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3 years ago

Look at Karen's attempt to solve the equation for y: y + 8 = 15, y = 15 + 8, y = 23.Describe the mistake that Karen made.

1 answer:

6 0

The mistake that Karen made was that in order to get the 8 to switch sides, it should have been subtracted rather than added. This is because it is positive on the left side and therefore must be negative when we switch it to the right side. A proper version of this problem would be below.

y + 8 = 15

y = 15 - 8

y = 7

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Circular tracts of land with diameters 900 meters, 700 meters and 600 meters are tangent to each other externally. There are hou

Rudik [331]

Answer:

$\alpha=69.28^o$

$\beta=61.26^o$

$\gamma=49.46^o$

$A=227980.26\ m^2$

Step-by-step explanation:

Triangle Solving

If we had a triangle will its three sides of known length, we can solve for the rest of the parameters of the triangle, i.e. the area, perimeter and internal angles.

The three circles have diameters 900 m, 700 m and 600 m and are tangent to each other externally. The distances from their centers (where houses are located) are the sum of each pair of the radius of the circles. Thus, the sides of the triangle are

$x=450+350=800$

$y=450+300=750$

$z=350+300=650$

The internal angles can be computed by using the cosine's law

$x^2=y^2+z^2-2yzcos\alpha$

$y^2=x^2+z^2-2xzcos\beta$

$z^2=x^2+y^2-2xycos\gamma$

Where \alpha, \beta and \gamma are the opposite angles to x, y and z respectively. Solving for each one of them:

$\displaystyle cos\alpha=\frac{y^2+z^2-x^2}{2yz}$

$\displaystyle cos\alpha=\frac{750^2+650^2-800^2}{2\cdot 750\cdot 650}$

$cos\alpha=0.3538$

$\alpha=69.28^o$

Similarly

$\displaystyle cos\beta=\frac{x^2+z^2-y^2}{2xz}$

$\displaystyle cos\beta=\frac{800^2+650^2-750^2}{2\cdot 800\cdot 650}$

$cos\beta=0.4808$

$\beta=61.26^o$

The other angle is computed now

$\displaystyle cos\gamma=\frac{x^2+y^2-z^2}{2xy}$

$\displaystyle cos\gamma=\frac{800^2+750^2-650^2}{2\cdot 800\cdot 750}$

$cos\gamma=0.65$

$\gamma=49.46^o$

The area can be found by

$\displaystyle A=\frac{1}{2}x.y.sin\gamma$

$\displaystyle A=\frac{1}{2}\cdot 800\cdot 750\cdot sin49.46^o$

$A=227980.26\ m^2$

8 0

3 years ago

Peter is saving money to buy an MP3 player. After one month, he has $85. After 3 months, he has $120. After 4 months, he has $15

Ahat [919]

It's asking how much money does he get each month

4 0

4 years ago

Given x = 5, y = -6, z = -2, evaluate z - yx

Andreyy89

Answer: 28

Step-by-step explanation: Plugging them in, it would be -2 - (-6)(5).

- 2 - (-30)

-2 + 30

8 0

3 years ago

What is the Volume of the Sphere?

IgorLugansk [536]

Answer:

7776 $\pi$

Step-by-step explanation:

Sphere Volume Formula = 4/3 times $\pi$ times r^2

r is the radius and in this case its 18.

4/3 times $\pi$ times 18^3

4/3 times 5832 times $\pi$

4 times 1944 times $\pi$

7776 times $\pi$

The volume of the sphere is 7776 $\pi$

7 0

2 years ago

The volume of oil in four different containers is shown below: container

sdas [7]

Let me help you!
What we have right now:
*A 5.25 milliliters container.
*A 5.29 milliliters container.
*A 5.27 milliliters container.
*A 5.23 milliliters container.
*Sue's measuring cup that can measure to the nearest tenth of a milliliter.

What we need to do:
*Find out the least amount of oil after Sue used her measuring cup to measure each oil container.

Solution:
Container A: 5.25mL ---> 5.3mL
Container B: 5.29mL ---> 5.3mL
Container C: 5.27mL ---> 5.3mL
Container D: 5.23mL ---> 5.2mL <---- This is what we are looking for!

Therefore, the correct answer and the container which has the least amount of oil is: D. 5.23 milliliters container.

I hope this helped you :>

6 0

3 years ago