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3 years ago

Plz I need help with geometry homework FIND THE ANGLES

Mathematics

1 answer:

Talja [164]3 years ago

3 0

Answer:

a = 36°
b = 36°
c = 72°
d = 72°
e = 108°
f = 16°
g = 74°
h = 70°

Step-by-step explanation:

You are expected to know and make use of the following relations:

vertical angles are congruent
angles of a linear pair are supplementary
angles of a triangle sum to 180°
alternate interior angles are congruent (at parallel lines)
corresponding angles are congruent (at parallel lines)
acute angles of a right triangle are complementary
base angles of an isosceles triangle are congruent

For this problem, it isn't always easiest to work the questions in order. It is best to start with the angles easiest to find from those given.

b and 144° are a linear pair, so b = 180° -144° = 36°

a and b are alternate interior angles, so a = b = 36°

2d and 144° are corresponding angles, so d = 144°/2 = 72°

e is the apex angle of an isosceles triangle with base angles 36°, so is 180° -2(36°) = 108° = e

f and 164° are a linear pair, so f = 180° -164° = 16°

g and f are complementary, so g = 90° -16° = 74°

g+h is a vertical angle with 144°, so is congruent to that. h = 144° -74° = 70°

c is the base angle of an isosceles triangle with b as the vertex angle. That means c = (180° -36°)/2 = 72°

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AysviL [449]

You can take x = a, 2y = b and then can apply the binomial theorem.

The expansion of given expression is given by:

Option D: $x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$ is

<h3>What is binomial theorem?</h3>

It provides algebraic expansion of exponentiated(integer) binomial.

According to binomial theorem,

$(a+b)^n = \sum_{i=0}^n ^nC_i a^ib^{n-i}$

<h3>How to use binomial theorem for given expression?</h3>

Taking a = x, and b =2y, we have n = 7, thus:

$(x+2y)^7 = \: ^7C_0x^0(2y)^7 + \: ^7C_1x^1(2y)^6 + \: ^7C_2x^2(2y)^5 + \: ^7C_3x^3(2y)^4 + \:^7C_4x^4(2y)^3 + \:^7C_5x^5(2y)^2 + \:^7C_6x^6y^1 + \: ^7C_0x^7y^0\\\\
(x+2y)^7 = 128y^7 + 448xy^6 + 672x^2y^5 + 560x^3y^4 + 280x^4y^3 + 84x^5y^2 + 14x^6y + x^7\\\\
(x+2y)^7 = x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$

Thus, Option D: $x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$ is correct.

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3 years ago

Peggy had three times as many quarters as nickels. She had $1.60 in all. How many nickels and how many quarters did she have?. .

Andru [333]

Let

n-------> the number of nickels

q------> the number of quarters

we know that

$1\ quarter=\$0.25\\1\ nickel=\$0.05$

$0.05n+0.25q=1.60$ ----> equation A

$q=3n$ ----> equation B

substitute equation B in equation A

$0.05n+0.25[3n]=1.60$

$0.05n+0.75n=1.60$

$0.80n=1.60$

$n=2$

Find the value of q

$q=3*2=6$

therefore

<u>The answer part a) is</u>

the number of nickels are $2$ and the number of quarters are $6$

<u>the answer Part b) is</u>

The expressions that represents the number of quarters is

$q=3n$

5 0

3 years ago

Read 2 more answers

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timurjin [86]

The table is an exponential function, and the equation that represents this function is $f(x) =2^x -1$

<h3>The equation of the table</h3>

The table is given as:

x F(x)

4 15

5 31

7 127

8 255

Rewrite the table as:

x F(x)

4 16 - 1

5 32 - 1

7 128 - 1

8 256 - 1

Express as a base of 2

x F(x)

4 2⁴ - 1

5 2⁵- 1

7 2⁷ - 1

8 2⁸ - 1

Notice that the function is 1 subtracted from 2 raised to the power of the input.

This is represented as:

$f(x) =2^x -1$

Hence, the equation of the table is $f(x) =2^x -1$

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2 years ago

What is the answer for 11 12

Vesnalui [34]

11.) our question issss.....
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420/7 = 60
sooooo answer is 60

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50 x __ = 0
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have a good one :)

merry christmas:D

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3 years ago

There is 12/15 of a pizza left. How many 3/10 pieces can be made from the leftover pizza? Show work please!

Katyanochek1 [597]

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Hence to find how many 3/10 pieces can be made from 12/15 pizza, we have to divide 12/15 by 3/10 or multiplying by its reciprocal 10/3, i.e.

12/15 times 10/3= 8/3 or 2 2/3

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So the answer is 2 three-tenths pieces can be made, and one-fifth pizza will be left out.

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3 years ago