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HACTEHA [7]
3 years ago
11

Liam and Kaiden are brothers who go to different schools. The school day is just as long at Liam's school as at Kaiden's school.

At Liam's school, there are 6 class periods of the same length each day. Kaiden's day is broken into 3 class periods of equal length. One day, it snowed a lot so both of their schools started late. Liam only had four classes and Kaiden only had two. Kaiden claims his school day was shorter than Liam’s was because he had only two classes on that day. Is he right?
PLEASE HELP!!
Mathematics
1 answer:
Triss [41]3 years ago
4 0

Answer:

He's not right

Step-by-step explanation:

L = 4/6 = 2/3

K = 2/3

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4 years ago
The height of a triangle is 5 cm shorter than its base. If the area of the triangle is 25 cm2, find the height of the triangle.
Olin [163]

Answer:

h = 5\ cm

Step-by-step explanation:

Let's call B at the base of the triangle and call h at the height of the triangle. Then we know that:

The height of a triangle is 5 cm shorter than its base. This means that:

h = B-5.

 The area of the triangle is 25 cm²

By definition the area of a triangle is:

A = 0.5Bh

For this triangle we know that A = 25\ cm^2 and h = B-5. We substitute these values in the equation and solve for B.

25 = 0.5B (B-5)

0.5B ^ 2-\frac{5}{2}B-25 = 0

Now we use the quadratic formula to solve the equation.

For an equation of the form ax ^ 2 + bx + c = 0 the quadratic formula is:

B=\frac{-b\±\sqrt{b^2-4ac}}{2a}

In this case note that:  a=0.5,\ \ b=-\frac{5}{2}\ \ c=-25

Then:

B=\frac{-(-\frac{5}{2})\±\sqrt{(-\frac{5}{2})^2-4(0.5)(-25)}}{2(0.5)}

B=\frac{\frac{5}{2}\±\sqrt{\frac{25}{4}+50}}{1}

B=\frac{5}{2}\±\frac{15}{2}

The solutions are:

B_1=\frac{5}{2}+\frac{15}{2}=10

B_2=\frac{5}{2}-\frac{15}{2}=-5

For this problem we take the positive solution.

B=10\ cm

Now we substitute the value of B in the equation to find the height h

h = 10-5

h = 5\ cm

6 0
3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Then the desired sum is ...

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Answer:

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Step-by-step explanation:

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