An arithmetic sequence has this recursive formula.

If the measure of angle BCD=51 degrees, solve for x.

BabaBlast [244]

Answer:

$x=5$

Step-by-step explanation:

step 1

Find the measure of angle EFD

In this problem I will assume that ABCD is a parallelogram

In a parallelogram opposite angles are congruent and consecutive angles are supplementary

so

$m\ angle BCD=m\angle BED=51^o$

$m\ angle FED=(1/2)m\angle BED=(1/2)51^o=25.5^o$ --- > given problem

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle EFD

$m\ angle FED+m\ angle FDE+m\ angle EFD=180^o$

substitute the given values

$25.5^o+55^o+m\ angle EFD=180^o$

$80.5^o+m\ angle EFD=180^o$

$m\ angle EFD=180^o-80.5^o$

$m\ angle EFD=99.5^o$

step 2

Find the measure of angle EFB

we know that

$m\angle EFB+m\angle EFD=180^o$ ---> by supplementary angles

we have

$m\ angle EFD=99.5^o$

substitute

$m\angle EFB+99.5^o=180^o$

$m\angle EFB=180^o-99.5^o$

$m\angle EFB=80.5^o$

step 3

Find the value of x

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle EBF

$m\ angle BEF+m\ angle EFB+m\ angle EBF=180^o$

we have

$m\angle BEF=m\ angle FED=25.5^o$

$m\angle EFB=80.5^o$

$m\angle EBF=(14x+4)^o$

substitute

$25.5^o+80.5^o+(14x+4)^o=180^o$

solve for x

Combine like terms

$(14x+110)^o=180^o$

$14x=180-110$

$14x=70$

$x=5$

4 0

2 years ago

If the square is 3 by 4 and shaded area is 5/8 by 3/7 what is the area of shaded region

mote1985 [20]

There is no picture added. I can not help with that then.

4 0

3 years ago

Luisa's current swimming record is 12% faster than it was last year. If her record last year was 4 minutes and 23 seconds, what

Elden [556K]

12% less since faster
100%-12%=88%

88% of 4 min and 23 sec=
0.88 times 263 seconds=
=231.44=3 minutes and 50 seconds rounded

3 mins, 50 seconds

7 0

2 years ago

If a logo of 6 ft and he needs a quart of paint for every 22 square ft how many quarte will he need for the whole logo

bulgar [2K]

Complete Question

If a logo has dimensions of 6 ft and 11ft, he needs a quart of paint for every 22 square ft. How many quarts will he need for the whole logo?

Answer:

3 quarts of paint

Step-by-step explanation:

The Logo is rectangular in shape, hence:

The area of a rectangle = Length × Width

The logo has dimensions of 6 ft and 11ft.

Area of the Logo = 6ft × 11ft = 66ft²

He needs a quart of paint for every 22 square ft

Hence:

22 ft² = 1 quart of paint

66ft² = x

Cross Multiply

22 ft² × x = 66 ft² × 1 quart

x = 66 ft² × 1 quart/22 ft²

x = 3 quarts of paint

Therefore, he will need 3 quarts of paint for the whole logo.

7 0

2 years ago

How do I solve for AB? (rounded to the nearest tenth)

kolbaska11 [484]

Answer:

The answer would be 8.1

Step-by-step explanation:

For the smaller triangle, you use the pythagorean theorem. a squared + b squared = c squared.

To find one of the legs, you do 5 squared - 3 squared = b squared.

25 - 9 = b squared. (BD)

16 = b squared

4 = b

Now for the bigger right triangle. You still use the same tactic.

7 squared + 4 squared = c squared (which is AB)

49 + 16 = c squared

65 = c squared

That means c would equal: square root of 65, which is 8.0622577483 which rounds to 8.1

7 0

1 year ago