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Posted in Mathematics

Which polynomial expression represents the area of the outermost square tile, shown below? A square shaped tile with length x plus three is shown x2 + 6x + 6 x2 + 9x + 6 x2 + 6x + 9 x2 − 6x + 9


I believe the correct answer from the choices listed above is the third option. The polynomial expression that represents the area of the outermost square tile would be x^2 + 6x + 9. The area of a square is calculated by the square of its side and the side of this square is given as x+3.

A = (x+3)^2 = x^2+6x+9

Related Questions

Posted in Mathematics

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.

Posted in Mathematics

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.

Posted in Mathematics

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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Posted in Mathematics

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

Posted in Mathematics

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

Posted in Mathematics

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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Posted in Mathematics

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.

Posted in Mathematics

Which test point holds true for y − 2x ≤ 1? (0, 2) (-2, 4) (1, 4) (5, 0)

So in order to find the correct answer, we can just easily plug in the values to check which ordered pair matches the given inequality above. So based on my solutions, the correct answer would be the last pair. 
 y − 2x ≤ 1
0 - 2(5)
 ≤ 1
0-10  ≤ 1
-10  ≤ 1
Hope this answer helps.

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Posted in Mathematics

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm? 4x < h < 10x 10x < h < 4x h = 4x h = 10x

Answer with explanation:

In a triangle sum of two sides , should always be greater than the third side.

Sides of the given triangle are, 3 x cm, 7 x cm and h cm.

1.

3 x + 7 x > h

→ 10 x > h

2.

3 x+ h > 7 x

→h > 7 x -3 x

→h> 4 x

3.

7 x + h > 3 x, which will be always true.

Combining 1, 2 and 3 we get

→4 x < h < 10 x

Option A

Posted in Mathematics

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

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)  = 
The answer is 
951.8 square kilometers.
                   

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Posted in Mathematics

What step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?

Mmk sweetie, if you have a compass and straightedge, you can totally do this! I'm going to try to talk you through this, it's not too hard: 

1. Take your straightedge (like a ruler or the side of a folder or notebook) and draw five lines on a piece of paper, just make sure none of them aren't the exact same size (not too hard.) 

2. Now you want to make segments the same length as your original lines. This is great, because you have a compass, and compasses are great at keeping the length of things! Open your compass and put the pointy end at one side of your first segment. Now open it until the pencil end is at the other end--you now have the length of your first segment (lock your compass, or be really careful with it to make sure it doesn't change how far open it is.) Next, on your new paper, where you're putting the congruent segments, draw a point. Put the pointy end of your compass on the point, then make a small, curved mark with the pencil side. Take your straight edge, and connect your point to any point on that small, curved line. Do this for all 5 of your lines. 

3. Remember that your compass keeps track of how long something is, so in order to figure out which ones are least (shortest) to greatest (longest) just look at how far you had to open your compass. The one where you had to open it very little is your least, and the one where you opened it very widely is your greatest, the others fall in between. 

4. Okay, this part sounds tricky but really is not. Choose what segment you want to double. Once more, put the pointy end at one point on the compass and open it so that the pencil part goes to the other end, lock your compass. Just like you did before, draw a point, put your pointy end of the compass on that point, now instead of making a small mark like you did before, swing your pencil all the way around your point, you will have created a circle with a radius of your original line. Now, take your straightedge and draw a line connecting one side of the circle to the other side, going through your original point--congratulations! You've just doubled your line segment. 

5. Again, this one sounds harder than it is, and there's probably a lot of ways to do it. Here's how I suggest--First, make a copy of your longest segment in the way described in #3, but draw your line lightly. Second, open your compass to the length of your smallest segment. Now instead of drawing a new line, put the pointy end on ONE point of your COPY of your longest segment, and swing to make a mark on the line you just created. Now, connect your mark from your short segment, to the other end of your longest segment, and voila! You've now created a segment equal to the difference between the two. Hope this helped!

Posted in Mathematics

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.

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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

Answer:

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.

?+8r^2s^4-3r^3s^3

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: ?+8r^2s^4-3r^3s^3, 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) s^5 cannot use as first term because its degree is less than 6.

2) 3r^4s^5 it can be use as degree is 9.

3r^4s^5+8r^2s^4-3r^3s^3 is the standard form.

3) -r^4s^6 it can be use as degree is 10.

-r^4s^6+8r^2s^4-3r^3s^3 is the standard form.

4) -6rs^5 it can be use as degree is 6.

-6rs^5+8r^2s^4-3r^3s^3 is the standard form.

Therefore, Option 2,3 and 4 are correct.

Posted in Mathematics

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 \boxed{ \ a + 3 \ and \ -2a^2 + 15a + 6 \ is \ -2a^3 + xa^2 + 51a + 18. \ }

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.

\boxed{ \ (a + 3)(-2a^2 + 15a + 6) = -2a^3 + xa^2 + 51a + 18. \ }

Work out the multiplication of terms carefully.

\boxed{ \ a(-2a^2 + 15a + 6) + 3(-2a^2 + 15a + 6) = -2a^3 + xa^2 + 51a + 18. \ }

\boxed{ \ -2a^3 + 15a^2 + 6a -6a^2 + 45a + 18 = -2a^3 + xa^2 + 51a + 18. \ }

\boxed{ \ -2a^3 + 9a^2 + 51a + 18 = -2a^3 + xa^2 + 51a + 18. \ }

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

\boxed{ \ 9a^2 = xa^2 \ }

Let us cross out a².

Hence, the value of x is 9.

Learn more

  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

Posted in Mathematics

Which ordered pair is a solution of the equation 2x − y = 9 (-4,1) (-2,5) (5,1) (6,-3)

In order to confirm if which ordered pair is a solution of the given equation above, we can just simply plug in the values.
So based on my solution, the correct answer would be the third option: (5,1) 
So let us try to plug in the values.
2(5) - 1 = 9
10 -1 = 9
9 = 9
So this is the correct one. Hope this answers your question.

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Posted in Mathematics

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!

Posted in Mathematics

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.
Hope this answers your question. Have a great day!

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Posted in Mathematics

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)

Posted in Mathematics

The soccer team voted on what they wanted to eat. there are 20 members on the team. six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs. which ratio represents the number of votes for hot dogs to chicken

Since there are 20 members in the soccer team. Then six members voted to eat pizza and 10 member voted to eat chicken and the rest is hotdog

Member voted for hotdog = 20 – 10 – 6 = 4

Ratio for hotdog to chicken is 10 : 4 or 5:2

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Posted in Mathematics

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

Identify the expression as a numerical expression or a variable expression. For a variable expression, name the variable. 1 × 12 A. numerical expression B. variable expression; a is the variable. C. variable expression; there is no variable. D. variable expression; l is the variable.

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

The expression above is an example of a numerical expression.


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

Posted in Mathematics

Convert 1.50 μm² to square meters.

The solution to the problem is as follows:

  1∙5µm² = ? m² 

1m * 1m = 1m² 
But 1m = 1,000,000µm = 1x10^6µm 
1x10^6µm * 1x10^6µm = 1m² 
1x10^12µm² = 1m² (Now, divide both sides by 1x10^12). 
1x10^12µm² /(1x10^12) = 1m² /(1x10^12) 
1µm² = 0∙000 000 000 001 m² (x both sides by by 1∙5). 
1∙5µm² = 0∙000 000 000 0015 m²
 
1∙5µm² = 1∙5x10^-12 m²


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

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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)

 a+b > c

case 2)

 a+c > b

case3)

 c+b > a

therefore

the answer is the option

B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Posted in Mathematics

Algebraic terms are separated by ______. Choose all that apply. 1)= 2)+ 3)x 4)÷ 5)-

Answer

1)=

2)+

5)-

Explanation

When letter or numbers are separated by multiplication or division can be combined to make one term.

In an algebra equation, terms are separated by an addition sign, subtraction sign or an equal sign. For example,

3a + 7b = 21.

This equation have 3 terms.

Posted in Mathematics

When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown? 2 + 7c – 4c2 – 3c + 4 –4c2 + 4c + 6 –7c2 + 10c + 6 –4c2 + 4c + 8 –7c2 + 7c + 6

Answer:

A) -4c^2 + 4c + 6

Step-by-step explanation:

The given polynomial is 2 + 7c – 4c^2 – 3c + 4

Add the like terms.

2 + 4 + 7c - 3c -4c^2

= 6 + 4c - 4c^2

Write it in a standard form

= -4c^2 + 4c + 6

Answer is A) -4c^2 + 4c + 6

Hope this will helpful.

Thank you.

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