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3 years ago

N the problem 4 × 12 = 48, which numbers are the factors?

Mathematics

1 answer:

Gre4nikov [31]3 years ago

5 0

The factor is, 4 and 12

A factor is a number that divides another number evenly with no remainder.

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Given: sin ∅= 4/5 and cos x = -5/13 ; evaluate the following expression. tan( ∅ - x )

Pavlova-9 [17]

By definition of tangent,

tan(θ - x) = sin(θ - x) / cos(θ - x)

Expand the sine and cosine terms using the angle sum identities,

sin(x ± y) = sin(x) cos(y) ± cos(x) sin(y)

cos(x ± y) = cos(x) cos(y) ∓ sin(x) sin(y)

from which we get

tan(θ - x) = (sin(θ) cos(x) - cos(θ) sin(x)) / (cos(θ) cos(x) + sin(θ) sin(x))

Also recall the Pythagorean identity,

cos²(x) + sin²(x) = 1

from which we have two possible values for each of cos(θ) and sin(x):

cos(θ) = ± √(1 - sin²(θ)) = ± 3/5

sin(x) = ± √(1 - cos²(x)) = ± 12/13

Since there are 2 choices each for cos(θ) and sin(x), we'll have 4 possible values of tan(θ - x) :

• cos(θ) = 3/5, sin(x) = 12/13 :

tan(θ - x) = -56/33

• cos(θ) = -3/5, sin(x) = 12/13 :

tan(θ - x) = 16/63

• cos(θ) = 3/5, sin(x) = -12/13 :

tan(θ - x) = -16/63

• cos(θ) = -3/5, sin(x) = -12/13 :

tan(θ - x) = 56/33

7 0

2 years ago

Read 2 more answers

2x^2-13x+20=2x 2 −13x+20

marta [7]

Answer:

Factor by grouping

( 2 x + 5 ) ( x + 4 )

6 0

3 years ago

The manager of a fashionable restaurant open Wednesday through Saturday says that the restaurant does about 29 percent of its bu

RideAnS [48]

Answer: The seasonal relatives is calculated are as follows:

Step-by-step explanation:

Given that,

restaurant only open from Wednesday to Saturday,

29 percent of its business on Friday
31 percent on Saturday night
21 percent on Thursday night.

∴ The remaining 19% of its business he does on Wednesday

Now, suppose that total production of sales in a given week be 'y'

So, average sales in a week = $\frac{y}{4}$

If we assume that y = 1

hence, average sales in a week = $\frac{1}{4}$

= 0.25

Now, we have to calculate the seasonal relatives,

that is,

= $\frac{Sales in a given day}{average sales in a week}$

Wednesday:

= $\frac{0.19}{0.25}$

= 0.76

Thursday:

= $\frac{0.21}{0.25}$

= 0.84

Friday:

= $\frac{0.29}{0.25}$

= 1.16

Saturday:

= $\frac{0.31}{0.25}$

= 1.24

8 0

4 years ago

What is the range of possible sizes for side x? _ < x < _

qwelly [4]

Answer:

2.8 < x < 5.8

Step-by-step explanation:

We must apply the Triangle Inequality Theorem which states that for any triangle with sides a, b, and c:

a + b > c

b + c > a

c + a > b

Here, let's arbitrarily denote a as 4.1, b as 1.3, and c as x. So, let's plug these values into the 3 inequalities listed above:

a + b > c ⇒ 4.1 + 1.3 > x ⇒ 5.8 > x

b + c > a ⇒ 1.3 + x > 4.1 ⇒ x > 2.8

c + a > b ⇒ x + 4.1 > 1.3 ⇒ x > -2.8

Look at the last two: clearly if x is greater than 2.8 (from the second one), then it will definitely be greater than -2.8 (from the third), so we can just disregard the last inequality.

Thus, the range of possible sizes for x are:

2.8 < x < 5.8

~ an aesthetics lover

8 0

3 years ago

Read 2 more answers

Please Help me with these 2 questions!!

qaws [65]

Answer:

3) Parabola

4) $y = 5x^2 + 7$ and $y = \frac{10}{x} +20$

4 0

2 years ago

Read 2 more answers