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4 years ago

Perform the following divisions. be sure all answers are reduced to lowest terms. 4/3 ÷ 1/2 =

Mathematics

1 answer:

Kobotan [32]4 years ago

7 0

The answer is 8 divide by 3

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The are of a shaded region is 118 ft squared. Which equation can be- used to find the value of X, in feet?

Triss [41]

Answer:

$x^2+ 18x -130=0$

Step-by-step explanation:

Given

See attachment for diagram

Required

The equation to find x

First, calculate the area of the big rectangle using:

$Area = Length * Width$

So:

$A_1 = (x + 6) * (3x - 2)$

The smaller rectangle

$A_2 = (x - 1) * (2x)$

The difference between this areas give the area of the shaded region.

So:

$A_1 - A_1 = 118$

$(x+6)*(3x-2) - (x-1)*2x = 118$

Open brackets

$3x^2 - 2x + 18x -12 -2x^2 +2x = 118$

Collect like terms

$3x^2 -2x^2- 2x +2x+ 18x -12 - 118=0$

$x^2+ 18x -130=0$

<em>The above equation can be used to solve for x</em>

4 0

3 years ago

How is this solved using trig identities (sum/difference)?

GenaCL600 [577]

FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

$cos \beta = -\frac{1}{2} \sqrt{3}$

$tan \beta= \frac{1}{3} \sqrt{3}$

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
$sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )$
$sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )$
$sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})$

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
$cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )$
$cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )$
$cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )$

Find tan (α - β)
$tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha tan \beta }$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}$

Simplify the denominator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5\sqrt{3}}{24})}$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the numerator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$
$tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the fraction
$tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})$
$tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}$

7 0

3 years ago

From 5 employees at a company, a group of 3 employees will be chosen to work on a project. How many different groups of 3 employ

Andrei [34K]

Hello,

aPb=b*(b-1)*(b-2)*....*(b-a+1) / a!

3P5=5*4*3/(3*2*1)=10

If we name the number of the employers 1,2,3,4,5

Here are the choices:

123,124,125,134,135,145,234,235,245,345 (total 10 choices)

8 0

3 years ago

Read 2 more answers

“twice the sum of a number and 6 is more than 84”

stealth61 [152]

Answer:

Step-by-step explanation:

2x+6=84

2x=78

find your own way

3 0

3 years ago

How many 2 thirds cups servings are in 4 cup container of food

garri49 [273]

There are 6 2/3 cup servings in a 4 cup container.

3 0

3 years ago