If f(x) = 3x - 4 and g(x) = x2, what is the value of f(3) - g(2)?

Answer:

Age of Anna = x years

Age of Jane i.e. Anna's sister = (x-y) years

a, What was the sum of their ages two years ago?

Solution,

Age of Anna two years ago = (x-2) years

Age of Jane two years ago = (x-y-2) years

Sum of their ages = x - 2 + x-y-2 = 2x - y -4

b. What will be the sum of their ages in 3 years?

Solution,

We have,

Present age of Anna = x years

Present age of Jane = (x-y) years

So,

Age of Anna after 3 years = (x+3) years

Age of Jane after 3 years = (x-y+3) years

Therefore,

Sum of their ages in 3 years = (x+3) +(x-y+3) = 2x - y+6

c. How old was Anna when Jane was born?

Solution,

Here,

According to question,

Jane is y years younger than Anna

So, Anna was y years when Jane was born.

[Suppose your age is 10 years and your brothers age is 14 years. You are 4 years younger than your brother. Also, his age was 4 years when you were born.]

The four rectangles can be painted with 7 different paints in 840 ways.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A={1,6} is 2, such as {1,6}, {6,1}, there are no other ways to arrange the elements of set A.

The formula for permutattion is;

\(P_r_n = \frac{n!}{(n-r)!} \\\)

where r = 4

n = 7

Substituting the values for n and r

\(P = \frac{7!}{(7-4)!}\)

\(P = \frac{7!}{3!}\)

P = 840 ways.

Learn more about permutations here: https://brainly.com/question/1216161

#SPJ1

For the application of the law of sine the true statement is that at least one side length and opposite angle pair must be known.

The law of sine is used to solve the sides and angles of a triangle.

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.

In other words,  the law of sines is defined as the ratio of side length to the sine of the opposite angle.

It holds for all the three sides of a triangle respective of their sides and angles.

Therefore, the law of sine can be expressed as follows:

a / sin A = b / sin B = c / sine C

Hence, the statement that is true is at least one side length and opposite angle pair must be known.

learn more on law of sine here: https://brainly.com/question/17145083

#SPJ1

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -1 = \cfrac{1}{3} ( x +2) \\\\\\ y-1=\cfrac{1}{3}x+\cfrac{2}{3}\implies y=\cfrac{1}{3}x+\cfrac{2}{3}+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{5}{3} \end{array}}\)

A swimming pool is 50 meters long, 15 meters wide, and 3 meters deep. What is the volume of the pool.

Length of the pool = 50 m

Width of the pool = 15 m

Depth of pool = 3 m

Volume of cuboid = Length x Width x Depth

For, the volume of the pool substitute the value of Length, Width and depth

Volume of Pool = 50 x 15 x 3

Volume of pool = 2250 m³

Volume of pool is 2250m³

Answer : B) 2250 cubic meter

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

Learn more about expression at https://brainly.com/question/1859113

#SPJ1

Answer:

Below

Step-by-step explanation:

L x H = area

(x+5) (x-2)   =   x^2 +3x -10  cm^2

Answer:

Answer is c

Step-by-step explanation:

Answer:

\(a(1) = 144\)

\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)

\(a(n) = - \frac{1}{6} a(n - 1)\)

The best representation of the mean number of sports played by middle school students is 2.75 sports and the MAD is about 0.84 sports.

To find the best representation of the mean number of sports played by middle school students, we need to calculate the median of the given data.

The median represents the central tendency of the data and is less affected by extreme values.

Arranging the means of the samples in ascending order, we have:

1, 1, 2, 2.5, 3, 3, 3.5, 4

Since there are eight values, the median will be the average of the fourth and fifth values:

(2.5 + 3) / 2 = 2.75

Variability in the Distribution

Summing up the absolute deviations:

1.75 + 1.75 + 0.75 + 0.25 + 0.25 + 0.25 + 0.75 + 1.25 = 6.75

To find the MAD, we divide the sum of the absolute deviations by the total number of data points:

MAD = 6.75 / 8 = 0.84

Therefore, the MAD is about 0.84 sports.

To learn more on Mean click:

https://brainly.com/question/31101410

#SPJ1

Answer:

1/10 of an million is 1000000 divided 10

Step-by-step explanation:

Answer:

a. N=11

D=12

b. N=1

D=7512

c. N=12

D=0

d. N= 1

D=978

The mean value theorem is used to link the average rate of change and the derivative of a function.

The value of V is 8.

The givenparameters are:

Mean value theorem states that:

If  [a,b] and

(a,b),

Then there is a point c in (a,b), such that:  

From the question, we understand that: f is differentiable

This means that:

avethat:

The equation becomes

Cross mltiply

o both side

From the question, we have:

By comparisons;

Hence, the value of V is 8.

Answer:

Step-by-step explanation:

area = ½(base)(height) = 2x²-2x-4

½(base)(x-2) = 2x²-2x-4

½(base) = (2x²-2x-4) ÷ (x-2) = 2x+2

base = 4x+4

The possible price for the items if the store sells $600 is (c) $40

From the question, we have the following parameters that can be used in our computation:

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

Read more about supply-demand graph at

https://brainly.com/question/14297698

#SPJ1

Answer:

120

Step-by-step explanation:

The prism shown is a rectangular prism with a height of 3 in a length of 5 in and a width of 8 in

The volume of a rectangular prism can easily be calculated by multiplying the height by the length by the width

So V = 3 * 5 * 8

3 * 5 = 15

15 * 8 = 120

V = 120

Therefore your answer is 120

Answer:

Option B is the correct answer

Step-by-step explanation:

Given that

\(\sin \theta =\frac{-1}{\sqrt{2}}\)

Value of sine function is negative in third and fourth quadrant

Hence this is true for

\(\theta =225^{0},315^{0}\)

Option B is the correct answer

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

for such more question on grams

https://brainly.com/question/13439286

#SPJ8

Answer:

Step-by-step explanation:

1/3 of a mile in 15 minutes. 1.333 (4/3) miles an hour

Answer:

im pretty sure its C

Step-by-step explanation:

Two numbers that can be used to find the area of the rectangle are:

So, we know that the formula for the area of the rectangle is:

Where l is length and b is breadth.

Therefore, two numbers that can be used to find the area of the rectangle are:

Know more about rectangles here:

https://brainly.com/question/25292087

#SPJ13

Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

The correct option is- A: (-1/2 , -√3/2) are the coordinates found using the terminal points t = 10pi/3.

On the unit circle, the terminal point. To find any terminal point on the unit circle which start at (1, 0), and determine the angle in degree or radian on the circle that travel counter clockwise whereas if angle is positive as well as clockwise if the angle is negative. The terminal point is the coordinate of the endpoint.

Given values:

t = 10pi/3

convert to degrees

t = 10*pi/3

t = 10*180/3

t = 600 degrees

Find quadrant of 600 degrees.

600 = 360+240

240 comes in III quadrant

Thus,  x-coordinate and y-coordinate are negative

Now,

240° = 180°+ 60°

60° is the angle for which terminal point are to be find.

Let ∅=60°

Consider unit circle

radius r = 1 units

Then,

x = -r*cos ∅

x = -cos 60

x = -(1/2)

And,

y = -r*sin ∅

y = -sin 60

y = -(√3)/2

Thus, the coordinates of the terminal point are found as  (-1/2 , -√3/2) by

t = 10pi/3.

Know more about the terminal points

https://brainly.com/question/3988149

#SPJ1

Answer:

Step-by-step explanation:

Pentagon

Answer: Pentagon

Step-by-step explanation: The shape has 5 sides so it's a pentagon

Answer:

  x = 10

Step-by-step explanation:

You want the value of x in triangle RST with angle bisector UT dividing RS into parts RU=3x and US=x+2, while RT=40 and ST=16.

The angle bisector divides the sides of the triangle proportionally;

  3x/40 = (x +2)/16

  6x = 5x +10 . . . . . . . multiply by 80

  x = 10 . . . . . . . . . subtract 5x

The value of x is 10.

<95141404393>

The slope is

\(\frac{-13-31}{1-(-10)}=-4 \)

So, the equation is

\(y+13=-4(x-1)

\)

The y-intercept is when x=0, so

\(y+13=-4(0-1) \\ \\ y+13=4 \\ \\ \boxed{y=-9}\)

Answer:

x-intercept:(2,0)

y-intercept:(0,-4)

Step-by-step explanation:

Answer:

C). Octagon.

Step-by-step explanation:

A cube has 6 plane faces. That would mean any plane slice that can intersect at most 6 of those faces, creating a hexagon. Not a single plane figure with more than 6 sides could be created by slicing a cube with a plane.

Therefore the answer is C, octagon.