we have:
M - $80.
Now she gives one third of that, then the leftover is:
(2/3)*(M - $80) + $80
We know that this is more than:
M - $200
Then we have the inequality:
(2/3)*(M - $80) + $80 > M - $200
And we can solve this for M.
(2/3)*M - (2/3)*$80 + $80 > M - $200
(1/3)*$80 + $200 > M - (2/3)*M
(1/3)*$80 + (1/3)*$200 > (1/3)*M
$280 > M
Then we conclude that there is less than $280 in the pile of money.
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A manufacturer makes ball bearings out of motel steel. it takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter
Answers
Using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.
According to the question,
It takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter.
Radius = 1/2 = 0.5 cm
volume V of one ball bearing is: V=(4/3)*π*r³
= 4/3 * π * (0.5)³
=0.524 cm³
In order to find number of ball bearings out of molten steel only if we divide the volume of steel by the volume of the ball bearing
5.24/0.524=10.
Hence, using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.
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HELP PLS PLS!!!! look at pic
Answers
Answer: [tex]\frac{2}{25} +\frac{11}{25}i[/tex]
Step-by-step explanation:
To get the following you have multiply the conjugate. [tex]\frac{(2-i)(3-4i)}{(3+4i)(3-4i)}[/tex]
60% of UCLA is girls. What perrcentage are boys
.
Answers
Answer:
40%
Step-by-step explanation:
Percent must be equal to 100, so if 60 are girls, then 40% must be boys.
Which of the following is a perfect square trinomial?
a. x^2+10x+25
b. x^2+6x+13
c. x^2+100
d. x^2+3x+9
Answers
Answer:
a. x² + 10x + 25
Step-by-step explanation:
because
(x + 5)² = (x + 5)(x + 5) = x² + 5x + 5x + 25 = x² + 10x + 25
so, it is a perfect square of (x + 5).
If you can please explain how you got your answer so I can understand, Thank you!
Answers
Answer:
3 2/5
Step-by-step explanation:
Each slash/mark on the number line is 1/5, meaning that 6 marks away is 3 2/5.
To further explain how I know each mark is 1/5, each question had a denominator of 5, and if you count each mark from 2 1/5 (2 2/5, 2 3/5, 2 4/5, 3, etc) you will eventually land on 4 evenly.
In the biblical account, adam lived to be how old?
a. 99
b. 122
c. 545
d. 930
Answers
A line passes through the points ( p , a ) and ( p , − a ) where p and a are real numbers. If p = 0 , what is the y-intercept? Explain your reasoning.
Answers
The y-intercept of the linear function is y = 0.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The y-intercept is given by (0,a) = (0,-a). From this, we have that for it to be a function, a = -a, and the only value that respects this condition is a = 0, hence the y-intercept of the linear function is y = 0.
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A DVD player costs $96.34, with sales tax included. What is the original price of the DVD player if the sales tax rate is 8.25%?
Answers
The original price of the DVD player if the sales tax rate is 8.25% is $88.79
Sales taxCost of DVD player including tax = $96.34Sales tax = 8.25%Original cost = 8.25%Total cost = original cost + (sales tax × original cost
96.34 = x + (8.5% × x)
96.34 = x + (0.085 × x)
96.34 = x + 0.085x
96.34 = 1.085x
x = 96.34 / 1.085
x = 88.7926267281105
Approximately,
x = $88.79
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Question 5 of 10
Identify an equation in slope-intercept form for the line parallel to y = 5x + 2
that passes through (-6, -1).
A. y = 5x + 29
B. y = -5x - 11
C. y = x +
OD. y = 5x - 29
SUMIT
Answers
Answer:
A
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is 5.
[tex]y+1=5(x+6) \\ \\ y+1=5x+30 \\ \\ y=5x+29[/tex]
If c(x) = 4x − 2 and d(x) = x² + 5x, what is (c.d)(x)?
4x³ + 18x² – 10x
x² + 9x-2
16x² + 4x-6
4x² + 20x-2
Answers
Answer:
[tex]4x^2+20x-2[/tex]
Step-by-step explanation:
To find (c.g)(x) we basically use the function d(x) as your variable, x, and plug it into c(x). So we replace every x in c(x) with the function d(x), [tex]x^{2} +5x[/tex]
c(g(x))=4(x^{2} +5x)-2
c(g(x))4[tex]x^2[/tex]+20x-2
A square metal sheet has the side length of 1 cm. À circular hole of radius 2/5 cm is drilled in the middle of the sheet.
How far the hole is from the edge of the sheet?
Answers
Step-by-step explanation:
Select the correct answer. which expression is equivalent to , if x > 0? a. b. c. d.
Answers
The equivalent expression of the expression is 128x^5y^6/2x^7y^5
How to determine the equivalent expression?The expression is given as:
128x^5y^6/2x^7y^5
Divide 128 by 2
64x^5y^6/x^7y^5
Apply the law of indices
64y^(6-5)/x^(7-5)
Evaluate the differences
64y/x^2
Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5
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Complete question
Select the correct answer. which expression is equivalent to 128x^5y^6/2x^7y^5 , if x > 0 and y > 0
A landscaping company is covering this trapezoid-shaped yard with grass seed. A trapezoid with base lengths of 6 meters and 7 meters, and height 4 meters. How much area will they need to cover with grass seed
Answers
Area covered with grass seed = 10.4[tex]m^{2}[/tex].
What is trapezoid geometry?
A quadrilateral with one set of parallel opposite sides is referred to as a trapezoid. It can have congruent sides (isosceles) and right angles (a right trapezoid), but neither is necessary.
Area of the trapezoid ={ (a+b)/2} +h
where a and b is base and h is height of the trapezoid geometry.
In the question,
a=6m , b=7m and h=4m.
According to the formula { (a+b)/2} +h.
Area covered with grass seed = {(6+7)/2} + 4
= 10.4[tex]m^{2}[/tex].
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Answer:
26
Step-by-step explanation:
GOT IT RIGHT`
Cora is wrapping a ribbon around a cylinder-shaped gift box. The box has a diameter of 15 inches and the ribbon is 60 inches long. Cora is able to wrap the ribbon all the way around the box once, and then continue so that the second end of the ribbon passes the first end. What is the central angle formed between the ends of the ribbon? Round your answer to the nearest tenth of a degree.
Answers
The central angle formed between the ends of the ribbon is 98.6°.
How to illustrate the angle?The circumference will be:
= πd
= 3.14 × 15 = 47.1
Ribbon = 60 - 47.1 = 12.9
Length of arc = x/360 × πd
12.9 = x/360 × 3.14 × 15
x = 98.6°
The angle is 98.6°
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Which term describes the red curve in the figure below?
• A. Hyperbola
B. Circle
C. Parabola
• D. Ellipse
Answers
When a plane intersects a cone and is perpendicular to the height of the cone, then it forms a circle. If the plane intersected the cone at an angle, we would have an ellipse.
A cone has a circular base. So, the answer to your question is B for circle.
Adding and Subtracting Functions
F(x)=x^2+4
G(x)=x-1
Find (g+f)(x)
Answers
Answer:
Step-by-step explanation:
[tex](g+f)(x)=g(x)+f(x)=x-1+x^2 +4=x^2 +x+3[/tex][tex]x^2 +x+3[/tex]
The difference between two integers is 8 and their product is 65. Assume that the larger of the two numbers is x. Write a quadratic equation in standard form that can be used to determine the value of x. Factor your equation from Part B and determine the possible solutions to your equation. Show your work. Write an expression for the second number.
Answers
A quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0.
The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5.
The value for the second number is 5
Word Problem Leading To Quadratic Equation.The general formula for quadratic equation in a in standard form is
a[tex]x^{2}[/tex] + bx + c = 0
Given that the difference between two integers is 8
Let the two integers = x and y,
and their product is 65. If the larger of the two numbers is x. Then,
x - y = 8 and xy = 65
Since we are looking for the value of x, make y the subject of formula in the first equation.
y = x - 8
Substitute y in the second equation.
x(x - 8) = 65
[tex]x^{2}[/tex] - 8x - 65 = 0
[tex]x^{2}[/tex] - 13x + 5x - 65 = 0
(x - 13)(x + 5) = 0
x = 13 or -5
We will ignore -5 since x is the larger number.
To get y Substitute x in the second equation.
xy = 65
13y = 65
y = 65/13
y = 5
Therefore, a quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0. The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5. The value for the second number is 5
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Please if anyone no math I really need help
Answers
Answer:
c
Step-by-step explanation:
option a (x-4) translates the graph 4 units right, not down
option b (x)-4 translates the graph 4 units down, not left
option c (x)+4 translates the graph 4 units up, so it is correct
option d (x+4) translates the graph 4 units left, not right
if the number is outside of the parentheses, like (x)+4 or (x)-4, the graph undergoes a vertical translation, and it moves up/down, with + meaning up and - meaning down
if the number is inside of the parentheses, like (x+4) or (x-4), the graph undergoes a horizontal translation, and moves left/right, with - meaning right and + meaning left
PLEASE ASAP NEEDED SO BADLY PLEASEE PLEASE
Answers
Answer:
[tex]6x^{2} -24x-10[/tex] with remainder -5
Answer:
[tex]6^2-24x-10-\frac{5}{x+4}[/tex]
In other words, [tex]6x^2-24x-10[/tex] is the answer and -5 is the remainder
Step-by-step explanation:
I used long division for this, and I uploaded an image for the steps. The final answer I got was [tex]6x^2-24x-10-\frac{5}{x+4}[/tex]