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3 years ago

<1 and <2 form a linear pair. The measure of <2 is six more than twice the measure of <1. Find the measure of <2

Mathematics

1 answer:

MrMuchimi3 years ago

7 0

Answer:

122 Degrees

Step-by-step explanation:

Since we are given that angle 1 and 2 make a linear pair:

angle 1 + angle 2 = 180 degrees ----------------------------(1)

We have also been told that angle 2 is 6 more than twice the measure of angle 1

Which means: angle 2 = (2*angle1) + 6 -------------------(2)

From putting the value of angle 2 in (1) from (2)

angle 1 + 2*angle 1 + 6 = 180

3*angle 1 = 174

angle 1 = 58 degrees -----------------------(3)

From (1) and (3):

angle 2 + 58 = 180

angle 2 = 122 degrees

Therefore, the measure of angle 2 is 122 degrees

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Bobby put 1/3 of his lawn mowing money into his savings and uses the remaining 2/5 to buy a video game. If he has $12 left, how

Alexeev081 [22]

Given:

Bobby put 1/3 of his lawn mowing money into his savings

He uses the remaining 2/5 to buy a video game.

He has $12 left.

To find:

The amount did he have at first.

Solution:

Let x be the initial amount.

Bobby put 1/3 of his lawn mowing money into his savings. So, the remaining amount is

$x-\dfrac{1}{3}x=\dfrac{2}{3}x$

He uses the remaining 2/5 to buy a video game. Then the remaining amount is

$Remaining=\dfrac{2}{3}x-\dfrac{2}{3}x\times \dfrac{2}{5}$

$Remaining=\dfrac{2}{3}x-\dfrac{4}{15}x$

$Remaining=\dfrac{10x-4x}{15}$

$Remaining=\dfrac{6x}{15}$

$Remaining=\dfrac{2x}{5}$

It is given that the remaining amount is $12.

$12=\dfrac{2x}{5}$

$12\times 5=2x$

$60=2x$

Divide both sides by 2.

$\dfrac{60}{2}=x$

$30=x$

Therefore, Bobby have $30 at first.

6 0

3 years ago

Which are the correct measures for

-BARSIC- [3]

Answer:

option c is the correct answer

Step-by-step explanation:

∠YXZ+117°=180°

∠YXZ=180°-117°

∠YXZ=63°

63°+36°+∠YZX=180°(sum of angles is 180)

99°+∠YZX=180

∠YZX=180-99

∠YZX=81

5 0

3 years ago

The sales tax for an item was $24.50 and it cost $490 before tax.

Ymorist [56]

The sales tax rate is 5%.

Step-by-step explanation:

Given,

Sales tax for an item = $24.50

Cost of item before tax = $490

Sales tax rate = $\frac{Sales\ tax}{Cost\ of\ item}*100\\$

$Sales\ tax\ rate=\frac{24.50}{490}*100\\\\Sales\ tax\ rate=\frac{2450}{490}\\\\Sales\ tax\ rate=5\%$

The sales tax rate is 5%.

Keywords: sales tax, percentage

Learn more about percentages at:

#LearnwithBrainly

3 0

3 years ago

Jason’s checkbook had a balance of $525.02 on May 5. On May 6, he wrote a check for $107.65 at the grocery store. On May 8, he w

blondinia [14]

Answer:

Jason has $244.37 in his bank account.

Step-by-step explanation:

This is simple addition and subtraction,

525.02 - 107.65 - 228.00 + 55.00 = bal

3 0

2 years ago

The volume of a cone is 763.02 cubic inches. The radius and height of the cone are equal. What is the radius of the cone?

Hoochie [10]

Answer:

The radius of the cone is 9cm

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cone

The volume of a cone is expressed as

V=1/3(πr²h)

We were told that the radius r and the height h are equal

I.e r=h

Substituting h=r in the formula we have

V= 1/3(πr²*r)

V =1/3(πr³)

To find the radius r let us substitute our given 763.02cm³ (note we assume unit in cm)

763.02= 1/3(3.142r³)

763.02= (3.142r³)/3

763.02*3=3.142r³

2289.06=3.142r³

r³=2289.06/3.142

r³= 728.54

r= ³√728.54

r= 8.99cm

≈r= 9cm

hope this helps

7 0

2 years ago