Solve the polynomial equation using division and factoring / the quadratic formula. Write the solution in simplest form. Show all work.
Answers
The polynomial is
[tex]\begin{gathered} x^3-8x^2-15x+54=0 \\ \text{and we are dividing it by x-2} \end{gathered}[/tex]Thus, we are left to factorize the quotient to obtain the remaining factors, let's do that
[tex]\begin{gathered} x^2-6x-27 \\ we\text{ try obtain 2 factors that sum to get -6, and multiply to get-27, } \\ \text{the numbers are 3 and -9} \\ x^2+3x-9x-27 \\ x(x+3)-9(x+3) \\ (x+3)(x-9) \end{gathered}[/tex]Thus, the polynomial in its simplest factorized form is;
[tex](x-2)(x+3)(x-9)[/tex]
Related Questions
Write each as an algebraic expressionthe product of a quarter of 3 more than a number a and 2 times a number b
Answers
1) Considering that "the product of a quarter of 3 more than a number a" can be written as:
[tex]\begin{gathered} \frac{1}{4}\times3+a \\ \\ \frac{3}{4}+a \end{gathered}[/tex]2) And for the second statement: "2 times a number b" can be written as:
[tex]2b[/tex]We can write them both as:
[tex]\begin{gathered} \frac{3}{4}+a \\ 2b \end{gathered}[/tex]If you can I would like the answer as soon as possible thank you
Answers
1) Gathering the data
a)
(4,112) and ( 6,168)
Picking those points and inserting them in the slope-intercept formula:
Now plugging one point (4,112) into the y=mx +b, to find out b, the linear coefficient:
112=28(4) +b
112=112 +b
b= 0
So, the function for that is f(x) = 28x
An item is $4,200. What is the sales if it is marked down 35%?
Answers
The first step is to find the discount applied (use percentage as decimal). Then, susbtract this to the original price
[tex]\begin{gathered} 4,200\cdot0.35=1,470 \\ 4,200-1,470=2730 \end{gathered}[/tex]The sales is $2,730
find the perimeter as a radical expression in simplest form
Answers
Answer:
The perimeter of the figure, in it's simplest form, is 2(1 + 5*sqrt(6)) feet
Step-by-step explanation:
The perimeter of a figure is the sum of all dimensions of the figure.
In this question, the perimeter is:
[tex]2+\sqrt{54}+\sqrt{54}+2\sqrt{24}[/tex]Adding like terms:
[tex]2+\sqrt{54}+\sqrt{54}+2\sqrt{24}=2+2\sqrt{54}+2\sqrt{24}[/tex]Now we have to factorize 54 and 24
Factorization of 54:
We go dividing by prime numbers.
54|2
27|3
9|3
3|3
1
So: 54 = 2*3*3*3 = 2*3³
Factorization of 24:
24|2
12|2
6|2
3|3
1
So 24 = 2*2*2*3=2³*3
Simplifying:
[tex]2+2\sqrt{54}+2\sqrt{24}=2+2\sqrt{2\ast3^3}+2\sqrt{2^3\ast3}^{}[/tex]Now we continue working to place in the simplest form
[tex]2+2\sqrt{2\ast3^3}+2\sqrt{2^3\ast3}=2+2\sqrt{2\ast3\ast3^2}+2\sqrt{2^2\ast2\ast3}[/tex]Now, for the radicals, we have that:
[tex]\sqrt{2\ast3\ast3^2}=\sqrt{6\ast9}=\sqrt{6}\ast\sqrt{9}=3\sqrt{6}[/tex][tex]\sqrt{2^2\ast2\ast3}=\sqrt{4\ast6}=\sqrt{4}\ast\sqrt{6}=2\sqrt{6}[/tex]Then
[tex]2+2\sqrt{2\ast3\ast3^2}+2\sqrt{2^2\ast2\ast3}=2+2\ast3\sqrt{6}+2\ast2\sqrt{6}[/tex]Finally:
[tex]2+2\ast3\sqrt{6}+2\ast2\sqrt{6}=2+6\sqrt{6}+4\sqrt{6}=2+10\sqrt{6}=2(1+5\sqrt{6})[/tex]The perimeter of the figure, in it's simplest form, is 2(1 + 5*sqrt(6)) feet
For f(x)=3x and g(x)=x+1(f o g)(x) =?
Answers
Answer
[tex](f\circ g)(x)=3x+3[/tex]Explanation
The composite function can be rewritten as:
[tex](f\circ g)(x)=f(g(x))[/tex]meaning that we have to replace all the x in f(x) with g(x).
In our case:
• f(x) = 3x
,• g(x) = x+1
Then, we can write and simplify it as:
[tex](f\circ g)(x)=3(x+1)[/tex][tex](f\circ g)(x)=3x+3[/tex]there is a group of 9 people ordering pizza if each person gets 2 slices and each pizza has 8 slices how many pizzas should they order ?
Answers
Total People = 9
Each person gets 2 slices, so 9 person will get:
9 * 2 = 18 slices
We would need 18 slices altogether.
Since each pizza has 8 slices, we can write:
1 pizza = 8 slices
2 pizza = 8 + 8 = 16 slices
3 pizza = 8 + 8 + 8 = 24 slices
Taking 2 pizza means we will have 16 slices, but we need atleast 18. So that is 2 short. We would need to order another pizza.
So we would need 2 + 1 =
O GEOMETRY Volume of a sphere The diameter, D, of a sphere is 13.2 mm. Calculate the sphere's volume, V. Use the value 3.14 for , and round your answer to the nearest tenth. (Do not round any intermediate computations Explanation Check D V = 0 mm 3 X Ś
Answers
Given:
The diameter of the sphere is
[tex]\begin{gathered} d=13.2mm \\ \\ r=\frac{d}{2} \\ \\ r=\frac{13.2}{2} \\ \\ r=6.6mm \end{gathered}[/tex]Required:
To find the volume of the sphere.
Explanation:
The formula for volume of sphere is
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ =\frac{4}{3}\times3.14\times(6.6)^3 \\ \\ =1203.64mm^3 \\ \\ =1203.6mm^3 \end{gathered}[/tex]Final Answer:
The volume of the sphere is
[tex]V=1203.6mm^3[/tex]Fill in the blanks for the resulting statement is true
Answers
Given:
[tex]f(x)=a(x-h)^2+k[/tex]Given equation is in thee general form.
Suppose a polynomial function of degree 4 with rational coefficients has the following given numbers as zeros. Find the other zero(s).
−i,
Answers
If a polynomial has rational coefficients, then irrational and complex roots must occur in conjugate pairs.
The conjugate of the complex number a + bi is a - bi; the conjugate of the irrational number a + b[tex]\sqrt{c}[/tex] is a - b[tex]\sqrt{c}[/tex].
with one root -i, another root must be i and with one root 7[tex]\sqrt{11}[/tex], another root must be -7[tex]\sqrt{11}[/tex].
Therefore the roots are conjugate pairs.
1. -i and i
2. 7[tex]\sqrt{11}[/tex] and -7[tex]\sqrt{11}[/tex]
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[tex]h = 50 - \frac{t} {5} [/tex]Please answer the following question
Answers
We are given that
[tex]h=50-\frac{t}{5}[/tex]We want to find h when t = 35
Solution
From
[tex]\begin{gathered} h=50-\frac{t}{5} \\ \text{put t = 35} \\ h=50-\frac{35}{5} \\ h=50-7 \\ h=43 \end{gathered}[/tex]Therefore, h = 43
Question 7 of 10 Kim earns 3 points for every correct answer on a test. The equation y 3r shows her total points, which depends on the number of correct answers. Select the graph with the correctly labeled axes for this situation.
Answers
Since Kim earns 3 points for every correct answer, in the horizontal axis we have the number of correct answers Kim got, and in the vertical axis we have the corresponding total of points that each number of correct answers is related.
Also, for each unitary increase in the x-axis, the y-axis increases 3 units, because each correct answer is worth 3 points.
The option that shows these relations is the graph in option D.
what is the fourth term of the sequence an = an - 1 + 11 when a1 = 4
Answers
Here, we want to calculate the fourth term of the sequence, given the formula for the nth term of the sequance and the first term of the sequence
From the formula given for the nth term, we will need to add 11 to the previous term
In this case, the first t
The sum of five times a number and eight is the number subtracted from 10. What is the number?
Answers
Step-by-step explanation:
Let the number be x
Sum of five times the number = 5x
Number subtracted from 10 = 10 - x
According to question,
5x + 8 = 10 - x
=> 6x = 2
=> x = 2/6 = 0.33
I have a figure of some triangles and I need to figure out the congruence statement but I don't understand how to tell
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it depends on the triangles that you have,you will use one of them (SAS,ASA,SSA) for example
-if you have that the triangles has two equal sides and their angle equal too you use SAS to conclude that the triangles are congruent.
-if you have that the triangles has two angles and the side between them equal, you conclude by ASA that the triangles are congruent.
-Finally, if you have that the triangles has two equal sides and a angle equal too, you conclude by SSA that they are congruent.
Which of the following mathematical properties is described by the statement, “whatever is done on one side of the equation must also be done on the other side of the equation”?Identity Property of AdditionAssociative PropertyCommunitive PropertyProperty of Equality
Answers
To find:
The name of the property:
Solution:
The given statement is "whatever is done on one side of the equation must also be done on the other side of the equation".
This is the statement for "Propert of Equality".
a right triangle has a hypotenuse that is 10ft long and a leg that is 6ft long. find the length of the unknown leg. make sure to include units in your answer and round to the ones place.
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So,
To find the missing leg we have to use phytagoras theorem.
Then:
Find the value of "X" and find the measure of the indicated line segment NM
Answers
Answer:
Explanation:
The tangent-secant theorem states that if the segments of a secant segment and a tangent segment share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.
We can go ahead and solve for x as shown below;
[tex]\begin{gathered} (x-3)16=(x+3)^2 \\ 16x-48=x^2+6x+9 \end{gathered}[/tex][tex]\begin{gathered} x^2-16x+6x+9+48=0 \\ x^2-10x+57=0 \end{gathered}[/tex]What's the answer to this question and can you please explain how that is the answer ?
Answers
A (-4, 3)
B(-4, 1)
C(-2, 1)
When you reflect about the y-axis, the coordinate becomes (-x, y)
A(-4, 3) ⇒ A' ( 4, 3)
B(-4, 1) ⇒ B' (4, 1)
C(-2, 1) ⇒ C' ( 2, 1)
To find the length of B'C', we will use the distance formula
[tex]|d|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]x₁=4 y₁= 1 x₂=2 y₂=1
substitute the coordinates in the above
[tex]|d|=\sqrt[]{(2-4)^2+(1-1)^2}[/tex][tex]=\sqrt[]{(-2)^2+0}[/tex][tex]=\sqrt[]{4}[/tex][tex]=2[/tex]Hence, the length is 2
The amount of paint needed to cover a wall is proportional to its area. The wall is rectangular and has an area of 6z2 + 6z square meters. Factor this polynomial to find possible expressions for the length and width of the width of the wall
Answers
Let A be the area of the wall.
Given that the amount of paint needed to cover a wall paint is proportinal to ts area, and the wall is rectangular with area
[tex]A=6z^2+6z\text{ ---- equation 1}[/tex]Since the wall has a rectangular shape, the area of the wall is evaluated as
[tex]\text{Area of rectangular wall = length}\times width[/tex]From equation 1,
[tex]A=6z^2\text{ + 6z}[/tex]simplify by factorization,
[tex]A\text{ = 6z(z+1)}[/tex]Since the length has a longer dimension than the width, we have
[tex]\begin{gathered} \text{length = 6z} \\ \text{breadth = z+1} \end{gathered}[/tex]Hence, the possible expressions for the length and width of the wall are
[tex]\begin{gathered} \text{length = 6z} \\ \text{width = z+1} \end{gathered}[/tex]
Bob spins a 5-sided spinner 200 times. What is the experimental probability of landing on a 4?a1/5b0.02c1/10d4/40
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From the data of the table, we know that 40 out of those 200 spins landed on a 4.
Therefore, the experimental probability (the probability we can calculate from experimental data) is:
[tex]\frac{40}{200}\rightarrow\frac{1}{5}[/tex]In this case, the experimental probability is the same as the theoretical probability. But it isn't always the case!
Answer: A. 1/5
The price of a gallon of gasoline is supposed to increase by 40% over the next year. If a gallon of gas costs $2.05 now, how much will it cost to buy 12 gallons of gas in one year?
Answers
If the price of a gallon of gasoline is supposed to increase by 40% over the next year and a gallon of gas costs $2.05 now, then the cost to buy 12 gallons of gas in one year is $34.44
The cost of one gallon of gas now = $2.05
In next year it will increase by 40%
Then the 40 percentage of $2.05 is
2.05×(40/100) = $0.82
The cost of one gallon of gas after one year = 2.05+0.82
= $2.87
The cost of 12 gallon of gas after one year = 2.87×12
= $34.44
Hence, if the price of a gallon of gasoline is supposed to increase by 40% over the next year and a gallon of gas costs $2.05 now, then the cost to buy 12 gallons of gas in one year is $34.44
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McKenzie has a 2 quart pitcher.she fills it up two times with juice.how many cups of juice was she able to make?
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Since McKenzie fills it up 2 times, then she has the equivalent to 4 quart pitcher. We know there are 4 cups in one quart, then she has
[tex]4\times4\text{ cups in 4 quart}=16\text{ cups in 4 quart}[/tex]Therefore, she will able to make 16 cups of juice.
If Rosie has 20 sweets and Chloe has 49 sweets how many sweets will Lewis get? Total number of sweets is 69 sweets.
Answers
Lewis will get zero sweets.
Explanation:
There are a total of 69 sweets and these are divided by Rosie and Chloe only. Rosie has 20 and Chloe gets the rest which is 49.
20 from Rosie and 49 from Chloe = 20 + 49 = 69. Therefore, a total of 69 sweets. Nothing is left for Lewis.
Which of the following logarithmic is equivalent to the logarithmic expression
Answers
Given,
The expression is,
[tex]\log (r)+\log (v)[/tex]By the properties of the logarithmic,
[tex]\begin{gathered} \log (a)+\log (b)=\log (ab) \\ \log (a)-\log (b)=\log (\frac{a}{b}) \\ \log a^b=b\text{ log a} \end{gathered}[/tex]So, according to the properties, the given expression becomes,
[tex]\log (r)+\log (v)=\log (rv)[/tex]Hence, the solution is log (rv).
An architect uses a scale of 2/3 inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint? how many inches?
Answers
Step 1
Given; An architect uses a scale of 2/3 inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint? How many inches?
Step 2
[tex]The\text{ scale is }\frac{2}{3}inch\text{ = 1 foot}[/tex]
Thus;
[tex]\begin{gathered} \frac{\frac{2}{3}}{1}=\frac{x}{24} \\ x=\frac{2}{3}\times24=16inches \end{gathered}[/tex]Answer;
[tex]16inches[/tex]Which statement best describes how to create the graph below fromparent function??
Answers
SOLUTION
The graph below helps answers the question
From the graph above, the black graph indicates f(x) = log(x), it was shifted 4 units down to get the red graph f(x) = log(x) - 4
Hence the answer is Shift the parent function, f(x) = log(x), down 4 units. Option A
Identify the polynomial that can be used to model the total cost.
Answers
Solution:
Given:
[tex]\begin{gathered} h(x)=0.42x^2+0.3x+4 \\ r(x)=-0.005x^2-0.2x+7 \end{gathered}[/tex]Hence, the total cost is;
[tex]\begin{gathered} q(x)=h(x)\cdot r(x) \\ q(x)=(0.42x^2+0.3x+4)(-0.005x^2-0.2x+7) \\ q(x)=0.42x^2(-0.005x^2-0.2x+7)+0.3x(-0.005x^2-0.2x+7)+4(-0.005x^2-0.2x+7) \\ q(x)=-0.0021x^4-0.084x^3+2.94x^2-0.0015x^3-0.06x^2+2.1x-0.02x^2-0.8x+28 \\ q(x)=-0.0021x^4-0.084x^3-0.0015x^3+2.94x^2-0.06x^2-0.02x^2+2.1x-0.8x+28 \\ q(x)=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28 \end{gathered}[/tex]Therefore, the polynomial that can be used to model the total cost is;
[tex]q(x)=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28[/tex]A rectangular garden is 21 feet long and 14 feet wide. A brick walk way with uniform width is going to be constructed around the garden. The brick walk way will have an area of 330 square feet. What should be the width of the brick walk way? Type in your answer to the nearest thousandth. The width of the walk way should be?
Answers
Answer:
3.862 feet
Explanation:
Let the uniform width of the walkway = x ft
From the diagram above, the area of the walkway will be:
[tex]2x(21+2x)+2(14x)[/tex]The brick walkway will have an area of 330 square feet. Therefore:
[tex]2x(21+2x)+2(14x)=330[/tex]We simplify the equation in order to solve for x:
[tex]\begin{gathered} 42x+4x^2+28x=330 \\ 4x^2+28x+42x-330=0 \\ 4x^2+70x-330=0 \end{gathered}[/tex]Next, solve for x:
[tex]\begin{gathered} 2(2x^2+35x-165)=0 \\ 2x^2+35x-165=0 \end{gathered}[/tex]Using the quadratic formula, we solve for x:
[tex]\begin{gathered} $$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$$ \\ x=\dfrac{-35\pm\sqrt{35^2-4(2)(-165)}}{2\times2} \\ =\dfrac{-35\pm\sqrt{1225-(-1320)}}{4} \\ =\dfrac{-35\pm\sqrt{2545}}{4} \\ x=\frac{-35+\sqrt{2545}}{4}\text{ or }x=\frac{-35-\sqrt{2545}}{4} \\ x=3.862\text{ or }x=-21.362 \end{gathered}[/tex]The width of the brick walkway should be 3.862 feet (correct to the nearest thousandth).
ABCD is parallelogram and m
Answers
We have the following:
In a parallelogram, the opposite angles are equal and the sum of all the angles is 360 degrees, therefore
[tex]\begin{gathered} \text{ABC}=\text{ADC} \\ \text{BCD}=\text{DAB} \\ 360=\text{ABC+ADC}+\text{BCD+DAB} \end{gathered}[/tex]solving:
[tex]\begin{gathered} 360=125+125+\text{BCD}+\text{BCD} \\ 2\text{BCD}=360-125-125 \\ \text{BCD}=\frac{110}{2} \\ \text{BCD}=55 \end{gathered}[/tex]Therefore,
An antique has a price tag of $440. The sales tax rate for the county is 8.5%. How much sales tax will be due?
Answers
Solution:
First, we need to find the tax
tax = price * tax rate
= 440 * 8.5%
= 440 * (0.085) = 37.4
So that, the correct answer is:
37.4