Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
g(x)-f(x)

The simplified expression is 8

To find the simplified form of the mentioned expression, we will first simplify the value in bracket. Then, multiply the powers to solve it.

As per the known fact, 4² and 2⁴ result to give the number 16.

Expression = (2⁴)³/₄

Now, again as per the known fact, the exponents can be multiplied.

Exponents = 4×(3/4)

Cancelling 4 as it is common in both numerator and denominator

Exponents = 3

Putting the resultant exponent back to the expression -

Expression = 2³

Taking cube -

Expression = 2×2×2

Performing multiplication

Expression = 8

Hence, the simplified form of expression is 8

Learn more about simplifying the expression -

https://brainly.com/question/1280754

#SPJ4

Answer: 4

Step-by-step explanation:

= Multiply -1 by -9 to change 9 to a positive number

= Add -5 to 9 (-5 + 9 = 4)

= 4

If the diameter of the circle is 18 feet, the circumference of the circle is 56.55 feet.

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

The diameter of a circle is 18 feet.

D = 18 feet

Now, the radius of the circle is half the diameter of the circle.

Therefore,

Diameter = 2 × Radius

Radius = Diameter / 2

D = 2r

r = D / 2

r = 18 feet / 2

r = 9 feet

Now, the circumference of a circle is given as:

Circumference = π × diameter

Circumference = π × 2r

Circumference = 2πr

Circumference = 2 × π × 9 feet

Circumference = 2 × 3.14159 × 9

Circumference = 56.55 feet

Learn more about circles here:

https://brainly.com/question/8952990

#SPJ9

A classmate writes the matrix at the right to represent a system and says that the solution is x = 2, y = 0. Classmate's error and how to describe it is mentioned as follows:

Given:

x = 2

y = 0

From this we can say that The second row of the matrix doesn't have a coefficient in the y column. The equation represented by second row is 0 = 0 and not y = 0.

Thus it is concluded that the equation represented by second row  is 0 = 0 not y = 0.

If you need to learn more about matrix, click here

https://brainly.com/question/28180105

#SPJ4

The binomial expansion for ( X + Y )⁴ is X⁴ + 4 X³(Y) + 6 X²(Y²) + 4 XY³ + Y⁴.

Use the binomial expansion theorem to find each term. The binomial theorem states ( a + b )ⁿ = ⁿ∑ _{k = 0} n C k ⋅ ( a^(n - k) × b^{k} ) .

⁴∑ _{k = 0} = ( 4 ! / [ ( 4 − k ) ! k ! ] ) × ( X )^{4 - k} × ( Y )^{k}

Expanding the summation.

( X + Y )⁴ = ( 4! / ( 4 − 0 )! 0! ) × ( X )⁴⁻⁰ × ( Y )⁰ + ( 4! /( 4 − 1 )! 1! ) × ( X )⁴⁻¹ × ( Y )¹ + ( 4! / ( 4 − 2 )! 2! ) × ( X )⁴ ⁻ ² × ( Y )² + ( 4! /( 4 − 3 )! 3! ) × ( X )⁴ ⁻ ³ × ( Y )³ + 4! / ( 4 − 4 )! 4! × ( X )⁴ ⁻ ⁴ × ( Y )⁴

Simplify the exponents for each term of the expansion.

( X + Y )⁴ = 1 × ( X )⁴ × ( Y )⁰ + 4 × ( X )³ × ( Y )¹ + 6 × ( X )² × ( Y )² + 4 × ( X )¹ × ( Y )³ + 1 × ( X )⁰ × ( Y )⁴

Therefore,

( X + Y )⁴ = X⁴ + 4 X³ (Y) + 6 X² (Y²) + 4 X Y³ + Y⁴

Learn more about binomial expansion here:

https://brainly.com/question/13602562

#SPJ9

Answer:

Yes

Step-by-step explanation:

Math, due tomorrow and i can't find the rate of enlargement of my dilation in transformation....

The factoring of the expression x² = 5 x + 14 is (x+2)(x-7)

By ordering the values, we get:

x²- 5x - 14 = 0

To solve this exercise, we have to follow the rules of factoring:

1. Looking for the a and b number that state the following equations:

Analyzing that (a*b) is a negative number, it means that (a) and (b) have different signs, and due to the results of (a+b) is negative the higher number has to be the negative one.  

The number could be:

a = 2

b = -7

Confirming:

a + b = 2 + (-7) = -5

a * b = 2 * (-7) = -14

2. Rewriting the factored expression (x+a)(x+b) with the obtained values, we get:

(x+2)(x-7)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

Learn more about factoring at brainly.com/question/24734894

#SPJ4

The area of the whole figure includes the areas of the rectangle and the two triangles and the value is 60 square units

The area of a shape is the amount of space on the shape.

For most regular shapes, the area is the product of their width and the length

Rectangle A

The dimensions of this rectangle are

Length = 8

Width = 10 - 5 = 5

The area of the rectangle is

Area = Length * Width

This gives

Area = 8 * 5

Evaluate the product

Area = 40

Triangle B

The dimensions of this rectangle are

Base = 6

Height = 10 - 5 = 5

The area of the triangle is

Area = 0.5 * Base * Height

This gives

Area = 0.5 * 6 * 5

Evaluate the product

Area = 15

Whole figure

The area of the whole figure is

Area = Rectangle A + Triangle B + Triangle C

This gives

Area =

Evaluate the product

Area = 40 + 15 + 5

Evaluate

Area = 60

Hence, the area of the whole figure is 60 square units

Read more about areas at

https://brainly.com/question/8409681

#SPJ1

Answer:

r = 2

Step-by-step explanation:

-12r + 16 = -8

Subtract 16 from both sides to isolate the r term.

-12r + 16 - 16 = -8 - 16

-12r = -24

Divide both sides by negative twelve.

-12r/-12 = -24/-12

Solve.

r = 2

Answer:

r=2

Step-by-step explanation:

sub 16 frome each side: -12r=-24

divide both sides by -12: r=2

would have made it more detailed but im lazy rn, have a good day

The correct answers of the statement are as follows;

Line a and b area parallel lines.

c is not parallel to a or b.

When parallel lines are cut by a transversal, angle relationships are formed. The angle relationship includes corresponding angles, alternate angles, vertically opposite angles etc.

Therefore, let's select the correct answer in the options.

m∠1 = m∠5

Therefore, the measure of angle 1 is equals to the measure of angle 5 because they are corresponding angles.

m∠4 = m∠5

Therefore, the measure of angle 4 is equals to the measure of angle 5 because they are alternate angles.

Hence, the correct answers of the statement are as follows;

learn more on parallel lines and angles here: https://brainly.com/question/11546031

#SPJ1

The solution of the given equation by rounding off it to the nearest ten-thousandth is 2.7182.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation: log x² = 2

We are given a logarithmic expression: log x² = 2        —- 1

We know that log x² = 2 log x and log (ab) = log a + log b

Using in equation 1, we have,

2 log x = 2

log x = 1

Using exponential on both sides, we have

e^(log x) = e^1

x = e

x = 2.7182

Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 2.7182.

To learn more about the round-off of a digit, visit the link given below:

https://brainly.com/question/4896544

#SPJ4

Answer:

0.030303...

Step-by-step explanation:

i put the dots because this is a repeating decimal

Answer:

0.03030303030303.

Answer:

The slope is 2.

Step-by-step explanation:

You can use the slope formula or pick two points, count up from one point then to the right. Use rise/run if you use the counting method.

The slope formula is y2-y1/x2-x1

Use the points (20, 20) and (30, 40)

Look at this link to understand how to use it.

https://brainly.com/question/28619876

Hope this helps!

Please mark as brainliest if correct!

Based on the fraction of their books that they have sold, the number of books that Alexander is left with is 30 books and the number of books that Sophia is left with is 11 books.

Alexander has sold 3/8 of the 48 books and so to find the number of books left, the formula is:

= 48 - (3/8 x 48 books)

= 48 - 18

= 30 books

The number of books that Sophia is left with is:
= 38 - (5/7 x 38)

= 38 - 27

= 11 books

Find out more on fractions at https://brainly.com/question/534634

#SPJ1

Answer:

1/2

Step-by-step explanation:

Point Form:

(

3

4

,

−

2

,

1

2

)

Equation Form:

x

=

3

4

,

y

=

−

2

,

z

=

1

2

The value of the term 9w using the slope of the line is found as 54.

As per the given question;

The slope of the line is given as;

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = m = -1/9

The two coordinates from where the line is passing is (w, -2) and (3, -3).

Thus,

(x₁, y₁) = (w, -2)

(x₂, y₂) = (3, -3)

Put the values in the slope equation;

m = (y₂ - y₁)/(x₂ - x₁) = -1/9

(-3 + 2)/(3 - w) = -1/9

Cross- multiplying the terms;

9(-3 + 2) = -(3 - w)

Simplifying;

-9 = -3 + w

w = 6

The value of 9w = 9×6

9w = 54.

Therefore, the value of 9w is found as 54.

To know more about the slope of the line, here

https://brainly.com/question/16949303

#SPJ9

Using the Segment Addition Postulate, considering the congruent segments and the trisection, the missing lengths of the segments are given by the following items:

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For this problem, two other concepts are important, given by the bullet points below:

CD = 12, hence, considering the trisection: (12/3) = 4.

CD is also congruent to CB, hence:

CB = 12.

CE = 6, and AE = 2CE, hence:

Due to the postulate, since DG = 8 and GE = 12, and the entire lengths are of 12, and considering the congruence:

More can be learned about the segment addition postulate at https://brainly.com/question/2134445

#SPJ1

Answer:

y=6x+3  

Step-by-step explanation:

Draw it on a graph, then use rise over run, 6/1 and you get 6.

Answer: download the app photo math and rewrite your equation and replace your variables with your numbers so the app can understand it. then just take a pic with it on the app and it will give you the answer. its a super useful app!

Step-by-step explanation:

Answer: 3/5

Step-by-step explanation:

First prime factor to get GCF:

36= 2 x 2 x 3 x 3

60= 2 x 2 x 3 x 5

GCF= 2 x 2 x 3 = 12

Therefore u divide each number by 12 to get your answer.

36/12=3     60/12=5

Fraction in lowest terms= 3/5

Answer: A i think

Step-by-step explanation:

The answer to the question is 3√10.

The concept used here is radical expressions

Radicals, like fractions, are often simplified till you have got the littlest attainable elements. 

Be conscious of what numbers square measurewithin the unconventional sign and that square measure not! Unless you'll be able to take the rootof the individual prime numbers, they have to stay beneath the unconventional.The same methodworks for variables beneath the unconventional.

On multiplying  5 and 18 we get expression as -√90

90 can be rewritten as 9×10

9 can further be written as 3²

On simplifying we get √9×10

Since 9 is the square root of 3 we can take 3 outside the square root sign.

So the final answer is 3√10.

Learn more about Square root here-https://brainly.com/question/3617398

#SPJ9

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

Work Shown:

[tex]\sqrt{\frac{81}{100}}\\\\\\\frac{\sqrt{81}}{\sqrt{100}}\\\\\\\frac{\sqrt{9^2}}{\sqrt{10^2}}\\\\\\\frac{9}{10}\\\\\\[/tex]

Therefore,  [tex]\sqrt{\frac{81}{100}}=\frac{9}{10}\\\\\\[/tex]

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

Explanation:

I broke up the single square root to make a fraction of square roots. Then I rewrote 81 as 9^2, and 100 as 10^2. This is so the square roots cancel out with the squares.

The general rule is that [tex]\sqrt{\text{x}^2} = \text{x} \ \text{ , where x} \ge 0[/tex]

We'll use 3/8 cup of macadamia nuts.

Describe ratios.

A ratio is defined as a/b where b is not equal to 0. Since a and b are separate portions of the two values, the total combined amount is expressed as (a + b).

Given:

3/4 cup of macadamia nuts are used in a banana macadamia nut bread recipe that Vincent created. We are aware of this based on the information provided.

The quantity of nuts needed if he decides to make only half the recipe is:

used macadamia nuts = 1/2 * 3/4

used macadamia nuts =3/8

Therefore, there will be 3/8cup of Macadamia nuts utilized.

To learn more about ratio visit:

https://brainly.com/question/1504221

The correct question is given below

"Vincent found a recipe for banana macadamia nut bread that uses 3/4 cup of macadamia nuts. If he only wants to make half the recipe, how many cups of macadamia nuts should be use?"

Carolyn will win the contest as the money raised by her is more than the money raised by Gershon.

We are given that:

For Carolyn:

Money given by parents = $ 100

Money she raises every day = $ 15

For Gershon:

Money given by parents = $ 50

Money he raises every day = $ 15

Let the number of days a contest lasts be x.

So, the equations for both will be:

For Carolyn:

100 + 15 x

For Gershon:

50 + 15 x

By comparing, we get that:

Money raised by Carolyn > Money raised by Gershon.

Therefore, we get that, Carolyn will win the contest as the money raised by her is more than the money raised by Gershon.

Learn more about equation here:

https://brainly.com/question/1214333

#SPJ9

After solving the equation, x = 15 is the value of x in 5-3x = -40 .

⇒ 5 - 3x = -40

⇒ - 3x = -40-5

⇒ - 3x =  -45

⇒ 3x = 45

⇒ x = 45/3

⇒ x = 15

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

Learn more about  linear equations

brainly.com/question/14323743

#SPJ4

Answer:

[tex] \sf \: x ≤ \frac{11}{6} \: or \: x> \frac{11}{3} [/tex]

Step-by-step explanation:

First question

6x-2≤9

Step 1: Add 2 to both sides.

6x−2+2≤9+2

6x≤11

Step 2: Divide both sides by 6.

6x/6 ≤ 11/6

x≤11/6

Second question

4+3x>15

Step 1: Simplify both sides of the inequality.

3x+4>15

Step 2: Subtract 4 from both sides.

3x+4−4>15−4

3x>11

Step 3: Divide both sides by 3.

3x/3 > 11/3

x> 11/3