MATHEMATICS HIGH SCHOOL

What polynomial identity will prove that 49 = (2+5)^2? (A. Difference of Squares; B. Difference of Cubes; C. Sum of Cubes; D. Square of a Binomial)

Answers

Answer 1

Answer:

Answer:

Option D is correct.

Square of binomials.

Step-by-step explanation:

Prove that: $49 = (2+5)^2$

Square of binomials states that the square of a binomial is always a trinomial.

Also, it will be helpful to memorize these patterns for writing squares of binomials as trinomials.

$(a+b)^2 = a^2+2ab+b^2$

Take RHS

$(2+5)^2$

Apply the square of binomial, we have;

$(2+5)^2 = 2^2+2 \cdot 2 \cdot 5 +5^2$

= 4 + 20 + 25 = 24 + 25 = 49 = LHS proved.

Therefore, Square of binomials identity will prove that $49 = (2+5)^2$

Answer 2

Answer: Hi,

(a+b)² = a²+2ab+b²

For a = 2 and b = 5

(2+5)² = 2²+2(2)(5)+5²
(2+5)² = 4+20+25
(2+5)² = 49

Answer:

D. Square of a Binomial

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Follow the directions to solve the system of equations by elimination.8x + 7y = 39
4x – 14y = –68

Answers

To solve a system of equation by elimination, the coefficients of the same variable of both equations must be equal. In this case, let's choose y.
In order to make the coefficient of y of the second equation be equal to 7, we divide it by 2. Resulting to:
2x - 7y = -34

Next, add the two solutions so that the y term is eliminated. The result is:
10x = 5
Then solve for x
x = 1/2

Substitute x to either of the solution to solve for y. The result is:
y = 5

Final answer:

The solution to the system of equations 8x + 7y = 39 and 4x – 14y = -68 via elimination is x = 0.5 and y = 5.

Explanation:

The two given equations are 8x + 7y = 39 and 4x – 14y = -68. The method for solving this is elimination.

First, modify the second equation by multiplying every term by 2.
This will give 8x - 28y = -136.
Now, you have two equations 8x + 7y = 39 and 8x - 28y = -136 that can be combined by subtraction: 8x - 8x + 7y - (-28y) = 39 - (-136).
Simplification gives 35y = 175, so y = 5.
Substituting y = 5 into the first equation, 8x + 7*5 = 39, which simplifies to 8x + 35 = 39, and then to 8x = 4, so x = 0.5.

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Which shows a perfect square trinomial?50y2 – 4x2
100 – 36x2y2
16x2 + 24xy + 9y2
49x2 – 70xy + 10y2

Answers

Answer:

C. $16x^2+24xy+9y^2$

Step-by-step explanation:

We have been given 4 expressions and we are asked to choose the expression that is a perfect square trinomial.

We know that a perfect square trinomial is in form: $a^2+2ab+b^2$ .

Upon looking at our given choices we can see that option C is the correct choice as we can write as:

$16x^2+24xy+9y^2=(4x)^2+2(4x\cdot 3y)+(3y)^2$

$16x^2+24xy+9y^2=(4x)^2+2(12xy)+(3y)^2$

$16x^2+24xy+9y^2=(4x)^2+24xy+(3y)^2$

Therefore, option C is the correct choice.

A perfect square trinomial is found in the expression where both the leading coefficients and the constant are both perfect squares. That only is the case with the third choice above. 16 is a perfect square of 4 times 4, and 9 is a perfect square of 3 times 3. We need to set it up into its perfect square factors and FOIL to make sure, so let's do that. Not only is 16 a perfect square in that first term, but so is x-squared. Not only is 9 a perfect square in the third term, but so is y-squared. So our factors will look like this:

(4x + 3y)(4x + 3y). FOIL that out to see that it does in fact give you back the polynomial that is the third choice down.

PLEEEEEEEEEEEEASE HELP ME WITH THIS! IT IS DUE TOMORROW!!!

Answers

Answer: They both equal 30

Solving Steps:
1. Solve for x
40-4x=50-8x
-4x+8x=50-40
4x=10
x=2.5

2. Find <1 and <2
40-4(2.5)
40-10
=30

What is the sum of the arithmetic sequence 149, 135, 121, …, if there are 28 terms?−1,204
−1,176
−1,148
−1,120

Answers

The sum of the arithmetic sequence is -1120.

What is arithmetic sequence?

"It is a sequence of numbers in which the difference between consecutive terms is constant."

What is the sum of arithmetic sequence?

" $S_n=(n)/(2)[2a +(n-1)d]$

where a as the first term,

d the common difference between the consecutive terms,

n is the total number of terms in the sequence."

For given question,

We have been given an arithmetic sequence 149, 135, 121,. . .

The first term of given arithmetic sequence is 149

⇒ a = 149

The common difference is,

⇒ d = 135 - 149

⇒ d = -14

There are 28 terms.

⇒ n = 28

Using the formula for the sum of an arithmetic sequence,

$\Rightarrow S=(n)/(2)[2a +(n-1)d]\n\n\Rightarrow S=(28)/(2)[2* (149) +(28-1)* (-14)]\n\n\Rightarrow S=14*[298-378]\n\n\Rightarrow S=14* (-80)\n\n\Rightarrow S=-1120$

Therefore, the sum of the arithmetic sequence is -1120.

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I needed my brother to help me with this one,so here is the answer.
The common difference is -14.

Let's simplify this by expressing each term as
163 - 14n
where n is the number of the term.

Then the sum of the 28 terms is
28 * 163 - 14 (1+2+3+...+28)
= 4,564 - 14 * 28 * 29 / 2
= -1,120

Hamburgers cost $2.50 and cheeseburgers cost $3.50 at a snack bar. Ben has sold no more than $30 worth of hamburgers and cheeseburgers in the first hour of business. Let x represent the number of hamburgers and y represent the number of cheeseburgers. The inequality 2.50x + 3.50y ≤ 30 represents the food sales in the first hour.If Ben has sold 4 cheeseburgers, what is the maximum value of hamburgers Ben could have sold?

Answers

Using the inequality
2.50x + 3.50y ≤ 30
substituting y with the number of cheeseburgers sold
2.5x + 3.5(4) ≤ 30
x = 6.4
The maximum number of hamburgers he can sell is 6

Answer:

The maximum value of hamburgers is $6$

Step-by-step explanation:

Let

x-------> the number of hamburgers

y-----> the number of cheeseburgers

we know that

$2.50x+3.50y\leq 30$ -------> inequality that represent the situation

For $y=4$

substitute in the inequality and solve for x

$2.50x+3.50(4)\leq 30$

$2.50x+14\leq 30$

$2.50x\leq 30-14$

$2.50x\leq 16$

$x\leq 6.4$

The maximum value of hamburgers is $6$

Janie uses a reflecting tool to reflect Point B onto Point A. Which of the following statements are true about the line of reflection?1. Reflection line is perpendicular to AB
2. Reflection line does not bisect AB.
3. Reflection line passes through the midpoint of BA.
4. Reflection line forms two equal angles with segment AB.

Answers

You can understand the concept of reflection by imagining a lake. Suppose a mountain is reflected on the lake across an imaginary horizontal line in the ground. This line is the Line of Symmetry. So, in this problem we need to solve four items. Therefore:

1. Reflection line is perpendicular to AB

This is true. To reflect Point B onto Point A, we need to take a Line of Symmetry perpendicular to the segment AB as illustrated in Figure 1. This line is the one in red and the blue square indicates that the red line and the segment AB are perpendicular.

2. Reflection line does not bisect AB

This is false. Instead, the line in red bisect the segment AB, that is, it divides the segment into two equal parts as indicated in Figure 2. The x in blue represents the point at which the red line bisects the segment.

3. Reflection line passes through the midpoint of BA.

This is true. Given that the red line divide the segment into two equal parts, then the point at which the red line bisects the segment is also called the midpoint (M) as indicated in Figure 3.

4. Reflection line forms two equal angles with segment AB.

This is true. As you can see in Figure 4, the two blue angles are equal and the two green angles are equal. So, reflection line forms two equal angles with segment AB. In fact, each of these angles measures 90 degrees. Accordingly, all these four angles are equal.

Hello,

1:TRUE
2:FALSE
3:TRUE
4:TRUE

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