A company produces items in small batches. The machinery needs to warm up before the items can be produced. The scatterplot show the time needed to produce batches of different number of items.

Answer:

The simplest form is [tex]\frac{x+2}{x^2+2}[/tex]

Explanation:

The given is: [tex]\frac{x^2 + x-2}{x^3-x^2+2x+2}[/tex]

1- For the numerator:

[tex]x^2+x-2[/tex] can be factorized to give (x-1)(x+2)

2- For the denominator:

[tex]x^3-x^2+2x-2[/tex]

We will factor this using grouping

Take [tex]x^2[/tex] as a common factor from the first two terms and [tex]2[/tex] as a common factor from the last two terms

This will give us:

[tex]x^3-x^2+2x-2[/tex] [tex]=x^2(x-1) + 2(x-1)[/tex]

Now, take (x-1) as a common factor:

[tex]x^3-x^2+2x-2[/tex] = (x-1)(x²+2)

3- Finally, getting the simplest form:

[tex]\frac{x^2+x-2}{x^3-x^2+2x-2}=\frac{(x-1)(x+2)}{(x-1)(x^2+2)}=\frac{x+2}{x^2+2}[/tex]

Hope this helps :)

The solution is [tex]\frac{x+2}{x^2+2}[/tex]

See the image attached

Answer:

1.08c or c + 0.08c

Step-by-step explanation:

The price of any used car plus 8% tax can be found by writing an expression. You can write an expression using a variable c where c is the price of the car. You will pay the 100% the whole price of the car and add on 8% of the price as tax. This means you pay 100 + 8 = 108% of the price c. This is 1.08c. Or you can also write it as c + 0.08c.

Given:

Brian scored 154 more than Colin

Colin’s score=141

Let Brian’s score be x

x= Colin’s score+ 154

x= 141 + 154

x=295

Brian’s score=x=295

Combined score= Brian’s +Colin’s

Combined score= 436

They have a combined score of 436 points

Data;

Let's write an equation showing Brain's score

[tex]x = 141+ 154\\x = 295[/tex]

Brain's score is equal to 295 points.

The sum of their combined score would be

Collin + Brain

[tex]141+295=436[/tex]

They have a combined score of 436 points.

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Answer:

48 X 3= 144 miles

Step-by-step explanation:

Answer:

144 miles

Step-by-step explanation:

First, let's use the distance formula which is distance = rate*time.

We know the rate is 48 miles and the time is 3 hours so if you were to plug it in to the formula you'd get distance = 48*3.

When you multiply 48 by 3 you get 144 which will be the distance.

➷ Just substitute 3 in:

2(3)^2 = 18

It would be 18

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Answer:

36

Step-by-step explanation:

2*3

6^2

6*6 = 36

Answer:

The standard form of the equation is y = 2x^2 + 16x + 25

Step-by-step explanation:

To find the standard form, first square the parenthesis.

y = 2(x + 4)^2 - 7

y = 2(x^2 + -8x + 16) - 7

Now distribute the 2

y = 2(x^2 + 8x + 16) - 7

y = 2x^2 + 16x + 32 - 7

Now combine like terms

y = 2x^2 + 16x + 32 - 7

y = 2x^2 + 16x + 25

Answer:

y = 2x^2 + 16x + 25

Answer:

y    = (5/4)x - 4

Step-by-step explanation:

As we move from (0, -4) to (4, 1), x increases by 4 and y increases by 5.

Thus, the slope of the line segment connecting these two points is

m = rise / run = 5/4.

Subbing these knowns into the point-slope formula for the equation of a straight line, we get:

y - 1 = (5/4)(x - 4), or

y     = (5/4)x - 5 + 1, or

y    = (5/4)x - 4

Let's check this out.  Determine whether or not (0, -4) satisfies the equation:

-4 = (5/4)(0) - 4

Yes, this is true; the equation is correct.

[tex]\huge\boxed{\text{$17$ miles}}[/tex]

This is a fairly simple problem. Just add all of the miles together:

[tex]\begin{array}{c}4+5+3+5\\9+8\\\boxed{17}\end{array}[/tex]

Answer:

17 miles in all.

Step-by-step explanation:

4+5+3+5=17

Answer:

15 cm

Step-by-step explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

[tex]\frac{BC}{EF} =\frac{AC}{DF}[/tex].

[tex]\frac{18}{x}=\frac{12}{10}[/tex]

To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

[tex]\frac{18}{x}=\frac{12}{10}\\ 18*10 = x*12 \\ 180 = 12x \\ 15 = x[/tex]

Answer:

two $20 and five $10

He has three $20 and four $10. Hope this helps!

Answer:

Choice 3

Step-by-step explanation:

Using V = πr^2 h

Choice 1. π2^2x6 = 75.4

Choice 2. π2.5^2x5 = 98.17

Choice 3. π3^2x4 = 113.1

Choice 4.  π3.2^2x3 = 96.51

[tex] {8}^{2} + {15}^{2} = 64 + 225 = 289 \\ {17}^{2} = 289 \\ \Rightarrow {8}^{2} + {15}^{2} = {17}^{2} \\ \Rightarrow A \: right \: triangle[/tex]

Answer:Yes

Step-by-step explanation:

a^2 + b^2 = c^2

C is the hypotenuse which is the longest side, b is the second longest and a is the shortest one

3 to a negative 3 would be 1/3^3 and then simplify to 1/27 so your answer is D

I can't read number 15, but number 16 is C

Step-by-step explanation:

1 1/3x=-8/3

Answer:

x=−2 is the answer

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2/3(x - 4) = 2x

(2/3) (x) + (2/3) (-4) = 2x      Distributed

2x/3  +  -8/3 = 2x

Step 2: Subtract 2x from both sides.

2x/3 + -8/3 = 2x

(2x/3) (-2x/1)  + -8/3 =0

-4x/3 + -8/3 = 0

Step 3: Add 8/3 to both sides.

-4x/3 = 8/3

Step 4: Multiply both sides by 3/(-4).

(3/-4)  (-4x/3) = ( 3/-4)  (8/3)

X= -2 because 3 x 8= 24   and  -4 x 3 = -12

24 Divided by -12 give -2

Hopes this helps!

ok if i am right  their are 0.3333 yards in a foot so if their is 14 feet it would be 4.66667

so your answer would go to the 4 1/2

Answer:

14 ft  >  4 1/2 yd.

Step-by-step explanation:

1 yard = 3 ft

so

4 1/2 yard = 4.5 x 3 = 13.5 ft so it's less then 14 ft or 14 ft is greater than 13.5 ft

answer

14 ft  >  4 1/2 yd.

3097 is the value you get when rounded off to nearest whole number

Answer:

C. [tex]x>0[/tex]

Step-by-step explanation:

Given: [tex]f(x)=log(8x)[/tex]

To find the domain of a logarithmic function, we need to take the argument, 8x, and set it greater to zero. This is because an argument of a logarithmic function cannot be zero or negative.

[tex]8x>0[/tex]

[tex]x>0[/tex]

So since x is greater than zero, we have just found out our domain:

Interval Notation: (0, ∞)

Set Notation: {[tex]x|x>0[/tex]}

The domain of the logarithmic function is,

⇒ x > 0

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that:

The function is,

⇒ F (x) = log₈ x

Now, To find the domain of a logarithmic function, we need to take the term, 8x, and set it greater to zero.

This is because an argument of a logarithmic function cannot be zero or negative.

Hence, We get;

8x > 0

x > 0

Thus, The domain of the logarithmic function is,

⇒ x > 0

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Answer:

[tex]1,125\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the triangular prism that will be covered with insulation is equal to the area of the two triangular faces plus the two lateral rectangular faces

so

[tex]SA=2[\frac{1}{2}(15)(15)]+2[(30)(15)]= 1,125\ ft^{2}[/tex]

Answer:

Top- 23 square cm

Bottom- 172.5 square m

Step-by-step explanation:

Let me know if you need an explanation

Answer:

yes

Step-by-step explanation:

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Answer:

Radius Squared

Step-by-step explanation:

Following answer is Pi

The area of a circle is π times the square of its radius.

A circle is a locus of a point in a plane such that its distance from a fixed point always remains constant. This fixed point is called the centre of the circle while the distance between the centre and the moving point is called the radius of the circle.

The area of a circle is given by [tex]A=\pi r^{2}[/tex]

Where [tex]\pi[/tex] is an irrational number with a value of 3.14159...... and r is the radius of the circle.

So, the area of a circle is π times the square of its radius.

Hence, the area of a circle is π times the square of its radius.

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f(5) is basically another way of saying x = 5, so we can plug 5 as x into the equation.

3(5) + 2

The answer is D. 17

Answer:

f(5) is basically another way of saying x = 5, so we can plug 5 as x into the equation.

3(5) + 2

The answer is D. 17

Step-by-step explanation:

QUESTION 4.

The given function is [tex]f(x)=48x^2-32x[/tex].

The highest common factor is [tex]16x[/tex].

We factor to obtain;

[tex]f(x)=16x(3x-2)[/tex]

QUESTION 5

The given function is

[tex]g(x)=20x^2-8x[/tex]

The highest common factor is 4x.

We factor to obtain;

[tex]g(x)=4x(5x-2)[/tex]

QUESTION 6.

The given function is [tex]h(x)=42x^3-35x^2[/tex].

The highest common factor is 7x.

We factor to obtain;

[tex]h(x)=7x^2(6x-5)[/tex]

Answer:

I believe your answer is 429.

Step-by-step explanation:

5 1/2 x 6 1/2 x 12 = 429

Answer:

6-n

Step-by-step explanation:

it is subtracting a number from 6

I hope this helps!

6-n because n is equivalent to a number

Answer:

B. She multiplied the dividend by 100 instead of 10.

Step-by-step explanation:

Ella had to divide[tex]1.848[/tex] by [tex]0.6[/tex]. To make it easier to divide, she thought of multiplying both the dividend and the divisor by 10.

Ella multiplied the divisor by 10 but mistakenly she multiplied the dividend by 100 instead of 10.

So her division problem changed totally.

Therefore, the correct answer option is B. She multiplied the dividend by 100 instead of 10.

Answer:

John gave Fred $48

Step-by-step explanation:

Let

x be the amount of dollars John gave fred

y1 be the amount of dollars Fred has at the end

y2 be the amount of dollars John has at the end

Fred has

y1 = - $12 + x

John has

y2 =  $84 - x

y1 = y2

- $12 + x =  $84 - x

2*x = $96

x = $48