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3 years ago

Find the length of “b”, to the nearest tenth, using the Pythagorean Theorem.

Mathematics

2 answers:

julia-pushkina [17]3 years ago

7 0

Answer:

b = square root of 125

Put into calculator and put to 1dp

Step-by-step explanation:

Pythagorean theorem is

a^2 + b^2 = c^2

The a and b are the two short sides and c is always the hypotenuse

We just put the numbers in

10^2 + b^2 = 15^2

Now we can rearrange so that b^2 is by its self on the left side

b^2 = 15^2 - 10^2

Now just solve by putting into calculator

b^2 = 125

And finally square root to get b^2 down to b

b = square root of 125

Put into calculator and put to 1dp

Tresset [83]3 years ago

3 0

Answer: b= 11.2

10^2 + b^2 = 15^2

100 + b^2 = 225

b^2 = 125

b= $\sqrt{125}$

b= 11.2

Step-by-step explanation:

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2 years ago

The water level in a lake decreased by 2 1/4 inches in march and increased by 1 5/8 inches in april. Determine wether the water

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Change in level is given by :

C = increase in level - decrease in level.

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2 years ago

If DB = 36 and AC = 3x - 3, what is the value of x?

algol13

Answer:

A.) 13

Step-by-step explanation:

Since DB =36, and AC is the same line, then AC = 36. The new equation is 36 = 3x - 3. Do inverse operation. Add 3 to both sides of the equation: 36+3=39 & -3+3=0. New equation is 39=3x. Finally divide. 39/3= 13.

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2 years ago

Solve for w, where w is a real number.

Ber [7]

Answer:

w= 9

Step-by-step explanation:

$\sqrt{ - 4w + 61} = w - 4$

Square both sides:

-4w +61= (w -4)²

$\boxed{(a - b)^{2} = a^2 -2ab + b^2 }$

Expand:

-4w +61= w² -2(w)(4) +4²

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Simplify:

w² -8w +16 +4w -61= 0

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Factorize:

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w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

Note:

-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

Why do we use negative square root?

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

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