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2 years ago

Find the exact length of the third side?

Mathematics

1 answer:

notka56 [123]2 years ago

3 0

Answer:

57 for the third side

Step-by-step explanation:

a = √(c² - b²)

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What is the best way to display data if there is a wide range and we want to see individual data?

Novosadov [1.4K]

Answer:
The correct option is;
b. Stem and leaf plot

Step-by-step explanation:
A stem-and-leaf plot shows the data shape and the densities of the different classes in a graphical form such that the information in the data such as the data characteristics are self displayed by the data numbers arranged in the stem-and-leaf plot. The stem-and-leaf plot keeps the raw numerical data, in the form they were obtained and by their arrangement, outliers are easily spotted.

5 0

3 years ago

Read 2 more answers

In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm

tangare [24]

Answer:

$AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm$

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

$AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm$

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

$\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD$

Consider right triangle CAH.By the Pythagorean theorem,

$CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8$

The length cannot be negative, so CD=8 cm and

$CA=\sqrt{3}CD=8\sqrt{3}\ cm$

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

$AB=2CA=16\sqrt{3}\ cm$

By the Pythagorean theorem,

$BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm$

3 0

2 years ago

A chef kept track of the number of apples people ate last week in his cafeteria. The results are shown here.

n200080 [17]

The correct answer is C) 10

5 0

2 years ago

Suppose p(a) = 0.40 and p(a 

sveticcg [70]

Between the probability of union and intersection, it's not clear what you're supposed to compute. (I would guess it's the probability of union.) But we do know that

$P(A\cup B)+P(A\cap B)=P(A)+P(B)$

For parts (a) and (b), you're given everything you need to determine $P(B)$ .

For part (c), if $A$ and $B$ are mutually exclusive, then $P(A\cap B)=0$ , so $P(A\cup B)=P(A)+P(B)$ . If the given probability is $P(A\cup B)=0.55$ , then you can find $P(B)=0.15$ . But if this given probability is for the intersection, finding $P(B)$ is impossible.

For part (d), if $A$ and $B$ are independent, then $P(A\cap B)=P(A)\cdot P(B)$ .

8 0

3 years ago

Translate the sentence into an inequality.

Vadim26 [7]

Answer:

9(n + 22) ≤ -15

Step-by-step explanation:

9 times the sum of a number and 22 is at most −15

Let n = number

Times = multiplication

Sum = Addition

9 * n + 22

We must add parenthesis on the end on 22 and before n

We must do this because it says 9 times the sum of a number and 22 which means that 9 is being multiplied by both n and 22

We would have 9(n + 22)

9(n + 22) is at most -15

At most meaning that -15 is the highest number that 9(n + 22) can equal

Because it says at most 9(n + 22) can equal -15 or anything less than -15

So at most can be replaced with ≤

9(n + 22) ≤ -15

4 0

2 years ago