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2 years ago

In ΔTUV, t = 410 cm, ∠U=27° and ∠V=78°. Find the length of v, to the nearest 10th of a centimeter.

Mathematics

1 answer:

telo118 [61]2 years ago

6 0

Answer:

$v \approx 415.2\,cm$

Step-by-step explanation:

The angle T is:

$\angle T = 180^{\circ} - 27^{\circ} - 78^{\circ}$

$\angle T = 75^{\circ}$

Now, the length of v is determine by the Law of Sines:

$\frac{410\,cm}{\sin 75^{\circ}} = \frac{v}{\sin 78^{\circ}}$

$v = (410\,cm)\cdot \left(\frac{\sin 78^{\circ}}{\sin 75^{\circ}} \right)$

$v \approx 415.2\,cm$

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At a bake shop, the cost of flour is $2.50 per pound and increases at a rate of $0.07 per month. The cost of cocoa is $6.00 per

Vesna [10]

Answer:

Step-by-step explanation:

We will find two equations for this system, one representing flour and the other representing cocoa. For the flour, we start with $2.50, and the cost goes up .07 per month, x. The equation for that is

y = .07x + 2.50

For the cocoa, the equation is written in the exact same way, but the cost goes down. Down is a negative thing while up is a positive thing. The cost starts at $6.00 and goes down .03 per month, x. The equation for that is

y = -.03x + 6.00

Comparing the first equation to the second, the .07 is positive because the cost goes UP that amount per month and the .03 is negative because the cost goes DOWN that amount per month. Get it?

If y is cost and we are tryong to find out where the cost is the same, we are looking for when y is the same. If the first y is equal to .07x + 2.50 and the second y is equal to -.03x + 6.00, and y is equal to y, then

.07x + 2.50 = -.03x + 6.00 (this is setting the first y equal to the second y). This is the system that describes how to find the number of months x when the cost y is the same. We'll solve it just for practice.

Combining like terms we get

.10x = 3.5 so

x = 35

Now back sub in what x equals to solve for y. If x = 35, then in the first equation,

.07(35) + 2.50 = y and

y = 4.95 (you could have used the second equation and subbed in 35 for x and you will get the exact same y value. Promise!)

What this answer tells us is that 35 months after the start of this pricing, the cost of flour will be the same as the cost of cocoa. But immediately after 35 months, the costs will not be the same anymore. It is only AT 35 months. At 36 months, the costs will be different.

7 0

2 years ago

Octagon PQRSTVWZ is a regular octagon with its center at point C.

REY [17]

Answer:

Option F is correct, i.e. "rotating 90° counterclockwise around point C."

Step-by-step explanation:

Given is the regular octagon PQRSTVWZ with its center at point C.

To map octagon PQRSTVWZ onto itself, we must provide such a transformation that should not change the size or coordinates of the vertices.

We can not use Translations, Reflections, and Dilations because they will change size and coordinates.

We can use only Rotations and that should be about the center C of the regular shape.

About center point C, and rotations of 90° does not change the orientation of the regular octagon, Both images would overlap each other.

Hence, option F is correct, i.e. "rotating 90° counterclockwise around point C."

8 0

2 years ago

In a race, Car #1 went an average of 165 miles per hour for x hours before dropping out. Car #2 went an average of 175 miles per

Akimi4 [234]

When you think about it. It's actually quite easy.
The number are the amount of miles, and the variables are the amount of hours. So we would just have to multiply them. So, by putting the number together we would be able to multiply them once we have the numbers for the variables. Since we dont have them, we can just make the inequality. It says that car 1 traveled at LEAST that of car 2. Showing that car 1 may have traveled farther. SOOOOO........ the inequality should look like this:

165x <span>≥ 175y</span>

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2 years ago

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Tony is 4 years younger than his brother josh and two years older than his sister Cindy. Tony also has a twin brother, Evan. All

Sholpan [36]

Let Tony's age = x

He is 4 years younger than his brother Josh, so Josh's age would be x + 4

He is 2 years older than his sister, so her age would be x - 2

He has a twin, which would be the same age, so the twins age is also x

They all add together to equal 66, so you get:

x + x + x+4 + x-2 = 66

Simplify:

4x +2 = 66

Subtract 2 from both sides:

4x = 64

Divide both sides by 4:

x = 64/4 = 16

Tony is 16 years old.

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2 years ago

A local diner has started selling cupcakes and is using the bar chart given below to keep track of how many are sold each day. H

stepladder [879]

Answer:

Step-by-step explanation:

the pattern is adding 4 each day

13 + 4 = 17

actually nvm i read it wrong

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2 years ago

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