6 times a certain number is added to 8, the result is 32
Which of the following equations could be used to solve the problem?
6x +32
6x5)= 32
6x=8 - 32
6x-8= 32

Answer:

[tex]f^{-1}[/tex](x) = [tex]\frac{x-3}{2}[/tex]

Step-by-step explanation:

Let y = f(x) and rearrange making x the subject

y = 2x + 3 ( subtract 3 from both sides )

y - 3 = 2x ( divide both sides by 2 )

[tex]\frac{y-3}{2}[/tex] = x

Change y back into terms of x, hence

[tex]f^{-1}[/tex](x ) = [tex]\frac{x-3}{2}[/tex]

Keep in mind that f(x) means the same thing as y so...

y = 2x + 3

To find the inverse operation you switch the places of x and y like so...

x = 2y + 3

Now you must solve for y. To start off you must subtract 3 to both sides.

x - 3 = 2y + 3 - 3

x - 3 = 2y

Now divide 2 to both sides to completely isolate y

(x - 3) / 2 = 2y / 2

[tex]\frac{1}{2} x - \frac{3}{2}[/tex] = y

OR

[tex]\frac{x}{2} -\frac{3}{2}[/tex] = y

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

3/7

Step-by-step explanation:

The total number of students in the play is 10.

The number of boys in the play is 7.

The remaining students in the play must be girls, so 10-7=3.

There are 3 girls in the play.

The ratio of girls in the play to boys in the play would be:

girls/boys= 3/7.

Answer:

Step-by-step explanation:

The no of girls is 3/10

Girls : boys

3/10 : 7/10

3 : 7

Answer:

1575 grams

Step-by-step explanation:

If a baker has 2,000 grams of flour and uses 425 grams of it, the mass will become 1575 grams.

2000 - 425 = 1575

Answer:

1575 grams of flour

Step-by-step explanation:

If he had 2000 grams of flour and used 425 grams of it, you have to subtract 2,000 by 425, which would equal 1,575 grams of flour left.

Answer:

∠PMA=55°

Step-by-step explanation:

see the attached figure with the letter X to better understand the problem

we know that

In the right triangle PXM

PX=LA=25 cm

XM=AM-15/2=25-7.5=17.5 cm

∠PMA=∠PMX

tan(∠PMA)=(PX)/(XM)

tan(∠PMA)=(25)/(17.5)

∠PMA=arctan((25)/(17.5))=55°

Answer:

The polyester in standard form with zero placeholders is

-x^6+0x^5+3x^4+-7x^3+4x^2+0x+-1

7th term -1

6th term 0x

5th term 4x^2

4th term -7x^3

3rd term 3x^4

2nd term 0x^5

1st term -x^6

Step-by-step explanation:

We want to write 4x^2-7x^3-x^6+3x^4-1 in descending order means want the exponents to being counting down.

6 is the highest exponent so lets rearrange this so that tern comes first:

-x^6+.....

5 is the highest but we are missing so now we have:

-x^6+0x^5+....

4 is the next highest and I see +3x^4 in our polynomial so that comes next:

-x^6+0x^5+3x^4+...

3 is the next highest and I see -7x^3 so that term comes next:

-x^6+0x^5+3x^4+-7x^3+....

2 is the next highest and I see +4x^2 so that term comes next:

-x^6+0x^5+3x^4+-7x^3+4x^2+...

1 is the next highest and we are missing an x term so the next term is +0x.....

-x^6+0x^5+3x^4+-7x^3+4x^2+0x+....

0 is the next highest and will be the last term we write. This is the constant tern, the term without the variable and that is -1.

-x^6+0x^5+3x^4+-7x^3+4x^2+0x+-1

Now I guess you are reading this from left to right when numbering the terms as first, second, and so on...

1st term -x^6

2nd term 0x^5

3rd term 3x^4

4th tern -7x^3

5th term 4x^2

6th term 0x

7th term -1

Answer:

B and C

Step-by-step explanation:

We are going to look at each choice:

Let's look at choice A.

f(5)=1

f(5) means look at function f and then see which piece contains x=5.

5>1 so we are looking at [tex]x^2[/tex] for x=5 which gives you [tex]5^2=25[/tex], this is not 1.

The answer is not A.

Let's look at choice B.

f(2)=4

f(2) means look at function f and then see which piece contains x=2.

2>1 so we are looking at [tex]x^2[/tex] for x=2 which gives you [tex]2^2=4[/tex], so this is true that f(2)=4.

Let's look at choice C.

f(1)=5

f(1) means look at function f and then see which piece contains x=1.

1=1 which means we are using [tex]5[/tex] for x=1, so f(1)=5 which is what choice C says so choice C is true.

Let's look at choice D.

f(-2)=4

f(-2) means look at function f and then see which piece contains x=-2

-2<1 so we use [tex]2x[/tex] for x=-2, so we get 2(-2)=-4 which is not 4 so f(-2)=4 is not true.

Answer: 88

Step-by-step explanation:

(8x2)=16/2=8

8x6=48

8x4=32

48+32+8=88

Answer:

112

Step-by-step explanation:

Answer:

The average rate of change is -6

Step-by-step explanation:

The formula for average rate of change is

[tex]=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

where

x₁=-1 and x₂=2

In this case we replace f(x) with z(x)

Substitute values of x₁ and x₂ in the formula given the function as

[tex]z(x)=-6x+2+3\\z(x)=-6x+5\\\\\\=\frac{z(x_2)-z(x_1)}{x_2-x_1} \\\\\\z(x_1)=z(-1)=-6*-1+5=6+5=11\\\\\\z(x_2)=z(2)=-6*2+5=-12+5=-7\\\\\\x_2-x_1=2--1=3\\\\Rateofchange=\frac{-7-11}{3} =\frac{-18}{3} =-6[/tex]

Answer:

(y - 7)

Step-by-step explanation:

"7 less than y" means just that.... that you have 7 fewer units then the value of y.

Expression for [tex]7[/tex] less than [tex]y[/tex] is equal to [tex]y-7[/tex].

" An expression is defined as the representation of the relation between variables and numbers using mathematical operation."

According to the question,

Given statement,

[tex]7[/tex] less than [tex]y[/tex]

Expression for the given statement is,

[tex]y - 7[/tex]

Hence, the expression for [tex]7[/tex] less than [tex]y[/tex] is equal to [tex]y-7[/tex].

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Answer:

1100 km

Step-by-step explanation:

The problem doesn't clearly state whether the 380,000 km is from the Earth's surface to the moon's center, or to the moon's surface.  Since we'll be rounding to 2 significant figures, it's not enough to make a difference, so I'll assume it's to the moon's center.

Draw circle representing the moon and earth.  Draw tangent lines from the earth's center to the edge of the moon.  The angle between these lines is the subtended angle.  Now draw a line representing the moon's radius from the center of the moon to the point where the tangent line intersects.  Notice this forms a right angle.

(See attached diagram)

Using trigonometry:

sin(θ/2) = r / (R + h)

r = (R + h) sin(θ/2)

Given that R = 6400 km, h = 380,000 km, and θ = 20' = 1/3 degrees:

r = (6400 + 380000) sin(1/6 °)

r = 1100

The moon's radius is 1100 km.

Answer:  southeast

Step-by-step explanation:

Draw a picture showing x to the left of y and z below y:

                                   x    y

                                         z

This results in z being south and east from x

If x is in west of y and y is in north of z,  direction of x with respect to z is South-east .

Given that x is in west of y and y is in north of z.

To obtain the direction of a respective person with respect to a given person, we draw the given image as mentioned in the question.

Drawing the required direction as per given in question -

                                  x    y

                                        z

Thus, we can clearly see that z is South-east direction of x.

Therefore, if x is in west of y and y is in north of z,  direction of x with respect to z is South-east .

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Answer:

40 combinations

Step-by-step explanation:

We just multiply the outcomes.

4*2*5=40

There are 40 different ways to redecorate.

4 colors of paint * 2 kinds of curtains * 5 colors of carpet

= 40 outcomes.

In the possibility principle, an outcome is a probable result of a test or trial. every possible final result of a selected experiment is precise, and one-of-a-kind results are together one of a kind (most effective final results will occur on each trial of the experiment).

To locate the total wide variety of consequences for two or greater occasions, multiply the variety of effects for every occasion collectively. that is referred to as the product rule for counting because it involves multiplying to discover a product.

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Answer:

[tex]3x^2-2x-6[/tex]

Step-by-step explanation:

[tex](f-g)(x)[/tex]

[tex]f(x)-g(x)[/tex]

So plug in your functions:

[tex][3x^2-2]-[2x+4][/tex]

Distribute:

[tex]3x^2-2-2x-4[/tex]

Combine like terms:

[tex]3x^2-2x-6[/tex]  There was only one pair of like terms -2 and -4.

Answer:

Part 41) The solution of the compound inequality is equal to the interval  [-1.5,-0.5)

Part 45) The solution of the compound inequality is equal to the interval

(-∞, -0.5] ∪ [1,∞)

Step-by-step explanation:

Part 41) we have

[tex]-4\leq 2+4x < 0[/tex]

Divide the compound inequality into two inequalities

[tex]-4\leq 2+4x [/tex] -----> inequality A

Solve for x

Subtract 2 both sides

[tex]-4-2\leq 4x [/tex]

[tex]-6\leq 4x [/tex]

Divide by 4 both sides

[tex]-1.5\leq x [/tex]

Rewrite

[tex]x\geq -1.5[/tex]

The solution of the inequality A is the interval -----> [-1.5,∞)

[tex] 2+4x < 0[/tex] -----> inequality B

Solve for x

Subtract 2 both sides

[tex]4x < -2[/tex]

Divide by 4 both sides

[tex]x < -0.5[/tex]

The solution of the inequality B is the interval ------> (-∞, -0.5)

The solution of the inequality A and the Inequality B is equal to

[-1.5,∞)∩ (-∞, -0.5)------> [-1.5,-0.5)

see the attached figure N 1

Part 45) we have

[tex]2x-3\leq -4[/tex]  or [tex]3x+1\geq 4[/tex]

Solve the inequality A

[tex]2x-3\leq -4[/tex]

Adds 3 both sides

[tex]2x\leq -4+3[/tex]

[tex]2x\leq -1[/tex]

Divide by 2 both sides

[tex]x\leq -0.5[/tex]

The solution of the inequality A is the interval ------> (-∞, -0.5]

Solve the inequality B

[tex]3x+1\geq 4[/tex]

Subtract 1 both sides

[tex]3x\geq 4-1[/tex]

[tex]3x\geq 3[/tex]

Divide by 3 both sides

[tex]x\geq 1[/tex]

The solution of the inequality B is the interval -----> [1,∞)

The solution of the compound inequality is equal to

(-∞, -0.5] ∪ [1,∞)

see the attached figure N 2

Answer:

y=3x+5

Step-by-step explanation:

To determine the slant asymptote you must perform polynomial division and also the degree of the numerator must be one greater than degree of the denominator for it to even exist.  (We do have that here by the way since degree of the top is 2 and the degree of the bottom is 1).

Let's begin the division process:

I'm using synthetic. You can also use long.

3 goes on the outside because we are dividing by x-3

3 |   3     -4      5

  |           9      15

    ----------------------

      3       5       20

So [tex]\frac{3x^2-4x+5}{x-3}=3x+5+\frac{20}{x-3}[/tex]

So the slant aymptote is y=3x-5 since 20/(x-3) approaches 0 as x approaches  infinity.

To find the slant asymptote of the given function, perform long division to divide the numerator by the denominator. As x approaches infinity, the slant asymptote is 3x + 5.

To find the slant asymptote of the function f(x) = (3x^2 - 4x + 5) / (x - 3), we need to determine what happens as x approaches positive or negative infinity. We can do this by dividing the numerator polynomial by the denominator polynomial using long division.

Performing long division, we get:

3x^2 - 4x + 5 / (x - 3) = 3x + 5 + (8 / (x - 3))

As x approaches infinity, the 8 / (x - 3) term becomes negligible and we are left with the slant asymptote:

f(x) = 3x + 5

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Answer:

The expression which will result in difference of two squares is:

 (–7x + 4)·(–7x – 4)

Step-by-step explanation:

We know that the formula of the type:

(a-b)(a+b)=a²-b²

i.e. it is a difference of two square quantities. (a^2 and b^2)

since,

a= -7x , b=4

(-7x+4)(-7x-4)= (-7x)² - (4)²

=(7x)² - 4²

So the expression is a difference of two square quantities:

(7x)² and (4)²

Hence the answer is (–7x + 4)·(–7x – 4)....

Answer:

C

Step-by-step explanation:

The surface area (A) of a sphere is calculated as

A = 4πr² ← r is the radius, here r = 12, hence

A = 4π × 12²

  = 4π × 144 = 576π units² → C

The surface area of the sphere is  576 square units. The correct option is B.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called as the surface area.

The surface area (A) of a sphere is calculated as

A = 4πr² ← r is the radius, here r = 12, hence

A = 4π × 12²

A= 4π × 144

A = 576π units²

Hence, the correct option is B.

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Answer:

1. mode

2. median

3. mean

Answer with explanation:

The equation of line having X intercept (-4,0) and Y intercept (0,2) is given by the formula

    [tex]\rightarrow \frac{x}{a}+\frac{y}{b}=1\\\\ \rightarrow \frac{x}{-4}+\frac{y}{2}=1\\\\ \rightarrow x -2 y= -4\\\\ x -2 y+4=0[/tex]

Answer:

-2 degrees

Step-by-step explanation:

If you work backwards you will eventually get -2

For example: -3 + 3 = 0, then 0 - 2 = -2, so on...........

Answer:

37.7 = h

Step-by-step explanation:

Area of a rectangle is base * height

A =bh

Substitute what you know

1059.37 = 28.1 * h

Divide each side by 28.1

1059.37/28.1 = 28.1 * h/28.1

37.7 = h

Answer:

see explanation

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 )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 5) and (x₂, y₂ ) = (2, 10)

m = [tex]\frac{10-5}{2+3}[/tex] = [tex]\frac{5}{7}[/tex], hence

y = [tex]\frac{5}{7}[/tex] x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation

Using (2, 10), then

10 = [tex]\frac{10}{7}[/tex] + c ⇒ c = 10 - [tex]\frac{10}{7}[/tex] = [tex]\frac{60}{7}[/tex]

y = [tex]\frac{5}{7}[/tex] x + [tex]\frac{60}{7}[/tex] ← in slope- intercept form

ANSWER

13.5

EXPLANATION

We write 6 cubed as 6³

We write 4 squared as 4²

The quotient of 6 cubed and 4 squared is written as

[tex] \frac{ {6}^{3} }{ {4}^{2} } [/tex]

We expand to obtain:

[tex] \frac{6 \times 6 \times 6}{4 \times 4} [/tex]

Cancel out the common factors to get,

[tex] \frac{3 \times 3 \times 3}{2} [/tex]

This simplifies to

[tex] \frac{27}{2} = 13.5[/tex]

Answer:

A 15

Step-by-step explanation:

In an isosceles trapezoid, each pair of base angles is congruent.

In this isosceles trapezoid, angles B and C are congruent, so their measures are equal.

m<B = m<C

60 = 3x + 15

Subtract 15 from both sides.

45 = 3x

Divide both sides by 3.

15 = x

x = 15

Answer:  The correct option is (A) 15.

Step-by-step explanation:  As shown in the attached figure below, ABCD is an isosceles trapezoid with AD parallel to BC.

Also, m∠B = 60°  and  ∠C = (3x +15)°.

We are to find the value of x.

Since ABCD is an isosceles trapezoid with AB and CD as the two legs, so we have

[tex]AB=CD\\\\\Rightarrow m\angle C=m\angle B~~~~~~~~~~~~~~~~~~~[\textup{Angles opposite to equal legs are equal}]\\\\\Rightarrow (3x+15)^\circ=60^\circ\\\\\Rightarrow 3x+15=60\\\\\Rightarrow 3x=60-15\\\\\Rightarrow 3x=45\\\\\Rightarrow x=\dfrac{45}{3}\\\\\Rightarrow x=15.[/tex]

Thus, the required value of x is 15.

Option (A) is CORRECT.

Answer:

Step-by-step explanation:

His chances of getting the purple one are 1/6

His chances of getting the blue one after drawing the purple one and not replacing are 1/5

The probability of both happening are 1/6 * 1/5 = 1/30

[tex]\huge{\boxed{\text{42 ounces}}}[/tex]

25% is equal to [tex]\frac{1}{4}[/tex], so multiplying it by 4 gets 100%.  This means we can multiply 10.5 by 4 to get 100% of the fiber the koala ate that day.

[tex]10.5*4=\boxed{42}[/tex]

Answer:

42 ounces

Step-by-step explanation:

So a koala absorbs 25% of fiber they eat.

A koala absorbed 10.5 ounces in a day.

Let x be the amount of ounces of fiber the source(s) actually contained that day.

So we have 25% of x is 10.5

As an equation that is .25x=10.5 or 1/4 *x=10.5.

.25x=10.5

To solve this equation you can divide both sides by .25 giving you

x=10.5/.25=42.

If you chose the other equation which is an equivalent equation you would multiply both sides by 4.

1/4 *x=10.5

x=4(10.5)

x=42

Answer:

Any equation of a line having a slope of 1/2.

Step-by-step explanation:

It appears that the question gives answer choices and this problem could have many solutions, but parallel lines have equal slopes. The slope of this line is 1/2 since it is in y=mx+b form where m is the slope. So a few examples of equations of lines parallel to the given equation would be y = 1/2x - 5 or y = 1/2x + 10 etc.

Answer:

-8

Step-by-step explanation:

If you want to find the fourth term in the sequence, or b(4), then you just plug in the value 4 for n, resulting in

b(4)=1(-2)^(4-1).

Simplifying, we get

b(4)=1(-2)^3

     =1(-2*-2*-2)

     =1(-8)

     =-8

Answer:

The area of triangle DEF is [tex]282\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

To find the scale factor, divide the height of triangle DEF by the height of triangle ABC

Let

z ------> the scale factor

[tex]z=\frac{13}{5}[/tex]

step 2

Find the area of triangle DEF

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the area of triangle DEF

y -----> the area of triangle ABC

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{13}{5}[/tex]

[tex]y=15\ cm^{2}[/tex]

substitute and solve for x

[tex](\frac{13}{5})^{2}=\frac{x}{15}[/tex]

[tex]x=(\frac{169}{25})(15)[/tex]

[tex]x=282\ cm^{2}[/tex]

Answer:

D. 9 inches

Step-by-step explanation:

By using proportionality theorem,

Triangle BLM ~ Triangle BAC

[tex] \frac{bm}{bc} = \frac{bl}{ba} [/tex]

as ba = bl + la and as bl = la

Therefore, bl + la = 2bl

[tex] \frac{bm}{bc} = \frac{bl}{2bl} [/tex]

Now, we get,

[tex] \frac{bm}{18} = \frac{1}{2} [/tex]

as bc = 18

Hence,

[tex]bm = 9 \: inches[/tex]

Answer: D. 9 inches

Step-by-step explanation:

Given : The midsegment of Δ ABC is line segment IM.

Such that for side BC ,  BM=MC         [ Show in the picture ]     (1)

and BC= BM+MC    (2)

The length of BC = 18 inches              (3)

From (1) and (2), we have

[tex]BC=MC+MC\\\\\Rightarrow\ BC=2MC[/tex]

Using (3), we have

[tex]2MC=18\text{ inches}\\\\\Rightarrow\ MC=\dfrac{18}{2}=9\text{ inches}[/tex]

Therefore, the length of MC = 9 inches.

Hence, D is the correct option.