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garik1379 [7]
2 years ago
11

Can a parallelogram have two 45 degree angles and two 75 degree angles? Why or why not?

Mathematics
2 answers:
Sergio [31]2 years ago
8 0

Answer:No, the sum of the parallelogram's four angles must be equal to 360

Step-by-step explanation:

All four of a parallelogram's angles must add up to 360. Here, the angles only add up to 45 * 2 + 75 * 2 = 240 degrees.

Also, two adjacent angles must add up to 180. Here, the two adjacent angles 45 and 75 only add up to 120 degrees.

enyata [817]2 years ago
5 0

Answer:

no

Step-by-step explanation:

A parallelogram has to have 4 angles that add to 360 degrees

45+45 + 75+75

90+150

240

This does not equal 360

No

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What is the solution to the following system of equations? x − 4y = 6 2x + 2y = 12 (0, 10) (10, 0) (6, 0) (0, 6)
frozen [14]

Answer:

(6,0)

Step-by-step explanation:

The given system has equations:

x-4y=6

2x+2y=12

Multiply the top equation by 2 to get:

2x-8y=12

2x+2y=12

Subtract the top equation form the bottom equation to get:

2x-2x+2y--8y=12-12

\implies 10y=0

\implies y=0

Put y=0 into x-4y=6

x-4*0=6

\implies x=6

Therefore the solution is (6,0)

4 0
3 years ago
Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X deno
Roman55 [17]

Answer:

a) P(X>np+3\sqrt{np(1-p)}=0.017

b) P(x>1)=0.190

c) P(Y>1)=0.651

Step-by-step explanation:

This a binomial experiment where success is denoted by parts that need rework.

X ∼ B(n, p); n = 20; p = 0.01

The expected value of X is: E(X) = np =20×0.01= 0.2

The variance is: Var(X) = np(1 − p) = 0.2 × 0.99 = 0.198,

The standard deviation SD(X)= \sqrt{0.198} ≈ 0.445

a) P(X>np+3\sqrt{np(1-p)}=P(X>0.2+3×0.445)=P(X>1.535)=P(X≥2)

Probability function is given by:

\frac{n!}{x!(n-x)!} *p^x*(1-p)^{(n-x)}

P(X≥2)=1-P(X<2)=1-P(X=1)-P(X=0)= 1 - \frac{20!}{1!(20-1)!} *(0.01)^{1}*(1-0.01)^{(20-1)}-\frac{20!}{0!(20-0)!} *(0.01)^{0}*(1-0.01)^{(20-0)}

P(X≥2)=1-0.165-0.818=0.017

b) p=0.04

P(x>1)=P(x≥2)= 1 - P(x=1) - P(x=0)= 1 - \frac{20!}{0!(20-1)!} *(0.04)^{1}*(1-0.04)^{(20-1)} - \frac{20!}{0!(20-0)!} *(0.04)^{0}*(1-0.04)^{(20-0)}

P(x>1)= 1 - 0.368 - 0.442=0.190

c) In this case we consider p=0.19 (Probability that X exceeds 1)

In this experiment Y is the number of hours and n= 5 hours.

Then, we check the probability in each hour:

P(Y>1)=1- P(Y=0)

P(Y=0)=\frac{5!}{0!(5-0)!} *(0.19)^{0}*(1-0.19)^{(5-0)}=0.349

P(Y>1)=1-0.349=0.651

3 0
2 years ago
2/5gal fill up 3/4 of a tank how many gallons will it take
Olin [163]

Answer:

8/15 gallons or 0.5333 gallons

Step-by-step explanation:

x = total

0.4 = 0.75x

0.4/0.75 = x

0.533 = x

0.533 = 8/15

5 0
2 years ago
Find the area of this regular polygon.<br> Round to the nearest tenth.<br> 8.65 mm<br> [? ]mm2
nadezda [96]

Answer:

Actually it's not polygon. it's a nonagon. With r=8.65mm″, the law of cosines gives us side a:

a=√{b²+c²−2bc×cos40°}

a=√{149.645−149.645cos40°}

Area Nonagon = (9/4)a²cos40°

=9/4[149.645−149.645cos40°]cot20°

=336.70125[1−cos(40°)]cot(20°)

Applying an identity for the cos(40°) does not get us very far…

= 336.70125[1−(cos2(20°)−1)]cot(20°)

= 336.70125[2−cos2(20°)]cot(20°)

= 336.70125[2−(1−sin2(20°))]cot(20°)

= 336.70125[1+sin2(20°)]cos(20°)sin(20°)

= 336.70125[cot(20°)+sin(20°)cos(20°)]mm²

3 0
3 years ago
Decrease £2123 by 8%
Gemiola [76]
Should be £1953.16 :)
3 0
2 years ago
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