Amelia bought a violin that was on sale for 15% off. If the original price was

In the adjoining figure , APB and AQC are equilateral triangles. Prove that PC = BQ. ( Hint : <img src="https://tex.z-dn.net/?f=

just olya [345]

Answer:

See Below.

Step-by-step explanation:

Statements: Reasons:

$\displaystyle 1)\text{ } \Delta APB \text{ and } \Delta AQC \text{ are equilateral triangles}$ Given

$\displaystyle 2) \text{ } m \angle PAB = 60$ Definition of equilateral.

$3)\text{ } m \angle QAC = 60$ Definition of equilateral.

$4)\text{ } m\angle PAB = m\angle QAC$ Substitution

$5)\text{ } m\angle PAC=m\angle PAB+m\angle BAC$ Angle Addition

$\displaystyle 6)\text{ } m\angle QAB=m\angle QAC+m\angle BAC$ Angle Addition

$7)\text{ } m\angle QAB=m\angle PAB+m\angle BAC$ Substitution

$\displaystyle 8)\text{ } m\angle PAC=m\angle QAB$ Substitution

$9)\text{ } PA=BA$ Definition of equilateral

$10)\text{ } AC=AQ$ Definition of equilateral

$\displaystyle 11)\text{ } \Delta PAC \cong \Delta BAQ$ Side-Angle-Side Congruence*

$\displaystyle 12)\text{ } PC=BQ$ CPCTC

* SAS Congruence:

PA = BA

∠PAC = ∠QAB

AC = AQ

6 0

2 years ago

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A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line?

beks73 [17]

Slope = (2 + 1) / (-5 - 10) = -3/15 = - 1/5

Equation

y - 2 = -1/5 (x + 5)

y - 2 = -1/5 x - 1

y = -1/5 x + 1

Answer

y = -1/5 x + 1

6 0

3 years ago

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Ethan rollerbladed a total of 623 \text{ km}623 km623, start text, space, k, m, end text over ddd days. He rollerbladed the same

Sever21 [200]

Answer:

Ethan rollerbladed each day $\frac{623}{d}$ kilometers.

Step-by-step explanation:

Given:

Ethan rollerbladed a total of 623 km over d days.

Now, to find the kilometers Ethan rollerblade each day.

Total number of distance rollerbladed = 623 km.

Total number of days = $d.$

As, Ethan rollerbladed each day the same distance.

Now, to get the distance Ethan rollerbladed in each day we divide total number of distance rollerbladed by total number of days:

$Ethan\ rollerbladed\ each\ day\ =\ \frac{Total\ number\ of\ distance\ rollerbladed}{Total\ number\ of\ days}$

$Ethan\ rollerbladed\ each\ day\ =\ \frac{623}{d}$

Therefore, Ethan rollerbladed each day $\frac{623}{d}$ kilometers.

5 0

2 years ago

I need some one to help me!! Is (7, 0) a solution to the equation y = x − 7?

Marianna [84]

Answer:

Yes

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Coordinates (x, y)

Step-by-step explanation:

Step 1: Define

Identify

Point (7, 0)

Equation y = x - 7

Step 2: Find

Substitute in point [Equation]: 0 = 7 - 7
Subtract: 0 = 0

Since 0 = 0 is true, then it would be a solution to the equation.

3 0

2 years ago

Joanna splits 3 pitches of water equally among her 8 plants.what fraction represents this division??

KATRIN_1 [288]

3/8.

Hope this helps!

6 0

2 years ago

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