All categories

3 years ago

How to find the measure of a triangle?

Mathematics

2 answers:

gulaghasi [49]3 years ago

8 0

Is it 1/2×b×h
to find the area
or
base×height

AleksAgata [21]3 years ago

6 0

Hi there! :)

Answer:

The answer is D. 83°

Step-by-step explanation:

You should know that the interior angles of a triangle always add up to 180°.

So, what you will need to do, is add all 3 angles together and create an equation (equal to 180). Then you need to solve this equation by isolating "x":

(8x + 12) + (55 - 3x) + (10x + 23) = 180

Get rid of all the parentheses

8x + 12 + 55 - 3x + 10x + 23 = 180

Add all similar terms together

8x - 3x + 10x = 15x

12 + 55 + 23 = 90

15x + 90 = 180

Subtract "90" from each side of the equation → 180 - 90 = 90

15x = 90

Divide each side of the equation by "15" → 90 ÷ 15 = 6

x = 6

Since you now know that the value of "x" is 6, you can now find the measure of the angle at George's position by replacing the "x" by 6:

10x + 23 = Measure of the angle at George's position

10(6) + 23

Multiply 10 by 6 → 10 × 6 = 60

60 + 23

Add 60 and 23 together → 60 + 23 = 83

83 = Measure of the angle at George's position

There you go! I really hope this helped, if there's anything just let me know! :)

You might be interested in

Solve the following equation. Show all your work.

horrorfan [7]

$\dfrac{x}{x - 2} + \dfrac{x - 1}{x + 1} = -1$

$(x - 2)(x + 1) \times \dfrac{x}{x - 2} + (x - 2)(x + 1) \times \dfrac{x - 1}{x + 1} = -1(x - 2)(x + 1)$

$(x + 1)x + (x - 2)(x - 1) = -1(x - 2)(x + 1)$

$x^2 + x + x^2 - 3x + 2 = -x^2 + x + 2$

$3x^2 - 3x = 0$

$3x(x - 1) = 0$

$x = 0~~~or~~~x - 1 = 0$

$x = 0 ~~~ or ~~~ x = 1$

Since neither 0 nor 1 cause a zero in a denominator in the original equation, 0 and 1 are acceptable as solutions.

Answer: x = 0 or x = 1

8 0

3 years ago

Mona is skating at a speed of 300 feet per minute. Lina is 1000 feet behind her. What should be her speed if she wants to catch

Allisa [31]

If we translate the facts into location equations, xM=Mona's location, xL=Lina's location, then we get:

xM(t) = 300t
xL(t) = v*t - 1000
xM(10)=xL(10)

Where v is Lina's speed we have to find.

Plugging them all together gives:

300*10 = 10v - 1000

Which can be solved:

3000 + 1000 = 10v
4000 = 10v
v=400

Lina should skate at 400 feet per minute!

4 0

3 years ago

In a random sample of 25 people, the mean commute time to work was 33.9 minutes and the standard deviation was 7.2 minutes. Ass

Phoenix [80]

Answer:

$33.9-1.32\frac{7.2}{\sqrt{25}}=31.999$

$33.9+1.32\frac{7.2}{\sqrt{25}}=35.801$

So on this case the 80% confidence interval would be given by (31.999;35.801)

And the margin of error is given by:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}}$

And replacing we got:

$ME = 1.32\frac{7.2}{\sqrt{25}} =1.9008$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=33.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.2 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.80 or 80%, the value of $\alpha=0.2$ and $\alpha/2 =0.1$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,24)".And we see that $t_{\alpha/2}=1.32$