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2 years ago

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Tim and Sue share a small pizza. Tim eats 2/3 of the pizza. Sue eats half as much of the pizza as Tim does. What fraction of the

pizza does Sue eat?

2 answers:

Luda [366]2 years ago

5 0

If he ate 2/3 of the pizza and she ate half as much as him that would be half of two thirds so one third or 1/3 of the pizza.

sergij07 [2.7K]2 years ago

5 0

If she ate half as much as tim that means she ate 1/3

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Ramona's backyard is fenced and represented by parallelogram YARD with measures in meters. She installed a 12-meters fence to se

Alisiya [41]

The fencing line x is the height of a rectangle triangle of base = y, hypothenuse of 9 m, so we use Pythagoras theorem to solve:

hyp^2 = height^2 + base^2
9^2 = x^2 + y^2
x^2 = 81 - y^2

we can see that x is also the height of another rectangle triangle of base = 15 - y, hypothenuse of 12 m, so we use Pythagoras theorem to solve:
hyp^2 = height^2 + base^2
12^2 = x^2 + (15 - y)^2

lets expand:
144 = x^2 + 225 - 30y + y^2

substitute x^2 from the first equation in the last:
144 = 81 - y^2 + 225 - 30y + y^2
144 = 81 + 225 - 30y
30y = -144 + 81 + 225
y = 5.4 m

substitute in the fence equation:
x^2 = 81 - y^2
x^2 = 81 - 5.4^2
x = 7.2 m that is the length of the fence

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2 years ago

Which number in the monomial 125x18y3z25 needs to be changed to make it a perfect cube?

andriy [413]

To make the monomial 125 x^18 y^3 z^25 a perfect cube, the entire expression should be reduced to a rational number when the cube root is taken. For the constant 125, the cube root is 5, so it doesn't need to be changed. For the variables, the exponents should be divisible by 3. The exponent of z is not divisible by 3. It can be subtracted with 1 or added with 2 to make the expression a perfect cube.

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2 years ago

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Henry is asked to find the exact value of cos 10pi/3. His steps are shown below.

nata0808 [166]

Answer:

<em>A) The reference angle should be </em><u><em> $\frac{\pi }{3}$ ,</em></u><em> and the sign of the value should be </em><u><em>negative.</em></u>

Step-by-step explanation:

cos( $\frac{10\pi }{3}$ )

Remove full rotations of 2π until the angle is between 0 and 2 $\pi$ .

cos( $\frac{4\pi }{3}$ )

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

-cos( $\frac{\pi }{3}$ )

The exact value of cos( $\frac{\pi }{3}$ ) is $\frac{1}{2}$ .

− $\frac{1}{2}$

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2 years ago

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Sitting on a park bench, you see a swing that is 100 feet away and a slide that is 80 feet away. The angle between them is 30 de

leva [86]

We are given : Distance of the swing = 100 feet.

Distance of slide = 80 feet.

Angle between swing and slide = 30 degrees.

We need to find the distance between the swing and the slide.

Distance of swing, distance of slide and distance between the swing and the slide form a triangle.

We can apply cosine law to find the distance between the swing and the slide.

c^2 = a^2 +b^2 - 2ab cos C

c^2 = 100^2 +80^2 - 2(100)(80) cos 30°

c^2 = 10000 + 6400 -2* 8000 $(\frac{\sqrt{3}} 2)}$

c^2 = 16400 - 8000 $\sqrt{3}$

c^2 = 16400 - 13856

c^2 = 2544

$c =\sqrt{2544}$

c= 50.44

c = 50 feet approximately.

<h3>Therefore, the approximate distance between the swing and the slide is 50 feet.</h3>

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2 years ago

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Yuliya22 [10]

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2 years ago

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