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2 years ago

Simplify the expression.

Mathematics

1 answer:

Inessa05 [86]2 years ago

7 0

Answer:

$\frac{-4}{x^5y^13}$

Step-by-step explanation:

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LMN is a right-angle triangle. Angle NLM=90. PQ is parallel to LM. The area of triangle PNQ is 8cm^2. The area of triangle LPQ i

likoan [24]

Answer:

The area of LQM is $48cm^2$

Step-by-step explanation:

Given

Area of PNQ = 8

Area of LPQ = 16

See attachment for triangles

The area of PNQ is calculated as:

$Area = \frac{1}{2} * PQ * PN$

Substitute 8 for Area

$8 = \frac{1}{2} * PQ * PN$

$PQ * PN = 16$

The area of LPQ is calculated as:

$Area = \frac{1}{2} * PQ * LP$

Substitute 16 for Area

$16= \frac{1}{2} * PQ * LP$

From the attachment:

$PN + LP =LN$

Make LP the subject

$LP = LN -PN$

So:

$16= \frac{1}{2} * PQ * (LN -PN)$

We have:

$16= \frac{1}{2} * PQ * (LN -PN)$ and $PQ * PN = 16$

Equate both expressions:

$\frac{1}{2} * PQ *(LN - PN) = PQ * PN$

Divide both sides by PQ

$\frac{1}{2} (LN - PN) = PN$

Multiply both sides by 2

$LN - PN = 2PN$

$LN= 3PN$

Since PNQ is similar to LNM, the following equivalent ratios exist:

$\frac{LM}{PQ} = \frac{LN}{PN}$

Substitute $LN= 3PN$

$\frac{LM}{PQ} = \frac{3PN}{PN}$

$\frac{LM}{PQ} = 3$

$LM = 3PQ$

Area of LQM is:

$Area = \frac{1}{2} * LM * LP$

This gives:

$Area = \frac{1}{2} * 3PQ * LP$

$Area = 3 *\frac{1}{2} *PQ * LP$

Recall that:

$16= \frac{1}{2} * PQ * LP$

So:

$Area = 3 *16$

$Area = 48cm^2$

5 0

2 years ago

Solve the System of Equations -4x + 9y = 14 12x - 10y = - 8

12345 [234]

Answer:

(1, 2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

-4x + 9y = 14

12x - 10y = -8

Step 2: Rewrite Systems

-4x + 9y = 14

Multiply everything by 3: -12x + 27y = 42

Step 3: Redefine Systems

-12x + 27y = 42

12x - 10y = -8

Step 4: Solve for y

Elimination

Combine 2 equations: 17y = 34
Divide 26 on both sides: y = 2

Step 5: Solve for x

Define equation: 12x - 10y = -8
Substitute in y: 12x - 10(2) = -8
Multiply: 12x - 20 = -8
Isolate x term: 12x = 12
Isolate x: x = 1

6 0

2 years ago

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Find the percent of each number 6% of 38

blondinia [14]

2.28 is the answer I got

first I divided 6 by 100

then multiplied that by 38 and that's how I got 2.28

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2 years ago

A car travels about 45 feet in one second. At this speed,

cluponka [151]

The correct answer for the giving question it number 4

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2 years ago

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Alex for school I need help whoever helps first will get brainlyist

gayaneshka [121]

Answer:

Well what do you need help on. :) Ill be happy to help.

Step-by-step explanation:

8 0

1 year ago

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