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sasho [114]
3 years ago
7

Find the values of x, y, and z. The diagram is not to scale.

Mathematics
2 answers:
adoni [48]3 years ago
7 0
Start by finding x.

All triangles have the property that their angles add up to 180°.

So you know from the diagram that:
36 + 63 + x = 180
Solve for x.

Similarly, looking at the larger triangle that holds the two smaller triangles, try solving for y. The top of the triangle is made up of 13° and 36°. 13 + 36 = 49.
So since we know the angles have to add up to 180°, we can solve for y in the equation:
63 + 49 + y = 180
Solve for y.

Lastly, solve for z using the same process! If you have any questions, just comment here. You've got this!
Kruka [31]3 years ago
5 0

we know that

The sum of the internal angles in the triangle must be 180 degrees

see the attached figure with letters to better understand the problem

Step 1

<u>Find the measure of the angle x</u>

In the triangle ABC

63\°+36\°+x\°=180\°

solve for x

99\°+x\°=180\°

x\°=180\°-99\°

x=81\°

therefore

<u>the answer Part a)  is</u>

the measure of angle x is 81\°

Step 2

<u>Find the measure of the angle z</u>

we know that

x+z=180\° --------> by supplementary angles

substitute the value of x

81\°+z=180\°

z=180\°-81\°

z=99\°

therefore

<u>the answer Part b)  is</u>

the measure of angle z is 99\°

Step 3

<u>Find the measure of the angle y</u>

In the triangle ACD

13\°+z\°+y\°=180\°

solve for y

13\°+99\°+y\°=180\°

112\°+y\°=180\°

y\°=180\°-112\°

y\°=68\°

therefore

<u>the answer Part c)  is</u>

the measure of angle y is 68\°

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Answer:

The left end approaches to + Infinite being an exponential function, and the right end to 0

Step-by-step explanation:

we have to remember the exponential function, the best way to find the answer is plotting the graph or arranging a table of values.

As you can see in the attached graph the y axis gets closer and closer to 0 as it moves forward in the x axis, and as it moves to the left the y axis starts increasing rapidly.

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Phoenix [80]

Question 1 Answer:

Aunt 1 and Grandma 1 would fill gift bags.

Mom and Aunt 2 would make centerpieces.

You and Grandma 2 would blow up balloons.

Since you are pairing up to complete the tasks, these pairs each have the shortest times in their respective categories and therefore are the most logical pairing to complete tasks.

Question 2 Answer:

We use algebra and our previous pairings to determine the length of each task.

<u>Gifts Bags --> 6/7 hours</u>

x = time together

\frac{1}{x} = rate of completion

Aunt 1 = \frac{1}{1.5} Grandma 1 = \frac{1}{2}

\frac{2}{3} +\frac{1}{2} = \frac{1}{x}

\frac{7}{6} = \frac{1}{x}

x = \frac{6}{7}

<u>Centerpieces --> 7/4 hours</u>

x = time together    \frac{1}{x} = rate of completion

Mom = \frac{1}{3.5} Aunt 2 = \frac{1}{3.5}

\frac{2}{7} + \frac{2}{7}  = \frac{1}{x}

\frac{4}{7} = \frac{1}{x}

x = \frac{7}{4}

<u>Balloons --> 15/16 hours</u>

x = time together    \frac{1}{x} = rate of completion

You = \frac{1}{1.5} Grandma 2 = \frac{1}{2.5}

\frac{2}{3} + \frac{2}{5}  = \frac{1}{x}

\frac{16}{15} = \frac{1}{x}

x = \frac{15}{16}

Shortest amount of time to complete all tasks is:

\frac{6}{7} + \frac{7}{4} + \frac{15}{16} = \frac{397}{112}  ≈ 3.54 hours

Converting hours to hours and minutes --> 3 hours 32 minutes

Therefore they must arrive by 5:28pm to complete the tasks in time to leave at 9:00pm.

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2 years ago
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pishuonlain [190]

\mathcal \pink{Answer}

\mathcal \green{3x = 30}

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