All categories

3 years ago

Find the length of b using the Pythagorean theorem

Mathematics

2 answers:

g100num [7]3 years ago

6 0

Answer:

b = 32 units

Step-by-step explanation:

by Pythagoras theorem,

(40)^2 = 24^2 + b^2

1600 = 576 + b^2

1600 - 576 = b^2

1024 = b^2

b = √1024

b = 32

Rus_ich [418]3 years ago

3 0

Answer:

the Pythagorean theorem states:

a^2 + b^2 = c^2 in your case a=24 and c=40

Step-by-step explanation:

24^2 + b^2 = 40^2

24x24 + b^2 = 40x40

(576 + b^2 = 1600)

b^2 = 1600 - 576

b^2 = 1024

b= √1024

b = 32

Final answer: 32

You might be interested in

Johanna can jog 3,000 feet in 5 minutes. If she jogs at the same rate, how many feet can she jog in 8 minutes? *

olya-2409 [2.1K]

The answer is B (4,800)

Why?

Because we divide 3,500 feet by 5 and that will give us 600. Why we had to divide is because we need to find how many feet in minutes. So we do 600 times 8 and that gives us 4,800. Please mark me as branlist! Hope this helped! :)

6 0

3 years ago

Peter mixes 4 1/2 cups of orange juice, 2 1/4 of ginger ale and 6 1/3 cups of strawberry lemonade to make some punch. What is th

ruslelena [56]

To add these amounts together, we must first find their least common multiple in order to get common denominators (b/c when you add fractions, the denominators must be the same).

We'll start by listing some of their multiples.
To do this, count by whatever the denominator is:
4 1/2 (denominator is 2): 2 4 6 8 10 12 14
2 1/4 (denominator is 4): 4 8 12 16
6 1/3 (denominator is 3): 3 6 9 12 15

Look and see which is the first multiple that all three denominators have. Circle them if it helps you. In this case, it's 12.

So now we have to multiply the denominators by whatever number it takes to reach 12, and multiply by the same number to the numerator:

4 1/2 (times 6 to both top and bottom) =
4 6/12

2 1/4 (times 3) = 2 3/12

6 1/3 (times 4) = 6 4/12

Add all these fractions together, and you get 12 13/12, which is equal to 13 1/12.

Thus, Peter makes a total of 13 1/2 cups.

Hope this made sense! tell me if anything is confusing/incorrect :))

8 0

3 years ago

The data shown represent the number of runs made each year during Bill Mazeroski’s career. Check for normality.

const2013 [10]

Answer:

The given data is not normal.

Step-by-step explanation:

We are given the following data:

30, 59, 69, 50, 58, 71, 55, 43, 3, 66, 52, 56, 62, 36, 13, 29, 17, 31

Condition for normality:

Mean = Mode = Median

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{800}{18} = 44.44$

Mode is the most frequent observation of the data.

Since all the value appeared once, there is no mode.

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data: 3, 13, 17, 29, 30, 31, 36, 43, 50, 52, 55, 56, 58, 59, 62, 66, 69, 71

Median =

$=\dfrac{9^{th}+10^{th}}{2} = \dfrac{50+52}{2}=51$

Since the mean, mode and median of data are not equal, the data is not normal.

7 0

3 years ago

Simplify (1-cos theta)(1+cos theta) over (1-sin theta) (1+ sin theta)

slega [8]

$\bf sin^2(\theta)+cos^2(\theta)=1\to 
\begin{cases}
cos^2(\theta)=1-sin^2(\theta)\\
sin^2(\theta)=1-cos^2(\theta)
\end{cases} \\\\
-------------------------------\\\\
\stackrel{\textit{difference of squares}}{\cfrac{[1-cos(\theta )][1+cos(\theta )]}{[1-sin(\theta )][1+sin(\theta )]}}\implies \cfrac{1^2-cos^2(\theta )}{1^2-sin^2(\theta )}\implies \cfrac{1-cos^2(\theta )}{1-sin^2(\theta )}
\\\\\\
\cfrac{sin^2(\theta )}{cos^2(\theta )}\implies tan^2(\theta )$

4 0

3 years ago

A survey asked 72 randomly chosen students if they were going to attend the school play twelve said yes, predict the number of s

Lilit [14]

72 people questioned , 12 are going . that means that 16.6..% of which are going , 16.6....% is equal to 1/6 so 210 x 6 = 1260 . the number of students that attend the school would be 1260 if im right but if its how many students attended the play then it would be a 1/6 of 210 which is 35

8 0

3 years ago