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3 years ago

If m∠4 = 35, find m∠2. Explain.

Mathematics

1 answer:

Bad White [126]3 years ago

4 0

Answer:

Option (1)

Step-by-step explanation:

From the picture attached,

Triangle CAB is a right triangle.

Therefore, m∠1 = 90°

Similarly, m∠ACD = 90°

m∠ACD = m∠ACB + m∠BCD = 90°

= m∠3 + m∠4 = 90°

Since m∠4 = 35°,

m∠3 + 35° = 90°

m∠3 = 90° - 35°

= 55°

In the triangle ABC,

m∠ACB + m∠CBA + m∠BAC = 180° [Property of a triangle]

m∠3 + m∠2 + m∠1 = 180°

55° + m∠2 + 90° = 180°

m∠2 + 145° = 180°

m∠2 = 180° - 145°

= 35°

Since, AB║CD and BC is a transverse,

Therefore, m∠2 = m∠4 = 35° [Alternate interior angles]

Option (1) is the correct option.

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I am greater than 320. You say my number if you start at 324 and count from 10 to 10. I have the same number of tens and ones.

Bess [88]

Answer:

344

Step-by-step explanation:

Um..... sorta confusing, but I think you are only allowed to increase by 10 each time, so then you need to add 20 to make 344, where the units digit and tens digit are the same

4 0

2 years ago

An unbalanced die is manufactured so that there is a 20% chance of rolling a “six." The die is rolled 6

SIZIF [17.4K]

Answer:

Probability of rolling at least 4 sixes is 0.01696.

Step-by-step explanation:

We are given that an unbalanced die is manufactured so that there is a 20% chance of rolling a “six." The die is rolled 6 times.

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......$

where, n = number trials (samples) taken = 6 trials

r = number of success = at least 4

p = probability of success which in our question is probability of

rolling a “six", i.e; p = 0.20

Let X = Number of sixes on a die

So, X ~ Binom(n = 6, p = 0.20)

Now, Probability of rolling at least 4 sixes is given by = P(X $\geq$ 4)

P(X $\geq$ 4) = P(X = 4) + P(X = 5) + P(X = 6)

= $\binom{6}{4} \times 0.20^{4} \times (1-0.20)^{6-4}+\binom{6}{5} \times 0.20^{5} \times (1-0.20)^{6-5}+\binom{6}{6} \times 0.20^{6} \times (1-0.20)^{6-6}$

= $15 \times 0.20^{4} \times 0.80^{2}+6 \times 0.20^{5} \times 0.80^{1}+1 \times 0.20^{6} \times 0.80^{0}$

= 0.0154 + 0.00154 + 0.000064

= 0.01696

Therefore, probability of rolling at least 4 sixes is 0.01696.

8 0

3 years ago

What is the slope of y=45x

Lapatulllka [165]

Answer:

45/1

Step-by-step explanation:

45x is the rate at which the line goes up

8 0

2 years ago

Ebony's gross income is $46 660 with allowable tax deductions of $4120. a What is Ebony's taxable income? b Calculate the amount

jasenka [17]

Answer:

(a) Ebony's taxable income = $42,540

(b) Amount of tax due = $5190.3

Step-by-step explanation:

Ebony's gross income = $46,660 (given)

Allowable tax deductions = $4,120 (given)

(a) Taxable Income = Gross income - Tax deductions

Ebony's taxable income = $46,660 - $4,120

Ebony's taxable income = $42,540

(b) Amount of tax due = 22% of Taxable Income,

Refer to the USA Tax Brackets for 2019 (See Attached image)

Amount of tax due = 10% on first $9,700 + 12% on ($39475-$9700) + 22% on ($42540-$39475).

Amount of tax due = 10% on first $9,700 + 12% on $29775 + 22% on $3065.

Amount of tax due = $970 + $3573 + $647.3

Amount of tax due = $5190.3

$95 * 4 = $380

Amount of tax owed = Amount of tax due - Amount of tax paid

Amount of tax owed = $5190.3 - $380 = $4810.3

3 0

3 years ago

Felicia wants to buy a new soccer ball. it is on sale for $12.60 She has one $10 bill,two $5 bills,three$1 bills,6 quarters,and

gladu [14]

One $10 bill, Two $1 bills, Two Quarters, Two Nickels

Two $5 bills, Two $1 bills, Two Quarters, Two Nickles

One $10 bill, One $1 bill, Six Quarters, Two Nickles

5 0

3 years ago