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10 days ago

Given: and bisect each other. Prove: Quadrilateral ABCD is a parallelogram. Proof: Statement Reason 1. and bisect each other. gi

ven 2. AE = EC BE = ED definition of bisection 3. m∠AEB = m∠CED 4. ΔABE ≅ ΔCDE SAS criterion 5. ∠ACD ≅ ∠CAB Corresponding angles of congruent triangles are congruent. 6. converse of Alternate Interior Angles Theorem 7. m∠BEC = m∠AED Vertical Angles Theorem 8. ΔBEC ΔDEA SAS criterion for congruence 9. DBC ≅ BDA Corresponding angles of congruent triangles are congruent. 10. converse of Alternate Interior Angles Theorem 11. Quadrilateral ABCD is a parallelogram. definition of a parallelogram 1 What is the reason for step 3 of this proof? A. Alternate Interior Angles Theorem B. Corresponding angles in congruent triangles are congruent. C. For parallel lines cut by a transversal, corresponding angles are congruent. D. Vertical Angles Theorem E.

Mathematics

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Jun and deron are applying for summer jobs at a local restaurant. after interviewing them, the restaurant owner says, "the proba

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<span>As the restaurant owner, The likelihood of hiring Jun is 0.7 => p(J) The likelihood of hiring Deron stands at 0.4 => p(D) The chance of hiring at least one of them is 0.9 => p(J or D) We can formulate the probability equation: p(J or D) = p(J) + p(D) - p(J and D) => 0.9 = 0.7 + 0.4 - p(J and D) p(J and D) = 1.1 - 0.9 = 0.2 Thus, the probability that both Jun and Deron are hired is 0.2.</span>

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categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay.

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This represents exponential growth

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The area of a square picture frame is 55 square inches. Find the length of one side of the frame. Explain to the nearest whole i

Inessa [12570]

We know that the area of a square picture frame measures 55 square inches. We need to calculate the length of one side of the frame. Let's denote the side length as x inches. The formula for the area of a square is x squared, and we can conclude that the area equals 55. Taking the square root of both sides, we see that 55 is nearer to 49, so x is approximately 7 inches.

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2 months ago

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?

Leona [12618]

Keep in mind that when factoring by grouping, we should divide the expression into two pairs that share some commonality. The goal is to create a common binomial factor after we factor each pair. It's important to mention that there can be multiple ways to pair the factors.

Let's explore the method of finding the factors of our expression through grouping:

Step 1. Identify shared multiples among the terms.

We can see that 4 and 8 are multiples of 2, 8 is a multiple of 4, and all are multiples of 1, suggesting various pairing options.

Step 2. Identify common variables.

Typically, we should pair variables that have the highest exponents to ensure that when factoring each group, we derive another common binomial factor.

Step 3. Factor each group; if it leads to another common binomial factor, you did it correctly. If it doesn't, try again.

Let's use these steps on our expression $4x^3+x^2-8x-2$

For step 1, we are grouping $4x^3$ and $-8x$ . Don't forget to pair the leftover factors too.

$(4x^3-8x)+(x^2-2)$

The common factor for the first group is $4x$ , which we will factor out.

$4x(x^2-2)+(x^2-2)$

Look at that! We obtained the common binomial factor $(x^2-2)$ . Sadly, $4x(x^2-2)+(x^2-2)$ isn't among our provided choices, so we'll attempt this again:

This time, let's group the higher variables from step 2: $4x^3$ and $x^2$

$4x^3+x^2-8x-2$

$(4x^3+x^2)+(-8x-2)$

The common factor in the first group turns out to be $x^2$ , and in the second one, it's -2, so we'll factor both of them out:

$(4x^3+x^2)+(-8x-2)$

$x^2(4x+1)-2(4x+1)$

Now, we have chosen option A.

Therefore, we can conclude that the correct answer is: A) x2(4x + 1) – 2(4x + 1)

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3 months ago