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3 years ago

Find the value of x. Show all work.

Mathematics

1 answer:

Inessa05 [86]3 years ago

8 0

Answer:

x = -8°

Step-by-step explanation:

Angle 2

Since the triangle is isosceles, Angle 2 is the same as the missing angle

So angle 2 would be:

180 - 34 = 2(angle 2)

So 146 = 2(x + 81)

146 = 2x + 162

146 - 2x = 162

-2x = 16

x = -8

Check

146 = 2(-8+81)

146 = 2(73)

146 = 146

Correct!

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The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

5 0

3 years ago

The question is in the screenshot.

Musya8 [376]

Answer:

v = 4

Step-by-step explanation:

a (-2) multiplied by t (3) = -6

-6 + u (10) = 4

5 0

3 years ago

Read 2 more answers

Fifteen more than four times a number is equal to the difference between 191 and four times the number. Find the number.

Semenov [28]

Answer:

The number would be 22.

Step-by-step explanation:

In order to solve for the number, we need to make both statements into numerical statements.

Fifteen more than four times a number = 15 + 4x

difference between 191 and four times the number = 191 - 4x

Now we set them equal to each other.

15 + 4x = 191 - 4x -----> Add 4x to each side

15 + 8x = 191 ------> Subtract 15 from both sides

8x = 176 -------> Divide by 8

x = 22

5 0

3 years ago

Find the prime factorization of 30

sattari [20]

Let us start dividing 30 by small prime numbers in increasing order .

the smallest prime number we use is 2

Let's divide 30 by 2 quotient is 15

so we get : 30 = 2* 15

15 is not a prime number , it can be factorized further .

now we start dividing 15

2 can not divide 15 so we move to next prime number that is 3

can 3 divide 15? yes .

we get a quotient 5

so 30 is now : 2* 15 = 2* 3*5

now we have to work on 5 but 5 is a prime number so we stop here .

the prime factorization of 30 is : 2* 3* 5

Answer : 2 *3*5

5 0

3 years ago

Read 2 more answers

Find the values of x,y, and z. The diagram is not to scale.

vazorg [7]

All the angles must add to 180degrees in a triangle.

180 = 59 + 35 + x
180 = 94 + x
86 = x

Supplementary angles x and z add to 180
180 = x + z
180 = 86 + z
94 = z

Now the last triangle is with angles 11, z, and y
they must add to 180 so...
180 = 11 + z + y
180 = 11 + 94 + y
180 = 105 + y
75 = y

Hope this helps!

3 0

3 years ago