How much of a stick of butter is 1/2 cup?

Fifty six students sing up to volunteer for the race . There were 4 equal groups of students , and each group had a different ta

andrey2020 [161]

There were 14 students per group.

8 0

3 years ago

drawbridge at the entrance to an ancient castle is raised and lowered by a pair of chains. The figure represents the drawbridge

jasenka [17]

Answer:

4.0 meters, ∠C = 39°, ∠A = 51°

Step-by-step explanation:

Firstly, our diagram shows us that the given triangle is actually a right triangle. So we can use the <em>Pythagorean Theorem</em> to solve for the height of the chain:

$a^{2} +b^{2} =c^{2}$

$(3.3)^{2} +b^{2} =(5.2)^{2}$

$b^{2} =(5.2)^{2}-(3.3)^{2}$

$b =\sqrt{(5.2)^{2}-(3.3)^{2}}$

$b=4.0187...$

$b=4.0 m$

Now, we can use the <em>Law of Cosines</em> to figure out one of the acute angles:

$c^{2} =a^{2} +b^{2} -2ab(cos(C))$

$(3.3)^{2} =(4.0)^{2} +(5.2)^{2} -2(4.0)(5.2)(cos(C))$

$cos(C)=\frac{(3.3)^{2}-(4.0)^{2} -(5.2)^{2}}{-2(4.0)(5.2)}$

$C=cos^{-1}( \frac{(3.3)^{2}-(4.0)^{2} -(5.2)^{2}}{-2(4.0)(5.2)})$

$C=39.3915...$

∠C = 39°

And since we know that all angles in a triangle add up to 180°:

∠A + ∠B + ∠C = 180

∠A + 90 + 39 = 180

∠A = 180 - 90 - 39

∠A = 51°

However, you should always review any answers on the Internet and make sure they are correct! Check my work to see if I made any mistakes!

7 0

2 years ago

Find the minimum and maximum possible areas for a rectangle measuring 4.15 cm by 7.34 cm. Round to the nearest hundredth. A. min

Shalnov [3]

This is probably in the context of a discussion of significant figures and accuracy.

When we record a measurement of 4.15 cm with two significant figures, that means we believe the exact value is in the range from 4.145 cm to 41.155 cm

Similarly 7.34 really means between 7.335 and 7.345 cm.

The minimum area rectangle is

$4.145 \times 7.335 = 30.403575 \approx 30.40$

The maximum area rectangle is

$4.155 \times 7.345 =30.518475 \approx 30.52$

Choice A

5 0

2 years ago

Read 2 more answers

What is the length of side x?

Vinil7 [7]

Answer:

x = 3

Step-by-step explanation:

In a 30-60-90 triangle the side between 60 and 90 degree angle is a, the side between 30 and 90 degree angle is a√3, and the hypotenuse is 2*a.

Given that the side that is supposed to be a is currently √3, we know that the missing side x must be:

a√3 (We know that a, in this case, is √3, so substitute)

x = (√3) * (√3)