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7 months ago

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Mathematics

1 answer:

Romashka-Z-Leto [24]7 months ago

4 0

Answer:

The slope is $\frac{-3}{5}$

Step-by-step explanation:

You know the slope is negative if you start on the left side and move right along the line. You are moving down hill. Down hill is a negative slope.

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If a² + b² = z and ab = y, which of the following is equivalent to 4z + 8y? Show all the steps.

Ivenika [448]

Answer:

The answer to your question is: (2a + 2b)²

Step-by-step explanation:

a² + b² = z

ab = y

Which is equivalent to 4z + 8y ?

Substitution

4(a² + b²) + 8(ab)

Simplify 4a² + 4b² + 8ab

Order 4a² + 8ab + 4b² It's a perfect square trynomial

Factorize (2a + 2b)²

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3 years ago

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Identify the gerund phrase, the direct object of the verb requires. The job requires getting your hair cut to a short, safe leng

Mekhanik [1.2K]

D is ur answer I think

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3 years ago

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Florida sales tax is 7%. How much money comes out of your pocket if u buy something for $100

liq [111]

Answer:

Step-by-step explanation:

If you use "Is over of" the equation will be ?/100*7/100, therefore after simplifying your answer is $7

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2 years ago

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Two sides of a triangle are as follows: 2 centimeters and 5 centimeters. Describe the possible lengths of the third side

Elden [556K]

Answer:

3cm < Third side < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values of third side are

4cm, 5cm,6cm

Step-by-step explanation:

This question can be solved using given by Triangle Inequality Theorem Given below.

Sum of two sides is always greater than value of third side
Difference of two sides is always less than value of third side

Given two sides are 2cm, 5cm

Sum of two sides = (2+5)cm = 7 cm

Difference of two sides = (5-2) = 3 cm

Let the third side be X

thus according to Triangle Inequality Theorem

X < Sum of two sides of given triangle

X < 7cm -----1

X > Difference of two sides

X > 3cm ----1

combining expression 1 and 2 we have

3cm < X < 7cm

Thus third side can take any value between 3cm and 7 cm

(note: excluding 3 cm and 7 cm)

If the value are integral then possible values are

4c, 5cm,6c

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2 years ago

Multiplying Powers with the Same Base

Luda [366]

Applying the product rule of exponents, each product of powers are matched with its simplified expression as:

1. $5 \times 5^3 = 5^4$

2. $5 \times 5^3 = 5^4$

3. $5^{-3} \times 5^{-3} = \frac{1}{5^6}$

4. $5^{-4} \times 5^{4} \times 5^0 = 5^0$

5. $5^{7} \times 5^{3} = 5^{10}$

To multiply the powers having the same base, we will apply the product rule for exponents.

<h3>What is the Product Rule for Exponents?</h3>

Base on the product rule for exponents, we have, $a^m \times a^n = a^{m + n} = a^{mn}$ .
In order to find the products of two given numbers that have the same base, the exponents would be added together.

1. $5^6 \times 5^{-4$

Add the exponents together

$5^6 \times 5^{-4} = 5^{(6) + (-4)}$

$5^6 \times 5^{-4} = 5^2$

2. $5 \times 5^3$

Add the exponents together

$5 \times 5^3 = 5^{(1 + 3)}$

$5 \times 5^3 = 5^4$

3. $5^{-3} \times 5^{-3}$

Add the exponents together

$5^{-3} \times 5^{-3} = 5^{(-3) + (-3)$

$5^{-3} \times 5^{-3} = 5^{-6$

$5^{-3} \times 5^{-3} = \frac{1}{5^6}$

4. $5^{-4} \times 5^{4} \times 5^0$

Add the exponents together

$5^{-4} \times 5^{4} \times 5^0 = 5^{(-4) + (4) + (0)$

$5^{-4} \times 5^{4} \times 5^0 = 5^0$

5. $5^{7} \times 5^{3}$

Add the exponents together

$5^{7} \times 5^{3} = 5^{10}$

In summary, applying the product rule of exponents, each product of powers are matched with its simplified expression as:

1. $5 \times 5^3 = 5^4$

2. $5 \times 5^3 = 5^4$

3. $5^{-3} \times 5^{-3} = \frac{1}{5^6}$

4. $5^{-4} \times 5^{4} \times 5^0 = 5^0$

5. $5^{7} \times 5^{3} = 5^{10}$

Learn more about product rule of exponents on:

brainly.com/question/847241

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1 year ago