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kifflom [539]
3 years ago
11

Choose two of the angles on ∆ABC, and locate the line segment between them. Draw a new line segment,DE , parallel to the line se

gment you located on ∆ABC. You can draw of any length and place it anywhere on the coordinate plane, but not on top of ∆ABC. From points D and E, create an angle of the same size as the angles you chose on ∆ABC. Then draw a ray from D and a ray from E through the angles such that the rays intersect. You should now have two angles that are congruent to the angles you chose on ∆ABC. Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.

Mathematics
1 answer:
Degger [83]3 years ago
5 0

Answer:

The two triangles are attached below.

Step-by-step explanation:

Let the ∆ABC be an isosceles right angled triangle.

The two angles will be 45° each.

The triangle ABC is attached below.

Now construct the triangle DEF according to the given instructions.

The two triangles are attached below.

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Find (fog)(2) and (f+g)(2) when f(x) =1/x and g(x) =4x+9
Dahasolnce [82]

( f o g)(2) = \frac{1}{17}

(f + g)(2) = \frac{35}{2}

<em><u>Solution:</u></em>

Given that:

f(x) = \frac{1}{x}\\\\g(x) = 4x + 9

To find: (fog)(2) and (f + g)(2)

By composite function,

( f o g)(x) = f (g(x))

Substitute g(x) = 4x + 9 in above formula,

( f o g)(x) = f(4x + 9)

To find (fog)(2) substitute x = 2 in above formula

( f o g)(2) = f(4(2) + 9)

( f o g)(2) = f(8 + 9) = f(17)

We know that f(x) = \frac{1}{x}

( f o g)(2) = f(17) = \frac{1}{17}

( f o g)(2) = \frac{1}{17}

<em><u>To find (f + g)(2)</u></em>

We know that,

(f + g)(x) = f (x) + g(x)

Therefore,

(f + g)(2) = f(2) + g(2)

Substitute x = 2 in f(x) and g(x)

(f + g)(2) = \frac{1}{2} + (4(2) + 9)\\\\(f + g)(2) = \frac{1}{2} + 17 = \frac{1+34}{2} = \frac{35}{2}

(f + g)(2) = \frac{35}{2}

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3 years ago
Helpppp meeeeee plssssss
saul85 [17]

Answer:

Second

Step-by-step explanation:

1 gallon = 23 miles

2 gallons = 46 miles

3 gallons = 69 miles

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5 0
3 years ago
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Mandy's baby brother weighs 15 lb. How many ounces does her baby brother weigh?
Leokris [45]

Answer:

240 oz

Step-by-step explanation:

we know that,

1 lb = 16oz

15lb = ?

15 * 16 = 240oz

7 0
3 years ago
A baseball is dropped from a glider 500 feet above the ground. The height (in feet) above the ground is modeled by the function
Sophie [7]

A) 436 ft

B) t = 5 sec

C) 5.60 s

Step-by-step explanation:

A)

The height of the ball at time t is given by the equation

h(t)=-16t^2+500

where

-16 ft/s^2 is the acceleration of the ball (acceleration of gravity, downward)

+500 is the initial height of the ball, at time t = 0

Here we want to find the height of the ball after 2 seconds, so at a time of

t = 2 s

Substituting into the equation, we find:

h(2)=-16\cdot 2^2+500=436 ft

B)

Here we want to find the time it takes for the ball to fall to a height of 100 feet above the ground, so the time t at which

h(t) = 100 ft

As stated in the text of the question, the height of the ball at time t is given by

h(t)=-16t^2+500

Since

h(t) = 100, we have

100=-16t^2+500

And solving for t we find:

16t^2=400\\t^2=25\\t=\pm 5

So, the correct solution is the positive one:

t = 5 sec

C)

The ball reaches the ground when the height of the ball has became zero:

h(t) = 0

The height of the ball at time t is given by

h(t)=-16t^2+500

And substituting

h(t) = 0

We get

0=-16t^2+500

And solving the equation for t, we find the time t at which the ball reaches the ground:

16t^2=500\\t^2=31.25\\t=\pm 5.6 s

So, the correct solution is the positive one:

t = 5.60 s

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What do you mean, the answer is 12 and we know that because we combine the numbers
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