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8090 [49]
2 years ago
5

In ΔDEF, \overline{DF} DF is extended through point F to point G, \text{m}\angle FDE = (2x+4)^{\circ}m∠FDE=(2x+4) ∘ , \text{m}\a

ngle DEF = (3x+3)^{\circ}m∠DEF=(3x+3) ∘ , and \text{m}\angle EFG = (7x-5)^{\circ}m∠EFG=(7x−5) ∘ . Find \text{m}\angle FDE.M∠FDE.

Mathematics
1 answer:
Sedaia [141]2 years ago
5 0

Answer:

<h3>18°</h3>

Step-by-step explanation:

See the diagram attached:

In a triangle, the sum of interior angles is equal to the exterior angle.

According the diagram, the sum of interior angles is given as:

Sum of interior = <FDE+<DEF

Given

<FDE = 2x+4

<DEF = 3x+5

Sum of interior = 2x+4+3x+5

Sum of interior = 5x+9

Exterior angle = <EFG = 7x-5

Equate the interior to the exterior and calculate the value of x:

5x+9 = 7x-5

Collect like terms

5x-7x = -5-9

-2x = -14

x = -14/-2

x = 7

Next is to get <FDE:

<FDE = 2x+4

<FDE = 2(7)+4

<FDE = 14+4

<FDE = 18°

Hence the measure of <FDE is 18°

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Cloud [144]

Answer:

See below

Step-by-step explanation:

<u>Sides of the garden</u>

  • 16 feet and 8 feet

<u>New dimensions of the garden</u>

  • 16 + 2x and 8 + x

<u>1. The area of the new garden</u>

  • (16 + 2x)(8 + x) =
  • 2x^2 + 32x + 128

<u>2. The difference in area </u>

  • 2x^2 + 32x + 128 - 16*8 =
  • 2x^2 + 32x

<u>3. x= 2 effect on the area</u>

  • 2*2^2 + 32*2 =
  • 8 + 64 =
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<u>4. Area difference = 160</u>

  • 2x^2 + 32x = 160
  • x^2 + 16x - 80 = 0
  • Solving we get positive root of 4 ft

<u>5. Area difference = 4 times</u>

  • 2x^2 + 32x = 128*3
  • 2x^2 + 32x - 384 = 0
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  • Solving we get positive root of 8 ft

3 0
3 years ago
Find h(g(n)) when h(n) = 2n + 5<br> and g(n) = n +4
Evgen [1.6K]

Answer:

2n+13

Step-by-step explanation:

h(g(n))\\h(n)=2n+5\\g(n)=n+4\\h(n+4)=2(n+4)+5\\=2n+8+5\\=2n+13

5 0
2 years ago
Find the equation of the line which passes through the point (-4,12) and is perpendicular to the given line. Express your answer
Vika [28.1K]

Answer:

y = 1/7x + 88/7

Step-by-step explanation:

y = mx +b

since it is perpendicular you have to get the negative reciprocal of the slope which is 1/7

y = 1/7x + b then you would plug in your points

12 = 1/7(-4) + b and then solve for b

12 = -4/7 + b

+ 4/7

88/7 = b

y = 1/7x + 88/7

8 0
3 years ago
1) Is 26,341 divisible by 3? If it is, write the number as the product of 3 and another factor. If not, explain.
yan [13]

Answer:

No

Step-by-step explanation:

26341 ÷ 3 = 8780.333333

because the product has a decimal of 8780 recurring 3, therefore 26341 is not divisible by 3

8 0
3 years ago
What is 11/12 - 2/3 <br> Subtracting Proper Fractions
alexgriva [62]

Answer:

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Step-by-step explanation:

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0.917 - 0.667 = 0.25

4 0
2 years ago
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