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3 years ago

In △XYZ , XZ=11 , YZ=8 , and m∠Z=31∘ .

Mathematics

1 answer:

Natalija [7]3 years ago

8 0

Answer:

The area of the triangle is 22.7 units²

Step-by-step explanation:

The formula of the area of a triangle using trigonometry is A = $\frac{1}{2}$ (a)(b) sin(C), where a , b are two sides in the triangle and C is the angle between these two sides

In Δ XYZ

∵ XZ = 11 units

∵ YZ = 8 units

∵ m∠Z = 31°

∵ ∠Z is between the two sides XZ and YZ

∴ We can use the formula above to find the area of Δ XYZ

∵ Area Δ XYZ = $\frac{1}{2}$ (XZ)(YZ) sin(Z)

∴ Area Δ XYZ = $\frac{1}{2}$ (11)(8) sin(31)

∴ Area Δ XYZ = 22.6616753 unit²

- Round it to the nearest tenth

∴ Area Δ XYZ = 22.7 units²

The area of the triangle is 22.7 units²

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A tree in John's backyard has been growing for 4 1/2 years. The tree is 4/5 meters tall. What is the unit rate in meters per yea

STatiana [176]

Answer:

5 127/200 meters

Step-by-step explanation:

4 1/2 = 4 5/10 | 4/5 = 8/10

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4 5/10 = 4.5 | 8/10 = 0.8

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4.8 divided by 0.8 = 5.625

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5.635 = 5 635/1000

635/1000 divided by 5 = 127/200

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5 + 127/200 = 5 127/200

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3 years ago

I'm so confused please helpppppppp How is C correct please show your work

777dan777 [17]

Answer:

Step-by-step explanation:

She makes $325 a week, so go to the 8th row, for weekly income of $300 to $400. She claims 2 exemptions, so go to the third column labeled 2. The value is 2. That means the $2 is withheld from her paycheck on top of the 6.25% for FICA. The total is therefore:

$2 + (0.0625) ($325)

$22.3125

Rounded to the nearest cent, that's $22.31.

3 0

3 years ago

Please help with the attached question. Thanks

Mademuasel [1]

Answer:

Choice A) $F(x) = 3\sqrt{x + 1}$ .

Step-by-step explanation:

What are the changes that would bring $G(x)$ to $F(x)$ ?

Translate $G(x)$ to the left by $1$ unit, and
Stretch $G(x)$ vertically (by a factor greater than $1$ .)

$G(x) = \sqrt{x}$ . The choices of $F(x)$ listed here are related to $G(x)$ :

Choice A) $F(x) = 3\;G(x+1)$ ;
Choice B) $F(x) = 3\;G(x-1)$ ;
Choice C) $F(x) = -3\;G(x+1)$ ;
Choice D) $F(x) = -3\;G(x-1)$ .

The expression in the braces (for example $x$ as in $G(x)$ ) is the independent variable.

To shift a function on a cartesian plane to the left by $a$ units, add $a$ to its independent variable. Think about how $(x-a)$ , which is to the left of $x$ , will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by $a$ units, subtract $a$ from its independent variable.

For example, $G(x+1)$ is $1$ unit to the left of $G(x)$ . Conversely, $G(x-1)$ is $1$ unit to the right of $G(x)$ . The new function is to the left of $G(x)$ . Meaning that $F(x)$ should should add $1$ to (rather than subtract $1$ from) the independent variable of $G(x)$ . That rules out choice B) and D).

Multiplying a function by a number that is greater than one will stretch its graph vertically.
Multiplying a function by a number that is between zero and one will compress its graph vertically.
Multiplying a function by a number that is between $-1$ and zero will flip its graph about the $x$ -axis. Doing so will also compress the graph vertically.
Multiplying a function by a number that is less than $-1$ will flip its graph about the $x$ -axis. Doing so will also stretch the graph vertically.

The graph of $G(x)$ is stretched vertically. However, similarly to the graph of this graph $G(x)$ , the graph of $F(x)$ increases as $x$ increases. In other words, the graph of $G(x)$ isn't flipped about the $x$ -axis. $G(x)$ should have been multiplied by a number that is greater than one. That rules out choice C) and D).

Overall, only choice A) meets the requirements.

Since the plot in the question also came with a couple of gridlines, see if the points $(x, y)$ 's that are on the graph of $F(x)$ fit into the expression $y = F(x) = 3\sqrt{x - 1}$ .

5 0

3 years ago

Read 2 more answers

At a regional soccer tournament, tickets for two adults and seven students cost $60. Tickets for three adults and eleven stude

den301095 [7]

Answer:

The price of an adult ticket is $9 and the price of a student ticket is $6

Step-by-step explanation:

Create a system of equations where x is the price of an adult ticket and y is the price of a student ticket:

2x + 7y = 60

3x + 11y = 93

Solve by elimination by multiplying the top equation by 3 and the bottom equation by -2, to cancel out the x terms:

6x + 21y = 180

-6x - 22y = -186

Add them together:

-y = -6

y = 6

Then, plug in 6 as y into one of the equations to solve for x:

2x + 7y = 60

2x + 7(6) = 60

2x + 42 = 60

2x = 18

x = 9

So, the price of an adult ticket is $9 and the price of a student ticket is $6

8 0

3 years ago

In a survey, four out of five people surveyed preferred creamy over chunky peanut butter. 120 people are shopping at the grocery

elixir [45]

Answer: Around 96 people would prefer creamy peanut butter.

Step-by-step explanation:

In the survey was found that 4 out of 5 preferred creamy over chunky peanut butter.

Then the relative frequency is:

4/5 = 0.8 prefer creamy peanut butter.

And we can assume that:

1/5 = 0.2 prefer chunky peanut butter.

We also could multiply these numbers by 100% to obtain the percentage forms:

0.8*100% = 80%

0.2*100% = 20%

Now, if there are 120 people in the grocery store, we can expect that the 80% will prefer creamy peanut butter.

Then we can expect that the number of people that prefers creamy peanut butter is:

N = (80%/100%)*120 = 0.8*120 = 96

Around 96 people would prefer creamy peanut butter.

3 0

2 years ago