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2 years ago

One integer is 5 less than another and their product is 84. Find the integers.

Mathematics

1 answer:

andrezito [222]2 years ago

5 0

The first integer is going to be x and the second one is going to be y.

We now turn the clues into equations:

x = y - 5

xy = 84

The substitution method:

(y - 5)y = 84

y^2 - 5y - 84 = 0

(y+7)(y-12) = 0

y = -7, 12.

If y = -7, then x = -12.

If y = 12, then x = 7

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the length of a rectangle is 2 cm more than 5 times the width. The perimeter 196 cm.Find the width and length

blondinia [14]

w(5)+2+w=196

5w+2+w=196

6w+2=196

6w=194

w=32 1/3

4 0

3 years ago

Please help! acellus

ch4aika [34]

Answer:

The number that belongs in the green box is equal to 909.

General Formulas and Concepts:
Algebra I

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem:
$\displaystyle a^2 + b^2 = c^2$

a is a leg
b is another leg
c is the hypotenuse

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 30

b = 3

c = x

Step 2: Find x

Let's solve for the general equation that allows us to find the hypotenuse:

[Pythagorean Theorem] Square root both sides [Equality Property]:
$\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}$

Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:

[Equation] Substitute in variables:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}$

∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.

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Learn more about Trigonometry: brainly.com/question/27707750

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Topic: Trigonometry

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2 years ago

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3 years ago

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kiruha [24]

Answer:

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Step-by-step explanation:

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2 years ago

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cake batter poured into a pan creates a circular batter pattern whose radius increases at a constant rate of 1 in/sec. at what r

docker41 [41]

Answer:

8 π .

Step-by-step explanation:

radius increases at a constant rate of 1 in/sec.

dr / dt = 1

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