Polynomial
[tex]f(x)=4x^3+13x^2+9x+2[/tex]Factor out the greatest common factor. Simplify the factors, if possible.6x4 - 42x3 + 12x2Select the correct choice below and fill in any answer boxes in your choice.O A. 6x4 - 42x3 + 12x2 =(Type your answer in factored form.)OB. There is no common factor other than 1.ih
You have to find the greatest common factor first.
To do so, do as follows:
[tex]6x^4-42x^3+12x^2[/tex]Factors of 6 are: 1, 2, 3, 6
Factors of 12 are: 1, 2, 3, 4, 6, 12
Factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The greates common factor is the greatest common factor shared by all values, in this case is 6
Now to factor it out you have to divide each term of the equation by it.
[tex](\frac{6x^4}{6})=x^4[/tex][tex](\frac{42x^3}{6})=7x^3[/tex][tex](\frac{12x^2}{6})=2x^2[/tex]The expression with the GCF factorized is then:
[tex]6(x^4-7x^3+2x^2)[/tex]A teacher receivesa monthly salary of $2800.00 What isheraunnual salary?
The year has 12 months, since the teacher receives a monthly salary of $2800, then his annual salary is:
[tex]2800\times12=33600[/tex]Answer:
$33600
"A quadrilateral is a square if and only if it has fourright angles."Which of the following terms provides acounterexample for why the biconditional statement is
Given statement: A quadrilateral is a square if and only if it has four right angles
Counterexample: A quadrilateral with four right angles can be also a rectangle. Then, not all quadrilaterals with four right angles are squares.
Answer: Rectangle
Commercial agents earn 5% of the cost of each product they sell. If an agent earsn $2000 for selling a product, what was the cost of the product?
Answer: 40,000
Step-by-step explanation: 5 (the earnings) times twenty is 100 (the total cost) and if we substitute 5 for 2000, the total is 40,000.
Answer: 40,000
Step-by-step explanation:
just because
Assume that a varies directly as b.When the value of a is 5,the value of b is 18.When the value of a is 22,what is the value of b?
In this case we have the proportion 18:5, then we have the equation
[tex]\begin{gathered} \frac{18}{5}=\frac{b}{22} \\ b=\frac{18}{5}\times22 \\ b=\frac{396}{5} \end{gathered}[/tex]Then, when a is 22, the value of b is 396/5 that is also equal to 79.2 or
[tex]79\frac{1}{5}[/tex]4 numbers that are divisible by both 2 and 9
A Number to be divisible by 2, the last digit must be even.
divisible by 9 = sum of the digits must be divisible by 9:
So, 4 numbers:
18,36,54,72
The polynomial P(x) = 5x^3 + 2x^2- 42 has ___ local maxima and minima
SOLUTION:
Case: Local maxima and local minima
Given:
[tex]P(x)=5x^3+2x^2-42^{}[/tex]Required: To find the local maxima and minima
Method:
[tex]\begin{gathered} P(x)=5x^3+2x^2-42^{} \\ \text{ } \end{gathered}[/tex]First the find the first derivative:
[tex]\begin{gathered} P^{\prime}(x)=15x^2+4x \\ we\text{ make P'(x) = 0} \\ 15x^2+4x=\text{ 0} \\ x(15x+4)=0_{} \\ x=0\text{ or 15x+4 =0} \\ x=\text{ 0 or x= }\frac{-4}{15} \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = 0. The points are {-1, 1}.
[tex]\begin{gathered} \text{when x=-1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(-1)=15(-1)^2+4(-1) \\ P^{\prime}(-1)=15(1)^2-4 \\ P^{\prime}(-1)=15^{}-4 \\ P^{\prime}(-1)=11 \\ \text{when x= 1} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(1)=15(1)^2+4(1) \\ P^{\prime}(1)=15^{}+4 \\ P^{\prime}(1)=19 \end{gathered}[/tex]Let us take the points in the immediate neighbourhood of x = -4/15. The points are {-1, 0}
[tex]\begin{gathered} \text{when x= 0} \\ P^{\prime}(x)=15x^2+4x \\ P^{\prime}(0)=15(0)^2+4(0) \\ P^{\prime}(0)=0^{}+0 \\ P^{\prime}(0)=0^{} \end{gathered}[/tex]Final answer:
The local minima is at x= 0 while the local maxima is at x= -4/15
It’s given that the shape is not a parallelogram but why?
They are two congruent triangles.
Find the values of A, B, and C in the table.Intervalfa) for a in Relation ofinterval fa) to x-axis(0, 1)f(-2)= -12below(-1, A)f(0)=Babove(A, 2)f (1.5) -0.6(2,)f(3) = 8above
From the first line of the table, it shows
[tex]f(-2)=-12[/tex]This means that
when x = -2, y = -12,
so
[tex]a=-2[/tex]Now,
Suppose there is a simple index of three stocks, stock X, stock Y, and stock Z. Stock X opens the day with 5000 shares at $4.10 per share. Stock Y opens the day with 2000 shares at $4.50 per share. Stock Z opens the day with 4000 shares at $3.60 per share. The simple index rises 3.4% over the course of the day. What is the value of the index at the end of the day? Round your answer the nearest hundred. A. $45,100 B. $43,900 C. $45,400 D. $44,800
Solution:
Step 1:
Calculate the total value of stock X
[tex]\begin{gathered} =5000\times\text{ \$}4.10 \\ =\text{ \$}20,500 \end{gathered}[/tex]Step 2:
Calculate the total value for Stock Y
[tex]\begin{gathered} =2000\times4.5 \\ =\text{ \$}9000 \end{gathered}[/tex]Step 3:
Calculate the total value for stock Z
[tex]\begin{gathered} =4000\times\text{ \$}3.60 \\ =\text{ \$}14,400 \end{gathered}[/tex]Step 4:
Calculate the total value of the shares but without the increase yet
[tex]\begin{gathered} 20,500+9000+14,400 \\ =\text{ \$}43,900 \end{gathered}[/tex]Step 5:
Calculate the increase in the simple index
[tex]\begin{gathered} =\frac{3.4}{100}\times43900 \\ =\text{ \$}1,492.60 \end{gathered}[/tex]Step 6:
Add the increase in the simple index to the total value of the shares
[tex]\begin{gathered} 43,900+1,492.60 \\ =\text{ \$}45,392.60 \\ \approx\text{ \$}45,400 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow\text{\$}45,400[/tex]OPTION C is the right answer
Answer:
45,400
Step-by-step explanation:
just took test AP3
The area of the trapezoid is 14 square feet. Write an equation that you can use to find the value of x
Explanation
the area of a trapezoid is equal to half the product of the height and the sum of the two bases.
[tex]A=(\frac{base1+base2}{2})\cdot\text{heigth}[/tex]then
Step 1
Let
base1=2x
base2=x
height= 2 ft
area= 14 square feet
replace,
[tex]\begin{gathered} A=(\frac{base1+base2}{2})\cdot\text{heigth} \\ 14=(\frac{2x+x}{2})\cdot\text{2 } \\ 14=(\frac{3x}{2})\cdot2 \\ 14=3x\rightarrow equation \\ divide\text{ both sides by 3} \\ \frac{14}{3}=\frac{3x}{3} \\ \frac{14}{3}=x \\ x=\frac{14}{3} \end{gathered}[/tex]then put 3x in the box.
I hope this helps you
2. The sum of the perimeters of similar quadrilaterals is 22.5 dm. Find the perimeters of the quadrilaterals if the similarity coefficient k = 1.25.
Given:
The sum of the perimeters of similar quadrilaterals is 22.5 dm. The similarity coefficient k = 1.25.
Required:
To find the perimeters of the quadrilaterals.
Explanation:
The quadrilaterals are similar and the similarity coefficient is k = 1.25.
If the quadrilateral is similar then the ratio of their corresponding sides is equal.
Let the perimeter of the one quadrilateral is x then the perimeter of the other quadrilateral will be 1.25x
Now
[tex]\begin{gathered} x+1.25x=22.5 \\ x(1+1.25)=22.5 \\ 2.25x=22.5 \\ x=\frac{22.5}{2.25} \\ x=10 \end{gathered}[/tex]Thus the perimeter of the one quadrilateral is 10dm.
The perimeter of the other quadrilateral = 1.25 x 10 = 12.5 dm
Final Answer:
Thus the perimeter of the quadrilaterals is 10dm and 12.5 dm.
Yolanda is riding in a bike race that goes through a valley and a nearby mountain range,The table gives the altitude (in feet above sea level) for the five checkpoints in the race,Use the table to answer the questions,CheckpointAltitude(feet above sea level)12,2242- 13731,5714-305218(8) How much lower is Checkpoints than check out 2909 i lower
Step 1
Write the given checkpoint altitude
Checkpoint 1 = 2224
Checkpoint 2 = -137
Checkpoint 3 = 1571
Checkpoint 4 = -39
Checkpoint 5 = -218
Step 2:
a) How much lower is checkpoint 5 than checkpoint 2
You will subtract checkpoint 5 altitude from checkpoint 2
[tex]\begin{gathered} =\text{ -137 - (-218)} \\ =\text{ -137 + 218} \\ =\text{ 81 f}eet \end{gathered}[/tex]b) Altitude of the top hill that is 365 above checkpoint 5.
[tex]\begin{gathered} \text{Altitude of the top hill = 365 - 218 } \\ \text{Altitude of the top hill 365 above checkpoint 5 = 147} \end{gathered}[/tex]Drag each tile to the correct box.Arrange the functions in ascending order, starting with the function that eventually has the least value and ending with the function thateventually has the greatest value.3x + 8+4+3x² + 63x4*
To answer the question we are going to graph the functions given:
From the graph we notice that the order will be:
[tex]\begin{gathered} 3x \\ 3x+8 \\ x^2 \\ x^2+6 \\ 4^x \\ 4^x+3 \end{gathered}[/tex]Find MK. ML = 8, LK = x + 2, MK = 4x - 2
From the given description, it appears that M, L, and K are collinear and the length of MK is equal to the sum of ML and LK.
To be able to find the length of MK let's first find the value of x using the equation of the sum of the lines.
[tex]\text{ }\bar{\text{ML}}\text{ + }\bar{\text{LK}}\text{ = }\bar{\text{MK}}[/tex]Let's plug in the values given in the description.
[tex]\text{ (8) + (x + 2) = 4x - 2}[/tex][tex]\text{ 8 + x + 2 = 4x - 2}[/tex][tex]\text{ x + 10 = 4x - 2}[/tex][tex]\text{ x - 4x = -2 - 10}[/tex][tex]\text{ -3x = -12}[/tex][tex]\text{ }\frac{\text{-3x}}{-3}\text{ = }\frac{\text{-12}}{-3}[/tex][tex]\text{ x = 4}[/tex]Let's plug in x = 4 in the equation for the length of MK = 4x - 2.
[tex]\text{ }\bar{\text{MK}}\text{ = 4x - 2}[/tex][tex]\text{ }\bar{\text{MK}}\text{ = 4(4) - 2}[/tex][tex]\text{ }\bar{\text{MK}}\text{ = 16 - 2}[/tex][tex]\text{ }\bar{\text{MK}}\text{ = 1}4[/tex]Therefore, the length of MK is 14.
Given the expression: 6x^10 - 96x^2Part A: Rewrite the expression by factoring out the greatest common factor.Part B: Factor the entire expression completely. Show the steps of your work.
According to factorization method, we have find out that by factoring out the greatest common factor, we can rewrite the expression as [tex]6x^{2}(x^{8}-16)[/tex] and by factoring the entire expression by difference of squares concept, we can rewrite the expression as [tex]6x^{2}(x^{4}+4)(x^{2}+2)(x^{2} -2)[/tex].
The given expression is -
[tex]6x^{10}-96x^{2}[/tex] ---- (1)
We have to -
A: Rewrite the expression by factoring out the greatest common factor.
B: Rewrite the expression by factoring the entire expression completely.
Solving for Part A:
From equation (1), we have
[tex]6x^{10}-96x^{2}[/tex]
Applying the distributive property, we can rewrite this as -
[tex]6x^{10}-96x^{2}\\=6x^{2} x^{8}-6x^{2}*16\\=6x^{2}(x^{8}-16)[/tex]------- (2)
This is the expression obtained by factoring out the greatest common factor that is [tex]x^{2}[/tex].
Solving for Part B:
From equation (2), we have
[tex]6x^{2}(x^{8}-16)[/tex]
Applying the difference of squares concept, we can rewrite this as -
[tex]6x^{2}(x^{8}-16)\\=6x^{2}[(x^{4} )^{2} -4^{2} ]\\=6x^{2}(x^{4}+4)(x^{4}-4)\\=6x^{2}(x^{4}+4)[(x^{2} )^{2}-2^{2} ]\\=6x^{2}(x^{4}+4)(x^{2}+2)(x^{2} -2)[/tex]
This is the expression obtained by factoring the expression completely.
Therefore, according to factorization method, we have find out that by factoring out the greatest common factor, we can rewrite the expression as [tex]6x^{2}(x^{8}-16)[/tex] and by factoring the entire expression by difference of squares concept, we can rewrite the expression as [tex]6x^{2}(x^{4}+4)(x^{2}+2)(x^{2} -2)[/tex].
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The length of a rectangle is 97 m and the width is 14 m find the area give your answer without units
The area of the rectangle is 1358
Explanation:length of the rectangle = 97m
width of the rectangle = 14m
Area of a rectangle = length × width
[tex]\begin{gathered} \text{Area = 97m }\times\text{ 14m} \\ Area\text{ }of\text{ the rectangle = }1358m^2 \end{gathered}[/tex]The area of the rectangle is 1358 (without units)
What is the value of x in the triangle?a right triangle with a short leg of length x and hypotenuse of length 3 times the square root of 2A. B. C. D. E.
Solution:
Given the right triangle below:
To solve for x, we use the trigonometric ratio.
In the above triangle, the angles at A and B are equal.
Thus, we have
[tex]\begin{gathered} \angle A+\angle B+\angle C=180(su\text{m of angles in a triangle\rparen} \\ \angle A=\angle B \\ thus, \\ 2\angle\text{B+90=180} \\ \Rightarrow2\angle\text{B=180-90} \\ 2\angle\text{B=90} \\ \Rightarrow\angle\text{B=45} \end{gathered}[/tex]From trigonometric ratio,
[tex]\sin\theta\text{=}\frac{opposite}{hypotenuse}[/tex]In this case, θ is the angle at B, which is 45; opposite is AC, and hypotenuse is AB.
Thus,
[tex]\begin{gathered} \sin45=\frac{x}{3\sqrt{2}} \\ \Rightarrow x=3\sqrt{2}\times\sin45 \\ =3\sqrt{2}\times\frac{1}{\sqrt{2}} \\ =3 \end{gathered}[/tex]Hence, the value of x is
[tex]3[/tex]The correct option is B
f (t) = 44 – 5 g(t) = 2t - 1 Find (f - g)(t)
To solve the given problems, we have to subtract the functions.
[tex](f-g)(t)=4t-5-(2t-1)[/tex]Then, we simplify
[tex](f-g)(t)=4t-5-2t+1=2t-4[/tex]Hence, the resulting function is 2t-4.using the values from the graph, compute the values for the terms given in the problem. Choose the correct answer. Age of car = 4 years Original cost = 13,850 The current market value is $ _
The current market value is $9086.98
In this problem, supposing a decay of 10% a year, and the original value of $13,850, the parameters are A(0) = 13850, r = 0.1.
Using exponential decay formula, the value of the car in 4 years is given by:
A(t) = A(0)(1 - r)^t
A(4) = 13850(1 - 0.1)^4
A(4) = 13850 * (0.9)^4
A(4) = 9086.98
Therefore, The current market value is $9086.98
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[tex]y = 3(x + 3)(x + 1)[/tex]Intercept form find the vertex
Answer:
(-2, -3)
Explanation:
If we have an equation with the form:
f(x) = ax² + bx + c
The vertex of the parabola is the point (-b/2a, f(-b,2a)).
So, to find the vertex, we need to write the equation y = 3(x + 3)(x + 1) as:
[tex]\begin{gathered} y=3(x+3)(x+1) \\ y=3(x^2+3x+x+3) \\ y=3(x^2+4x+3) \\ y=3x^2+12x+9 \end{gathered}[/tex]Then, the value of a is 3 and the value of b is 12. It means that -b/2a is equal to:
[tex]-\frac{b}{2a}=-\frac{12}{2(3)}=-\frac{12}{6}=-2[/tex]And f(-b/2a) = f(-2) is equal to:
[tex]\begin{gathered} y=3x^2+12x+9 \\ f(-2)=3(-2)^2+12(-2)+9 \\ f(-2)=3(4)-24+9 \\ f(-2)=12-24+9 \\ f(-2)=-3 \end{gathered}[/tex]Therefore, the vertex is the point (-2, -3)
Solve the right triangle. Round decimal answers to the nearest tenth. find RSfind RTfind angle T
Δ RST shown in the picture is a right triangle, we know the measure of ∠R and ∠S, and the length of side ST.
To determine the length of the missing angle, you have to remember that the sum of the inner angles of a triangle add up to 180º
Then we can calculate the measure of ∠T as follows:
[tex]\begin{gathered} \angle R+\angle S+\angle T=180 \\ 57+90+\angle T=180 \\ 174+\angle T=180 \\ \angle T=180-174 \\ \angle T=33º \end{gathered}[/tex]The measure of the missing angle is ∠T=33º
To determine the lengths of the missing sides RS and RT, you have to use the trigonometric ratios of sine, cosine, and tangent. These ratios are defined as follows:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypothenuse} \\ \cos \theta=\frac{adjacent}{hypothenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]"θ" represents the angle of interest.
Using ∠R as a point of reference, side ST is across this angle so it is the side of the triangle "opposite" to it.
Side RS is next to ∠R, so it is the side "adjacent" to it.
The trigonometric ratio that shows the relationship between the opposite and adjacent sides to an angle is the tangent. Using the definition of the tangent you can determine the length of RS as follows:
[tex]\tan R=\frac{RS}{ST}[/tex]-First, write the expression for RS, which means that you have to pass "ST" to the left side of the equal sign by applying the opposite operation to both sides of it.
[tex]\begin{gathered} ST\tan R=ST\cdot\frac{RS}{ST} \\ ST\tan R=RS \end{gathered}[/tex]-Replace the expression with the values of ∠R and ST:
[tex]\begin{gathered} 15\cdot tan57=RS \\ 23.09=RS \\ RS\approx23.1 \end{gathered}[/tex]Side RS measures 23.1
Side RT is the longest side of the triangle, and thus, its hypothenuse. To determine its length using ∠R and side ST, you have to apply the definition of the sine:
[tex]\sin R=\frac{ST}{RT}[/tex]-Pass the term RT to the other side of the equation to take the term out of the denominators place:
[tex]\begin{gathered} RT\cdot\sin R=RT\frac{ST}{RT} \\ RT\cdot\sin R=ST \end{gathered}[/tex]-Next, divide both sides by the sine of R to write the expression for RT
[tex]\begin{gathered} RT\cdot\frac{\sin R}{\sin R}=\frac{ST}{\sin R} \\ RT=\frac{ST}{\sin R} \end{gathered}[/tex]-Now replace the expression with the values of ∠R and ST to determine the length of RT
[tex]\begin{gathered} RT=\frac{15}{\sin 57} \\ RT=12.58 \\ RT\approx12.6 \end{gathered}[/tex]Side RT measures 12.6
A business person invests $3,367 at 5% compounded semiannually for two years. What is the future value of the investment, and how much interest will they earn over the two-year period?
The future value of the investment will be $3712.1 and they will earn interest of $345.1 over the two-year period.
Given that business person invests $3,367 at 5% compounded semiannually for two years.
p = $3,367
r = 5%
t = 2 years
A = P(1+r/100)ⁿ
Substitute the values of p,r, and t in the formula,
A = 3,367(1 + 5/100)²
A = 3,367(1 + 0.05)²
A = 4.700 (1.05)²
A = 3712.1175
Rounded to the nearest cent
A = $3712.1
Total interest = A - p = 3712.1 - 3,367 = $345.1
Therefore, the future value of the investment will be $3712.1 and they will earn interest of $345.1 over the two-year period.
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What would be the equation for this line? 80 60 40 20 time in minutes 2 3 4 5 6 7 8 9 X distance in miles
the equation of the line is given as follows,
first we take points on this line
A(2,20)
and
B (4,40)
so, the equation of the line is,
[tex]y-20=\frac{40-20}{4-2}(x-2)[/tex][tex]\begin{gathered} y-20=\frac{20}{2}(x-2) \\ y-20=10x-20 \\ y=10x \end{gathered}[/tex]thus, the equation of the line is
y = 10x
the table shows the number of hours worked and the total amount that each of the four people earned one weekendwhose pay rate was the best whose pay rate was the worst Based on the chart.
pay rate = money earned/hours worked
Gary's pay rate: $37/4 = $9.25 per hour
Tara's pay rate: $54.9/6 = $9.15 per hour
Lamont's pay rate: $27.6/3 = $9.2 per hour
Darius' pay rate: $46.5/5 = $9.3 per hour
best pay rate: Darius
worst pay rate: Tara
use the information given to answer the question.consider the textbook and its mathematical label.part Awhich statement is true?the answer questions is in the image
Solution:
Given the textbook and its mathematics label as shown below:
From the above shape of the book and label, the textbook takes the shape of a rectangular prism, while its label is rectangular in shape.
Thus, the textbook is best represented by a rectangular prism, while the label is best represented by a rectangle.
The third option is the correct answer.
Can you please help and Copy the pictures and put the answers
x = -1/2, y = -6
x = 0, y = -3
x = 1/2, y = -2
x = 1, y = -3
x = 3/2, y = -6
Explanation:We trace each point on the x-axis to the corresponding point on the y-axis to have the following
x = -1/2, y = -6
x = 0, y = -3
x = 1/2, y = -2
x = 1, y = -3
x = 3/2, y = -6
What is the volume of a cylinder whose base diameter is 10 cm and whose height is 12 cm? Round your answer to the nearest tenth.
Solution
We are given the following
Diameter = 10cm
Radius = 10/2 = 5cm
Height = 12cm
Therefore, the Volume will be
[tex]\begin{gathered} Volume=\pi r^2h \\ \\ Volume=\pi(5^2)(12) \\ \\ Volume=\pi\times25\times12 \\ \\ Volume=300\pi \\ \\ Volume=942.5cm^3\text{ \lparen to the nearest tenth\rparen} \end{gathered}[/tex]Therefore, the answer is
[tex]\begin{equation*} 942.5cm^3\text{ } \end{equation*}[/tex]Find the shape, or rate of change, from the following table?
ANSWER
C. -6
EXPLANATION
The rate of change is the change in the dependent variable when the independent variable changes 1 unit. In this case, all columns in the table have a change in the x variable of 1, so the difference between each column in the y-row is the rate of change,
[tex]m=-9-(-3)=-15-(-9)=-21-(-15)=-6[/tex]Hence, the rate of change is -6.
it take Sarah to 1/2 AJ to make a birdhouse how much of the birdhouse will be built after 2/5 day choose the model that correctly illustrates the problem 2/5 ÷ 1/2
After 2/5 days Sarah can build 4/5 of a birdhouse.
It is given that Sarah can build birdhouses at the rate of 1/2 day per birdhouse.
Now let us use unitary method to calculate the number of birdhouses she can make in the given amount of time in a day.
Sarah takes 1/2 day to make 1 birdhouse
Sarah takes 1 day to make 1 ÷(1/2) birdhouse
Sarah takes 2/5 day to make 1÷ 1/2 × 2/5 birdhouse
Hence Sarah will make
= 1 ÷ 1/2 × 2/5
= 4/5 birdhouse
The unitary approach is a technique for solving problems that requires first figuring out how much one unit costs, then multiplying that amount to get the answer.
Therefore Sarah will take 2/5 days to make 4/5 of a birdhouse.
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