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8 months ago

Find the measure of ZB.

1 answer:

6 0

The sum of the inside angles of a triangle, always sum up to 180 degrees. Using this information, we can create the following equation for this problem:

$(3x-2)\text{ +(6}x\text{+11)+(5}x\text{ +3) = 180}$

Adding up all terms with 'x' and adding the other together, we have the following equation:

$\begin{gathered} (3x+6x+5x)+(11+3-2)=180_{} \\ 14x+12=180 \\ 14x=180-12=168 \end{gathered}$

Solving this last equation for 'x', we have the following:

$\begin{gathered} 14x=168 \\ x=\frac{168}{14}=12 \end{gathered}$

Then, the final answer for the 'x' value is twelve!

You might be interested in

a certain triangle has a perimeter of 3067 mi. the shortest side measures 71 mi less than the middle side and the longest side m

UkoKoshka [18]

Answer:

The measure of the shortest side is 851 miles

Step-by-step explanation:

Let

x ----> the measure of the shortest side

y ---> the measure of the middle side

z ---> the measure of the longest side

we know that

The perimeter of triangle is equal to

$P=x+y+z$

$P=3,067\ mi$

$3,067=x+y+z$ ----> equation A

the shortest side measures 71 mi less than the middle side

$x=y-71$ ----> equation B

the longest side measures 372 mi more the the middle side

$z=y+372$ ----> equation C

substitute equation B and equation C in equation A

$3,067=(y-71)+y+(y+372)$

solve for y

$3,067=3y+301\\3y=2,766\\y=922$

Find the value of x

$x=y-71\\x=922-71\\x=851$

therefore

The measure of the shortest side is 851 miles

6 0

2 years ago

For a certain candy, 20% of the pieces are yellow, 15% are red, 20% are blue, 20% are green, and the rest are brown. a

OLEGan [10]

Answer:

Step-by-step explanation:

Based on the question we are given the percentages of each of the types of candies in the bag except for brown. Since the sum of all the percentages equals 75% and brown is the remaining percent then we can calculate that brown is (100-75 = 25%) 25% of the bag. Now we can show the probabilities of getting a certain type of candy by placing the percentages over the total percentage (100%).

Brown: $\frac{25}{100}$
Yellow or Blue: $\frac{20}{100} +\frac{20}{100} = \frac{40}{100}$ ....add the numerators

Not Green: $\frac{80}{100}$ .... since the sum of all the rest is 80%

Stiped: $\frac{25}{100}$ .... there are 0 striped candies.

Assuming the <u><em>ratios/percentages</em></u> of the candies stay the same having an infinite amount of candy will not affect the probabilities. That being said in order to calculate consecutive probability of getting 3 of a certain type in a row we have to multiply the probabilities together. This is calculated by multiplying the numerators with numerators and denominators with denominators.