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eimsori [14]
3 years ago
10

To solve 2x + 9 = 21, what is the first step?

Mathematics
1 answer:
Oxana [17]3 years ago
4 0
D.) Subtracting 9 from each side.
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Prove: cot(x) sec^4(x) = cot(x) +2tan(x) + tan^3(x)
masha68 [24]
\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\qquad\qquad 
sec(\theta)=\cfrac{1}{cos(\theta)}\quad\qquad  1+tan^2(\theta)=sec^2(\theta)\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}
\qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\\\\
-------------------------------\\\\
cot(x)sec^4(x)=cot(x)+2tan(x)+tan^3(x)\\\\
-------------------------------\\\\

\bf \textit{so, let's do the left-hand-side}\\\\
cot(x)sec^2(x)sec^2(x)\implies cot(x)[1+tan^2(x)][1+tan^2(x)]
\\\\\\
cot(x)[1^2+2tan^2(x)+tan^4(x)]
\\\\\\
cot(x)+2tan^2(x)cot(x)+tan^4(x)cot(x)
\\\\\\
cot(x)+2\cdot \cfrac{sin^2(x)}{cos^2(x)}\cdot \cfrac{cos(x)}{sin(x)}+\cfrac{sin^4(x)}{cos^4(x)}\cdot \cfrac{cos(x)}{sin(x)}
\\\\\\
cot(x)+2\cdot \cfrac{sin(x)}{cos(x)}+\cfrac{sin^3(x)}{cos^3(x)}\implies \boxed{cot(x)+2tan(x)+tan^3(x)}
8 0
3 years ago
Staples recently charged $3.79 per ream (package of 500 sheets) of regular paper and $5.49 per ream of paper made of recycled fi
Ipatiy [6.2K]
<h3>Given</h3>

regular paper costs $3.79 per ream

recycled paper costs $5.49 per ream

$582.44 was spent for 116 reams

<h3>Find</h3>

the numbers of reams of each type that were purchased

<h3>Solution</h3>

Let r and g represent the numbers of reams of regular and recycled ("green") paper, respectively.

... r + g = 116 . . . . . . . . 116 reams were purchased

... 3.79r + 5.49g = 582.44 . . . . this is the total cost of the purchase

Solve the first equation for r and substitute that into the second equation.

... r = 116 - g

... 3.79(116 - g) + 5.49g = 582.44 . . . . . use the expression for r

... 1.70g + 439.64 = 582.44 . . . . . . . . . simplify

... g = (582.44 -439.64)/1.70 = 84 . . . . subtract the constant, divide by 1.70

... r = 116 -84 = 32 . . . . . . . . . . . . . . . . . use the equation for r

32 regular reams and 84 recycled reams were purchased

3 0
3 years ago
The area of a playing card is 48 square centimeters. It is 8 centimeters tall. How wide is it?
il63 [147K]

Answer:6

Step-by-step explanation:

Area of a rectangle = length × width

Length = 8

Breadth = ?

Area = 48

L × B = Area

8 × B = 48

Divide both sides by 8

B = 48 ÷ 8

B = 6

3 0
3 years ago
Find the lateral area of a cylinder
Dovator [93]

Answer:

314 cm^2

Step-by-step explanation:

(=^w^=)

A= 2*pi*r*h

A=2*pi*5*10

A=314.16 cm^2

7 0
3 years ago
Read 2 more answers
31)The scale on a map shows that 5 centimeters = 2 kilometers.
Sonbull [250]

Answer:

13.5 cm

Step-by-step explanation:

if 5 cm is 2 km, then 10 cm is 4 km. To find one km you do half of 5 cm. which is 3.5 cm. So 10+3.5=13.5

8 0
4 years ago
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