Find the domain of the function. (Enter your answer using interval notation.)

Answer:

f(x)⁻¹ = -5/3x - 5

Step-by-step explanation:

y = -3/5x - 3

x = -3/5y - 3

x + 3 = -3/5y

(x + 3)(-5/3) = y

-5/3x - 5 = y

Answer: Simon has a higher chance of winning

Step-by-step explanation: The possibility of Smith winning is 16/52 and the possibility of Simon pulling an even card is 20/52.

(20/52 is more than 16/52)

Answer:

Simon has a higher chance of winning

Step-by-step explanation:

Answer:

-2/3

Step-by-step explanation:

To find the slope, pick two points on the line, and use the slope formula

( 0,50) and  (30,30)

m = ( y2-y1)/(x2-x1)

   = (30-50)/(30-0)

    = -20/30

   = -2/3

Answer:

m = -2/3

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Find 2 coordinates

(0, 50)

(60, 10)

Step 2: Plug into formula

m = (10 - 50)/(60 - 0)

m = -40/60

m = -4/6

m = -2/3

-10x+38

Let's simplify step-by-step.

- 2(x – 3) +40-2r + 8)

Distribute:

= (-2)(x) + (-2)(-3) + (4)(-2x) + (4)(8)

= -2x + 6+ - 8x + 32

Combine Like Terms:

= -2x + 6 + - 8x + 32

= (-2x + - 8x) + (6 + 32)

-10x + 38

The simplified form of the algebraic expression  -2(x-3)+4(-2x+8) is -10x+38.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given algebraic expression -2(x-3)+4(-2x+8), when simplified it can be written as,

[tex]-2(x -3) + 4(-2 x + 8)\\\\=-2x +6-8x+32\\\\=-10x+38[/tex]

Hence, the simplified form of the algebraic expression -2(x-3)+4(-2x+8) is -10x+38.

Learn more about Expression:

https://brainly.com/question/13947055

Answer:

8.46

Step-by-step explanation:

Answer:

8.46

Step-by-step explanation:

6+0 =6

3+1=4

4+4=8

No carryovers

Answer:

circumference is 40.84 and the area is 132.73

Step-by-step explanation:

Answer:

The tank can hold  4423.36 feet³ of water.

Step-by-step explanation:

Given that,

Height = 22 feet

Diameter = 16 feet

We need to calculate the maximum amount of water

Using formula of volume

[tex]V=\pi r^2h[/tex]

Where, h = height of cylinder

r = radius of cylinder

Put the value into the formula

[tex]V=\pi\times(8)^2\times 22[/tex]

[tex]V= 4423.36\ feet^3[/tex]

Hence, The tank can hold  4423.36 feet³ of water.

Answer:

(d/2)^2 pi

Step-by-step explanation:

To find the area of a circle the formula is A=pi times radius sqaured. Since we do not have the radius we need to find it. The radius will always be half the diameter hence the (d/2). This will give us the radius, next is just to complete the area formula by squaring the radius and multiplying it by pi.  i hope this helps :)

The circle's area, in function of it's diameter, is given by:

[tex]A = \frac{\pi d^2}{4}[/tex]

----------------------

[tex]A = \pi r^2[/tex]

[tex]A = \pi r^2[/tex]

[tex]A = \pi (\frac{d}{2})^2[/tex]

[tex]A = \pi \frac{d^2}{4}[/tex]

[tex]A = \frac{\pi d^2}{4}[/tex]

Which is the area of a circle of diameter d.

A similar problem is given at https://brainly.com/question/16891462

Answer:

Hey there!

A rational number is any number that can be expressed as a fraction.

Hope this helps :)

Answer:

D.

Step-by-step explanation:

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333 (the threes go on forever). A rational number comes to an end at some point, even if the end is long, it will eventually stop.

Answer:

Distance AB is 18.79 units

Step-by-step explanation:

Given two points with coordinates as:

A= (-4,7)

B= (-12, -10)

To find:

Distance AB = ?

Solution:

To find the distance between two points with given coordinates, we can use Distance formula.

Distance formula  is given as:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the two coordinates whose distance is to be find out.

[tex]x_1 = -4\\y_1 = 7\\x_2 = -12\\y_2 = -10[/tex]

[tex]AB = \sqrt{(-12-(-4))^2+(-10-7)^2}\\\Rightarrow AB = \sqrt{(-8)^2+(-17)^2}\\\Rightarrow AB = \sqrt{64+289}\\\Rightarrow AB = \sqrt{353}\\\Rightarrow \bold{AB = 18.79\ units }[/tex]

Distance AB is 18.79 units

Answer:

AB = 18.8 units

Step-by-step explanation:

If there are two points (x1,y1) and (x2,y2) on the coordinate plane.

distance between those two points = [tex]\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }[/tex]

given points are

A= (-4,7)

B= (-12, -10)

[tex]AB = \sqrt{(-4 -(-12))^{2} + (7-(-10))^{2} }\\AB = \sqrt{(-4 +12)^{2} + (7+10)^{2} }\\AB = \sqrt{(8)^{2} + (17)^{2} }\\AB = \sqrt{64 + 289 }\\AB = \sqrt{353 }\\AB = 18.79[/tex]

Thus, length of AB is 18.79 units

since, value of hudredth of unit is 9 which is greater than 9 then rounding the value to nearest tenth of unit we increase the value at tenth of unit place by that is 7 becomes 8

length of AB  to the nearest tenth of a unit is 18.9 units

Answer: 37.07

because 35.7+1.37 is 37.07

Answer:

250

Step-by-step explanation:

I looked up s=d/t calculator and it is the calculator soup link

Answer:

70 [tex]\sqrt{3}[/tex]

Step-by-step explanation:

300    

6            50

|    \          |      \

2     3      5      10

                         |    \

                         5     2

2×5=10

10×7=70

70[tex]\sqrt{3}[/tex]

Answer:

70√3

Step-by-step explanation:

7√300 =

7√100*3

7√10*10*3     (√100=√10²=10)

7*10√3

70√3

This isn't an answer, rather a suggestion.

I would use the website desmos to help you out. But it won't help you forever like when you do quizzes or tests.

Directions:

Make the variable "y" all by itself. It need to be solo. For example for problem 34, negate 3 on each side and you will have "y=1/2(x+2)+3".

From there, plug in numbers into the x variable. (I suggest using common factors of "2" since the number your multiplying is 1/2.

Again using 34,

y=1/2(x+2)+3

y=1/2(2+2)+3

y=1/2(2+2)+3

y=1/2(4)+3

y=2+3

y=5

The coordinates are (2,5). Plot the coordinate.

Repeat the process.

x > 5

x ∈ [ 5 ; + oo )

–6x + 15 < 10 – 5x

15 - 10 < 6x - 5x

5 < x

x > 5

x ∈ [ 5 ; + oo )

Answer: x>5

Step-by-step explanation:

Given

-6x+15<10-5x

Add 6x on both sides (Addition property of equality)

-6x+15+6x<10-5x+6x

15<10+x

Subtract 10 on both sides (Subtraction property of equality)

15-10<10+x-10

5<x

x>5

Hope this helps!! :)

Please let me know if you have any question

Answer:

It means multiply the 2 numbers.

Step-by-step explanation:

(316)(18) means 316 * 18

= 5688.

The outcome of the given expression is 5724

The given expression:

(316)(18)

To find:

the outcome of the expression:

The outcome of the given expression is obtained by multiplying them out.

[tex](318)(18) = 318 \times 18 = 10(318) + 8(318) = 3180 + 2544 = 5724[/tex]

Thus, the outcome of the given expression is 5724

Learn more here: https://brainly.com/question/16787713

Answer:

2

Step-by-step explanation:

Answer:

-4x²y + 17xy² - 15xy

Step-by-step explanation:

Step 1: Write out expression

6x²y + 8xy² - 10x²y - 15xy + 9xy²

Step 2: Combine like terms (x²y)

-4x²y + 8xy² - 15xy + 9xy²

Step 3: Combine like terms (xy²)

-4x²y + 17xy² - 15xy

Answer:

[tex]28-17y[/tex]

Step-by-step explanation:

[tex]3(y+6)+5(2-4y)[/tex]

Expanding:

[tex]3y+18+10-20y[/tex]

[tex]28-17y[/tex]

Answer:

-17y+18

Step-by-step explanation:

[tex]3(y+6)+5(2-4y)\\= (3*y + 3*6) + (5*2 - 5*4y)\\= 3y + 18 + 10 - 20y\\= -20y + 3y +18 +10\\=-17y+28[/tex]

Answer:

integers contain 0, all negative and +ve whole number!!

Since -3/5 is not a whole number so not an integer!

Step-by-step explanation:

Answer:

La pregunta no está completa. Explicaré las propiedades de funcionamiento de los números racionales.

Explanation:

Las principales propiedades de los números racionales son:

- Propiedad de cierre

- Propiedad de conmutatividad

- Propiedad asociativa

- Propiedad distributiva

La propiedad de cierre establece que para dos números racionales cualesquiera xey, x + y, x-y, x * y, y x / y también será un número racional.

La propiedad de conmutatividad establece que para dos números racionales cualesquiera xey, x + y = x + y; x - y ≠ y - x; x * y = y * x; x / y ≠ y / x.

La propiedad asociativa establece que para cualesquiera tres números racionales dados x, y y z, (x + y) + zyx + (y + z) son iguales.

La propiedad distributiva establece que para tres números cualesquiera x, y y z, x × (y + z) = (x × y) + (x × z).

Answer:

Overtime hours = [h - 40] hours

Step-by-step explanation:

Given:

Weekly hour work = 40 hours per week

Total hour work = h hours

Find:

Overtime hours

Computation:

Overtime hours = Total hour work - Weekly hour work

Overtime hours = [h - 40] hours

Answer:

740

Step-by-step explanation:

Let the AP be a, a+d, a+2d, a+3d, ...

The  term of AP is given by:

[tex]t n =a+(n-1)d[/tex]

We are given that the third term is 7.

[tex]t 3=7[/tex]

⇒  [tex]a+(3-1)d=7[/tex]

⇒[tex]a+2d=7 ---(1)[/tex]

Also, the seventh term is 2 more than three times the third term.

[tex]t7=3t3+2[/tex]

⇒[tex]a+ (7-1)d=3(a+(3-1)d)+2[/tex]

⇒[tex]a+6d=3(a+2d)+2[/tex]

⇒[tex]a+6d=3a+6d+2[/tex]

⇒[tex]-2a=2[/tex]

⇒[tex]a=-1[/tex]

We can put it in (1)

[tex]a+2d=7[/tex]

⇒[tex](-1)+2d=7[/tex]

⇒[tex]2d=8[/tex]

⇒d=4

Now, the Sum of n terms of an AP is given by the formula:

[tex]sn=\frac{n}{2}(2a+(n-1)d)[/tex]

So, Sum of first 20 terms would be:

[tex]s 20=\frac{20}{2}(2(-1) +(20-1) x 4)[/tex]

⇒[tex]s20=10(-2+19 x 4)[/tex]

⇒[tex]s 20=10 x(-2+76)[/tex]

⇒[tex]s 20= 10 x 74[/tex]

⇒[tex]s 20=740[/tex]

Thus, The Sum of first 20 terms of the AP is 740.

Answer:

The amount invested at 7% is $12,000 while the amount invested at 10% is $8,000

Step-by-step explanation:

The given parameters are;

The total amount Hank invested = $20,000

The interest earned in one year = $1640

Hank invested part of the $20,000 at 7% interest and part of the $20,000 at 10%

Let the part invested at 7% = X and the part invested at 10% = Y, we have;

7% of X + 10% of Y = $1640 which gives;

0.07×X + 0.1×Y = $1640.....................(1)

X + Y = $20,000.................................(2)

Multiply equation (1) by 10 and subtract equation (1) from equation (2) to get;

X + Y - 10×(0.07×X + 0.1×Y) = $20,000 - 10×$1640

X - 0.7·X - Y - Y = $20,000 - $16,400 = $3,600

0.3·X = $3,600

X = $3,600/0.3 = $12,000

X = $12,000

Y = $20,000 - X = $20,000 - $12,000 = $8,000

Y = $8,000

Therefore, the amount invested at 7% = $12,000 and the amount invested at 10% = $8,000.

Answer:

$8,000 at 10%

$12,000 at 7%

Step-by-step explanation:

Let the part invested at 10% = x

Let the part invested at 7% = $20,000 - x

7% = 0.07

10% = 0.10

Hank invested a total of $20,000, part at 7%

0.07(20000 - x)

And part at 10%

0.10(x)

Hence, we have:

0.10x + 0.07(20000 - x) = 1640

0.10x + 1400 - 0.07x = 1640

0.10x - 0.07x = 1640 - 1400

0.03x = 240

x = 240/0.03

x = 8000

Hence, the amount he invested at 10% = $8,000

The amount he invested at 7% =

$20,000 - x

= $20,000 - $8,000

= $12,000

3b^3+2b^2+13b+14

Just add like terms

If u have any questions just ask

Answer:

1.2

Step-by-step explanation:

[tex]s/1.5 = .8\\s = 1.5 * .8\\s = 1.5 *4/5\\s = 6 /5\\s=1.2[/tex]

Answer:

462 pounds

Step-by-step explanation:

weighs 42 pounds

    and the water 11 times more

 so, 42*11 = 462 pounds

Answer:

6 hours represents [tex]\frac{3}{4}[/tex] of the 8-h work shift.

Step-by-step explanation:

The fraction of the employee's work shift is equal to the given time divided by the work shift. That is:

[tex]x = \frac{6\,h}{8\,h}[/tex]

[tex]x = \frac{6}{8}[/tex]

[tex]x = \frac{3}{4}[/tex]

6 hours represents [tex]\frac{3}{4}[/tex] of the 8-h work shift.

Answer:

Step-by-step explanation:

The product of two even numbers is even.

Let m and n be any integers so that 2a and 2b are two even numbers.

The product is 2a(2b) = 2(2ab), which is even.