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3 years ago

Lines AB and CD and are parallel. Find the measures of the three angles in triangle ABF.

Mathematics

1 answer:

Airida [17]3 years ago

3 0

Answer: ∠B = 42° ∠A = 23° ∠F = 115°

Step-by-step explanation:

∠B≅∠C alternate interior angles 42°

∠CDF is supplementary to ∠CDE,

so m∠CDF = 23° and ∠FAB≅∠CDF so m∠FAB= 23°

also ∠A ≅ CDE corresponding angles 157° ∠FAB is suplementary to ∠A

so 180 - 157 = 23 gives the m∠FAB

The sum of the angles of a triangle is 180°, so m∠AFB = 180 -(23 +42)

180- 65 = 115 = m∠F

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Andrea, Justin, and Virginia went to an office supply store. Andrea bought 6 pencils, 7 markers, and 8 erasers. Her total was $1

olga2289 [7]

Answer:

$x=0.25\,,\,y=1.75\,,\,z=0.25$

Step-by-step explanation:

Let $x,y,z$ denotes number of pencils, markers, erasers respectively.

For Andrea:

$6x+7y+8z=15.75\,\,\,(i)$

For Justin:

$6x+8y+5z=16.75\,\,\,(ii)$

For Virginia:

$5x+5y+7z=11.75\,\,\,(iii)$

On subtracting equations (i) and (ii), we get

$(6x+7y+8z)-(6x+8y+5z)=15.75-16.75\\-y+3z=-1\\y-3z=1\\y=1+3z$

Put $y=1+3z$ in equation (i)

$6x+7(1+3z)+8z=15.75\\6x+29z=8.75\,\,\,(iv)$

Put $y=1+3z$ in equation (iii)

$5x+5(1+3z)+7z=11.75\\5x+22z=6.75\,\,\,(v)$

Multiply equation (iv) by 5 and equation (v) by 6 and then subtract both the equations.

$5(6x+29z)-6(5x+22z)=5(8.75)-6(6.75)\\13z=3.25\\z=\frac{3.25}{13}=0.25$

Put $z=0.25$ in equation $y=1+3z$

$y=1+3(0.25)=1.75$

Put $y=1.75\,,\,z=0.25$ in equation (i)

$6x+7(1.75)+8(0.25)=15.75\\6x+12.25+2=15.75\\6x=1.5\\x=0.25$

8 0

3 years ago

A poll asks shoppers at the mall how many cups of water they typically drink in a day. The results of the poll are listed below.

juin [17]

Answer:

D 9.5

Step-by-step explanation:

Write data in increasing order.

3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11

Find the median

3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11

Median is 8

Lower half of the data is : 3, 5, 5, 6, 6, 6, 7, 7, 8, 8,

First quartile is the median of the lower half of the data=6+6 /2 =6

Upper half of the data is: 8, 8, 8, 9, 9, 10, 10, 10, 10, 11

The Third quartile is the median of the upper half=9+10 / 2 = 9.5

3 0

3 years ago

Read 2 more answers

At one time the price of gasoline was $1.279 a gallon. Then the price

ELEN [110]

Answer:

1.6627 (money wise, $1.66)

Step-by-step explanation:

Since its 130%, you know there was already a whole increase. So first you would do 1.279 + 1.279, which would give you 2.558. Then you need to calculate 30% of 1.279 for the rest of the increase. That gives you 0.3837 Add 2.558 and 0.3837 together, which would give you 2.9417. To get the INCREASE, you would have to subtract the new total from the original price, so 2.9417 - 1.279. This would give you 1.6627.

5 0

3 years ago

Write the equation of the line in point-slope form that has slope 3 and passes through (2, -5)

Fynjy0 [20]

Answer:

y = 3x - 11

Step-by-step explanation:

Step 1:

y = mx + b Slope Intercept Form

Step 2:

y = 3x + b Input Slope

Step 3:

- 5 = 3 ( 2 ) + b Input x and y values

Step 4:

- 5 = 6 + b Multiply

Step 5:

- 11 = b Subtract 6 on both sides

Answer:

y = 3x - 11

Hope This Helps :)

5 0

3 years ago

What is least 1.11, 0.111,1.01,1.001

Elan Coil [88]

0.11 is the least amount.

8 0

3 years ago