If f (x) = 2x2 + 3 and g(x) = *2 - 7, find (f + g)(x).

A polynomial more than 3 terms is read as trinomial.

A polynomial is an equation that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates.

Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.

hence, a polynomial more than 3 is trinomial or cubic.

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Based on the gallons of apple juice brought by the students, and the serving per gallon, the number of students that would have some apple juice is  15 students

First, find the total amount of juice that the students brought of apple juice:

= 1 ½ + 3 ½

= 3/2 + 7/2

= 10 / 2

= 5 gallons

If each serving is in a 1/2 cup, then the number of students that would be able to get some apple juice is:

= Number of gallons of juice / Number of cups per serving

= 5 ÷ ⅓

= 5 x 3/1

= 15 / 1

= 15 students

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From the given figure a pair of lines that appear to parallel are AG and CJ.

The line segments AG, BH and CJ and DF is transversal.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

12. A pair of lines that appear to parallel are AG and CJ.

13. A perpendicular is a straight line that makes an angle of 90° with another line.

Here, the perpendicular lines are DF and BH.

14. When two or more lines meet at a common point, they are known as intersecting lines. The point at which they cross each other is known as the point of intersection.

Here, AG and DF, BH and DF, CJ and DF are intersecting lines.

Therefore, from the given figure a pair of lines that appear to parallel are AG and CJ.

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Answers:

Zeros: -2 and 1

Factored form: P(x) = (x+2)(x+2)(x-1)

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

Explanation:

One way to show that c = -2 is a zero or root of P(x) is to plug it in as the x value and simplify. If we get P(x) = 0, then that input is a root.

P(x) = x^3+3x^2-4

P(-2) = (-2)^3+3(-2)^2-4

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

P(-2) = -8+12-4

P(-2) = 4-4

P(-2) = 0

In short, the input x = -2 leads to the output P(x) = 0.

This confirms -2 is a root of P(x). By extension, this tells us that (x+2) is a factor of P(x).

We can determine the other factor using synthetic division as shown in figure 1. See the image below.

The synthetic division table shows us getting a remainder of 0, as highlighted in yellow.

The other stuff in pink represents the coefficients of the quotient.

We have the coefficients 1, 1, -2 which forms 1x^2+1x-2 and that simplifies to x^2+x-2

This further factors to (x-1)(x+2) because we're looking for two numbers that a) multiply to -2 and b) add to 1. Use the FOIL rule to expand (x-1)(x+2) and you should get x^2+x-2 again. This helps confirm the factorization was done correctly.

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

In short, we found that P(x) = (x+2)(x^2+x-2) and it fully factors to P(x) = (x+2)(x+2)(x-1)

Each factor leads to a root.

x+2 = 0 leads to the root x = -2

x-1 = 0 leads to the root x = 1

Visually, each root is an x intercept where the curve either crosses the x axis or touches it before bouncing away. See figure 2 below.

If the researcher employs a repeated measures design with 15 participants per condition, the study will require 15 participants

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Answer:

0.45

Step-by-step explanation:

2.75+ 2.80= 5.55

6-5.55= 0.45

I hope this helps! :) If it does could you please mark me brainliest?

Answer:

Step-by-step explanation:

answer: 9/20

formulate 2 3/4 + 2 4/5 - 6

sorry if im wrong.

The fifth and the twenty fifth terms of the arithmetic sequence are a5 = - 45 and a25 = - 1725

A group of integers that are arranged in a particular order and share a difference between each term is known as an arithmetic sequence. For instance, the common difference between the numbers 3, 9, 15, 21, and 27 in mathematics is 6. The term "arithmetic progression" can refer to an arithmetic sequence..

The given expression is [tex]6n - 3n^2[/tex]

The 5th term that is n = 5

thus the given expression will become

[tex]6n-3n^2[/tex]

which is equal 6×5 - 3 (5)²

= 30 - 3 × 25

= 30 - 75

= - 45

The 25th term is n = 25

Thus the given expression that is [tex]6n-3n^2[/tex]

= 6 × 25 - 3× ( 25) ²

= 150 - 3 × 625

= - 1725

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There will be 6 two-digit numbers having an odd number of factors.

According to the question,

We have the following information:

There are two-digit numbers.

It means that the list of numbers is from 10 to 99.

Now, we have to find the numbers with the odd number of factors.

We know that odd numbers are the numbers which are not divisible by 2. For example, 1, 3, 5, etc. are odd numbers.

Note that 1 is also included as a factor.

Now, the numbers with odd number of factors will be the perfect squares as 1 will be added to them and the numbers will become odd.

So, the perfect two-digit square numbers are 16, 25, 36, 49, 64 and 81.

Now, we can prove that these numbers satisfy the given conditions by taking factor of any one number.

Let's take 25. The factors of 25 are 1, 5, and 5. So, in total there are 3 factors.

Hence, there are 6 two-digit numbers having an odd number of factors.

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Answer:

ignoring the decimal. The order from greatest to least is 2, 4, 5, 6, and 8

Solution

Given the probability of event A happening is P(A) = 7/10

the probability of event A not happening P(A') = 1 - 7/10 = 3/10

The answer is 3/10

Answer:

Q (- 1, 6 )

Step-by-step explanation:

use the midpoint formula to find the coordinates of M then equate the x and y coordinates with the actual coordinates of M

P (11, - 10) and let Q = (x, y ) , then

[tex]\frac{11+x}{2}[/tex] = 5 ( multiply both sides by 2 )

11 + x = 10 ( subtract 11 from both sides )

x = - 1

and

[tex]\frac{-10+y}{2}[/tex] = - 2 ( multiply both sides by 2 )

- 10 + y = - 4 ( add 10 to both sides )

y = 6

coordinates of Q = (- 1, 6 )

Step-by-step explanation:

7. the additive property of equality. we can add the same thing to both sides, and the equality stays true. it is like a balance with 2 cups. it is balanced, and we add the same weight to both sides. it remains balanced.

8. the commutative property of equality.

a = b, therefore b = a.

the simplest of all principles and properties.

imagine what would be the consequence, if that

were not true.

it would mean for example that you give the cashier in a store some money to pay for something, but the amount the cashier receives is not the same amount you have given the cashier. booom !

Using the properties of ratio and proportion we can find the value as  [tex]\frac{x+1}{x-1}[/tex] .

A theorem built on the idea of proportions enables a computation procedure that is speedier and requires fewer expansions.

The given ratio is of the form x = a /b

This can be written in the form of

[tex]\frac{x}{1} = \frac{a}{b}[/tex]

Now we have to find the value of [tex]\frac{a+b}{a-b}[/tex].

Using the componendo and dividendo rule we get:

Adding the denominator to the numerator to get the new numerator and subtracting the denominator from the numerator to get the new denominator.

Mathematically:

[tex]\frac{a+b}{a-b} = \frac{x+1}{x-1}[/tex]

Therefore this is the required result.

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The trash dumpster fee was 60 dollars.

The lengths of the base and height of the garden in the other scale drawing is 9.6 cm and 14.4 cm

The scale from a garden to the illustration is stated as 8 feet to 1 centimeter in the question. The drawing's base and height are each 2.4 cm long and 3.6 cm tall, respectively.

As a result, the lengths of the garden's base and height are, respectively, 2.4*8 ft (19.2 ft) and 3.6*8 ft (28.8 ft).

We now know that the scale is 2 feet to 1 centimeter between the same garden and another drawing.

Thus, the lengths of the base and the height of the other drawing are 19.2/2 cm. = 9.6 cm. and 28.8/2 cm. = 14.4 cm. respectively.

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Answer:

324

Step-by-step explanation:

1) substitute the 5 into the formula

n=5     [tex]a_{n}=4[/tex]×[tex]3^{5-1}[/tex]

2) simplify

5-1 = 4

[tex]3^4[/tex] = 81

4×81 = 324

Hope this helps, have a great day!

Answer:

5th term = 324

Step-by-step explanation:

[tex]a_n \: = \: 4 \: \cdot \: {3}^{n - 1} [/tex]

Where, n = 5

[tex]a_5 \: = \: 4 \: \cdot \: {3}^{5 - 1} [/tex]

[tex]a_5 \: = 4 \: \cdot \: {3}^{4} [/tex]

[tex]a_5 \: = 4 \: \cdot \: 81[/tex]

[tex]a_5 \: = \: 324[/tex]

Answer:

it should be a 90-degree angle or right triangle

Step-by-step explanation:

Composition Functions

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

The Solution.

Your company partially funds 85% of the total coverage. That gives

The percent of the insurance coverage that will be paid by you is

Thus, the correct answer is 15%.

Answer:

y = (3/2)x - 12

Step-by-step explanation:

The equation of a line is expressed in the form y = mx + c, where m is the gradient (slope) and c is the y-intercept. Simply substitute your values into this form:

y = (3/2)x - 12

Answer:

The answer is -71.124

Step-by-step explanation:

Since there is a subtraction sign next to a negative it becomes addition.

so the equation becomes -95.004 + 23.88 which were going to flip around to 23.88 - 95.004

So,

     23.880

  -  95.004

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

       -71 .124

If Mandi has 8 dog biscuits, she has 7 dog bowls and each dog bowl gets the same number of dog biscuits, then the number of dog biscuits in each bowl is 1.14 biscuits

Number of dog biscuits that Mandi has = 8 dog biscuits

Number of dog bowls that Mandi has =  7 dog bowls

Each dog bowl get the same number of dog biscuits.

To find the number of dog biscuits in each bowl we have to do the division

Number of dog biscuits in each bowl = Number of dog biscuits that Mandi has ÷ Number of dog bowls that Mandi has

Substitute the values in the equation

= 8/7

= 1.14 biscuits

Hence, if Mandi has 8 dog biscuits, she has 7 dog bowls and each dog bowl gets the same number of dog biscuits, then the number of dog biscuits in each bowl is 1.14 biscuits

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Given:

17 people apply for the position of an engineer.

22 people apply for the position of a manager.

Number of ways to fill the positions is 374.

The requested probability is 0.99974

The likelihood of an event happening is gauged by probability. Many things are impossible to completely predict in advance. Only the likelihood of an event occurring, or how probable it is to happen, can be predicted using probability. Tossing a coin, for instance, has a chance of coming up heads or tails.

TOTAL NUMBER OF POSSIBLE HANDS..

WE HAVE 52 CARDS WITH 4 SUITS AND 13 CARDS PER SUITE.

WHEN WE ARE DEALT A 5 CARDER, DISREGARDING THE ORDER OF DEAL,WE HAVE

C[52,5] TOTAL NUMBER OF POSSIBLE HANDS =52!/[47!×5!]=[52× 51 × 50 ×49× 48× (47!) ]/[5! ×47!]=

=[52× 51× 50× 49×48]/ [5!] = 2598960

ROYAL FLUSH

THIS COULD BE OF ANY SUIT ...

SO WE HAVE 4 POSSIBILITIES

ONCE A SUIT IS CHOSEN THE THEN THE OTHER POSSIBILITY IS TO ONLY GET

A,K,Q,J,10 IN THAT SUIT, OF EACH OF WHICH, THERE IS ONLY ONE CARD IN THE PACK

SO THERE IS ONLY 1*1*1*1*1=1 WAY

SO TOAL NUMBER OF POSSIBILITIES ARE 4^ * 1 = 4 WAYS

SO PROBABILITY = 4/2598960 = 0.00000154 ..........ANSWER

PROBABILITY = 0.00000 ...ANSWER

TWO PAIR OR BETTER

THERE ARE ...4+36+624+3744+5108+10200+54912+123552-198180

HENCE PROBABILITY = 198180/2598960=0.0762536

-0.07625...........ANSWER

WE CAN GET 4 OF A KIND OR BETTER IN 4+36+624= 664 WAYS

SO LOSING HANDS TO 4 OF A KIND ARE =2598960-664-2598296

SO PROBABILITY = 2598296/2598960-0.9997445

=0.99974...........ANSWER

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Answer:

if there are 12 cubes, there must be 3 rows of 4 since its a prism. 1288 square root is 35. something

Step-by-step explanation: