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DedPeter [7]
3 years ago
10

Point 6 is on line segment FH. Given FG=8 and GH=11, determine length FH

Mathematics
1 answer:
Pie3 years ago
7 0

Answer:

GH = 20

Step-by-step explanation:

We have that

FH = FG + GH ← substitute values

4x + 8 = x + 5x

4x + 8 = 6x ( subtract 4x from both sides )

8 = 2x ( divide both sides by 2 )

4 = x

Hence GH = 5x = 5 × 4 = 20GH = 20

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The corners of a meadow are shown on a coordinate grid. Ethan wants to fence the meadow. What length of fencing is required?
Nuetrik [128]

Answer:

34.6 units

Step-by-step explanation:

The lenght of fencing required is the total distance between point A to B, B to C, C to D, and D to A. That is the distance between all 4 corners of the meadow.

The coordinates of the corners of the meadow is shown on a coordinate plane in the attachment. (See attachment below).

Let's use the distance formula to calculate the distance between the 4 corners of the meadow using their coordinates as follows:

Distance between point A(-6, 2) and point B(2, 6):

AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

A(-6, 2)) = (x_1, y_1)

B(2, 6) = (x_2, y_2)

AB = \sqrt{(2 - (-6))^2 + (6 - 2)^2}

AB = \sqrt{(8)^2 + (4)^2}

AB = \sqrt{64 + 16} = \sqrt{80}

AB = 8.9 (nearest tenth)

Distance between B(2, 6) and C(7, 1):

BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

B(2, 6) = (x_1, y_1)

C(7, 1) = (x_2, y_2)

BC = \sqrt{(7 - 2)^2 + (1 - 6)^2}

BC = \sqrt{(5)^2 + (-5)^2}

BC = \sqrt{25 + 25} = \sqrt{50}

BC = 7.1 (nearest tenth)

Distance between C(7, 1) and D(3, -5):

CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

C(7, 1) = (x_1, y_1)

D(3, -5) = (x_2, y_2)

CD = \sqrt{(3 - 7)^2 + (-5 - 1)^2}

CD = \sqrt{(-4)^2 + (-6)^2}

CD = \sqrt{16 + 36} = \sqrt{52}

CD = 7.2 (nearest tenth)

Distance between D(3, -5) and A(-6, 2):

DA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

D(3, -5) = (x_1, y_1)

A(-6, 2) = (x_2, y_2)

DA = \sqrt{(-6 - 3)^2 + (2 - (-5))^2}

DA = \sqrt{(-9)^2 + (7)^2}

DA = \sqrt{81 + 49} = \sqrt{130}

DA = 11.4 (nearest tenth)

Length of fencing required = 8.9 + 7.1 + 7.2 + 11.4 = 34.6 units

8 0
3 years ago
PLEASE HELP ME, EASY MATH QUESTION !!!! (no links), beainliest xtra points profile thanks, thanks, 5star rating ((IF CORRECT))
Keith_Richards [23]

Answer:

1) A) Increases

2) C) Stays the same

Step-by-step explanation:

1) A) Increases (94 to 95)

2) C) Stays the same (95)

8 0
2 years ago
The number of ways 8 cars can be lined up at a toll booth would be computed from
stepladder [879]

Answer: c. 8!

Step-by-step explanation:

We know , that if we line up n things , then the total number of ways to arrange n things in a line is given by :-

n! ( in words :- n factorial)

Therefore , the number of ways 8 cars can be lined up at a toll booth would be 8! .

Hence, the correct answer is c. 8! .

Alternatively , we also use multiplicative principle,

If we line up 8 cars , first we fix one car , then the number of choices for the next place will be 7 , after that we fix second car ,then the number of choices for the next place will be 6 , and so on..

So , the total number of ways to line up 8 cars = 8 x 7 x 6 x 5 x 4 x 3 x 2 x1 = 8!

Hence, the correct answer is c. 8! .

5 0
3 years ago
I need help with 1-9 please!
Margaret [11]

1-First let’s list the numbers between 210 to 220, except the even ones since they’re a multiple of 2:

211; 213; 215; 217; 219

Let’s remove 213, and 219 because they’re multiples of 3 (2+1+3=6; 2+1+9=12), 215 is multiple of 5, so let’s remove it.

That leave’s is with 211, and 217.

We can remove 217, because it’s a multiple of 7, leaving us with 211.

2- It’s deductive reasoning, because you started with a more general idea.

3- {-7, -6, -5, -4, -3, -2, -1, 0, 1}

4- {x e R, x>=-2}

5-{-1, 0, 1}

6- {x∣-4≤ x ≤6}

7- [-20, ♾ )

8- On a number line, make a circle around -1, and continue the line to minus infinity.

9- On a number line, make a circle on -3, and continue to minus infinity. Make a ring on 0, and continue to infinity.

8 0
2 years ago
Verify the identity.
olga nikolaevna [1]

Answer:

from left hand side:tan^2/secx=(,sin^2x/cos^2x)/(1/cosx)=sin^2x/cosx=sinx×sinx/cosx=sinx.tanx=right hand side.verified.

3 0
2 years ago
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