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The binomials shown below will be multiplied to produce a quadratic trinomial. (x + p)(x + q) Which part of the trinomial will equal the sum of p and q? A. The constant term B. The coefficient of the x-term C. The degree D. The coefficient of the x2-term

I believe the correct answer from the choices listed above is option B. The part of the trinomial will equal the sum of p and q would be the coefficient term. We do it as follows:

(x + p)(x + q)
x^2 + px + 1x +pq
x^2 + (p+q)x + pq

Hope this answers the question. Have a nice day.

Related Questions

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If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial. true or false

The Factor theorem states that  for any polynomial f(x) if f(c)=0 then x-c is a factor of the polynomial f(x).

If any polynomial f(x) is divided by x-a and remainder is 0 that means f(a)= 0 .In other words we can say x-a is a factor of the polynomial f(x).So the statement :If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial is True.

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4. Which of the following sets of numbers is a Pythagorean triple? A. 4, 5, 6 B. 8, 15, 17 C. 5, 12, 14 D. 8, 24, 25 Suppose a triangle has side lengths 6, 7, and 10. Which of the following best describes this triangle? A. obtuse B. acute C. right D. Cannot be determined.

Here are the answers to the given questions above:
4. When we say pythagorean triple, this would consists of three positive integers a, b, and c, such that a2 + b2 = c2. So for the given numbers above, the set that is considered a pythagorean triple would be B.  8, 15, 17.
5. The correct answer for this question would be option D. It cannot be determined whether the triangle is obtuse, acute or right if the given values are the side lengths. It should be angles. Hope this answer helps.

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For f(x)=2x+1 and g(x)=x^2-7, find (f-g)(x)

I hope this helps you

(f-g)(x)=2x+1-(x^2-7)

(f-g)(x)=2x+1-x^2+7

(f-g)(x)= -x^2+2x+8

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A quadratic equation is shown below: 9x2 - 36x + 36 = 0 Part A: Describe the solution(s) to the equation by just determining the discriminant. Show your work. (3 points) Part B: Solve 2x2 - 9x + 7 = 0 using an appropriate method. Show the steps of your work and explain why you chose the method used.(4 points)

For part A:
9x² - 36x + 36 = 0
9(x² - 4x + 4) = 0
9(x-2)(x-2) = 0
Radicand = Discriminant = 36² - 4(9)(36) = 0
there is 1 real zero that repeats itself)

zero is x=2.

Use factoring. Factors of 7 are 1 and 7
2x²-9x+7 = 0

(2x-7)(x-1) = 0
2x-7 = 0              (x-1)=0
2x = 7x=1
x = 7/2
Your solutions are x = 1 and x = 7/2

I hope my answers helped you

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Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h? h = (– b)÷ r h = – b ÷ r h = ÷ r – b h = ÷ r

For the answer to the question above, first we must enlist the given

p = take home pay
r = rate of dollars per hour
h = number of hours worked
b = bonus

So now we can find h and let us start with the formula.

p = 0.7(rh + b)

p = 0.7*r*h + 0.7b

p - 0.7b = 0.7rh

So the answer for this problem is

h = (p-0.7b)/0.7r

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The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, which system of inequalities could represent the values of a and b? A. a + b ≥ 30 b ≥ a + 10 B.a + b ≥ 30 b ≤ a – 10 c. a + b ≤ 30 b ≥ a + 10 D. a + b ≤ 30 b ≤ a – 10

I believe the correct answer from the choices listed above is option A.  If b is the greater integer, then the system of inequalities that could represent the values of a and b would be a + b ≥ 30 and b ≥ a + 10. Hope this answers the question. Have a nice day.

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1. Which set of ordered pairs in the form of (x,y) does not represent a function of x? (1 Point) A. (1, 1.5), (2, -1.5), (3, 1.5), (4, 1.5) B. (0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5) C. (1, 1.5), (-1, 1.5), (2, 2.5), (-2, 2.5) D. (1, 1.5), (-1, -1.5), (2, 2.5), (-2, 2.5)

Based on the given set of ordered pairs above, the set of ordered pairs in the form of (x,y) that does not represent a function of x would be option B. Why is this so? if you notice, the number 1 in the x is being repeated so this means this is not a function. Hope this answer helps.

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Drey makes \$10 an hour plus \$15 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week. Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. Part C: Drey earned \$490 in 1 week. How many hours (regular plus overtime) did he work?

For the answer to the question above, let us solve the first for
Part A. \$10 x 40 hours= \$400 (\$10x = W) X= 40 hours a week

Part b. \$10 x 40 hours = \$400 + \$15 x Y=S (\$10x=\$400 +\$15y=S) Y= number of hours overtime. Since he gets \$15 for working more than 40 hours you take the number of hours over time and multiply it by 15.

Part c.  Now that he made \$490 in 1 week you know that he worked for 40 hours at a rate of \$10 an hour. But that's only \$400, so we need to figure out 15 times what is equal to 90. 15 times six is equal to 90 which means that Drey worked for 46 hours

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What is f(x) = 2x2 + 28x – 5 written in vertex form?

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. We do as follows:

f(x) = 2x^2 + 28x – 5
f(x) = 2(x^2 + 14x) – 5
f(x) = 2(x^2 + 14x + 49) – 5 - 98
f(x) = 2(x + 7)^2 – 103

Hope this answers the question. Have a nice day.

Posted in Mathematics

Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?

For the answer to the question above, I'll show my to solution to the answer below.
average rate of change is
(f(5) - f(1))/(5 - 1) =

(17 - 5^2 - (17 - 1^2))/4 =

(17 - 25 - 17 + 1)/4 =
So the answer for this problem is
-6
I hope my answer helped you. Feel free to ask for more questions.

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Match Term Definition Line Segment A) a series of points that extend in two directions without end Plane B) two lines that intersect at 90° angles Perpendicular Lines C) lines that lie in the same plane and do not intersect Line D) a flat surface that extends infinitely and has no thickness Parallel Lines E) part of a line that has two endpoints

The correct matches are as follows:

Line Segment
E) part of a line that has two endpoints

Plane
D) a flat surface that extends infinitely and has no thickness

Perpendicular Lines
B) two lines that intersect at 90° angles

Line
A) a series of points that extend in two directions without end

Parallel Lines
C) lines that lie in the same plane and do not intersect

Hope this answers the question. Have a nice day.

Posted in Mathematics

A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that best represents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer. Hint: Use the formula, f(x) = P(1 + r)x

For the answer to the question above, I think the formula you is wrong. The x must be in exponential form. It must look like this

f(x) = P(1 + r)^x
Now we can solve.

Given:
P = 2000
r = -0.06

f(x)  =  2000 (1 - 0.06)^x
=  2000 (0.94)^x

2000 (0.94)¹² =

2000 (0.476)  =
951.8 square kilometers.

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The sum of the angle measures of any triangle is 180 degrees. Suppose that one angle in a triangle has a degree measure of 7x+3 and another has a degree measure of 3x-6 . Write an expression for the degree measure of the third angle in the triangle.

The sum of the angle measures of any triangle is 180 degrees. It should be that a + b + c = 180. For this problem, we are given the two angles which we assume to be a and b so,

180 =
7x+3 + 3x-6 + c
c = 180 - (
7x+3 + 3x-6)
c = 180 - (10x - 3)
c = 177 - 10x

Hope this answers the question. Have a nice day.

Posted in Mathematics

Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Check all that apply. + 8r2s4 – 3r3s3 s5 3r4s5 –r4s6 –6rs5

Option 2,3 and 4 are correct.

Step-by-step explanation:

To find : Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Check all that apply.

Solution :

The polynomials in standard form is written from higher degree to lower degree i.e. in descending order.

The given polynomial has degree 6: , and it can be ordered respect any of the two variables either r or s.

Adding a new term as first term needs to have degree equal or greater than 6.

1) cannot use as first term because its degree is less than 6.

2) it can be use as degree is 9.

is the standard form.

3) it can be use as degree is 10.

is the standard form.

4) it can be use as degree is 6.

is the standard form.

Therefore, Option 2,3 and 4 are correct.

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The product of a + 3 and –2a2 + 15a + 6 is –2a3 + xa2 + 51a + 18. What is the value of x? a. 3 b. 9 c. 12 d. 15

9

Further explanation

Given:

The product of

Question:

What is the value of x?

Problem solving:

We will solve the case about the distributive property of multiplication.

Let's rewrite and arrange the multiplication equation as follows.

Work out the multiplication of terms carefully.

Note the coefficient of the term a² on the left-hand side. Let us equate with a similar term on the right side.

Let us cross out a².

Hence, the value of x is 9.

1. Factoring methods brainly.com/question/2568692
2. Changing the subject in a formula brainly.com/question/291105
3. All the steps to get R as a subject  brainly.com/question/4703807#

Keywords: the product, the value of x, the distributive property of multiplication, the coefficient of the term a²

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What is the range of the function f(x) = 3x2 + 6x – 9

I have a solution here however with a slight change in the equation:

f(x)=3x^2-6x+1

My solution is:

The domain is all real numbers--there are no restrictions like a square root or variable in the denominator

this is a U shape parabola and you want to find the bottom point, it is at the vertex

x=-b/2a =- (-6) /2 (3) =1
f(1) =3(1)^2 -6(1) +1 =3-6+1 =-2
the minimum is (1, -2)
so the range is all real numbers >= -2

By examining my solution, you could just answer the problem on your own! I hope it helps!

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Find the multiplicative inverse of 6 + 2i.

The solution to the problem is as follows:

First thing to do is get rid of the i. Multiplying by 6 - 2i will do this

( 6 + 2i)(6 - 2i) = 6^2 - (2i)^2 = 36 - 4(-1) = 36 + 4 = 40

Dividing by 40 gets you 1

(6 + 2i) (6-2i)/40 = 1

The answer is (6 - 2i)/40 = (3 - i)/20

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

Solve the equation for y 2x+6y=13

So here is how we are going to solve for y for the given equation above:
2x+6y=13
Next, transfer 2x to the right side and it will look like this:
6y=13-2x
Now, divide both sides by 6, and it will look like this:
y=13-2x
--------
6
So, this is the final answer for y.

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Which of the binomial is a factor of this trinomial x2-7x-44?

I hope this helps you

x^2-7x-44

x -11

x +4

(x-11)(x+4)

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What is 20 time 4 equal?

20 x 4 = 80

hope this helps you

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The y-coordinate of the y-intercept is the _____ term in the equation of the line.

For the answer to the missing term in the question above, the question is as simple as its answer. The right answer is constant.
I hope my answer helped you. Feel free to ask more questions. Have a nice day!

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What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12? (–∞, –3] [–3, ∞) (–∞, 15] [15, ∞)

The solution to the problem is as follows:

solve for x :

−3(6−2x)≥4x+12

−18+6x≥4x+12

2x≥30

x≥15

So the answer is D ) 15 to +infinity

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

Which CANNOT be used in a proof? A. Theorems B.Postulates C.Properties D.Undefined Terms

The best and most correct answer among the choices provided by the first question is the fourth choice or letter D.

Undefined terms cannot be used as a proof in mathematics.

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

Which of the following is the statement of the triangle inequality theorem? A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle. B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. C. The longest side of a triangle is opposite the largest angle. D. The largest angle of a triangle is between the two longest sides.

we know that

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

Let

a,b,c------> the length sides of a triangle

The theorem states that three conditions must be met

case 1)

case 2)

case3)

therefore