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3 years ago

Which expressions correctly represent the area of the triangle XYZ?

Mathematics

1 answer:

Evgen [1.6K]3 years ago

6 0

Answer:

Options (2) and Option (1)

Step-by-step explanation:

Area of the ΔXYZ = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(XZ)h$

= $\frac{1}{2}(18)h$

By applying sine rule in the ΔYPZ,

sin(38°) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

sin(38°) = $\frac{h}{14}$

h = 14[sin(38°)]

Therefore, area of the given triangle = $\frac{1}{2}(18)(14)sin(38)$

By applying sine rule in ΔYPZ,

sin(58°) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

sin(58°) = $\frac{h}{10}$

h = 10sin(58°)

Area of ΔXYZ = $\frac{1}{2}(18)(10)sin(58)$

Therefore, Options (2) and Option (1) are the correct options.

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The volume of the oblique cylinder is 24 ft3.

Assoli18 [71]

Answer:

A: The height of the cylinder is 3.4 ft.

C: The diameter of the cylinder is about 3 ft.

E: A right cylinder with the same height and radius as this oblique cylinder would also have a volume of 24 ft3.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

How do you solve this equation: -2m+3=|15+m|

Elden [556K]

Any number inside the modulus sign becomes positive. This means $|15+m|=|-(15+m)|=|-15-m|$ and so we have,

$-2m+3=|15+m| \Rightarrow \left \Big\{ {{-2m+3=15+m} \atop{-2m+3=-15-m}} \right$

Solving these gives us

$-2m+3=15+m \Rightarrow m=-4$

$-2m+3=-15-m \Rightarrow = m=18$

However if we check the second solution in the original equation we obtain $-2(18)+3=|15+18| \Rightarrow -33=33$ . This is false and so $m=18$ can't be a solution.

Therefore the only solution is $m=-4$ .

(Note: I'm not sure why the second solution didn't work but when there's a modulus sign involved it always pays to check your final answers to be sure. I'll have a think about it but in case you find out before I do, I'd be interested to know in the comments.)

8 0

3 years ago

Use the Venn diagram to calculate probabilities. Circles A and B overlap. Circle A contains 15, circle B contains 10, and the in

grin007 [14]

Answer:

$(B) P(B)=\dfrac{16}{31}$

Step-by-step explanation:

From the Venn diagram, n(AUB)=31

The given probabilities in the option are calculated below:

$P(A)=\dfrac{21}{31}\\\\P(B)=\dfrac{16}{31}\\\\P(A|B)=\dfrac{P(A\cap B)}{P(B)}= \dfrac{6/31}{16/31} =\dfrac{6}{16}=\dfrac{3}{8} \\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{6/31}{21/31} =\dfrac{6}{21}=\dfrac{3}{7}$

The only correct option is the probability of B which is $\frac{16}{31}$

8 0

4 years ago

A roller coaster begins at 45 feet above ground level. Then it descend 52 feet. Find the height of the coaster after the first d

ioda

Answer:

-7 feet above the ground

Step-by-step explanation:

8 0

3 years ago

Anaya makes 14 baskets during her game. Some of these baskets were worth two points and others were worth three points. In total

Valentin [98]

Answer:she made 12 two points basket.

Step-by-step explanation:

Let x represent the number of baskets that were worth two points.

Let y represent the number of baskets that were worth three points.

Anaya makes 14 baskets during her game.

This means that

x + y = 14

Some of these baskets were worth two points and others were worth three points. In total she scored 30 points. His means that

2x + 3y = 30 - - - - - - - - - -1

Substituting x = 14 - y into equation 1, it becomes

2(14 - y) + 3y = 30

28 - 2y + 3y = 30

- 2y + 3y = 30 - 28

y = 2

Substituting y = 2 into x = 14 - y, it becomes

x = 14 - 2

x = 12

7 0

3 years ago