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3 years ago

Lisa's weekly pay increases from $525 to $546 Calculate her percentage pay increase.

Mathematics

1 answer:

Lana71 [14]3 years ago

6 0

546 - 525 = 21

21 is 4% of 525.

Lisa gained a 4% pay increase.

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Sort the property that characterizes either a trapezoid or a kite

balu736 [363]

Trapezoid:

•Can have congruent diagonals. •Has one pair of opposite, parallel sides.

Kites:

•Has congruent adjacent sides.

•Has perpendicular diagonals.

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3 years ago

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

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2 years ago

Given a triangle MTN, prove that

cupoosta [38]

Answer:

$\angle m + \angle t + \angle n = 180$

Step-by-step explanation:

Required

Show that:

$\angle m + \angle t + \angle n = 180^o$

To make the proof easier, I've added a screenshot of the triangle.

We make use of alternate angles to complete the proof.

In the attached triangle, the two angles beside $\angle m$ are alternate to $\angle t$ and $\angle n$

i.e.

$\angle 1 = \angle t$

$\angle 2 = \angle n$

Using angle on a straight line theorem, we have:

$\angle 1 + \angle m + \angle 2 = 180$

Substitute values for (1) and (2)

$\angle t + \angle m + \angle n = 180$

Rewrite as:

$\angle m + \angle t + \angle n = 180$ -- proved

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2 years ago

Anna earns $9 an hour babysitting. She wants to buy a 16 GB iPad that is $120. Anna has saved $45 so far. How many more hours of

natta225 [31]

Its 8.33 but go ahead and put 9

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3 years ago

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Please I need your help

Svetllana [295]

Answer:

249mm

Step-by-step explanation:

You find volume of the overall figure- 11 x 3 x 13= 429

Then find volumes of missing parts of overall complete figure and subtract from the overall volume....

5 x 4 x 3= 60

429-60=369

-------------------------------------

8 x 5 x 3= 120

369-120= 249

Hope this helped!! Hope you got it- please leave a rating and mark as Brainliest. Thank You :) (I really want to go to sleep right now, would have explained further, sorry)

8 0

3 years ago