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3 years ago

Which are partial products for 68 × 43?

Mathematics

1 answer:

IrinaVladis [17]3 years ago

6 0

The product 68 × 43 can be written as the sum ...

... 68 × 43 = 60×40 + 60×3 + 8×40 + 8×3

Of these four partial products, only two are listed in your list of answer choices:

... B. 8 × 3 = 24

... C. 8 × 40 = 320

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Select the equation that is equivalent to the equation: y-3=2(x+5).

jeyben [28]

Y - 3 = 2(x+5)
y - 3 = 2x + 10
-3 - 10 = 2x - y
-13 = 2x - y

D) 2x - y = -13

6 0

3 years ago

Please someone help me to prove this..

Pachacha [2.7K]

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the following Sum to Product Identities:

$\sin x+\sin y=2\sin \bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\sin x-\sin y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x+\cos y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x+\cos y=-2\sin \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)$

<u>Proof LHS → RHS</u>

$\text{LHS:}\qquad \qquad \qquad \dfrac{\sin 5-\sin 15+\sin 25 - \sin 35}{\cos 5-\cos 15- \cos 25 + \cos 35}$

$\text{Reqroup:}\qquad \qquad \qquad \dfrac{(\sin 25+\sin 5)-(\sin 35 + \sin 15)}{(\cos 35+\cos 5)-(\cos 25 + \cos 15)}$

$\text{Sum to Product:}\quad \dfrac{2\sin \bigg(\dfrac{25+5}{2}\bigg)\cos \bigg(\dfrac{25-5}{2}\bigg)-2\sin \bigg(\dfrac{35+15}{2}\bigg)\cos \bigg(\dfrac{35-15}{2}\bigg)}{2\cos \bigg(\dfrac{25+15}{2}\bigg)\cos \bigg(\dfrac{25-15}{2}\bigg)-2\cos \bigg(\dfrac{35+5}{2}\bigg)\cos \bigg(\dfrac{35-5}{2}\bigg)}$ $\text{Simplify:}\qquad \qquad \dfrac{2\sin 15\cos 10-2\sin 25\cos 10}{2\cos 20\cos 15-2\cos 20\cos 5}$

$\text{Factor:}\qquad \qquad \dfrac{2\cos 10(\sin 15-\sin 25)}{2\cos 20(\cos 15-\cos 5)}$

$\text{Sum to Product:}\qquad \dfrac{\cos 10\bigg[2\cos \bigg(\dfrac{15+25}{2}\bigg)\sin \bigg(\dfrac{15-25}{2}\bigg)\bigg]}{\cos 20\bigg[-2\sin \bigg(\dfrac{15+5}{2}\bigg)\sin \bigg(\dfrac{15-5}{2}\bigg)\bigg]}$

$\text{Simplify:}\qquad \qquad \dfrac{\cos 10[2\cos 20\sin (-5)]}{\cos 20[-2\sin 10\sin 5]}\\\\\\.\qquad \qquad \qquad =\dfrac{-2\cos10 \cos 20 \sin 5}{-2\sin 10 \cos 20 \sin 5}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 10}{\sin 10}\\\\\\.\qquad \qquad \qquad =\cot 10$

LHS = RHS: cot 10 = cot 10 $\checkmark$

8 0

3 years ago

Identify the terms and the coefficients of the expression 8p + 2q + 7r

skelet666 [1.2K]

Terms: 8p, 2q, 7r

Coefficients: 8, 2, 7

5 0

3 years ago

IMAX Movie Prices. There were 322 people at a recent showing of the IMAX 3D movie "300". Admission was $8.75 each for adults and

dsp73

Answer:

218 adults and 104 children attended.

Step-by-step explanation:

From the information given, you can write the following equations:

x+y=322 (1)

8.75x+6y=2531.50 (2), where:

x is the number of adults

y is the number of children

First, you can solve for x in (1):

x=322-y (3)

Then, you can replace (3) in (2) and solve for y:

8.75(322-y)+6y=2531.50

2817.5-8.75y+6y=2531.50

2817.5-2531.50=8.75y-6y

286=2.75y

y=286/2.75

y=104

Finally, you can replace the value of y in (3) to find x:

x=322-104

x=218

According to this, the answer is that 218 adults and 104 children attended.

8 0

3 years ago

What is the slope of a line that passes through (-4,6) and (-9, -11)? Simplify your answer if possible.

cupoosta [38]

Answer:

Step-by-step explanation:

5 0

3 years ago