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3 years ago

Is the decimal expansion of this fraction repeating or terminating?

Mathematics

1 answer:

NikAS [45]3 years ago

5 0

Answer:

terminating decimal

Step-by-step explanation:

Well 9÷5 is 1.8 and since it has an end it is terminal

For example 2÷9 is repeating because the answer is 0.222222222...

But since 9÷5 is just 1.8 it stops and doesn't continue

Terminal examples: 0.2, 2.6, 5.8, 0.465, ect.

Repeating examples: 0.2222222...., 0.23232323232323...., 0.399999999999..., ect.

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If JKLM is a rhombus, MK = 30, NL = 13, and mZMKL = 41°, find each measure.

oksian1 [2.3K]

Answer:

$NK = 15$

$JL = 26$

$KL = 19.85$

$\angle JKM =49$

$\angle JML =41$

$\angle MLK = 90$

$\angle MNL =90$

$\angle KJL =41$

Step-by-step explanation:

Given

$MK = 30$

$NL = 13$

$\angle MKL = 41$

Solving (a): NK

MK is a diagonal and NK is half of the diagonal. So:

$NK = \frac{1}{2} * MK$

$NK = \frac{1}{2} * 30$

$NK = 15$

Solving (b): JL

JL is a diagonal, and it is twice of NL.

$JL = 2 * NL$

$JL = 2 * 13$

$JL = 26$

Solving (c): KL

To solve for KL, we consider triangle KNL where:

$\angle KNL = 90$

and

$KL^2 = NL^2 + NK^2$

$KL^2 = 13^2 + 15^2$

$KL^2 = 394$

$KL = \sqrt{394$

$KL = 19.85$

Solving (d - h):

To do this, we consider triangle JKN

$\angle KNL = \angle LNM = \angle MNJ = \angle JNK = 90$ -- diagonals bisect one another at right angle

Alternate interior angles are equal. So:

$\angle MKL = \angle KMJ = \angle KJL = \angle JLM = 41$

Similarly:

$\angle MKJ = \angle KML = \angle MJL = \angle JLK = 90 - 41$

$\angle MKJ = \angle KML = \angle MJL = \angle JLK = 49$

So:

$\angle JKM =49$

$\angle JML =41$

$\angle MLK = \angle MLJ + \angle JLK$

$\angle MLK = 49 + 41$

$\angle MLK = 90$

$\angle MNL =90$

$\angle KJL =41$

5 0

3 years ago

A triangle has an area of 36 cm². The base and height are scaled by a factor of 5.

ahrayia [7]

Triangle Area = .5 * (base * height)
36 = (base * height) / 2
So let's say base = 9 height 8
If base and height are scaled by a factor if 5 than
base = 45 height 40 and
area = .5 * (45 * 40)
area = 900

Basically, the area increases by a factor of 25.
The base increases by 5 and the height increases by 5 so the area increases by 5*5 = 25

4 0

3 years ago

A rectangular room is 3 meters longer than it is wide, and its perimeter is 22 meters. Find the dimension of the room. The lengt

lyudmila [28]

Answer:

Width = 4 m

Length = 7 m

Step-by-step explanation:

given:

perimeter of a rectangle = 22m

L = 3 + W

perimeter = 2L + 2W

perimeter = 2 (3 + W) + 2W

22 = 6 + 2W + 2W

22 - 6 = 4W

W = 16 / 4

W = 4 m

L = 3 + W

L = 3 + 4

L = 7 m

check:

perimeter = 2L + 2W

22 = 2(7) + 2(4)

22 = 14 + 8

22 = 22 ---- OK

4 0

3 years ago

Please help me find the function rule, i dont know what to do!! I will give big brain

Vesnalui [34]

The answer is Y=4x+5

6 0

2 years ago

3) Lane and Zack purchased a house for $245,000 in 2016. The house loses 4% of its value each year,

alina1380 [7]

Answer:

$138,345

Step-by-step explanation:

This is a compound decline problem, which will be solve by the compound formula:

$F=P(1-r)^t$

Where

F is the future value (value of house at 2030, 14 years from 2016)

P is the present value ($245,000)

r is the rate of decline, in decimal (r = 4% = 4/100 = 0.04)

t is the time in years (2016 to 2030 is 14 years, so t = 14)

We substitute the known values and find F:

$F=P(1-r)^t\\F=245,000(1-0.04)^{14}\\F=245,000(0.96)^{14}F=138,344.96$

Rounding it up, it will be worth around $138,345 at 2030

8 0

3 years ago