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3 years ago

In exercises 1 and 2, find m<1 and m<2. Tell which theorem you used in each case.

Mathematics

1 answer:

solniwko [45]3 years ago

8 0

Answer:

m∠2 = 78°

Step-by-step explanation:

From the given picture,

lines 'm' and 'n' are the parallel lines and line 't' is the transverse line.

∠1 and angle with the measure of 78° are corresponding angles.

Therefore, m∠1 = 78°

m∠1 = m∠2 [Vertical angles are equal]

m∠2 = 78°

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Two types of shipping boxes are shown below.

devlian [24]

Answer:

B. 3 square feet

Step-by-step explanation:

The formula for surface area is:

2lw+2lh+2wh

Box F's surface area is just plugging in those variables

2(3)(3)+2(3)(3)+2(3)(3)=54

Box J's surface area is the same way

2(2)(4.5)+2(2)(3)+2(4.5)(3)=57

The difference is 57-54=3

The answer is B. 3 square ft

7 0

3 years ago

on Monday it rained 1 3/4 of an inch and on Tuesday it rained 2 2/3 of an inch. how many inches did it rain altogether?

iogann1982 [59]

Answer:

4 5/12

Step-by-step explanation:

Convert to mixed fraction 7/4 + 8/3

Find common denominator, 12

21/12 + 32/12

add numerators (21+32)/12 = 53/12

reduce fraction 4 5/12

8 0

3 years ago

Given that 1 foot<br> 0.3048 meter and 1 rod = 16.5 feet, 1 rod is about how many meters?

Lostsunrise [7]

Answer:

5.0292 meters

Step-by-step explanation:

.3048 meters per foot times 16.5 feet

8 0

3 years ago

Property of 5x+1=1+5x

Mariulka [41]

Answer:

Commutative property

4 0

3 years ago

A geometric sequence is shown below.

mestny [16]

Answer:

An explicit representation for the nth term of the sequence:

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

It means, option (B) should be true.

Step-by-step explanation:

Given the geometric sequence

$-\frac{1}{2},\:-2,\:-8,\:-32,...$

A geometric sequence has a constant ratio, denoted by 'r', and is defined by

$f_n=f_1\cdot r^{n-1}$

Determining the common ratios of all the adjacent terms

$\frac{-2}{-\frac{1}{2}}=4,\:\quad \frac{-8}{-2}=4,\:\quad \frac{-32}{-8}=4$

As the ratio is the same, so

r = 4

Given that f₁ = -1/2

substituting r = 4, and f₁ = -1/2 in the nth term

$f_n=f_1\cdot r^{n-1}$

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

Thus, an explicit representation for the nth term of the sequence:

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

It means, option (B) should be true.

8 0

2 years ago