Answer:
$2,649.50
Step-by-step explanation:
s
If f(x) = 3x-2 and g(x) = x +1, find (f+g)(x).
Answer:
[tex]\huge\boxed{\sf (f+g)(x) = 4x - 1}[/tex]
Step-by-step explanation:
Given functions:f(x) = 3x - 2g(x) = x + 1Solution:Add both functions
(f+g)(x) = 3x - 2 + x + 1
Combine like terms
(f+g)(x) = 3x + x - 2 + 1
(f+g)(x) = 4x - 1
[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex](f+g)(x)=4x-1[/tex]
Step-by-step explanation:
FunctionsFunctions written in equation form usually have several parts:
nameinputMathematical rule/expression that tells what the function does to the input to give an output.So, for instance, [tex]g(x)=x+1[/tex] has a name of "g", has an input of "x", and has a rule that it adds 1 to the input to get the output.
The name of the function should tell what rule to follow (look for the equation with that function name), or it may give some details on what the function does.
Dealing with so many different problems, functions often get a default name of "f", "g", or "h".
If a function is special and/or used commonly, it will sometimes get a special name (like the natural logarithm function "ln").
This functionIn this case, the function is (f+g)(x). The function name means that the result of each function, f and g, will be added together, while using the same input "x" for both functions.
[tex](f+g)(x)=f(x)+g(x)\\=(3x-2)+(x+1)\\=3x+(-2)+x+1\\=4x+(-1)\\=4x-1[/tex]
So, given these two functions for "f" and "g", [tex](f+g)(x)=4x-1[/tex]
A bike store marks up the wholesale cost of all bikes they sell by 30%. calvin wants to buy a bike that has a price log of 123.50. what was the wholesale cost of the bike?
The wholesale cost of the bike is 95.
Wholesale price is the price charged for a product as sold in bulk to large trade or distributor groups as opposed to what is charged to consumers.
The selling price is how much a buyer pays for a product or service.
The profit formula is used to calculate the amount of gain that has been made in a transaction
Profit = Selling Price (S.P.) - Cost Price (C.P.)(here it is the wholesale price)
Given =
Selling Price = 123.50Wholesale price = ?Profit = 30% of wholesale priceSubstituting it in the profit formula we get
0.3 x wholesale price = 123.50 + wholesale price
1.3 x wholesale price = 123.50
Wholesale price = [tex]\frac{123.50}{1.3}[/tex] = 95
Thus the wholesale cost of the bike is 95.
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Can someone help with these geometry questions? It’s question 2, 3, 4 & 5, I gotta have answers fast pls :(
Answer:
Hey! I am gona help you.
BC ≅ EF
DE ≅ AB
Angle C ≅ Angle F
Angle D ≅ Angle A
Hope it might help!
Note -2,3 can't be solved as there is no figure given here.
prove that the value of each expression is divisible by the given number 8^10-2^27 is divisible by 14
Answer:
Proof below
Step-by-step explanation:
General Strategy:Find factors of divisorUse algebraic properties to reveal those factors in the given expression.Divisibility
A number, p, is divisible by another number, d, if and only if there is some non-negative integer, n, such that n*d=p.
To prove that, 300 is divisible by 10 because, 30 is a non-negative integer, and 10*30=300.
Strategies for Divisibility by a composite number
Note that in the previous example, 10 is a composite number. This means that both one 2 and one 5 (the full list of 10s factors) had to be factored out of the 300.
In the given problem, we are to prove that the number is divisible by 14. Observe 14 is composite with factors of 2 and 7.
Properties of exponentsSince the expression is given with exponents, it will be helpful to recall a few exponent properties to algebraically manipulate the expression.
Recall the following property of exponents:
[tex]x^{a}*x^{b}=x^{(a+b)}[/tex] [tex](x^{a})^{b}=x^{ab}[/tex]Finding a factor of 14 in the given expressionOriginal expression...
[tex]8^{10}-2^{27}[/tex]
Recognizing 8 as a power of 2...
[tex](2^3)^{10}-2^{27}[/tex]
Simplifying and rewriting so that both terms are powers of 2...
[tex]2^{30}-2^{27}[/tex]
Observing that both terms have 27 twos as factors...
[tex]2^{27}*2^{3}-2^{27}[/tex]
Factoring out 27 twos...
[tex]2^{27}*(2^{3}-1)[/tex]
Simplifying the expression in the parenthesis:
[tex]2^{27}*(8-1)[/tex]
[tex]2^{27}*(7)[/tex]
Knowing that we also need a factor of 2, use properties of exponents, and associative property of multiplication...
[tex](2^{26}*2^1)*7[/tex]
[tex]2^{26}*(2^1*7)[/tex]
[tex]2^{26}*(2*7)[/tex]
[tex]2^{26}*14[/tex]
Since 2^26 is a non-negative integer, the original expression is divisible by 14.
xan any one help please
Answer:
Sophie.
Step-by-step explanation:
15. 30 in Italian minus 15 in German.
The mapping diagram shows a functional relationship. A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (8, 4), (negative two-thirds, 3), (11, negative 1), (4, one-half). Complete the statements. f(4) is . f(x) = 4 when x is .
Answer:
its 1/2 and 8
Step-by-step explanation:
got it right
what is the value of 2x^2 - 4x + 5 when x is -3
Answer:
35
Step-by-step explanation:
2x9+12+5=35
4 Determine and justify the strength of each of the following inductive arguments. (a) Premise: The 20 numbers that were randomly chosen from a box that contains 25 cards labeled with prime numbers of less than 100 are odd numbers. Conclusion: All prime numbers are odd numbers. (b) Premise 1: All the employees that have worked at least 15 years and above in Syarikat LMN will receive the excellent service rewards. Premise 2: Pak Hamid has worked in the LMN Company for 23 years. Conclusion: Pak Hamid will be awarded an excellent service. (c) Premise: Faisal had consecutively scored 'A' for his Mathematics subject for the last three examinations. Conclusion: Faizal will also score 'A' during the next term examination.
Pak Hamid has worked more than 15 years. The correct premise and conclusion is B.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
Premise: The 20 numbers that were randomly chosen from a box that contains 25 cards labeled with prime numbers of less than 100 are odd numbers.
Conclusion: All prime numbers are odd numbers.
Both premise and conclusion are incorrect because 2 is an even prime number.
Premise 1: All the employees that have worked at least 15 years and above in Syarikat LMN will receive the excellent service rewards.
Premise 2: Pak Hamid has worked in the LMN Company for 23 years.
Conclusion: Pak Hamid will be awarded an excellent service.
Both premise and conclusion are correct. Because Pak Hamid has worked more than 15 years.
Premise: Faisal had consecutively scored 'A' for his Mathematics subject for the last three examinations.
Conclusion: Faizal will also score 'A' during the next term examination.
The conclusion is incorrect because all the exams are independent to each other.
Then the correct premise and conclusion is B.
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For the following exercises, solve each inequality and write the solution in interval notation.
32. | x − 4 | ≥ 8
Answer:
The solution of the given set in interval form is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].
Step-by-step explanation:
It is given in the question an inequality as [tex]$|x-4| \geq 8$[/tex].
It is required to determine the solution of the inequality.
To determine the solution of the inequality, solve the inequality [tex]$x-4 \geq 8$[/tex] and, [tex]$x-4 \leq-8$[/tex]
Step 1 of 2
Solve the inequality [tex]$x-4 \geq 8$[/tex]
[tex]$$\begin{aligned}&x-4 \geq 8 \\&x-4+4 \geq 8+4 \\&x \geq 12\end{aligned}$$[/tex]
Solve the inequality [tex]$x-4 \leq-8$[/tex].
[tex]$$\begin{aligned}&x-4 \leq-8 \\&x-4+4 \leq-8+4 \\&x \leq-4\end{aligned}$$[/tex]
Step 2 of 2
The common solution from the above two solutions is x less than -4 and [tex]$x \geq 12$[/tex].
The solution set in terms of interval is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].
What is the smallest positive integer $n$ for which $n^2$ is divisible by 18 and $n^3$ is divisible by 640
The smallest positive integer n for which n^2 is divisible by 18 and n^3 is divisible by 640 is 120
The modulo (or "modulus" or "mod") is the remainder after dividing one number by another.
The smallest integer is 120, since:
[tex]120^{2}[/tex] mod 18 = 0, (reminder after dividing [tex]120^{2}[/tex] by 18 is 0) and
[tex]120^{3}[/tex] mod 640 = 0 (reminder after dividing [tex]120^{3}[/tex] by 18 is 0)
Hence, The smallest positive integer n for which n^2 is divisible by 18 and n^3 is divisible by 640 is 120.
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9. Evaluate 14(-6x +10) - 16x - 100x + 140 for x = -2.
Answer:
680
Step-by-step explanation:
14(-6x +10) - 16x - 100x + 140 for x = -2.
14(-6(-2) + 10) - 16(-2) - 100(-2) + 140
14(12 + 10) + 32 + 200 + 140
14(22) + 372
308 + 372
680
A new computer loses 1/3 of its value every year. Which graph- a, b, c, or d – could represent the relationship between the year and the computers value? Justify your choice.
The graph which represents the relationship between the year and the computers value is; Choice A.
Which graph represents the relationship?According to the task content, it follows that the computer loses 1/3 of its value every year. Hence, it follows that the value of the computer each year is 2/3 of its previous value.
Hence, the relationship can best be modelled by an exponential function, a decay function to be more specific and can best be represented by Choice A.
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Simplify the following:
A.
(-x)^4/4x * 8(-x)^-3/x^-3/4
Answer:
Answer for (a) -2x^4/3
Answer for (b) 2^5x/4^3x
Answer:
a. [tex]-2x\sqrt[3]{x}[/tex]
b. [tex]\frac{1}{2^x}[/tex]
Step-by-step explanation:
a.
Original equation:
[tex]\frac{(-x)^4}{4x}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]
So (-x)^4 can be seen as (-x * -x) * (-x * -x), which becomes x^2 * x^2 = x^4, the negatives cancel out of the degree is even. So it becomes:
[tex]\frac{x^4}{4x}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]
Cancel out one of the x's on the left fraction:
[tex]\frac{x^3}{4}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]
Rewrite the exponent in the numerator: [tex]a^{-x} = \frac{1}{a^x}[/tex]
[tex]\frac{x^3}{4}*\frac{8*\frac{1}{-x^3}}{x^{-\frac{4}{3}}}[/tex]
Simplify the numerator:
[tex]\frac{x^3}{4}*\frac{\frac{8}{-x^3}}{x^{-\frac{4}{3}}}[/tex]
Keep numerator, change division to multiplication, flip the denominator:
[tex]\frac{x^3}{4}*\frac{8}{-x^3} * \frac{1}{x^{-\frac{4}{3}}}[/tex]
multiply the denominator using the exponent identity: [tex]x^a*x^b=x^{a+b}[/tex]
[tex]\frac{x^3}{4}*\frac{8}{-x^{\frac{5}{3}}}[/tex]
Multiply the numerators and denominators:
[tex]\frac{8x^3}{-4x^{\frac{5}{3}}}[/tex]
Use the fact that: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] to divide the x^3 and x^(5/3) and divide the 4 by the -8
[tex]-2x^{\frac{4}{3}}[/tex]
Rewrite the exponent using the exponent identity: [tex]x^{\frac{a}{b}} = \sqrt[b]{x^a}=\sqrt[b]{x}^a[/tex]
[tex]-2\sqrt[3]{x^4}[/tex]
Rewrite as two radicals: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex]
[tex]-2\sqrt[3]{x^3} * \sqrt[3]{x}[/tex]
Simplify:
[tex]-2x\sqrt[3]{x}[/tex]
b.
[tex]2^{2x}\div4^{3x}*64^{\frac{x}{2}}[/tex]
Rewrite the 4 as 2^2
[tex]2^{2x}\div(2^2)^{3x}*64^{\frac{x}{2}}[/tex]
Use the exponent identity: [tex](x^a)^b=x^{ab}[/tex]
[tex]2^{2x}\div2^{6x}}*64^{\frac{x}{2}}[/tex]
Use the exponent identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]2^{2x-6x} = 2^{-4x}[/tex]
Rewrite this part using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = \frac{b}{a^x}[/tex].
[tex]\frac{1}{2^{4x}} * 64^{\frac{x}{2}}[/tex]
Multiply:
[tex]\frac{64^{\frac{x}{2}}}{2^{4x}}[/tex]
rewrite 64 as 2^6
[tex]\frac{(2^6)^{\frac{x}{2}}}{2^{4x}}[/tex]
Use the identity: [tex](x^a)^b=x^{ab}[/tex]
[tex]\frac{2^{3x}}{2^{4x}}[/tex]
Use the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]2^{-x}[/tex]
rewrite using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = \frac{b}{a^x}[/tex]
[tex]\frac{1}{2^x}[/tex]
Every year, the value of a surveying machine depreciates by 25 % of its value in the previous year.
If the value of the machine was $ 11 250 in 2012, find its value in 2010.
Answer:
$17578.13
Step-by-step explanation:
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Given x|7|8|9|10|
f|10|13|x|5|
if the mean is 8 find x ,mean variance
Answer:
X=11
Step-by-step explanation:
Find the zero of the given polynomial :
[tex]p(x) = {x}^{2} + 1[/tex]
Answer:
x = i, -i
Explanation:
p(x) = x² + 1
To set a polynomial to zero, p(x) = 0.
⇒ x² + 1 = 0
relocate variable
⇒ x² = -1
square root both sides
⇒ x = ±√-1
breakdown
⇒ x = √-1, -√-1
simplify if x = √-a then √a i
⇒ x = i, -i
Answer:
+i , -i
Step-by-step explanation:
Zero of the polynomial:p(x) =0
x² + 1 = 0
x² = -1
Take square root both sides,
[tex]\sf x = \sqrt{-1}\\\\x =\sqrt{i^2}\\[/tex]
x = ± i
Zeros of the polynomial:
x = +i , -i
please help me out with this
Answer:
25
Step-by-step explanation:
sin © =36/(35+x)=21/35
36/(35+x)=21/35
x=(36*35/21)-35
x=25
Step-by-step explanation:
SOLUTION::
please watch the image for explanation
The eleventh term of an AP is four times the second term. If the sum of the first seven terms of the AP is 175, find the first term and the common difference.
Step-by-step explanation:
a11 = 4 × a2
a + 10d = 4 × (a + d)
a + 10d - 4d = 4a
a + 6d = 4a
6d = 4a - a
6d = 3a
(6/3)d = a
2d = a ----- eq. 1
now, sum of 7 terms = s7 = 175
7/2 {2a+6d} = 175
7/2 { (2 × 2d ) + 6d} = 175
7 ( 4d + 6d ) = 175 × 2
7 ( 10d ) = 350
70d = 350
d = 350/70
d = 5
Now from eq. 1,
2d = a
2(5) = a
a = 10, d = 5
THANK YOU........
Please answer with everything needed i appreciate everyones help:00
Answer:
y = 5
Step-by-step explanation:
Step-by-step explanation:
the slope of a line is the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.
when the slope is 0, it means the y coordinate change is 0 for all points. that means y is a constant. and the line is a horizontal line.
to go through (-2, 5) this constant y has to be the y value of the point.
so,
y = 5
that's it. that is the whole equation for that line, because the slope m is 0. what remains is the y-axis intercept (y = 5).
Express the radical using the imaginary unit i
Answer:
[tex]\huge\boxed{\sf \pm 10i}[/tex]
Step-by-step explanation:
Given radical:[tex]\pm \sqrt{-100}[/tex]
We can write it as:
[tex]\pm \sqrt{-1 \times 100} \\\\\pm \sqrt{-1} \times \sqrt{100} \\\\\underline{We \ know \ that:}\ i =\sqrt{-1} \\\\\pm i \times 10\\\\\boxed{\pm 10i}\\\\\rule[225]{225}{2}[/tex]
The price of a technology stock was $9.69 yesterday. Today, the price rose to $9.80. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
Percent increase was 1.1%Step-by-step explanation:
Step 1Find the price increase in number:
$9.80 - $9.69 = $0.11Step 2Find the percent increase, relevant to initial price:
$0.11/$9.69 × 100% = 1.1% (rounded to the nearest tenth)Use the digits 1-20, at most one time each, to create a true statement for polynomial below.
(the _ are blanks that need to be filled in)
_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2
The complete equation of the polynomial is 2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2
How to complete the blanks?The equation is given as:
_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2
Complete the blanks using alphabets
ax(x^2 - bx) + cx^3 = dx(ex^2 + fx) - x^2
Open the brackets
ax^3 - abx^2 + cx^3 = dex^3 + dfx^2- x^2
Factorize the expression
(a + c)x^3 - abx^2 = dex^3 + (df - 1)x^2
By comparison, we have:
a + c = de
-ab = df - 1
Rewrite the second equation as:
ab + df = 1
So, we have:
a + c = de
ab + df = 1
Set a = 2 and c = 10.
So, we have:
a + c = de ⇒ de = 2 + 10 ⇒ de = 12
ab + df = 1 ⇒2b + df = 1
Express 12 as 3 * 4 in de = 12
de = 3 * 4
By comparison, we have:
d = 3 and e = 4
So, we have:
2b + df = 1
This gives
2b + 3f = 1
Set b = 11.
So, we have:
2 * 11 + 3f = 1
This gives
22 + 3f = 1
Subtract 22 from both sides
3f = -21
Divide by 3
f = -7
Hence, the complete equation is:
2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2
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For the following exercises, determine whether the relation is a function.
2. {(5, 2), (6, 1), (6, 2), (4, 8)}
Answer:
The given relation {(5,2),(6,1),(6,2),(4,8)} is not a function.
Step-by-step explanation:
The relation {(5,2),(6,1),(6,2),(4,8)} is given.
It is required to determine whether the given relation is a function.
To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.
Step 1 of 1
The given relation is {(5,2),(6,1),(6,2),(4,8)}.
The set of the first components of each ordered pair is called the domain.
From the relation, the domain is {5,6,6,4}.
The set of the second components of each ordered pair is called the range.
From the relation, the range is {2,1,2,8}.
The domain of the function does not have a unique range. So, the given relation is not a function.
The circle above has an area of 36π and is divided into 8 congruent regions. What is the perimeter of one of these regions?
A) 6+1.5π
B) 6+2π
C) 12+ 1.5π
D) 12+2π
The perimeter of each region is 12 + 1.5π if a circle with an area of 36π is divided into 8 congruent regions
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let r represent the area of the circle, hence:
Area = πr²
36π = πr²
r = 6 units
Perimeter = 2πr = 2π(6) = 12π
The circle has 8 congruent regions, hence:
Perimeter of each region = 6 + 6 + 12π/8 = 12 + 1.5π
The perimeter of each region is 12 + 1.5π if a circle with an area of 36π is divided into 8 congruent regions
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Deepika has drawn a rhombus and a square, each with side length 5 cm. Which of these will be different for both the shapes?
1. lengths of the two diagonals
2. angles between the two diagonals
3. lengths of the adjacent sides
4. angles between the adjacent side
The difference for both the rhombus and square are as follows;
Lengths of the two diagonalsAngles between the two diagonalsAngles between the adjacent sideProperties of a square?All the sides are equal.Opposite sides are parallel.All the angles are 90 degrees each.The diagonal bisect each otherProperties of a rhombusAll the sides are equal.Opposite sides are parallel.All the angles are not 90 degrees.The length of the diagonals are not the same.Therefore, the difference for both the shapes(square and rhombus)are as follows:
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what is 5500 divided by 785
Answer:
785 Remainder 5
Step-by-step explanation:
What is the Value of the expression? 2 (1/4)^2
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
2 ( [tex]\frac{1}{4}[/tex] )²
= 2 × [tex]\frac{1}{16}[/tex] ← cancel 2 and 16 by 2
= 1 × [tex]\frac{1}{8}[/tex]
= [tex]\frac{1}{8}[/tex]
assigning oxidation numbers , please help!!
Answer:
c is 1
o is q
h is 2
in ch3
c is 2 h is 3
and finally o is 1
How many solutions exist for the given equation?
3(x – 2) = 22 – x
zero
one
two
infinitely many
Answer:
C. Infinitely many
Step-by-step explanation:
First, find x.
3(x-2)=22-x
Use distributive property.
3x-6=22-x
Add x to both sides.
4x-6=22
Add 6 to both sides.
4x=28
Divide 4 from both sides.
x=7
Plug in 7 for x into the original equation.
3(7-2)=22-7
3(5)=22-7
15=15
Since 15 does equal 15, the answer has infinitely many solutions.
Hope this helps!
If not, I am sorry.
In a study to add a new feature to a software program, the programmer introduced two categories, men and women, in the survey she conducted. Is the study observational or experimental? if it is an experiment, what is the controlled factor?.
The given study is observational study
To gauge how strongly two variables are related to one another, correlation coefficients are used.
A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient. The values are in the -1.0 to 1.0 range. There was a measurement error in the correlation if the estimated value was larger than 1.0 or lower than -1.0. Perfect negative correlation is shown by a correlation of -1.0, and perfect positive correlation is shown by a correlation of 1.0. A correlation of 0.0 indicates that there is no linear link between the two variables' movements. Finance and investing can benefit from the usage of correlation statistics.
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