Answers
The correct answer is
[tex](\frac{f}{g})(x)=-x^2+x-1[/tex]To solve this, first let's write the division:
[tex]f(x)=x^4-x^3+x^2,g(x)=-x^2\Rightarrow(\frac{f}{g})(x)=\frac{x^4-x^3+x^2}{-x^2}[/tex]Now we can factor out a x^2 on the top and the bottom of the expression:
[tex](\frac{f}{g})(x)=\frac{x^4-x^3+x^2}{-x^2}\Rightarrow(\frac{f}{g})(x)=\frac{x^2(x^2-x+1)}{x^2(-1)}[/tex]Now we can cancel out and divide by (-1), or the same thing, multiply by (-1):
[tex](\frac{f}{g})(x)=\frac{x^2(x^2-x+1)}{x^2(-1)}=-(x^2-x+1)=-x^2+x-1[/tex]Then the answer is (f/g)(x) = -x^2 + x - 1. That's the third option
Related Questions
6 1/9to a mixed number is?
Answers
Answer: It's already a mixed number; if your talking about improper fractions it is 55/9
Step-by-step explanation:
6x9+1
6x9=54+1=55/9
Answer:
55/9
Step-by-step explanation:
Because 9 x 6 is 55 then + 1 is 55
help pleaseeee. I need it quick
Answers
x: -3 -2 -1 0 1 2 3 4
y: 6 0 -4 -6 -6 -4 0 6
You plug in x into the equation and you get the value of y. Then graph the points: (-3, 6) (-2, 0) (-1, -4) (0, -6) (1, -6) (2, -4) (3, 0) (4, 6).
Hope it helps! :D
A company surveyed 1200 people. Twice as many females as males. How many each were surveyed
Answers
Females: X
Males: Y
X=2Y because "Twice as many females as males"
The total surveyed are:
[tex]x+y=1200[/tex][tex]2y+y=1200[/tex]Then we have:
[tex]3y=1200[/tex][tex]y=\frac{1200}{3}=400[/tex]From the first equation:
[tex]x=1200-y=1200-400=800[/tex]So, males are 400 and females are 800.
A model for the potential through the heart (between sinoatrial node and atrioventricular node) for an individual is…. Where P(v) is the new voltage (in millivolts) after 1 second given a previous voltage v and u is a positive constant called the updating potential. A. Calculate, including units, the value of P(100): ______ mV B. Find the average rate of change in P on the interval [30, 120] (the answer will contain u). = __________ D. The system is said to be in equilibrium at a value for v for which P(v) = v. For what range of values or u does this system have an equilibrium? (Use interval notation) __________
Answers
The model is given in the question.
a. The value of P(100) is
[tex]P(100)=0.7\times100=70mV[/tex]b. The average rate of change in P on the interval [30,120] is
[tex]A=\frac{P(120)-P(30)}{120-30}=\frac{0.7\times120-(0.7\times30+u)}{90}[/tex][tex]A=\frac{84-21-u}{90}=\frac{63-u}{90}[/tex]c. The graph of P (v) is represented the linear function.
Yes it represents a linear function.
A dinner plate has 25.12 inches of metal around it's edge. What is the radius of the plate?
Answers
Assuming your teacher wants you to use 3.14 for pi, then,
C = circumference = perimeter around the circle
C = 2*pi*r
r = C/(2*pi)
r = (25.12)/(2*3.14)
r = 4 inches is the radius
The radius of the circle is 4 inches
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the centre for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
Given data ,
Let the circumference of the circle be = A
Now , Circumference A = 25.12 inches
The circumference of circle = 2πr
π = 3.14
Substituting the values in the equation , we get
2πr = 25.12
Divide by π on both sides , we get
2r = 8
Divide by 2 on both sides , we get
r = 4 inches
Therefore , the value of r is 4 inches
Hence , The radius of the circle is 4 inches
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MODELING WITH MATHEMATICS The top of the slide is 12 feet from the ground and has an angle of depression of 53°.What is the length of the slide? Round your answer to the nearest whole number.12 ft53AThe slide is aboutfeet long.
Answers
Solution:
From the given figure;
[tex]\begin{gathered} Opposite=12\text{ feet} \\ Hypotenuse=length\text{ of slide} \\ \theta=53\degree \end{gathered}[/tex]Applying SOHCAHTOA
[tex]\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \sin53\degree=\frac{12}{Hypotenuse} \\ Hypotenuse=\frac{12}{\sin53\degree} \\ Hypotenuse=15.02562=15\text{ feet \lparen nearest whole number\rparen} \end{gathered}[/tex]Hence, the slide is about 15 feet long
What is the greatest common factor of this expression?
12m + 18m2
A.
2m
B.
6m
C.
6
D.
2
Answers
Answer:
I think the answer is B because when you check the factors, you get 6 then you add your unit
Helen borrowed $2,500 for home repairs. She paid back 24 payments of$115 each. How much did she pay in interest on the loan?a. $108.96b. $4.79c. $2,760d. $260
Answers
To solve this problem, we will compute the total amount Helen paid back and we will subtract $2,500 from it.
To determine the total amount she paid back we multiply the number of payments by the amount of each payment:
[tex]T=24\times115\text{dollars}=2760\text{ dollars.}[/tex]Subtracting $2,500 from the above result we get:
[tex]2760-2500=260\text{dollars.}[/tex]Answer: Option d.
on a certain hot summer day 629 people use the public swimming pool The daily prices are $1.25 for children and $2.50 for adults The receptionist for admission totaled $1,200 how many children and how many adults swim at the public pool that day
Answers
Let the number of children be "c" and the number of adults be "a".
There are a total of 629 adults and children.
Thus, we can write an equation:
[tex]c+a=629[/tex]Price of each children admit is 1.25 and each child admit is 2.50 for a total of $1200.
Thus, we can write an equation to represent this information as:
[tex]1.25c+2.50a=1200[/tex]We can solve the system of 2 equations we got and find out the values of "a" and "c".
Solving the first equation for c:
[tex]\begin{gathered} c+a=629 \\ c=629-a \end{gathered}[/tex]We substitute it into second equation and figure out a:
[tex]\begin{gathered} 1.25c+2.50a=1200 \\ 1.25(629-a)+2.50a=1200 \\ 786.25-1.25a+2.50a=1200 \\ 1.25a=1200-768.25 \\ 1.25a=413.75 \\ a=\frac{413.75}{1.25} \\ a=331 \end{gathered}[/tex]Now, we simply find out c:
[tex]\begin{gathered} c=629-a \\ c=629-331 \\ c=298 \end{gathered}[/tex]Answer:
Children = 298Adults = 331step by step on how to solve -887.4 (-0.1) & -6 × 3.3
Answers
The numbers have opposite signs, so the result of the multiplication will be negative i.e -19.8.
We are given two mathematical expressions to be solved. An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.
The first expression is solved below :
E1 = -887.4(-0.1)
We need to multiply the two numbers with each other. Both the numbers are negative, so the result of the multiplication will be positive.
E1 = 88.74
The second expression is solved below :
E2 = -6 × 3.3
This is a simple multiplication of two real numbers. The numbers have opposite signs, so the result of the multiplication will be negative.
E2 = -19.8
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Construct an appropriate triangle to find the missing values
Answers
This can be solved using trigonometry.
What is trigonometry?
Trigonometry is a field of mathematics that examines correlations between triangle side lengths and angles (from the Ancient Greek words "trigonon" and "metron"). The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord computation. Trigonometry has been used historically in fields including geodesy, surveying, celestial mechanics, and navigation. Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric similarities are frequently employed to rewrite trigonometrical statements.
Using trigonometric relations,
cos 30° = cos π/6 rad = √3/2
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Use the standard normal distribution to find the probability P(z < –2.08)
Answers
P(z < -2.08) = 0.018763
Explanations:From the standard normal distribution table, we can check the probability given any z-score
Therefore, checking P(z < -2.08) from the standard normal distribution:
P(z < -2.08) = 0.018763
Raymond places four colored blocks in a bag. The colors are red, blue, yellow and green. Without looking, he reaches into the bag andpulls one block out.What is the probability that the block he pulls out will be yellow?A. 1/4. B.1/3. C.3/1. D.4/1
Answers
Given:
Total number of colored blocks in the bag = 4
Given that Raymond picks one block out without looking(randomly), let's find the probability it is a yellow block.
Probablity can be said to be the likelihood of the occurence of an event.
Given:
Number of yellow blocks = 1
To find the probability that the blocks he pulls out will be a yellow block, apply the formula below:
[tex]P(\text{yellow)}=\frac{\text{Number of yellow blocks}}{Total\text{ number of blocks}}[/tex]Thus, we have:
[tex]P(\text{yellow)}=\frac{1}{4}[/tex]Therefore, the probability thatvthe block he pulls out will be yellow is ¼
ANSWER:
[tex]A\text{. }\frac{1}{4}[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
its 5
Step-by-step explanation:
f
dddd
Solve: (2,1); m=undefined. Answer has to be in slope intercept form, so y=mx+b. SHOW ALL WORK SO I CAN HAVE A BETTER UNDERSTANDING :)
Answers
Answer:
x = 2
Step-by-step explanation:
So this seems kind of a trick question. This is why. The given slope is undefined. That means this is a vertical line. Vertical lines cannot be written in slope-intercept form,
y = mx+b.
Vertical lines have the equation "x = anumber" It literally cannot be written in the form y=mx+b.
The point given is (2,1) this is in the form (x,y) so x is 2 and y is 1. We are interested in the x.
x is 2 is written as:
x = 2 This is the equation of the lines through (2,1) with m=undefined.
Greg graduated in the bottom 9% of his class. If the mean was 585 and the standard deviation was 134, and the distribution was normal, what was Greg's raw score?
Answers
Greg's raw score in the test is 405
How to determine the raw score of the test?The given parameters are
Mean = 585Standard deviation = 134Proportion, p = bottom 9%The above implies that
z = P(p < 0.09)
From z tables of probabilities, we have
z = -1.34
The z-score of the data value is calculated using the following formula
z = (raw score - mean value)/standard deviation
Substitute the given parameters in the above equation
-1.34 = (raw score - 585)/134
This gives
-180 = raw score - 585
So, we have
raw score = 585 - 180
Evaluate
raw score = 405
Hence, the raw score is 405
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Find the lateral area of a right cylinder with a diameter of 6.4 yards and a height of 16.2 yards. Round to the nearest tenth.
Answers
You can use the following formula in order to calculate the Lateral area of the right cylinder given in the exercise:
[tex]LA=2\pi rh[/tex]Where "LA" is the lateral area of the cylinder, "r" is the radius and "h" is the height.
In this case you know that its diameter is:
[tex]d=6.4yd[/tex]Since the diameter of a circle is twice the radius:
[tex]2r=6.4yd[/tex]Knowing that the height of the cylinder is:
[tex]h=16.2yd[/tex]You can substitute values into the formula and then evaluate, in order to find the lateral area:
[tex]\begin{gathered} LA=\pi(6.4yd)(16.2yd) \\ LA\approx325.7yd^2 \end{gathered}[/tex]Then, the answer is:
[tex]LA\approx325.7yd^2[/tex]90 divided by 5(3x2)-1=
Answers
The solution of expression 90 ÷ [5 (3×2) - 1} is,
90 ÷ [5 (3×2) - 1} = 3.10
We have to given that,
An expression to simplify as,
⇒ 90 ÷ [5 (3×2) - 1}
We can simplify the expression as,
⇒ 90 ÷ [5 (3×2) - 1}
⇒ 90 ÷ [5 ×6 - 1]
⇒ 90 ÷ [29]
⇒ 3.10
Therefore, The solution of expression 90 ÷ [5 (3×2) - 1} is,
90 ÷ [5 (3×2) - 1} = 3.10
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Part 2: Multiple Choice Must show all work to get full credit.
Answers
The correct value of x is -6, as determined by the equation KL + LM = KM. As a result, Option C is correct.
What is an equation and what type is it?Equations are classified into two types: identities and conditional equations. An identity holds true for all variable values. A conditional equation is only true for specific variable values. An equation is formed by joining two expressions with an equals sign ("=").From the given figure,
KL + LM = KM
15 + 2x + 10 = x + 19
2x + 25 = x + 19
x = -6
Therefore, the correct value of x is -6 which is obtained from the given equation KL + LM = KM. So, Option C is correct.
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Elsie has just finished polishing some of her antique penny collection. She has twelve pennies, each with a different date. To store her coins she has purchased many plain black bags, and wishes to put the same number of coins in each bag. She has no restriction on the number of bags she can use. In how many possible ways can she store her coins
Answers
The possible ways Elsie (combinations) can store her 12 coins in the bags she purchased is 6 ways
What is a combination in mathematics?A combination is the number of possible arrangements.
The number of coins = 12 coins
The number of black bags = Many
Number of coins per bag = The same number of coins
Required;
The number of ways Elsie can store her coins
Solution;
The ways the coins can be stored is given by the factors of 12 which are; 1, 2, 3, 4, 6, and 12
The coins can therefore be stored as follows;
1 coin per bag to give 1 × 12 = 12 bags of coins2 coins per bag to give 12 ÷ 2 = 6 bagsShared into 3 coins each to give 12 ÷ 3 = 4 bags 4 coins to give 12 ÷ 4 = 3 bags6 coins each to give 12 ÷ 6 = 2 bags12 coins in each bag to give 12 ÷ 1 = 1 bagsThe possible number of ways Elsie can store the coins is 6 ways
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Help mee pleasee!!
thank you <3
Answers
The linear equation y = -500x + 5000 models the price-sales relationship for the toy and the daily sales of the toy would be $1250 if the price is set at $7.50.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The line must pass through points (6, 2000) and (8,1000) which is given in the question.
We have to determine the slope of the line :
m = (y₂ - y₁)/(x₂ -x₁ )
m = (1000 - 2000)/(8 - 6)
m = -1000/2
m = -500
This represents new assistants per year
So with through points (6, 2000) and (8,1000), the equation becomes
y - 2000 = -500(x -6)
y = -500x + 3000 + 2000
y = -500x + 5000
Using this equation to predict the daily sales of the toy if the price is set at $7.50.
Assume that the ratio of change in price to change in daily sales is constant and let x be the price of the toy and y be the number of sales.
Substitute the value of x = 7.50
y = -500(7.50) + 5000
y = -56000 + 294000
y = 1250
Hence, the daily sales of the toy would be $1250 if the price is set at $7.50.
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Use the Factor Theorem to find the zeros of f(x) = x³+4x² - 4x - 16 given that (x - 2) is afactor of the polynomial.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given polynomial function
[tex]f(x)=x^3+4x^2-4x-16[/tex]STEP 2: Apply the factor theorem
A polynomial function f(x) has a factor (x-a) if and only if f(a) = 0, this means that (x-2) will be a factor if and only if f(2)=0.
By checking,
[tex]\begin{gathered} f(2)=2^3+4(2^2)-4(2)-16 \\ f(2)=8+16-8-16=0 \end{gathered}[/tex]Hence, (x-2) is a factor and the first zero is 2
STEP 3: We divide the polynomial by its factor to get the quotient expression
[tex]\frac{x^3+4x^2-4x-16}{(x-2)}=x^2+6x+8[/tex]STEP 4: we find out the factors of the quotient
If f(a) is zero, this means that a must be a factor of 16
The factors of 16 are 1,2,4,8,16
[tex]\begin{gathered} x^2+6x+8=(x+4)(x+2) \\ f(-4)=(-4^2)+6(-4)+8=16-24+8=0 \\ f(-2)=(-2)^2+6(-2)+8=4-12+8=0 \end{gathered}[/tex]Hence, (x+4) and (x+2) are also factors of the polynomial.
Therefore, the zeroes of the given function are:
[tex]2,-4,-2[/tex]Health and Fitness Masha is training for a marathon. She is doing
tempo runs to increase her speed. In tempo runs, a runner varies
their pace during the run. Masha jogs 1 mile, then runs at a fast pace
for 11 miles. She finishes by walking 2 miles to cool down. Write a
numerical expression to model the number of miles Masha runs,
walks, or jogs.
Answers
The numerical expression to model the number of miles Masha runs, walks, or jogs is 14.
What is meant by numerical expression?Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.
The rule should state something along the lines of: "When simplifying, parentheses must be simplified first, followed by all exponents, all multiplication, and ultimately, all addition."
Based on the given conditions, formulate: 2 + 1 + 11
Calculate the sum or difference: 3 + 11
Calculate the sum or difference: 14
Therefore, the numerical expression to model the number of miles Masha runs, walks, or jogs is 14.
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The measure of an angle is 28.5°. What is the measure of its complementary angle?
Answers
When the measure of an angle is 28.5° then the angle measure of its complementary angle will be 61.5°.
What is complementary angle?They are referred to as complementary angles when the sum of two angles is 90 degrees. For instance, the angles of 30 degrees and 60 degrees complement one another.
If we know the measurement of one angle, we can easily find the unknown angle because the sum of complementary angles equals 90 degrees.
As an illustration, if one of the two angles is 45 degrees, then the formula is:
x + 45 = 90
x = 90 - 45 = 45°.
If 2 complementary angles adds up to 90°
So the complementary angle of 28.5° is
90° - 28.5° = 61.5°
Thus, the angle measure of its complementary angle will be 61.5°.
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May I please get help with this for I am confused S to hash by my original and final points of the figure and where I should Rotate it to 270° clockwise
Answers
ANSWER:
Point in original figure (2, -3)
Point in final figure (-3, -2)
STEP-BY-STEP EXPLANATION:
The first thing is to determine the original point of the figure on the graph, which would be:
[tex]P(2,-3)[/tex]The rule for 270° counterclockwise rotation is as follows:
[tex](x,y)\rightarrow(y,-x)[/tex]We apply it in this case, and the new point would be:
[tex]P(2,-3)\rightarrow P^{\prime}(-3,-2)[/tex]We represent the result on the graph, as follows
A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses.
4, 19, 7, 15, 13, 4
Find the mean number of hours for these students.
If necessary, round your answer to the nearest tenth.
Answers
Answer:
10.3
Step-by-step explanation:
To calculate the mean we need to:
(4 + 19 + 7 + 15 + 13 + 4)/6
10.33333,...
Round to nearest tenth: 10.3
Studying for a test, need some help solving this question
Answers
Solution
Part A
To find C
[tex]_{\angle\text{ C+}\angle A+\angle B=180^0(Sum\text{ of angles in a triangle\rparen}}[/tex][tex]\begin{gathered} \angle C+33.84+19.32=180 \\ \angle C+53.16=180 \\ \angle C=180-53.16 \\ \angle C=126.84^0 \\ \end{gathered}[/tex]Part B
To find a
Using sine rule
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex][tex]\begin{gathered} \frac{sin33.84}{a}=\frac{sin126.84}{13.95} \\ cross\text{ multiply} \\ asin126.84=13.95sin33.84 \\ divide\text{ both side by sin126.84} \\ \\ a=9.70672 \end{gathered}[/tex]Part C
To find b
Using sine rule
[tex]\begin{gathered} \frac{sin33.84}{9.70672}=\frac{sin19.32}{b} \\ \\ \\ b=5.76683 \end{gathered}[/tex]multiple fractions (reduce to lowest terms or tenths)61/2×41/4
Answers
Answer:
312.6
Explanation:
Given the expression
61/2 * 41/4
Multiply both numerator and denominator
= 61/2 * 41/4
= (61*41)/(2*4)
= 2501/8
= 312.625
To nearest tenth 61/2 * 41/4 = 312.6
Using Euler's formula, how manyedges does a polyhedron with 20faces and 12 vertices have?? ] edgesEuler's Formula: F + V = E + 2Enter
Answers
SOLUTION:
Case: Euler's formula
Given:
Faces= 20
Vertices =12
Euler's formula: F + V = E + 2
Required: To find the number of Edges
Method:
Step 1: Recreate the formula to isolate E
F + V = E + 2
E = F+V - 2
Step 2: Plug in the value of the variables
E = F+V - 2
E= 20 + 12 - 2
E = 30
Step 3:
The value of E is 30
Final answer:
The Polyhedron has 30 edges
4x3 − 6x2 − 28x Is this a special product?
Answers
ANSWER:
It is not a special product
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]4x^3-6x^2-28x[/tex]Among the special products we have:
The sum and difference of same terms
The square of a binomial
The cube of a binomial
Let's factor the expression to determine if it satisfies any of the above:
[tex]\begin{gathered} 2x\cdot\left(2x^2-3x-14\right? \\ 2x^{2}-3x-14 \\ -3x=4x-7x \\ 2x^2+4x-7x-14 \\ 2x\left(x+2\right?-7\left(x+2\right? \\ 2x\cdot\left(x+2\right)\cdot\left(2x-7\right) \end{gathered}[/tex]Therefore, we can determine that it does not belong to the group of special products.
