Given that f(x)=x+9 and g(x)=4x
Evaluate:
a) fg(2)
b) gf(2)

Answer:

The width of the rectangle is 5 meters, while the length of the rectangle is 12 meters.

Step-by-step explanation:

Given that the perimeter of a rectangle is twice the sum of its lenght and its width, and the perimeter is 34 meters and its lenght is 2 meters more than twice its width, to determine the length and width of the rectangle the following calculation must be done:

(2X + 2 + X) x 2 = 34

(3X + 2) x 2 = 34

6X + 4 = 34

6X = 34 - 4

X = 30/6

X = 5

(2x5 + 2 + 5) x 2 = 34

(10 + 2 + 5) x 2 = 34

17 x 2 = 34

34 = 34

Therefore, the width of the rectangle is 5 meters, while the length of the rectangle is 12 meters.

Answer:

50

Step-by-step explanation:

2000/40=50

Answer:

The train travels 50 miles per hour

Step-by-step explanation:

You can solve this by dividing 2,000 by 40.

Answer:

the answer for a is 38 over 45 that is the total fraction of her money that she spent in the local shop for b the answer is 7/45

This came about as for a when we added the total number of expenditures that CeCe had made that is 1/3 + 2/5 + 1/9 and that is 38/45 so that is the fraction of money that she said that she spent in the local shop.

as for b it said what fraction of sissies money does she have left and we know that the total fraction is 38 over 45 and we are going to subtract it from 1.

and that will give us 7/45

Answer:

[tex]y = 8 - 8\sin(2x) [/tex]

Answer:

The Measure of angle 1 is 68

The Measure of angle 2 is 112

The Measure of angle 3 is 68

The Measure of angle 4 is 112

Step-by-step explanation:

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 6

Step-by-step explanation:

The slope will be perpendicular to equation through A and B because of the 90 degree angle at B.

Lines that are perpendicular have opposite reciprocal slopes.

The slope of the line we know is 2 (The slope is the number before the x). The opposite reciprocal is -[tex]\frac{1}{2}[/tex].

Now that we have the slope we need a point on the line. They give us that point at (0,6)  We will use the y value of 6 and the x value of 0 from the point given to find the y-intercept.

slope (m) = -  [tex]\frac{1}{2}[/tex]

y = 6

x = 0

We will substitute all of this information into y = mx + b to solve for b (y-intercept)

y = mx + b

6 = - [tex]\frac{1}{2}[/tex] (0) + b

6 = b

Now that we have the slope (- [tex]\frac{1}{2}[/tex]) and the y-intercept (6) we can write the equation

y = - [tex]\frac{1}{2}[/tex] x + 6

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c  m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

BC is perpendicular to AB

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{BC}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

the line BC has point C at (0, 6 ) ⇒ c = 6

y = - [tex]\frac{1}{2}[/tex] x + 6 ← equation of line BC

Complete the table with values 3, 2, 24 and 10 respectively

The constant of proportionality is the ratio of the y value to the x value i.e.

constant of proportionality (k) = y/x

The table can be completed by determining the constant of proportionality. That is:

k = y/x

where y = hours and x = magnets

k = 4/12 = 1/3

when y = 1:

1/3 = 1/x

x = 3

when x = 6:

1/3 = y/6

y = 2

when y = 8:

1/3 = 8/x

x = 24

when x = 30:

1/3 = y/30

x = 10

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Answer:

oof...so sorry bro...

Step-by-step explanation:

9- left side of 10

-4 - right side of -5

2 - two points to the right of zero

so sorry if i am wrong..

Answer:

x = 19

Step-by-step explanation:

3(x - 9) = 30

Divide both sides by 3 to isolate the binomial.

x - 9 = 10

Add 9 to both sides to isolate x.

x = 19

Check your answer by plugging x = 19 back into the equation.

3(x - 9) = 30

3(19 - 9) = 30

Subtract.

3(10) = 30

Multiply.

30 = 30

Your answer is correct.

Hope this helps!

Answer:

x = 19

Step-by-step explanation:

First, we must distribute 3(x-9) = 30

[tex]3x - 27 = 30[/tex]

Now, that we've distributed this equation, we can proceed.

Secondly, since there is a subtraction sign in front of 27, we must do the opposite, addition.

Add 27 to 27 and 30:

[tex]3x - 27 = 30[/tex]

[tex]-27 + 27 = 0[/tex]

[tex]30 + 27 = 57[/tex]

Furthermore, -27 + 27 is 0, so it cancels itself out. Also, since we added 30 and 27 and got 57, replace 30 with 57.

[tex]3x = 57[/tex]

Lastly, divide 57 by the number in front of coefficient, 3.

[tex]57/3=19[/tex]

Therefore, [tex]x=19.[/tex]

**TO MAKE THIS MORE UNDERSTANDING, THIS IS HOW YOUR EQUATION SHOULD LOOK WHILE SOLVING**

The volume of a rectangular box can be found by multiplying the length, width, and height of the box together. So if the volume of the box is x³+x²-4x-4 cubic inches, the length is x+1 inches, and the width is x-2 inches, we can set up the equation h = (x³+x²-4x-4) ÷ (x²-x-2).

The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height of the box. This formula can also be written as V = l×w×h.

In the question you provided, the volume of the rectangular box is given as x³+x²-4x-4 cubic inches, and the length and width are given as x+1 inches and x-2 inches, respectively. With this information, we can set up an equation using the formula for the volume of a rectangular box:

(x+1)(x-2)(h) = x³+x²-4x-4

where h is the height of the box in inches. To solve for h, we can divide both sides of the equation by (x+1)(x-2) to get:

h = (x³+x²-4x-4) ÷ (x+1)(x-2)

And Now we can simplify the expression using standard algebraic operations.

h = (x³+x²-4x-4) ÷ (x²-x-2)

You can now substitute any value of x to find the height of the box.

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Answer:

First Question - 74.25

Second Question - 23.92

Hope this helps you out

The given parametric equation represents the graph mentioned in Option A.

A parametric equation is defined as a kind of equation that inherit an independent variable called a parameter, and where dependent variables are defined as continuous functions of the parameter.

here,
For equation, x = t cos (t), y = t, z = t sin(t), t ≥ 0.
Since,

x² + y² = t²cos²(t) + t² sin²t
x² + y² = t²
x² + y² = z²

Here, the x-z cross-section of the curve is a circle. But as t accumulates, the radius of the circle also advances in the y direction, and those circular cross-sections extend as the value of the parameter t increase.
The curve will draft as circles in x-z planes while moving towards y direction and also the radius of those circular cross sections increases at the same rate as its advancement towards y direction.

Thus, the given parametric equation represents the graph mentioned in Option A.

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Explanation:

There are 170 million martians surveyed, note the "170" in the bottom right hand corner.

Of this total, there are 48 million who have completed 4 (or more) years of college. Refer to the bottom of the "4 or more" column.

This must mean that 170 - 48 = 122 million martians have not completed 4 or more years of college. This figure of 122 is effectively the sum of nearly everything in the bottom row, except for the 48 and the 170. In other words, 27+51+44 = 122.

We divide the values 122 over 170, and reduce fully, to get the answer we're after.

122/170 = (2*61)/(2*85) = 61/85

This can be thought of as "if we had 85 million people total, then 61 million of them did not complete 4 or more years of college".

Side note: 61/85 = 0.7176 = 71.76% approximately

The probability that a randomly selected martian, has not completed four years (or more) of college is P = 0.72.

We want to find the probability that a randomly selected martian over the age 25, is not completed over 4 years of studies.

In the table, we can see that we have a total of 170 Martians.

Of these 170, only 48 have completed more than 4 years of college.

Then: 170 - 48 = 122 have not completed 4 years or more.

Then the probability that a randomly selected martian has not completed 4 years or more of college is:

P = 122/170 = 0.72

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Answer:

Average speed: 698 kmh^-1

Step-by-step explanation:

In 1440 earth days, there are 34560 hours (1440 × 24)

Solving for the average speed, km/h

[tex]\frac{24~130000km}{3450hr}[/tex] ≈ [tex]698.21 km[/tex]

so, the average speed is [tex]698 kmh^{-1}[/tex]

[tex]---------[/tex]

hope it helps..

have a great day!!

Answer:

[tex]x = 19[/tex]

Step-by-step explanation:

Given

[tex]\angle 1 = 4x + 9[/tex]

[tex]\angle 2 = x - 14[/tex]

See attachment

Required

Find x

From the attached image, we have:

[tex]\angle 1 +\angle 2 = 90[/tex]

Because the sum of both angle corresponds to the right angle between n and m

So, we have:

[tex]4x + 9 + x - 14 = 90[/tex]

Collect like terms

[tex]4x + x = 90 - 9 +14[/tex]

[tex]5x = 95[/tex]

Divide by 5

[tex]x = 95/5[/tex]

[tex]x = 19[/tex]

Answer:

[tex]\displaystyle x=\frac{1}{5}y^2[/tex]

Step-by-step explanation:

[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]

Answer:

I believe the answer is D.

[tex]\huge\boxed{Answer\hookleftarrow}[/tex]

D

[tex]\huge\boxed{Explanation\hookleftarrow}[/tex]

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identification of the expression 4x- 2y + 6 = 2x is

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, a linear expression 4x-2y + 6 = 2x

Coefficient:

Coefficients are the numbers by which the variables in an equation are multiplied

Thus, the Coefficient terms for this equation = 4x, -2y, 2x

Constants:

the constant is the part of the expression that does not vary with the value of x and y.

Thus, constant terms for this equation = 6

variable terms:

These are the terms that vary at the different values of x and y.

Thus, variable terms for this equation = 4x, -2y

Like terms:

Terms that have identical variable parts (same variable(s) and same exponent(s))

thus, Like terms for this expression = 4x, 2x

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Answer:

D

Step-by-step explanation:

ummm.....

Answer:

120 and 90

Step-by-step explanation:

let one number be x and the other y

x + y = 210 (sum = 210)

x - y = 30 (difference = 30)

add the two equations together

2x = 240

divide both sides by 2 to isolate x

x = 120

plug into 1st equation

120 + y = 210

subtract 120 from both sides

y = 90

We take the 2 numbers as 'x' and 'x-30' in order to find those numbers

We plug the values into the given equation

[tex]x + x - 30 = 210\\2x - 30 = 210\\\\2x = 240\\x = \frac{240}{2} \\x = 120\\x - 30 = 120 - 30 = 90\\[/tex]

[tex]120 - 90 = 30[/tex]

Hence , the two numbers are 120 and 90

Answer:

Each book cost 222 - 15 = 207 / 9 = 22.88 dollars.

Answer:

615.75m cubed

Step-by-step explanation:

Answer: -14

Step-by-step explanation:

As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.

Given that it has three sides and three vertices, a triangle is a polygon. It is one of the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon because it has three sides and three corners. The points at which the three sides of the triangle converge are referred to as its corners. Three triangle angles can be multiplied to get 180 degrees.

given

p is the midpoint of GI

GP = PI , PN = AP ( as mid point )

∠APG = ∠IPN ( as vertical opp. angle )

∠A = ∠N ( given )

so by ASA congruency ΔAPG = ΔIPN

As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.

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The ordered pair (x, y) for the given line can be obtained from the graph as (-4, 1).

A straight line can be written in the form of an equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

The graph of the line is given.

In order to find the coordinate of a point do as follows,

Draw a perpendicular line from any point on the line to the x-axis.

The intersection of this line with the x-axis will give the x-coordinate.

Similarly, find the y-coordinate by drawing a perpendicular line to the y-axis.

Applying the above procedure, a point is obtained as (-4, 1).

Hence, the ordered pair for the line shown in the graph is (-4, 1).

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