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3 years ago

Which of the following is a correct equation based on the triangle shown?

Mathematics

1 answer:

levacccp [35]3 years ago

4 0

Answer:

Correct choice is B

Step-by-step explanation:

Unknown leg x in right triangle is opposite to the angle of the measure of 50°. Use the definition of the sine of the angle:

$\sin \alpha=\dfrac{\text{opposite leg}}{\text{hypotenuse}}.$

Hence,

$\sin 50^{\circ}=\dfrac{x}{12}\Rightarrow 0.766=\dfrac{x}{12}.$

You might be interested in

25 – 4.33<br>7 + (1 - 100)

Sidana [21]

Answer:

25 – 4.33 = 20.67

7 + (1 - 100) = -92

Step-by-step explanation:

First one) Simply use your knowledge of integers and decimals to solve this. You can even start by drawing a number line and practising with that before beginning to do harder problems.

Second one) Just like the first one but use PEDMAS, BEDMAS or BODMAS and make sure to solve the brackets first.

6 0

3 years ago

Find the other two vertices of a square with one vertex (0, 0) and another vertex (4, 2). Can you find another answer?

Margarita [4]

It is given that two vertices of square are (0,0) and (4,2).

Now the problem is that you haven't given that whether these two vertices are adjacent vertices or opposite vertices of the square.

1. By Supposing that these two are adjacent vertices of Square

The third vertex will be at (-4,2) which lies in third quadrant.

Suppose the coordinate of fourth vertex be (x,y).

Mid point of line joining (4,2) and (-4,2) is{ [4+(-4)]/2,(2+2)/2} is (0,2).

Mid point of line joining (x,y) and (0,0) is (x/2,y/2).

Since diagonals of square bisect each other,

∵ x/2=0

⇒x=0

and

y/2=2

⇒y=4

So, The Coordinate of fourth vertex is (0,4).

Now coming back to second condition if these are two opposite vertex of Square.

Let the third coordinate be (a,b).

Length of diagonal= $\sqrt{(4-0)^2+(2-0)^2}=\sqrt20=2\sqrt5$

Now,let side of Square be A.

Then length of Diagonal of square =√2 A

⇒√2 A=2√5

⇒A =√10

As third vertex is (a,b).

Using distance formula

a² + b²=10 -------------(1)

(a-4)²+ (b-2)²=10 --------------(2)

Solving expression (1) and (2), we get

⇒a²+ b²=(a-4)² +(b-2)²

⇒2a + b =5

⇒b=5-2a

Putting the value of b in (1),we get

⇒a² +(5-2a)²=10

⇒a²+25+4a²-20a =10

⇒5a²-20a+15=0

⇒a² - 4a + 3=0

Splitting the middle term,we get

⇒(a-3)(a-1)=0

⇒a=3 ∧ a=1

we get b=5-2×1=3 and b=5-2×3=5-6=-1

So,the other vertex are (1,3) and(3,-1).

3 0

3 years ago

Battery packs in electric go-carts need to last a fairly long time. The run-times (time until it needs to be recharged) of the b

pav-90 [236]

Answer:

The minimum level for which the battery pack will be classified as highly sought-after class is 2.42 hours

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 2, \sigma = 0.33$