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4 years ago

Find the measure of each angle: Complementary angles with measures (5x)° and (4x−18)°.

1 answer:

7 0

Complentary angles add to 90 degrees
so
5x+4x-18=90
9x-18=90
add 18 both sides
9x=108
divide both sides by 9
x=12

5x is one angle
5x=5(12)=60 degrees

the other one is 4x-18
4x-18=4(12)-18=48-18=30

the angles are 60 degrees and 30 degrees
and x=12 degree

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Which set of numbers could represent the lengths of the sides of a right triangle?

DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

$\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2$ .

In this case,

$\text{longest side}^2 = 17^2 = 289$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}$ .

In other words, indeed $\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2$ . Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

Factor out the common factor $2$ to simplify the calculations.

$\text{longest side}^2 = 20^2 = 400$

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = 11^2 = 121$ .

<h3> $\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}$ .</h3>

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

6 0

4 years ago

Sam invests £1800 in the bank for four

KIM [24]

Answer:

£2088

US$ 2,536.48 dollars (2021)

Step-by-step explanation:

4% of 1800 = 72

72 x 4 = 288

1800 + 288 = 2088

He has £2088 at the bank after 4 year

8 0

3 years ago

please provider answer? A train travels 160160 km in the same time that a plane covers 720720 km. If the speed of the plane is 2

lys-0071 [83]

T=time
d=st
r=train speed
p=plane speed

<span>160=rt
</span><span>720=pt

speed of plan is 20kmph less than 5 times speed of train
p=5r-20

we notice that 160 times 4.5=720
times first equaton by 4.5

720=4.5rt
720=pt
set equal
4.5rt=pt
divide both sides by t
4.5r=p
sub </span><span>p=5r-20 for p
4.5r=5r-20
minus 4.5r from both sides
0=0.5r-20
add 20 to both sides
20=0.5r
times 2 both sides
40=r

sub back</span><span>
p=5r-20
p=5(40)-20
p=200-20
p=180

plane is 180kmph
train is 40kmph
</span>

3 0

3 years ago

I need help with my math who can help or wnats to

nignag [31]

Answer:

I can help!!

Step-by-step explanation:

6 0

4 years ago

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50 POINTS! PLEASE HELP!

Sauron [17]