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2 years ago

Find the length of the third side. If necessary, write in simplest radical form.

Mathematics

1 answer:

melisa1 [442]2 years ago

4 0

$\text{Apply Pythagorean theorem,}\\\\~~~~~~~~\text{Hypotenuse}^2=\text{Base}^2 + \text{Perpendicular}^2\\\\\implies 9^2 = \text{Base}^2 + \left(2\sqrt{14} \right)^2\\\\\implies 81 = \text{Base}^2 + 56\\\\\implies \text{Base}^2 = 81-56\\\\\implies \text{Base}^2 = 25\\\\\implies \text{Base} = \sqrt{25}\\\\\implies \text{Base} = 5\\\\\text{The length of the third side is 5 units.}$

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mixas84 [53]

Answer:

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Ques 17)

$\dfrac{3w^2+7w-7}{w^2+8w+15}+\dfrac{2w^2-9w+4}{(2w^2+9w-5)(w^2-w-12)}\\ \\=\dfrac{3w^2+7w-7}{w^2+8w+15}+\dfrac{(2w-1)(w-4)}{(2w-1)(w+5)(w+3)(w-4)}\\\\=\dfrac{3w^2+7w-7}{(w+3)(w+5)}+\dfrac{1}{(w+3)(w+5)}\\\\=\dfrac{3w^2+7w-7+1}{(w+3)(w+5)}\\\\=\dfrac{(3w-2)(w+3)}{(w+5)(w+3)}\\\\=\dfrac{3w-2}{w+5}$

Ques 18)

Let the blank space be denoted by the quantity 'x'.

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Ques 19)

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3 years ago

if the probability of picking a green marble from a bag of green and red marbles is 0.3. if i choose a marble 100 times and repl

vfiekz [6]

Answer:

30 marbles would be green

Step-by-step explanation:

green chance is 0.3

red chance 0.7

.3 times 100

30 green marbles is what you would expect

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3 years ago

What is f (0) for the function f (a) = 2a + 3

vovangra [49]

F(0)= 2* 0 +3

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f(0)=3

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3 years ago

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Randy has to raise $50.00 to repair his bicycle. He is only $1.00 short. He has only $1 and $5 bills. If he has one more $1 bill

Nezavi [6.7K]

Answer:

Randy has eight $5 bills and nine $1 bills

Step-by-step explanation:

Randy needs $50.00

And we know that he his only $1.00 short, so he has $49.00

let's define:

x = number of $1 bills that he has

y = number of $5 bills that he has.

then:

x*$1 + y*$5 = $49

We know that he has one more $1 bills than $5 bills.

we can write this as

x = y + 1

So we have a system of two equations and two variables:

x*$1 + y*$5 = $49

x = y + 1

First we can see that the variable "x" is isolated in the second equation, now we can replace that in the other equation:

x*$1 + y*$5 = $49

(y + 1)*$1 + y*$5 = $49

now we can solve this for y.

y*$1 + $1 + y*$5 = $49

y*($1 + $5) = $49 - $1 = $48

y*$6 = $48

y = $48/$6 = 8

He has 8 $5 bills

and we know that:

x = y + 1

x = 8 + 1 = 9

he has 9 $1 bills.

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3 years ago

Lorie correctly determines that for the triangles below, the statement pg and the statement both describe the relationship betwe

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Answer:

The correct option is 1.

Step-by-step explanation:

Two triangles are called similar if all the corresponding angles are congruent or all corresponding sides are in same proportion.

In triangle MNO and triangle RTS.

$\angle M\cong\angle R=54.4^{\circ}$ (Given)

$\angle N\cong\angle T=71.2^{\circ}$ (Given)

According to the angle sum property, the sum of all interior angles of a triangle is 180 degree. Since two corresponding angles are congruent, therefore third angle is also congruent.

$\angle O\cong\angle S=54.4^{\circ}$

Since all corresponding angles are congruent, therefore the triangles MNO and RTS similar.

The triangle are congruent by AA rule of similarity. Each triangle has two congruent angles, therefore both triangles are similar. Option 1 is correct.

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3 years ago

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