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Sav [38]
3 years ago
5

Please help (CORRECT ANSWERS ONLY)

Mathematics
1 answer:
german3 years ago
7 0

-2(8m+8) = -16

-16m - 16 = -16

His first mistake lies in his distribution. When multiplying -2 * 8, he made it a positive 16, when he should have made it a negative 16.

-16m - 16 = -16

Add 16 to each side.

-16m = 0

Divide that by -16

m = 0

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
Given the piece wise function show below, select all that are true​
NeTakaya

Answer:

Option (C) and (D)

Step-by-step explanation:

Given piecewise function is,

f(x) = 2x, x < 1

        5, x = 1

        x^{2}, x > 1

Option (A),

x = 5 means x > 1

So the function will be,

f(x) = x^{2}

f(5) = (5)²

     = 25

Therefore, f(5) = 1 is not correct.

Option (B),

x = -2 means x < 1

f(x) = 2x will be applicable.

f(-2) = 2(-2) = -4

Therefore, f(-2) = 4 is not correct.

Option (C)

For x = 1,

f(1) = 5

Therefore, f(1) = 5 is the correct option.

Option (D)

x = 2 means x > 1 and the function defined will be,

f(x) = x²

f(2) = 2²

     = 4

Therefore, f(2) = 4 will be the correct option.

Options (C) and (D) will be the answer.

7 0
3 years ago
How many inches represent 1 mile? Convert the map scale to a unit rate. 3/10in = 7/8mi
mote1985 [20]
I think it is 1357inchs

8 0
3 years ago
Which measures would be the side lengths of a right triangle?
pav-90 [236]

Answer:

Answer choice B.

Step-by-step explanation:

Remember the 3:4:5 rule.

3 0
3 years ago
What it means by that
denpristay [2]
Example A means

For every #of felt pieces you multiply that by the cost of one piece of felt to see how much you spent

Example
Felts cost $3 a piece
You get 7 pieces

7 x 3= 21

You spent $21 on felt
3 0
3 years ago
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