Given the following functions, find each of the values: f(x)=x2+3x−10 g(x)=x+5 (f+g)(−5)= ______ (f−g)(3)= _______
Answers
Answer:
(f+g)(-5)
(f+g)(x) = x²+3x-10+x+5
(f+g)(-5) = (-5)² + 3(-5)-10+(-5)+5
= 25-15-10-5+5 = 0
(f-g)(3)
(f-g)(x) = x²+3x-10 - (x+5)
= x²+3x-10-x-5
= x²+2x-15
(f-g)(3) = (3)²+2(3)-15
= 9+6-15 = 0
Related Questions
The compound interest formula states that if P dollars are invested at an annual interest rate of r, compounded n times per year, then A, the amount of money presentIf $10.500 is invested at 8 % compounded monthly, how much will this investment be worth in 22 years? Round youranswer to two decimal placesafter tyears, is given by A = P(1+2)
Answers
Step 1
State the compound interest formula
\(A=P(1+\frac{r}{n})^{t\times n}\)where;
\(\begin{gathered} P=10500 \\ r=\frac{8}{100}=0.08 \\ t=22 \\ n=12 \end{gathered}\)Step 2
Find the amount after 22 years
\(A=10500(1+\frac{0.08}{12})^{12\times22}\)\(\begin{gathered} A=10500\times5.778587511 \\ A=\text{ \$60675.16887} \\ A\approx\text{ \$60675.17} \end{gathered}\)Answer;
\(\text{ \$60675.17}\)4) Jose paid $4.98 in sales tax on an item that cost $62 before tax.
At that rate, how much would he pay in sales tax for an item that
costs $28.00 before tax?
Answers
Answer:
net is before tax
gross is after
Answer:
≈ $2.25
Step-by-step explanation:
This can be solved in two different ways.
1. Use ratios:
4.98/62 = x/28x = 4.98*28/62 x ≈ $2.252. Find the tax percent:
4.98/62*100% = 8.03%And apply this to $28
$28*8.03/100 ≈ $2.25Please help.
Henry is making a quilt using panels that are 2/3 foot by 2/3 foot. The quilt is 6 feet long and 4 2/3 feet wide. What is the area of the quilt?
Answers
Answer:
3 2/3 square feet.
Step-by-step explanation:
You just need to multiply 6 and 4 2/3. To do this you have to change both of them into improper fractions so 6 would be 21/3 and 4 2/3 would be 14/3. If you cross cancel the 21/3 will become 7/3 and the 14/3 will become 14/1. Now you have to multiply across and you should get 98/3. To change the improper fraction into a mixed number you have to divide 98 and 3 so you can get 3 2/3. Therefore, the answer to the area of the quilt is 3 2/3 square feet.
Solve: 6^2х-3 = 6^-2x+1 x = -1 х = 0 x= 1 х = 4
Answers
Answer:
\( \huge \boxed {x = 1}\)
Step-by-step explanation:
Both bases are the same so you will be able to solve the equation from exponent and exponent.
\(2x - 3 = - 2x + 1 \\ 2x + 2x = 1 + 3 \\ 4x = 4 \\ x = 1\)
Answer Check
Substitute x = 1 in the equation.
\( {6}^{2(1) - 3} = {6}^{ - 2(1) + 1} \\ {6}^{2 - 3} = {6}^{ - 2 + 1} \\ {6}^{ - 1} = {6}^{ - 1} \)
Both are same each sides. Therefore the equation is true.
Solve the equation. Remember to check for extraneous solutions.
x-5/x+5=6/x+5 +5
Answers
⇒The first step is to eliminate the fraction by multiplying all the terms with the lowest common denominator.
⇒In this case the lowest common denominator is (x+5), meaning all the terms will be multiplied by (x+5)
⇒\(\frac{x-5}{x+5} (x+5)=\frac{6}{x+5} (x+5)+5(x+5)\)
⇒Multiply out the brackets.
\(x-5=6+5(x)+5(5)\\x-5=6+5x+25\)
⇒Group the like terms together and simplify.
\(x-5x=6+25+5\\-4x=36\\\frac{-4x}{-4} =\frac{36}{-4} \\x=-9\)
⇒∴ x=-9
a continuous random variable x has a uniform distribution between 5 and 25 (inclusive), then p(x = 15) = 0.05. a. true b. false
Answers
Answer:
Step-by-step explanation:
The probability of a continuous random variable taking any specific value is always zero, so the statement p(x = 15) = 0.05 is false.
What is the slope of the line that passes through
the points (-4, -8) and (-8,-6)?
Answers
Answer:
-0.5 or -1/2
Explanation:
\( \frac{y2 - y1}{x2 - x1} \)
to find the slope
-2
4 up, 2 to the left. 4/2 = 2, but becuase it is going down to the right, you make it negative.
Please make me the brainliest. Thank you
Please help! Write the slope-intercept form equation of the trend line
Answers
Answer:
y= -1/3x+9.2
Step-by-step explanation:
I believe that it is 9.2 although it could be another number in the 9's.
The slope is (rise) -1 and (run) 3 and the line crosses the y-intercept at what it looks like 9.2
Lines l and m are parallel.
Which statement is always true?
Group of answer choices
A 90° rotation will map line l onto line m.
Line l can be reflected over a horizontal line to map onto line m.
Line l can be reflected over a vertical line to map onto line m.
Line l can be translated to map onto line m.
Answers
Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.
Do you have any explanations as to why the lines L and m are parallel?L and m are not parallel because the sum of the co-interior angles on the same side of the transversal does not equal 180 degrees.In the event when two lines, l and m, are in the same plane but do not cross, they are said to be parallel.We are aware that the equivalent angles are equal if they are parallel and a transversal is drawn to intersect them both. Accordingly, these are x and y. As a result, we can conclude that x and y are equivalent if l and m are parallel.If two lines, l and m, are in the same plane and do not cross one another, then they are parallel.To learn more about Lines refer to:
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For the series below calculate the sum of the first 3 terms, S3, and find a bound for the error. Make sure to include at least several decimals for accuracy when the problem is graded.∑
[infinity]
n
=
1
(
(
−
1
)
n
400
n
0.6
)
Answers
The sum of the first three terms in the series is -557.921 and a bound for the error is approximately 865.474.
What is series?
In mathematics, a series is the sum of the terms of a sequence. It is represented by the sigma notation (∑), which indicates that a sequence of terms is being added together.
To calculate the sum of the series and find the bounds for the error, let's break down the problem step by step.
The series can be represented as:
\(\sum_{n=1}^{\infty} [(-1)^n * 400*n^{0.6}]\)
To find the sum of the first three terms, S3, we need to calculate the values for n = 1, 2, and 3 and then sum them up.
For n = 1:
\((-1)^1 * 400 * 1^{0.6\) = -400
For n = 2:
\((-1)^2 * 400 * 2^{0.6\) = 564.189...
For n = 3:
\((-1)^3 * 400 * 3^{0.6\) = -721.110...
Now, let's calculate the sum of the first three terms, S3:
S3 = -400 + 564.189 + (-721.110) = -557.921
The sum of the first three terms, S3, is approximately -557.921.
To find a bound for the error, we can use the Alternating Series Estimation Theorem. The theorem states that the error in approximating an alternating series is less than or equal to the absolute value of the next term.
In this case, the next term of the series would be for n = 4:
\((-1)^4 * 400 * 4^{0.6\) = 865.474...
The bound for the error is given by the absolute value of this term:
|Next Term| = |865.474...| ≈ 865.474
Therefore, a bound for the error is approximately 865.474.
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4 is multiplied by the difference of 5 and a number. 4 is multiplied by the difference of 5 and a number
Answers
The expression “4 is multiplied by the difference of 5 and a number” can be simplified to 4(5 - x) or 4 * (5 - x).
The expression that represents the problem "4 is multiplied by the difference of 5 and a number" is 4(5 - x), where x is the unknown number.
In this expression, the difference of 5 and a number is first calculated, and then the result is multiplied by 4.
This can also be written as 4 * (5 - x), which is equivalent to the original expression.
So the answer to the question is 4(5 - x) or 4 * (5 - x).
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Coordinate matrix for differentiation Let L :P2P be the linear transformation given by L(p(t)) = 5p"(t) + 1p' (t) + 3p(t) + 3tp(t). Let E = (C1, C2, C3) be the basis of P2 given by el(t) = 1, ez(t) = t, ez(t) = ť. and let F = (f1, 82, 83, fa) be the basis of P3 given by fi(t) = 1, fz(t) = t, fz(t) = {2, fa(t) = {'. Find the coordinate matrix LFE of L relative to the ordered bases & and F. LFE = Save & Grade 2 tries left Save only
Answers
The coordinate matrix LFE of L relative to the ordered bases E and F is given by:
LFE=12,3,0,12,3,0,0
LFE =
[[5, 1, 3, 3],
[0, 0, 3, 0],
[0, 0, 0, 0]]
This matrix can be obtained by computing the entries of LFE in terms of the components of L with respect to the basis E and then expressing those components with respect to the basis F. The elements of LFE are computed as follows:
LFE[1,1] = L(e1) = = 5 + 1 + 3 + 3 = 12
LFE[1,2] = L(e2) = = 0 + 0 + 3 + 0 = 3
LFE[1,3] = L(e3) = = 0 + 0 + 0 + 0 = 0
LFE[2,1] = L(f1) = = 5 + 1 + 3 + 3 = 12
LFE[2,2] = L(f2) = = 0 + 0 + 3 + 0 = 3
LFE[2,3] = L(f3) = = 0 + 0 + 0 + 0 = 0
LFE[3,1] = L(f4) = = 0 + 0 + 0 + 0 = 0
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Tara's family raises honey bees and sells the honey at the farmers' market. to get ready for market day, tara fills 28 equal sized jars with honey. she brings a total of 14 cups of honey to sell at the farmers' market. use an equation to find the amount of honey each jar holds. to write a fraction, use a slash ( / ) to separate the numerator and denominator.
Answers
The amount of honey each jar holds is 1/2 cup by jar
To solve this exercise we have to perform a mathematical operation of division with fractions:
Information about the problem:
Jars filled = 28 jarsCups brought = 14 cupsTo find the amount of honey each jar holds we state the following equation:
Amount of honey by jar = Cups brought / Jars filled
Amount of honey by jar = 14 cups /28 jar
Simplifying to its minimum expression, we have:
Amount of honey by jar = 7 cups / 14 jar
Amount of honey by jar = 1 cup / 2 jar
Amount of honey by jar = 1/2 cup by jar
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
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Need help plzzzzzzzzzzzzzzz
Answers
Answer:
never, never
Step-by-step explanation:
a *( 1/a)
Rewriting
a/a *1
1
This is not equal to -1
ab
Both a and b are negative
(-) * (-) = positive
Never,never
#1
If a is negative
a(1/a)=a/a becomes
-a/-aWhuch yields 1 not -1
#2
a and b are negative
We know
(-)(-)=(+)So their product can't be negative
Find the value of z.
Answers
2z = 15
z = 7.5
Ms. Apple bought a new chair that was 25% off and saved $14. What was the sale price of the chair? What was the original price?
Answers
Answer:
Original price was $56
Step-by-step explanation:
If $14 is 25% then to find 100% multiply $14 by 4
then you will get $56
d) (2x - 5) (5x - 2) = 0
Answers
Answer:
10x^2-29x+10 is the answer of the question..Please use distributive property to solve it
Thank you
Using the formula for the nth-degree Taylor Polynomial
1. Find the 4th degree Taylor polynomial for tan x centered at x = 0.
2. Find the 10th degree Taylor polynomial centered at x = 1 of the function f (x) = 2x2 − x + 1.
Answers
The 4th degree Taylor polynomial for tan(x) centered at x = 0 is T4(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7.
The 10th degree Taylor polynomial centered at x = 1 for the function f(x) = 2x^2 - x + 1 is T10(x) = -15 + 23(x-1) + 12(x-1)^2 + 8(x-1)^3 + 32(x-1)^4 + 16(x-1)^5 + 32(x-1)^6 + 16(x-1)^7 + 32(x-1)^8 + 16(x-1)^9 + 32(x-1)^10.
To find the 4th degree Taylor polynomial for tan(x) centered at x = 0, we can use the Maclaurin series expansion of tan(x) and truncate it at the 4th degree. The general formula for the nth degree Taylor polynomial is given by Tn(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + ... + (f^n(0)/n!)x^n. Plugging in the derivatives of tan(x) at x = 0, we can simplify the expression and obtain T4(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7.
For the function f(x) = 2x^2 - x + 1, we need to find the 10th degree Taylor polynomial centered at x = 1. Using the same formula as above, we can evaluate the function and its derivatives at x = 1 and plug them into the Taylor polynomial formula. Simplifying the expression gives T10(x) = -15 + 23(x-1) + 12(x-1)^2 + 8(x-1)^3 + 32(x-1)^4 + 16(x-1)^5 + 32(x-1)^6 + 16(x-1)^7 + 32(x-1)^8 + 16(x-1)^9 + 32(x-1)^10. This is the 10th degree polynomial approximation of the function f(x) centered at x = 1.
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An investment will pay $150 at the end of each of the next 3 years, $250 at the end of Year 4,$400 at the end of Year 5 , and $500 at the end of Year 6 . If other investments of equal risk earn 8% annually, what is its present value? Its future value? Do not round intermediate calculations, Round your answers to the nearest cent:
Present value: $ _______
Future value: $ ______
Answers
Given data are: Payment of $150 at the end of each of the next 3 years,Payment of $250 at the end of Year 4,Payment of $400 at the end of Year 5,Payment of $500 at the end of Year 6,Rate of interest = 8% annually
Hence, the Present Value of the investment is $382.20
Present value and future value of investment Formula used: PV = Pmt/(1+r)^n,
FV = Pmt((1+r)^n-1)/r
Let's find the Present Value of the Investment: Given, n = 3 years
Pmt = $150
Rate = 8% annually
PV = 150/(1+8%)³
PV = $382.20
Let's find the Future Value of the Investment: Given, n1 = 3 years
Pmt1 = $150
Rate = 8% annually
n2 = 1 year
Pmt2 = $250
n3 = 1 year
Pmt3 = $400
n4 = 1 year
Pmt4 = $500
FV = (150((1+8%)³-1)/8%)+((250+400+500)(1+8%)³)
FV = $1579.51
Hence, the Future Value of the investment is $1579.51.
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I have never understood these. Help.
Answers
Answer:
5 sqrt(5)
Step-by-step explanation:
sqrt(125)
sqrt( 25*5)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt(25) sqrt(5)
5 sqrt(5)
Answer:
5√(5)
Step-by-step explanation:
Notice that 125 is 25×5
If you couldn't do it use the prime factorization.
Prime numbers are 2,3,5.....
125 isn't divisible by 2 and 3 so we'll go with 5.
● 125 ÷ 5 = 25
Againg 25 is divisible by 5
● 25÷5 = 5
5 is divisible by 5
● 5÷5=1
So 125= 5×5×5 = 5^2 × 5
● √(125)= √(5^2×5) = 5√(5)
NEED HELP
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer as a ratio in simplified form by filling in the boxes.
Answers
The constant of proportionality from the proportional relationship is 3/2
What is Proportional RelationshipA proportional relationship is a mathematical relationship between two variables in which their ratio is always equal. In other words, if x and y are in a proportional relationship, then y/x is always equal to a constant value, called the constant of proportionality. This can be expressed mathematically as y = kx, where k is the constant of proportionality and x and y are the variables in the relationship.
To determine the constant of proportionality, we need to use the proportional relationship given.
y = kx
k = constant of proportionality
3/8 = k(1/4)
Solve for k
k = [(3/8) / (1/4)]
k = 3/2
k = 1.5
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The difference of a number and 8 is 46 less the number. Find the number
Answers
Answer:
unsolvable
Step-by-step explanation:
n-8=46-n
n=(46-n)+8
n=54-n
Answer:
54
Step-by-step explanation:
you add 8+46 and you can check with 54-46=8
An urn containing 14 marbles of which 4 are blue and 10 are red, a marble is selected at random. What is the probability that a. The marble is blue b. The marble is red
Answers
On solving the provided question, we can say that Probability (marble in blue) = 4/14 and Probability (marble in red ) = 10/14
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
total marble = 14
total red = 4
total blue = 10
Probability (marble in blue) = 4/14
Probability (marble in red ) = 10/14
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GEOMETRY HELP PLEASE!! WILL MARK BRAINLEIST!
5
Answers
AC=BD
64 units=10x+24
64-24=10x
40=10x
X=40 divided by 10= 4
hope it helps:)))
The names of the automobile manufacturer of the car that you drive is what type of variables ( scales of measurement)
Answers
The type of variable that represents the names of the automobile manufacturers would be the categorical variable.
What are variables in research work?A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.
There are various types of variables that include the following:
categorical variables.Nominal variables. Ordinal variables. Numeric variables. Continuous variables. Discrete variables.Learn more about variables here:
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Consider a fractal line with fractal dimension D. The mean-square distance between monomers u and v along this line is ⟨(R(u)−R(v))2⟩=b2(v−u)2/D. Calculate the mean-square end-to-end distance R2 and radius of gyration Rg2 for this fractal line. Determine the ratio R2/Rg2 symbolically and then calculate this ratio for fractal dimensions D=1,1.7 and 2 .
Answers
The mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).
The mean-square end-to-end distance for the fractal line is as follows.⟨R2⟩ = ⟨(R(u)- R(v))^2⟩ for u = 0 and v = L where L is the length of the line.⟨R2⟩ = b²/L^2.D.L = b².L^(1-D).
Thus, the mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).
The radius of gyration Rg is defined as follows.
Rg² = (1/N)∑_(i=1)^N▒〖(R(i)-R(mean))〗²where N is the number of monomers in the fractal line and R(i) is the position vector of the ith monomer.
R(mean) is the mean position vector of all monomers.
Since the fractal dimension is D, the number of monomers varies with the length of the line as follows.N ~ L^(D).
Therefore, the radius of gyration for the fractal line is Rg² = (1/L^D)∫_0^L▒〖(b/v^(1-D))^2 v dv〗 = b²/L^2.D(1-D). Thus, Rg² = b².L^(2-D).
The ratio R²/Rg² is given by R²/Rg² = L^(D-2).
When D = 1, R²/Rg² = 1/L. When D = 1.7, R²/Rg² = 1/L^0.7. When D = 2, R²/Rg² = 1/L.
This provides information on mean-square end-to-end distance and radius of gyration for fractal line with a given fractal dimension.
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SOMEONE HELP WITH THIS PLS
Answers
Answer:
0.1218
Step-by-step explanation:
the answers are “2/1” ”4/2” “2/4 2/4” “1/2”
Answers
I probably think it is 4/2
If a resource gives you a pessimistic estimate of 10 days and an optimistic estimate of 6 days. What is the standard deviation?
Answers
The standard deviation can be calculated using the formula: Standard deviation = (pessimistic estimate - optimistic estimate) / 6. Therefore, the standard deviation is 0.67.
The standard deviation is a measure of the spread or variability of a set of data. It quantifies the amount of dispersion or deviation from the average or mean. In this case, we are given a pessimistic estimate of 10 days and an optimistic estimate of 6 days. To calculate the standard deviation, we need to find the difference between these two estimates. The difference is 10 - 6 = 4 days.
Since the range between the optimistic and pessimistic estimates is 6 days, we divide the difference by 6 to normalize it. So, 4 / 6 = 0.67.
Therefore, the standard deviation is 0.67. This means that the actual value is likely to deviate from the average estimate by approximately 0.67 days. A smaller standard deviation indicates less variability, while a larger standard deviation indicates more variability.
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The graph of a function h Is shown below.
Find one value of x for which h (x)=-4 and find h (1).
(a)
(b)
One value of x for which h(x) =
h(1) =
= -4:
X
3
Answers
Step-by-step explanation:
the picture asks for similar things as your text but got other numbers.
let's do both.
first the picture :
find g(0) and one value of x for which g(x) = 0.
g(0) means that x = 0.
so, we find x = 0 on the x-axis (it is where the y-axis intersects) and then go straight up or down until we meet or intersect the function curve.
in our case we go up and intersect the curve at y = 2.
and that is the result.
y = g(x), it is a named variable for the function result, nothing else.
so,
y = g(0) = 2
to find a value of x for which g(x) = 0 means we go along the x-axis (these are all the points for which y = 0) until the x-axis intersects with the curve.
and that is here at x = -1.
now for your text :
we repeat the same principles.
but now, we need to use imaginary lines that go parallel to the x- and y-axis.
your text now calls the function h(x), but since I have no other information, I assume it is the same line function in the picture.
for which value of x is h(x) = -4 ?
remember, y is just the variable that stands for the function result.
so, we are asking for
y = h(x) = -4
imagine a horizontal line through y = -4.
where does it intercept the line h(x) ?
at that point we go straight up or down (in our case up) to the x-axis and read the x-value there : -3
so,
y = h(-3) = -4
to find h(1) we find x = 1 on the x-axis, and from there we go straight up or down (in our case up) parallel to the y-axis until we intersect the function curve.
from there we go straight left out right (in our case left) to the y-axis and read the y-value there : 4
so,
y = h(1) = 4