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3 years ago

Angle G and H are vertical angles. If angle G is 45 degrees and angle H is 2x degrees, what is the value of x?

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

6 0

Answer:

x = 22.5

Step-by-step explanation:

Vertical angles are congruent by the vertical angles theorem. Therefore is angle G is 45 degrees, then that means that angle H must be 45 degrees as well.

The value of x can be found by making the expression that represents angle H (2x) equal to 45 in an equation to solve for x.

2x = 45

Divide both sides by 2.

x = 22.5

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Suppose a package delivery company purchased 14 trucks at the same time. Five trucks were purchased from manufacturer A, four fr

nikklg [1K]

Answer:

Step-by-step explanation:

Given that a package delivery company purchased 14 trucks at the same time. Five trucks were purchased from manufacturer A, four from manufacturer B, and five from manufacturer C. The cost of maintaining each truck was recorded.

No of companies = 3

No of items in total = 14

Total df = 17-1=16

degrees of freedom between groups = 3-1 =2

Hence degrees of freedom for denominator

= $16-2 =14$

5 0

3 years ago

Christian's car used 15 gallons to travel 270 miles. How far can he travel on 11 gallons?

kumpel [21]

Answer:

198

Step-by-step explanation:

270/15 gives us 18, his miles per gallon. multiply that by 11, and you get 198.

5 0

2 years ago

A restaurant sells tea for $1.50 plus $0.05 per refill a gas station store sells tea for $0.50 plus $0.50 per refill?

lutik1710 [3]

Answer:

Part a) $y=0.05x+1.50$

Part b) $y=0.50x+0.50$

Part c) The graph in the attached figure

Part d) see the explanation

Step-by-step explanation:

The complete question is

A restaurant sells tea for $1.50 plus $0.05 per refill. A gas station store sells tea for $0.50 plus $0.50 per refill.

Part a) Write a linear function for the price of tea at restaurant

Part b) Write a linear function for the price of tea at gas station store

Part c) Graph both equations

Part c) Compare the lines in terms of slope and y-intercept

Let

y -----> the price of tea in dollars

x -----> the number of refills

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value (value of y when the value o x is equal to zero)

Part a)

At restaurant

we have that

The slope or unit rate is equal to

$m=\$0.05\ per\ refill$

The initial value or y-intercept is equal to

$b=\$1.50$

substitute

$y=0.05x+1.50$

Part b)

At gas station store

we have that

The slope or unit rate is equal to

$m=\$0.50\ per\ refill$

The initial value or y-intercept is equal to

$b=\$0.50$

substitute

$y=0.50x+0.50$

Part c) Graph both equations

we know that

The easiest way to graph a line is with two points

Find the intercepts of the line

At restaurant

$y=0.05x+1.50$

The y-intercept is the point (0,1.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

$0=0.05x+1.50$

$x=-30$

The x-intercept is the point (-30,0)

Plot the points and join to graph the line

see the attached figure

At gas station store

$y=0.50x+0.50$

The y-intercept is the point (0,0.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

$0=0.50x+0.50$

$x=-1$

The x-intercept is the point (-1,0)

Plot the points and join to graph the line

see the attached figure

Part c) Compare the lines in terms of slope and y-intercept

The slope or unit rate at the restaurant is less than the slope at the gas station store

$\$0.05\ per\ refill < \$0.50\ per\ refill$

The initial value or y-intercept at the restaurant is greater than the initial value at the gas station store

$\$1.50 > \$0.50$

3 0

3 years ago

Distance formula (-5,5) and (1,-2)

UNO [17]

(-2-5)^2+(1--5)^2
49+36
Sq rt of 85= 9.2

5 0

3 years ago

X + 1 > -5( 7-2x) I need help please.

Ede4ka [16]

Answer:

x<4

Step-by-step explanation:

$x + 1 > -5( 7-2x) \\\\\mathrm{Expand\:}-5\left(7-2x\right):\quad -35+10x\\x+1>-35+10x\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\x+1-1>-35+10x-1\\\\Simplify\\x>10x-36\\\\\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}\\x-10x>10x-36-10x\\Simplify\\-9x>-36\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\left(-9x\right)\left(-1\right)$

$\mathrm{Divide\:both\:sides\:by\:}9\\\frac{9x}{9}$

5 0

2 years ago