If f(x) = 3x – 2 and g(x) = 2x + 1, find (f + g)(x).

Put your answer in standard form with no spaces.

If Lamont withdraws $2,750 monthly, he will be 66 years old (after 134.326 months) when the money runs out.

We can calculate the number of monthly withdrawals using an online finance calculator.

It determines the number of periods it will take for the investment to be exhausted, given an interest rate of 3.8%.

I/Y (Interest per year) = 3.8%

PV (Present Value) = $300,500

PMT (Periodic Payment) = $-2750

FV (Future Value) = $0

Results:

N = 134.326 months

Years = 11 years (134.326/12)

Age at FV = $0 is 66 years (55 + 11)

Sum of all periodic payments = $-369,397.09 (134.326 x $-2,750)

Total Interest = $68,897.09

Thus, making a monthly withdrawal of $2,750 will exhaust the investment when Lamont turns 66.

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The correct option is option: rotation 90°counterclockwise about the origin.

What is transformation?

A transformation is generally the shifting of the picture for manipulating the shape or position of a point, a line, or a geometric figure.

Transformation is a process by which the orientation or size of a given picture is changed without any effect on the shape.

A rotation is one kind of transformation in which the object rotates about a fixed point or line. The direction of rotation is clockwise or anticlockwise.

It is clear from the figure that

the triangle ∆ABC is mapped over triangle ∆A'B'C' by rotating every point 90° from 2nd quadrant to 3rd quadrant by the rotation of  90° counterclockwise about the origin.

Therefore triangle is rotated 90°counterclockwise about the origin.

Answer:

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The line doesn't go through the origin (0, 0). Therefore, it does not have a constant of proportionality. (even though it has a constant slope)

Also, it's a trick question. The answer is false because the statement is a negative.

True! all proportional graphs must go through 0,0 (origin point) and go a steady direction!

Answer: 1,200 and 1,100

Step-by-step explanation:

For to the nearest hundred

1,183 = 1,200

1,145 = 1,100

He defined quality as a speedy procedure and document security through the use of a web interface, and the data was safely backed up to Amazon S3.

Houston determined that his potential customers, who would be his target demographic, were already technically savvy, but that because of the product's simplicity and the advent of the internet, it could fast increase.

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Answer:

Vertical acute angles are a pair of acute angles formed by two intersectin lines.

The answer is

6, 12

hope this helps!

Answer:

Step-by-step explanation:

To find the lowest price per ounce, we must find the unit rate (how much does it cost to buy 1 unit of something).

The way to do this is divide the price by the quantity.

Option 1) [tex]\frac{1.65}{26/5} = 1.65 * 5/26 = 8.25/26 = 33/104[/tex]

For the first option, every ounce costs $33/104.

Option 2) [tex]\frac{10.4}{26} = 0.4 = \frac{4}{10}[/tex]

For the second option, every ounce costs $4/10.

Since we know that 33/104 is less than 4/10, option 1 is more worth it as every ounce costs less than option 2.

Answer:

26 selfies included Brianna

Step-by-step explanation:

Simply multiply the total amount of selfies (104) by the fraction of which included her BFF Brianna (1/4):

[tex]104*\frac{1}{4} =26[/tex]

The statement that is true about linear functions is the slope of function one is positive and the slope of function two is negative. The correct option is A.

A graph that has a straight line is called a linear function.

Given:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Given that the 1st graph has a positive slope; as x increases, the y-value also increases. So, the 1st graph should have a positive slope.

The given equation is our second line;

y = -4x  

Using,

y = mx + b

We see that our slope m = -4. Therefore, the 2nd graph has a negative slope.

Therefore, the correct option is A.

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The question is incomplete. Your most probably complete question is given below:

A) The slope of function one is positive and the slope of function two is negative.

B) Both functions have a negative slope.

C) Both functions have a positive slope.

D) Both functions have the same slope.

Integer represents the change in the height of the elevator, in meters, every second is 25200.

The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Given Data

The main elevator in the Willis Tower descends 420 meters in 60 seconds.

Distance = 420meters

Time = 60 seconds

Speed = distance (time)

Speed = 420(60)

Speed = 25200

Integer represents the change in the height of the elevator, in meters, every second is 25200.

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At x=1 in the domain f(x)=0.

The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

Keep in mind that a fraction's denominator (bottom) cannot be zero when determining the domain.

A square root must have a positive number under it.

At the points where the function's graph and the x-axis connect, f(x)=0.

You can see from the diagram that the function's graph crosses the x-axis three times:

1)between -3 and -2

2)between -1 and 0;

3)at x=1.

Since x=1 is the value of x from the domain, then correct choice is option C.

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Answer: negative

Step-by-step explanation:

When graphing the points on a coordinate plane, the line falls as it moves from left to right. This means that the line has a negative slope.

Answer:

negative

Step-by-step explanation:

The most appropriate choice for mean, median and mode will be given by-

Value of m = 20

What is mean, median and mode?

Mean of a data set gives the average value of the data set

Mean is calculated by the dividing sum of all observations by the number of observations.

Median is the middle value of the data set when the data set is arranged in ascending or descending order

Mode is the value of the data set which has the highest frequency

Here,

Let the number of integers be n

mean = 22

Sum = 22 x n

       = 22n

Now m is replaced by m + 10

New sum = 22n + 10

New mean = 24

New sum = 24n

By the problem,

22n + 10 = 24n

24n - 22n = 10

2n = 10

n = [tex]\frac{10}{2}[/tex]

n = 5

Now mode of 5 numbers = 32

Smallest number = 10

Data set = {10, x, m, 32, 32}

Now , if m is replaced by m - 8, the new median is m - 4

Since 5 is odd, m - 4 is a member of this data set

So x = m-4 (As m- 8 < m - 4, so on replacing m by m-8 will shift m - 8 to second place and x to third place as the data set is arranged in ascending order)

Data set  = {10, m-4, m, 32, 32}

Mean = [tex]\frac{10+(m-4)+m+32+32}{5}[/tex]

[tex]22 = \frac{70 + 2m}{5}\\70 + 2m = 22 \times 5\\70 + 2m = 110\\2m = 110 - 70\\2m = 40\\m = \frac{40}{2}\\m = 20[/tex]

Value of m = 20

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Complete Question

A list of integers has mode 32 and mean 22. The smallest number in the list is 10. The median m of the list is a member of the list. If the list member m were replaced by m+10, the mean and median of the new list would be 24 and m+10, respectively. If were m instead replaced by m-8, the median of the new list would be m-4. What is m?

(A)16 (B) 17 (C) 18 (D) 19 (E) 20

105 4/61 105 with a remainder of 4

2 to the power of 5 can be written as

[tex]$2^{5}[/tex] = 2 2 2 2 2 2 = 32.  Power is defined as a base number multiplied by its exponent, where the base number is the factor multiplied by itself and the exponent is the number of times the same base number is multiplied.

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Answer: S and T.

Step-by-step explanation:

I watched a video on how to do this just to answer, so it might not be right LOL. But since the angles are the same if you draw them from each other they both show the angles are equal which means the lines are parallel.

Answer:6x² - 5x + 3 - (3x² + 8x - 4) = 3x² - 13x + 7

i hope this helped

〒▽〒

Answer:

7+w

Step-by-step explanation:

I think this is the answer hope it helped

The right way to write digit 182136 without knowing the other factor is by; moving the decimal points 3 places to the left.

It is given that the digits in the product of 0.48 and a decimal number between 350 and 400 are 182136. Note that 0.48 is simply 48/100.

Hence, consider the decimal number between 350 and 400. The number will include one decimal place, so if it's 350.1, we may express it as 3501/10.

When we multiply 48/100 by 3501/10, the denominator is 1000, which is three decimal points to the left of the result.

As a result, the right method to express the answer supplied to us is 182.136, which was accomplished by shifting the decimal point three spaces to the left.

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Answer:

-3

Step-by-step explanation:

To make the equation have infinitely many solutions, we need to make both sides equal.

i will use variable y in place of blank

-x + 20 + yx = -4x + 20

-x + yx = -4x

yx = -3x

y = -3

now we can check the answer

-x + 20 - 3x = -4x + 20

-4x + 20 = -4x + 20

0 = 0

this means there are infinitely many solutions

Three combination of gift card you have purchased is 1 gift card for $10 and 14 gift card for $15 ; 4 gift card for $10 and 12 gift card for $15; 16 gift card for $10 and 4 gift card for $15

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

10 + 210 = 220

40 + 180 = 220

160 + 60 = 220

Three combination of gift card you have purchased is 1 gift card for $10 and 14 gift card for $15 ; 4 gift card for $10 and 12 gift card for $15; 16 gift card for $10 and 4 gift card for $15

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{2\implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{2}}}[/tex]

so we're really looking for the equation of a line with a slope of -1/2 and that it passes through (4 , 6)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y-6=- \cfrac{1}{2}x+2\implies {\Large \begin{array}{llll} y=- \cfrac{1}{2}x+8 \end{array}}[/tex]

We have to blend two brands of dressing with different proportions of vinegar. We want to obtain a mix of 230 cubic milimiters with a proportion of 11% of vinegar.

We can call A to the amount of dressing with 8% vinegar and B the amount of dressing with 13% vinegar.

Then, if the volume of the mix is 230 mm³, we can write:

We can obtain another equation by looking at the amount of vinegar in the mix.

The amount will be the volume of the mix (230 mm³) times the proportion of vinegar (11% or 0.11 in decimal).

This amount of vinegar will be contributed by the vinegar of each brand. The first brand will contribute with a volume of A times 0.08 and the second brand will contribute with B times 0.13.

We can write this as a equation like this:

We now have a system of linear equations (two equations and two unknowns).

We can replace B from the second equation by using the first equation:

Knowing A = 92 mm³, we can find B as:

Answer:

First brand: 92 mm³

Second brand: 138 mm³

The location of the eagle's nest at 1,284 feet and the diving speed of the eagle of 88 feet/seconds gives;

First part;

The function that gives the height of the eagle after a seconds is presented as follows;

h(a) = 1,284 - 88•a

Second part;

After 7 seconds, the eagles height is; 668 feet

A function maps an input element to one output element or value

First part;

The given parameters are;

Initial height of the eagle = 1,284 feet

Speed at which the eagle can dive, v = 88 feet/second

Required; The eagles height after 7 seconds of diving

Solution;

Height reached, h, which is the same as distance traveled, is given by the equation;

Distance = Speed, v × Time, a

The height reached by the eagle is given by the difference between the initial height and the distance traveled.

Distance traveled by the eagle = 88 × a

Eagles height = Initial height - 88 × a

Therefore, the eagles height, h, after t seconds is given by the equation;

Second part;

The eagle's height reached after 7 seconds

Solution;

The height reached after 7 seconds is found by plugging in a = 7 in the function for the height as follows;

h(7) = 1,284 - 88×7 = 668

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Considering the provided information and that the volume of a cuboid is the result of multiplying the width by the length by the height, we obtain the following:

Volume of a cuboid= Width * Length * Height

Volume of a cuboid= 3.4cm * 6.2cm * 5cm

Volume of a cuboid= 105.4 cm³

Finally we obtain that the volume of the cuboid is 105.4 cm³

The value of M is 20.

What is Line segment?

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

M is the midpoint of line PQ.

The value of P = 14

The value of Q = 26

Now,

Since, M is the midpoint of overline PQ.

So, By the definition of midpoint, we can formulate;

M = 14 + 26 / 2

M = 40 / 2

M = 20

Therefore, The value of M is 20.

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The simplification of the given expression is [tex]2^{\frac{1}{12} }[/tex].

Given expression:

[tex]\frac{8^{\frac{1}{4} }*4^{\frac{1}{6} }}{2^{\frac{1}{6} }}[/tex]

Exponents

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 8 is multiplied by itself 3 times, i.e. 8 × 8 × 8. This can be written as [tex]8^3[/tex]. Here, 3 is the exponent and 8 is the base. This can be read as 8 is raised to power 3.

We know that,

8 is the cube of 2 and 4 is the square of 2, hence, we can write,

[tex]\frac{(2^3)^{\frac{1}{4} }*(2^2)^{\frac{1}{6} }}{2^{\frac{1}{6} }}[/tex]

Using the properties of exponents, we can write,

[tex]\frac{(2)^{\frac{3}{4} }*(2)^{\frac{2}{6} }}{2^{\frac{1}{6} }}[/tex]

Simplifying this further, we can write,

[tex]\frac{2^{(\frac{3}{4}*\frac{2}{6}) }}{2^{\frac{1}{6} }} = \frac{2^{\frac{1}{4} }}{2^{\frac{1}{6} }} = 2^{\frac{1}{4}-\frac{1}{6} }=2^{\frac{3-2}{12} }=2^{\frac{1}{12}}[/tex]

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The equation of the line is: y = 9.

To write the equation of a line in point-slope form, where (a, b) is a point on the line, and m is the slope, the equation can be expressed as:

y - b = m(x - a).

Given:

Two ponts on a line, (-4, 9) and (-1, 9)

Find the slope (m):

Slope of the line, m = change in y / change in x = (9 - 9)/(-4 -(-1))

Slope (m) = 0/-3 = 0

Substitute m = 0, and (a, b) = (-1, 9) into y - b = m(x - a):

y - 9 = 0(x - (-1))

y - 9 = 0(x + 1)

y - 9 = 0

y = 9

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The equation Ar = Q, where A is the quantity of the solution, r is the percent concentration of the substance in the solution, and Q is the quantity of the substance in the solution, can be used to solve percent mixture problems.

y=-2x+3

y=mx+c

y  intercept

x=0

y=(-2(0)+3

=3

x=0

y=3

slope=-2

y=-1x+3

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