When you multiply a function by -1 what is the effect on its graph

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

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:

[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:

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

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:

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]

The transformation which do not describe a rigid motion transformation is:

           Option: C

   C. dilating a figure by a scale factor of 1/4

Rigid motion transformation is a transformation in which the shape and size of the figure is preserved i.e. it remains the same.

A)

Translating a figure 5 units right.

We know that in the translation transformation the shape and size of the figure remains the same only the location of points are changed.

B)

Rotating a figure 90 degrees.

In rotation the shape and size is preserved.

Hence it is a rigid transformation.

C)

dilating a figure by a scale factor of 1/4

This is not a rigid transformation because the size of the figure is changed.

since the scale factor is less than 1.

Hence, the transformation is a reduction of the original figure.

D)

reflecting a figure across the x-axis.

The reflection is also a rigid transformation.

since it preserves the shape and size of the object.

Answer:

The correct answer is C.

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:

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:

-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:

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

Answers: Ten millions

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:

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:

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:

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:

I have to assume that the 24, the 72, and the 18 are feet.

If those are the dimensions of a rectangular prism, like a box, a crate,

or a humongous block of ice, then

           Volume = (length) x (width) x (height) =

                            (24-ft) x (72-ft) x (18-ft) =  31,104 cubic ft

If those numbers are inches, then here's the easy way to handle it:

      24 inches  =  2 ft

      72 inches  =  6 ft

      18 inches  =  1.5 ft

              Volume  =  (length) x (width) x (height) =

                                    (2ft) x (6ft) x (1.5ft)  =  18 cubic feet

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:

18 and 19

Step-by-step explanation:

Consecutive positive integers have a difference of 1 between them

let n and n + 1 be the 2 integers, then

n(n + 1) = 342, that is

n² + n = 342 ( subtract 342 from both sides )

n² + n - 342 = 0 ← quadratic equation in standard form

(n + 19)(n - 18) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 19 = 0 ⇒ n = - 19

n - 18 = 0 ⇒ n = 18

However, n > 0 ⇒ n = 18 and n + 1 = 18 + 1 = 19

The 2 integers are 18 and 19

[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:

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 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:

1. mode

2. median

3. mean

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 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:

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:

You need to draw a horizontal line that goes through the point (0,4).

Step-by-step explanation:

Slope of zero means it does not go up or down. It looks like this ↔, but stretched out to the two sides of the graph.

A line with a slope of zero is flat and does not rise or fall. To graph this line, draw a horizontal line through the given y-coordinate.

A line with a slope of zero means that the line is flat and has no rise or fall. To graph a line with a slope of zero passing through the point (0,4), you would draw a horizontal line through the y-coordinate 4. Since the slope is zero, the line will not change in the vertical direction.

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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:

∠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°