is -1 a rational number.

Answer:

10 m

Step-by-step explanation:

15m - 5m = 10 m

both numbers have m which are alike

Answer: 10m

Step-by-step explanation: you subtract five from fifteen

Answer:  B. g(x) = –4(x – 3)2

Step-by-step explanation: To apply the changes to the equation of a vertical stretch of 4 and a translation of 3 units to the right, as well as the correct answer would be choice B.

The reason for this is when you apply a vertical stretch, because it changes the y-values (which causes it to vertically stretch or appear skinnier when graphed), you would multiply 4 to f(x) which would look like 4x^2.

Then, since you have a reflection over the x-axis, you must multiply a -1 to f(x) to reflect it over the x-axis which would result in -4x^2.

Finally, it also asks to shift the graph right 3 which by moving it right, you change the x values meaning you will perform f(x-3) to achieve this (subtract the value from x when you move right, and add the value to x when you move left).

Answer:

r≈4.775

Step-by-step explanation:

the formula for this is: r=(3V /4π)^⅓

Step-by-step explanation:

"Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.)"

Given one of the roots, we can use either long division or grouping to factor each cubic equation into a binomial and a quadratic.  I'll use grouping.

Then, we can either factor or use the quadratic equation to find the remaining two roots.

1. x³ − 7x + 6 = 0; 1

x³ − x − 6x + 6 = 0

x (x² − 1) − 6 (x − 1) = 0

x (x + 1) (x − 1) − 6 (x − 1) = 0

(x² + x − 6) (x − 1) = 0

(x + 3) (x − 2) (x − 1) = 0

The remaining two roots are both real: -3 and +2.

2. x³ − 3x² + 25x + 29 = 0; -1

x³ − 3x² + 25x + 29 = 0

x³ − 3x² − 4x + 29x + 29 = 0

x (x² − 3x − 4) + 29 (x + 1) = 0

x (x − 4) (x + 1) + 29 (x + 1) = 0

(x² − 4x + 29) (x + 1) = 0

x = [ 4 ± √(16 − 4(1)(29)) ] / 2

x = (4 ± 10i) / 2

x = 2 ± 5i

The remaining two roots are both imaginary: 2 − 5i and 2 + 5i.

3. x³ − 4x² − 3x + 18 = 0; 3

x³ − 4x² − 3x + 18 = 0

x³ − 4x² + 3x − 6x + 18 = 0

x (x² − 4x + 3) − 6 (x − 3) = 0

x (x − 1)(x − 3) − 6 (x − 3) = 0

(x² − x − 6) (x − 3) = 0

(x − 3) (x + 2) (x − 3) = 0

The remaining two roots are both real: -2 and +3.

"Find all the zeros of the function"

For quadratics, we can factor using either AC method or quadratic formula.  For cubics, we can use the rational root test to check for possible rational roots.

4. f(x) = x² + 4x − 12

0 = (x + 6) (x − 2)

x = -6 or +2

5. f(x) = x³ − 3x² + x + 5

Possible rational roots: ±1/1, ±5/1

f(-1) = 0

-1 is a root, so use grouping to factor.

f(x) = x³ − 3x² − 4x + 5x + 5

f(x) = x (x² − 3x − 4) + 5 (x + 1)

f(x) = x (x − 4) (x + 1) + 5 (x + 1)

f(x) = (x² − 4x + 5) (x + 1)

x = [ 4 ± √(16 − 4(1)(5)) ] / 2

x = (4 ± 2i) / 2

x = 2 ± i

The three roots are x = -1, x = 2 − i, x = 2 + i.

6. f(x) = x³ − 4x² − 7x + 10

Possible rational roots: ±1/1, ±2/1, ±5/1, ±10/1

f(-2) = 0, f(1) = 0, f(5) = 0

The three roots are x = -2, x = 1, and x = 5.

"Write the simplest polynomial function with integral coefficients that has the given zeros."

A polynomial with roots a, b, c, is f(x) = (x − a) (x − b) (x − c).  Remember that imaginary roots come in conjugate pairs.

7. -5, -1, 3, 7

f(x) = (x + 5) (x + 1) (x − 3) (x − 7)

f(x) = (x² + 6x + 5) (x² − 10x + 21)

f(x) = x² (x² − 10x + 21) + 6x (x² − 10x + 21) + 5 (x² − 10x + 21)

f(x) = x⁴ − 10x³ + 21x² + 6x³ − 60x² + 126x + 5x² − 50x + 105

f(x) = x⁴ − 4x³ − 34x² + 76x − 50x + 105

8. 4, 2+3i

If 2 + 3i is a root, then 2 − 3i is also a root.

f(x) = (x − 4) (x − (2+3i)) (x − (2−3i))

f(x) = (x − 4) (x² − (2+3i) x − (2−3i) x + (2+3i)(2−3i))

f(x) = (x − 4) (x² − (2+3i+2−3i) x + (4+9))

f(x) = (x − 4) (x² − 4x + 13)

f(x) = x (x² − 4x + 13) − 4 (x² − 4x + 13)

f(x) = x³ − 4x² + 13x − 4x² + 16x − 52

f(x) = x³ − 8x² + 29x − 52

Answer:

The answer is, 1,2,4, and 8

Step-by-step explanation:

Answer:Answer:

81 miles

Step-by-step explanation:

From the question 7/10 of the trip has been said to be downhill. It therefore means that 3/10 is not downhill.

Miles = 270

Downhill = 7/10

Not downhill = 3/10

Now we have To calculate Miles that are not downhill (uphill)

But first I calculated for the number of downhill miles

270x7/10

Downhill = 189 miles

To get the number of not downhill miles

I subtracted 189 from the total number of miles on the question.

270 - 189

= 81 Miles.

Therefore 81 Miles of the trip are not downhill.

If you have anymore questions or need clarity please let me know on the comment section. Thank you and Good luck!

Step-by-step explanation:

Answer:

a=-1

b=10

Step-by-step explanation:

Answer:

a: -1

b: 10

edge 2020

Answer:    2a - 10

Step-by-step explanation:

a represents the number of students in the art club.

The number of students in a school's math club is ten less than twice the number of students in the art club.

ten less = - 10

twice the number of students in the art club = 2*a

2a - 10 = the number of students in the math club

Answer:

10.67% increase

Step-by-step explanation:

We can find percent increase with (difference/original) x 100

7.47 - 6.75

= 0.72 (difference)

(0.72/6.75) x 100

= 10.67% increase

third

hope it helps you

Answer: (6^-8/7^-12)

Step-by-step explanation:

In this type of problems, you apply the laws of indices which stated that

( a²/b²)³ =( a²×³/b²×³)

= ( a6/b6)

From this question now, applying the above principle

(6²/7³)-4

= (6²×-⁴/7³×-⁴)

= (6^-8/7^-12)

So the answer is C

Answer:

x=(k+3)/y

Step-by-step explanation

First, we simplify by adding 3 to both sides of the equation

xy-3+3=k+3

Now it's xy=k+3

To get x we divide both sides by y

So x=(k+3)/y

Answer:

[tex]x = \frac{k + 3}{y} [/tex]

Step-by-step explanation:

Do all u can to make x stand alone.

Just obey the rules of fhe operations when they cross the equal sign.

Answer:

4 you dumba**. Jesus christ

Step-by-step explanation:

Answer:

[tex]\frac{7}{2}[/tex]in

Step-by-step explanation:

First you must set up an equation. [tex]\frac{1}{2}x=\frac{7}{4}[/tex]

Then, you must solve for x.          [tex]x=\frac{7}{2}[/tex]

Answer:

Hey there!

The big square has an area of 6x6 or 36 units.

However, we subtract 8 to get 28 because the 8 white squares do not count.

Let me know if this helps :)

Answer:

28units²

Step-by-step explanation:

6² = 36

36 - 8 = 28

Part A

1 hour = 60 minutes

0.5 hours = 30 minutes (multiply both sides by 0.5)

11.5 hours = 11 hours + 0.5 hours

11.5 hours = 11 hours + 30 minutes

11.5 hours = 11 hours, 30 minutes is the answer

========================================

Part B

20% = 20/100 = 0.20

The lion sleeps 20% more than the cat, which means the lion sleeps 0.20*11.5 = 2.3 hours more

This leads to 11.5 + 2.3 = 13.8 hours being the total time the lion sleeps

1 hour = 60 minutes

0.8 hours = 48 minutes (multiply both sides by 0.8)

13.8 hours = 13 hours + 0.8 hours

13.8 hours = 13 hours + 48 minutes

13.8 hours = 13 hours, 48 minutes is the amount of time the lion sleeps

Answer: B

Step-by-step explanation:

When you are multiplying exponents, if the base is the same, then you can directly add the exponents together.

We can see that both bases are 6. That means we can add the exponents.

[tex]3+\frac{1}{4}[/tex]                             [common denominator]

[tex]\frac{12}{4}+\frac{1}{4}[/tex]                            [add]

[tex]\frac{13}{4}[/tex]

Now, we know that the answer will be [tex]6^1^3^/^4[/tex].

Answer:

A reduce the fraction is

5\1

Answer:

C. 4i-2

Step-by-step explanation:

EDGE 2020

Answer:

x = -3 and y = 7 or x = 1 and y = -1

Step-by-step explanation:

Answer:

it will be one out six to roll a four

Step-by-step explanation:

there is one being rolled to be a 4 out of six

f(x) = 3x – 2, g(x) = 7 – x2.

3f(1) - 49(-2)

Substitute the given value into the function and evaluate.

101

The value of 3f(1) - 49(-2) for the given function f(x) = 3x – 2 will be 101.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

Given the function,

f(x) = 3x – 2

Now,

f(1) = 3(1) - 2 = 1

So,

3f(1) - 49(-2) = 3×1 - 49(-2)

⇒ 3 + 98 = 101

Hence "The value of 3f(1) - 49(-2) for the given function f(x) = 3x – 2 will be 101".

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Answer:

[tex]x=\frac{55}{3},\:y=\frac{22}{3}[/tex]

Step-by-step explanation:

Solve by Substitution ;

[tex]\begin{bmatrix}x+2y=33\\ x-y=11\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:x+2y=33:\quad x=33-2y\\\\\mathrm{Subsititute\:}x=33-2y\\\\\begin{bmatrix}33-2y-y=11\end{bmatrix}\\\\Simplify\\\begin{bmatrix}33-3y=11\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:33-3y=11:\quad y=\frac{22}{3}\\\mathrm{For\:}x=33-2y\\\\\mathrm{Subsititute\:}y=\frac{22}{3}\\x=33-2\times\frac{22}{3}\\\\x=\frac{55}{3}\\\\x=\frac{55}{3},\:y=\frac{22}{3}[/tex]

Answer:

b

Step-by-step explanation:

Complete Question  

Find the average value of the function over the given interval. (Round your answer to three decimal places.) f(x) = 12e^x, [−6, 6] Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)

Answer:

The  average is  

  [tex]AV  =  403[/tex]

The value of  x is

   [tex]x =  4[/tex]

Step-by-step explanation:

From the question we are told that

  The equation is  [tex]f(t) =  12e^x[/tex]

  The  points consider is  [-6 , 6]

Generally the average value of the function over the given interval is mathematically represented as

          [tex]AV  =  \frac{1}{z-w} \int\limits^ z_w {f(x)} \, dx[/tex]

          [tex]AV  =  \frac{1}{ 6 - (-6)}  \int\limits^{6}_{-6} { 12e^x} \, dx[/tex]

          [tex]AV  =  \frac{1}{12 } e^x| \left 6} \atop {-6}} \right.[/tex]

          [tex]AV  = e^6 -e^{-6}[/tex]

          [tex]AV  =  403[/tex]

Generally when the function equal the average we have that

        [tex]f(x) =  12e^{x} =  403[/tex]

        [tex]e^{x} =  34[/tex]

          [tex]x =  ln(34)[/tex]

        [tex]x =  4[/tex]

Answer:

Infinite Amount of Solutions

Step-by-step explanation:

Step 1: Write out equation

2a + 6 = 2a + 5 + 1

Step 2: Combine like terms

2a + 6 = 2a + 6

Here we see that we have the same slope and same y-intercept or the same equation. When this happens, our solution set is infinite amount of solutions, as any value a can be plugged in and would be true.

Answer: 0.68

Step-by-step explanation:

given data:

ABC market share = 30%

number of customers surveyed = 800

probability that more than 32% prefers ABC

Solution:

32% of 800

= 256 persons

p ( x ≥ 256 )

= 1 - ( 256/800 )

= 1 - 0.32

= 0.68

the probabiliy that more than 32% of those who carried out the survey would prefer ABC brand is 0.68.

Answer:

2/5 is greater

Step-by-step explanation:

to compare you need to make them common denominator, and that could be10. to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2. this will turn it into 4/10. 4/10 is greater than 3/10

The solution is : 2/5> 3/10

2/5 is greater than 3/10

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

Here, we have,

the given fractions are,

2/5 and 3/10

now, we have,

to compare you need to make them common denominator,

and that could be10.

to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2.

i.e. 2*2/5*2

=4/10

this will turn it into 4/10.

now, we get,

4/10 is greater than 3/10

Hence, 2/5> 3/10 , 2/5 is greater than 3/10.

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