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Ray Of Light [21]
4 years ago
12

Increase £20 by 15%

Mathematics
1 answer:
goblinko [34]4 years ago
7 0
Well 15% of £20 is three so maybe add that onto 20?
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If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?
eduard

Answer:

cos(\alpha+\beta)=-\frac{84}{85}

Step-by-step explanation:

we know that

cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)

Remember the identity

cos^{2} (x)+sin^2(x)=1

step 1

Find the value of sin(\alpha)

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

cos(\alpha)=-\frac{8}{17}

Find the value of sine

cos^{2} (\alpha)+sin^2(\alpha)=1

substitute

(-\frac{8}{17})^{2}+sin^2(\alpha)=1

sin^2(\alpha)=1-\frac{64}{289}

sin^2(\alpha)=\frac{225}{289}

sin(\alpha)=-\frac{15}{17}

step 2

Find the value of cos(\beta)

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

sin(\beta)=-\frac{4}{5}

Find the value of cosine

cos^{2} (\beta)+sin^2(\beta)=1

substitute

(-\frac{4}{5})^{2}+cos^2(\beta)=1

cos^2(\beta)=1-\frac{16}{25}

cos^2(\beta)=\frac{9}{25}

cos(\beta)=\frac{3}{5}

step 3

Find cos⁡ (α + β)

cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)

we have

cos(\alpha)=-\frac{8}{17}

sin(\alpha)=-\frac{15}{17}

sin(\beta)=-\frac{4}{5}

cos(\beta)=\frac{3}{5}

substitute

cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})

cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}

cos(\alpha+\beta)=-\frac{84}{85}

4 0
3 years ago
Bob,Cal,and Pete each made a stack of baseball cards.Bob's stack was 0.2 meter high.Cal's stack was 0.24 meter high.Pete's stack
AlekseyPX

Answer:

0.24 > 0.18

Step-by-step explanation:

Given that,

Bob's stack = 0.2m

Cal's stack = 0.24m

Pete's stack = 0.18m

To find?

A number sentence.

<em>A simple sentence is a string/collection of words that contain a subject and a verb whereas a number sentence is a sentence that consist of </em><em>mathematical operation</em><em> like +, -, /, * together with an equality such as =, <, >, and like a sentence it also tell a fact.</em>

<em> </em>So, the number sentence that compares cal's stack of cards to Pete's stack is

<h2>0.24 > 0.18</h2>

<em />

<em />

<em>  </em>

6 0
3 years ago
Read 2 more answers
Introduction to the Quadratic Formula
vredina [299]

Answer:

Any questions for us

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5 0
3 years ago
Which statement best describes how to determine whether f(x) = 9 - 4x^2 is an odd function?
OverLord2011 [107]

Answer:

Which statement best describes how to determine whether f(x) = 9 - 4x^2 is an odd function?

4 0
3 years ago
If Y varies directly with X solve the following :
BARSIC [14]

Answer:

a) x = -270

b) y = 304/9 or y = 33.78

c) x = -37.8

Step-by-step explanation:

y varies directly with x so y = kx

a)

y = kx

k = y/x

k = 10/-30 = -1/3

So

y = -1/3 x

If y = 90 then

90 = -1/3 x

x = 90 *(-3) = -270

b)

k = y/x

k = -19/-4.5

k = 38/9

So

y = 38/9 x

If x = - 8 then

y = 38/9 *(-8)

y = 304/9 or y = 33.78

c)

k = y/x

k = -4.3 / 12.9

k = - 1/3

So

y = -1/3 x

If y = 12.6 then

12.6 = -1/3 x

x = 12.6 *(-3)

x = -37.8

5 0
3 years ago
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