subtract and simplify​

You may consider a function with domain [tex](0,\infty)[/tex] and switch [tex]x\mapsto -x[/tex]

For example, we know that

[tex]y=\log(x)[/tex]

can only be evaluated for positive values of the argument. This means that

[tex]y=\log(-x)[/tex]

can also be evaluated only for positive values of the argument, i.e.

[tex]-x>0 \iff x<0 \iff x \in (0,\infty)[/tex]

To give another example, you may consider a function with domain [tex][0,\infty)[/tex], consider its inverse to remove 0 from the domain, and finally switch again [tex]x\mapsto -x[/tex]:

[tex]\sqrt{x} \implies D = [0,\infty)\\\dfrac{1}{\sqrt{x}} \implies D = (0,\infty)\\ \dfrac{1}{\sqrt{-x}} \implies D = (-\infty,0)[/tex]

Answer: D

Step-by-step explanation:

For this case we must find the product of the following expressions:

[tex]\frac {3x} {x + 1} * \frac {x} {x-7}[/tex]

So:

[tex]\frac {3x ^ 2} {x ^ 2-7x + x-7} =\\\frac {3x ^ 2} {x ^ 2-6x-7}[/tex]

So, we have to:

[tex]\frac {3x} {x + 1} * \frac {x} {x-7} = \frac {3x ^ 2} {x ^ 2-6x-7}[/tex]

Answer:

[tex]\frac {3x ^ 2} {x ^ 2-6x-7}[/tex]

Option C

Answer:

The area of rectangle C is 2

Step-by-step explanation:

Using a scale factor of [tex]\frac{1}{5}[/tex] yields the side lengths of 1 and 2

[tex](1)(2)=2[/tex]

Answer:

2 square units

Step-by-step explanation:

hello

The scale factor or linear scale factor is the ratio between the length of the same side in two similar figures.

in the graph we have  a rectangle with width 5 units and long 10 units, and we know the scale factor is 1/5

[tex]S_{f}=\frac{width(C)}{width(B)}\\ \\Width(B)*S_{f} =width(C)=5 units *\frac{1}{5} \\\\Width(C) =\frac{5}{5} units =1 unit[/tex]

[tex]S_{f} =\frac{length (C)}{length(B)} \\\\\\length(C)=length(B)*S_{f}\\length(C)=(10*\frac{1}{5})[/tex]

[tex]Length(C) =2 units\\\\ the area is A=w*l\\\\A=1 unit * 2 units\\\\\\[/tex]

A=2 square units

I hope it helps

Answer:

[tex]64.3=\frac{1}{3}(B)(7)[/tex]

Step-by-step explanation:

we know that

The volume of a cone (bird feeder) is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the cone

In this problem we have

[tex]V=64.3\ cm^{3}[/tex]

[tex]h=7\ cm[/tex]

substitute

[tex]64.3=\frac{1}{3}(B)(7)[/tex]

[tex]192.9=(B)(7)[/tex]

[tex]B=192.9/(7)=27.56\ cm^{2}[/tex]

The equation that can be used to determine the area of the circular lid needed to cover the bird feeder is 64.3 = 1/3 x b x 7.

A cone is a three-dimensional shape that consists of a circular base and a vertex.

Volume of a cone = 1/3πr²h

Area of a circle = πr²

πr = 64.3 = 1/3 x b x 7

To learn more about the volume of a cone, please check: https://brainly.com/question/13705125

#SPJ5

Answer:

C. [tex]f(x)=\sqrt[3]{-x} -1[/tex]

Step-by-step explanation:

Consider graph of the parent function (red curve in attached diagram)

[tex]g(x)=\sqrt[3]{x}[/tex]

First, multiply it by -1 to get function

[tex]h(x)=-\sqrt[3]{x}[/tex]

Then translate the graph of the function h(x) 1 unit down, then you'll get the function

[tex]f(x)=-\sqrt[3]{x} -1\\ \\ \text{or}\\ \\f(x)=\sqrt[3]{-x} -1[/tex]

The graph of the function f(x) is represented by the blue curve in attached diagram

Answer:

42.5%

Step-by-step explanation:

Answer:

42.5

Step-by-step explanation:

34/80×100/1

=340/8

=42.5

Step-by-step explanation:

[tex] \sqrt{x + 10} - 1 = x \\ \sqrt{x + 10} = x + 1 \\ (x + 10) = (x + 1) {}^{2} \\x + 10 = {x}^{2} + 2x + 1[/tex]

Answer:

[tex]x=44[/tex]

Step-by-step explanation:

[tex]\frac{x}{4}+4=15 \\ \\ \frac{x}{4}=11 \\ \\ x=44[/tex]

His sister is 8 and he is 20.

let's say z represents liz. we can make an equation where z+12=4z.

Solve for that and z is equal to 4. Now that was 4 years ago. She should be 8 now?

I hope this is correct because my brain isn't doing so well today.

Answer:

Adam is 20 years old and Liz is 8 years old.

Step-by-step explanation:

Let present age of Adam = x years

Let present age of Liz = y years

Now we will make the equations.

x = y + 12 -------------(1)

For second equation

( x-4) = (y-4) × 4

x-4 = 4y - 16

x = 4y + 4 - 16

x = 4y - 12 -----------------(2)

By substitution method, we  substitute  the value of  x  from equations (1) to equation (2).

y + 12 = 4y - 12

y - 4y + 12 = -12

-3y = -12 -12

3y = 24

y = 8

Now we put the value of y in equation (1)

x = 8 + 12 = 20

Therefore, Adam is 20 years old and Liz is 8 years old.

Answer:

B

Step-by-step explanation:

Answer:  13

Step-by-step explanation:  1st - Distribute the -1 through to the x + -1*(5+x) first:  8 + -1*[x + -1*(5+x)] = 8 + [-1*x  +  -1*-1*(5+x)]

= 8 + [-x + -1*-1 *(5+x)]

Multiply the two -1s that are in front of the (5+x).  Negative x Negative = positive

Minus the paranthesis

Do PEDMAS

8 + [-x + 5 + x]  <- -x +x = 0

                = 8 + [0 + 5]  <- 0 and 5 are like terms and will be combined

                = 8 + 5 = 13

Answer:

Jason's collection: 21 books.

Nathan's collection 24 books.

Step-by-step explanation:

Let number of books owned by Jason be j books and that for Nathan be n books.

So we have the system:

6j + 1/3 n = 134.........(1)

1/3j + n = 31................(2)

Multiply the first equation by -3. We get:

-18j - n = -402............(3)

Adding (2) + (3):

-53/3 j = -371

j = -371 * 3 / -53

j =  21.

Now substitute j = 21 in equation (2):

1/3(21) + n = 31

n = 31 - 7 = 24

n = 24.

-Hello There-

ANSWER: 10 Is 40% Of 25

EXPLANATION

What is 40% of 25?

Y is 40% of 25

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 40% * 25

Converting percent to decimal:

p = 40%/100 = 0.4

Y = 0.4 * 25

Y = 10

Have A Great Day!

Be Safe,

TheBlueFox

There is 336 ways the runners can finish first, second, and third.

Answer:

Yes, the answer provided is correct.

Step-by-step explanation:

Angles TRV and SRW are vertical angles, so they are the same value.

The angle of 110° and the angle labelled as 1 form 180°, so we have

[tex]<1> = 180-110=70[/tex]

The same holds for the angle labelled 2 and the 115° angle:

[tex]<2> = 180-115=65[/tex]

Angle 1, 2 and 7 are the interior angles of a triangle, so they sum to 180. We can deduce

[tex]<7> = 180-70-65=45[/tex]

Angles 5 and 7 are corresponding angles, so they have the same measure.

Remember that a complex number has the form a + bi. You need to figure out what a and b need to be. Since −3i is an imaginary number, it is the imaginary part (bi) of the complex number a + bi. This imaginary number has no real parts, so the value of a is 0.

ANSWER

Yes

EXPLANATION

The number

[tex]3i[/tex]

can be rewritten as

[tex]0 + 3i[/tex]This is of ty form

[tex]z = a + bi[/tex]

where 0 is the real part and 3i is the imaginary or complex part.

[tex]3i[/tex]

is therefore a complex number. It is purely imaginary because the real part is zero.

Answer: 15 ounces

Step-by-step explanation:

We need to find the unit rate for each of the prices/ounces,

0.89/10 = 0.089

1.29/15 = 0.086

2.26/18 = 0.125...

3.39/32 = 0.1059375

The answer is:

B. 15 ounces

Because the unit rate(cost per ounce) is 0.086 cents per ounce which is less than:

A. 0.086

C. 0.126

D. 0.106

Answer:

17.4 i believe

Step-by-step explanation:

Answer: OPTION C.

Step-by-step explanation:

Given a function f(x), the range of the inverse of f(x) will be the domain of the function f(x) and the range of the domain of f(x) will be the range of the inverse function.

For example, if the point (2,1) belongs to f(x), then the point (1,2) belongs to the inverse of f(x).

Observe that in the graph of the function f(x) the point (-3,1) belongs to the function, then the point (1,-3) must belong to the inverse function.

Therefore, you need to search the option that shown the graph wich contains the point (1,-3).

Observe that the Domain f(x) is (-∞,0) then the range of the inverse function must be (-∞,0).

This is the graph of the option C.

Answer:

Not safe

Step-by-step explanation:

Using the sine ratio in the right triangle

let the angle be x, then

sinx° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{16.5}{17}[/tex]

x = [tex]sin^{-1}[/tex] ([tex]\frac{16.5}{17}[/tex] ) ≈ 76.1°

Since 76.1° > 70° then not safe at this height

Answer:

[tex]LA=755\ m^{2}[/tex], [tex]SA=785\ m^{2}[/tex]

Step-by-step explanation:

Part 1) Find the lateral area of the given prism

we know that

The lateral area of the prism is equal to

[tex]LA=PL[/tex]

where

P is the perimeter of the triangular base

L is the length of the prism

Find the perimeter P

[tex]P=5+6+11.21=22.21\ m[/tex]

we have    

[tex]L=34\ m[/tex]

substitute

[tex]LA=(22.21)(34)=755\ m^{2}[/tex]

Part 2) Find the surface area of the given prism

we know that

The surface area of the prism is equal to

[tex]SA=2B+LA[/tex]

where

B is the area of the triangular base

LA is the lateral area of the prism

Find the area B

[tex]B=(1/2)(5)(6)=15\ m^{2}[/tex]

we have

[tex]LA=755\ m^{2}[/tex]

substitute

[tex]SA=(2)(15)+755=785\ m^{2}[/tex]

Answer:

Step-by-step explanation:

Look at the picture.

It's a net of right rectangular prism.

We have three pairs of rectangles:

7ft × 8ft

7ft × 18ft

8ft × 18ft

The formula of an area of a rectangle l × w:

A = lw

Calculate the areas:

A₁ = (7)(8) = 56 ft²

A₂ = (7)(18) = 126 ft²

A₃ = (8)(18) = 144 ft²

The Surface Area :

S.A. = 2A₁ + 2A₂ + 2A₃

Substitute:

S.A. = 2(56) + 2(126) + 2(144) = 652 ft²

The total cost y varies directly with the number of hours x needed to complete a job, with a direct variation coefficient of 100.

When analyzing the variation between two variables, specifically how y varies with x, we consider whether the relationship is direct or inverse. In the scenario provided, where it takes 10 workers 24 hours to do a job, if we let x represent the number of hours it takes to get the job done and y represent the total cost to the customer, we can establish that as the number of hours increases, the total cost also increases, assuming workers are paid by the hour. This suggests a direct variation.

Given that widget workers receive $10 per hour, the cost y to the customer for x hours of work would be 10 workers × $10 per hour × x hours. So, y = 10 × 10 × x = 100x. Hence, the relationship between y and x is directly proportional with a coefficient of variation of 100.

Answer:

y=9x+1.6

Step-by-step explanation:

bring the 10.6 over by adding it to both sides

Answer:

bro ur wrongf its y – 10.6 = 9(x – 1)

Step-by-step explanation:

BRO U BOT

Answer:

$445.32

Step-by-step explanation:

see picture attached

i hope this helped !!

Answer:

Two solutions.

Answer:

(x, y ) → (x - 8, y + 11)

Step-by-step explanation:

L(7, - 3) and L'(- 1, 8)

The x-coordinate 7 → - 1 , that is a shift of - 8

The y- coordinate - 3 → 8, that is a shift of + 11

The rule to translate LMN → L'M'N' is

(x, y ) → (x - 8, y + 11 )

You must use Pythagorean theorem, which is [tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are both legs (the two legs are the sides that form a perpendicular right angle) while c is the hypotenuse (side opposite the right angle)

In this case...

a = y

b = 8

c = 12

^^^Plug these numbers into Pythagorean theorem

[tex]y^{2} +8^{2} =12^{2}[/tex]

Simplify as much as possible

[tex]y^{2}[/tex] + 64 = 144

Isolate y by subtracting 64 to both sides

[tex]y^{2}[/tex] + (64 - 64) = 144 - 64

[tex]y^{2}[/tex] = 80

Further isolate y by taking the square root of both sides. This will take away the square from the left side

y = [tex]\sqrt{80}[/tex]

[tex]\sqrt{80}[/tex] <<< Can be further simplified

4√5 = y

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

hi so finding the volume you need to do

pi times R² times height

Step-by-step explanation:

hopes this will help u  outttttt