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nekit [7.7K]
2 years ago
10

Find the length of x.

Mathematics
1 answer:
jenyasd209 [6]2 years ago
6 0
This is one of the photos I used to answer, I’m going to send the second one

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Question 3 Determine the leg lengths between the two points: (6, -3) and (-2,4).
Shalnov [3]

Answer:

9

Step-by-step explanation:

→You can use the Pythagorean Theorem to solve this, by plugging in the numbers, like so:

\begin{gathered}a^2+b^2=c^2\\x^2+(x-3)^2=(x+3)^2\end{gathered}

a

2

+b

2

=c

2

x

2

+(x−3)

2

=(x+3)

2

x^2+x^2-6x+9=x^2+6x+9x

2

+x

2

−6x+9=x

2

+6x+9

→Subtract x^2-6x+9x

2

−6x+9 from both sides:

x^2 = 12xx

2

=12x

→Subtract 12x from both sides:

x^2 -12x=0x

2

−12x=0

→Factor out x:

x(x-12)=0x(x−12)=0

→Separate, set = to 0, and solve:

\begin{gathered}x = 0\\x -12=0\end{gathered}

x=0

x−12=0

→ Add 12 to both sides: x = 12x=12

→So we have 0 and 12, as our answers. However, we cannot have 0 as a side length, since this would not be possible.

→All we need to do is take 12, and plug it into the equation for the shortest leg.

\begin{gathered}x - 3=?\\12-3=9\end{gathered}

x−3=?

12−3=9

3 0
2 years ago
Rebecca and dan are biking in a national park for three days they rode 5 3/4 hours the first day and 6 4/5 hours the second day
likoan [24]

Answer:

Rebecca and Dan need to ride 7\frac{9}{20}\ hrs. on the third day in order to achieve goal of biking.

Step-by-step explanation:

Given:

Goal of Total number of hours of biking in park =20 hours.

Number of hours rode on first day = 5\frac34 \ hrs.

So we will convert mixed fraction into Improper fraction.

Now we can say that;

To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.

5\frac34 \ hrs. can be Rewritten as \frac{23}{4}\ hrs

Number of hours rode on first day = \frac{23}{4}\ hrs

Also Given:

Number of hours rode on second day = 6\frac45 \ hrs

6\frac45 \ hrs can be Rewritten as \frac{34}{5}\ hrs.

Number of hours rode on second day = \frac{34}{5}\ hrs.

We need to find Number of hours she need to ride on third day in order to achieve the goal.

Solution:

Now we can say that;

Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.

framing in equation form we get;

Number of hours she need to ride on third day = 20-\frac{23}{4}-\frac{34}{5}

Now we will use LCM to make the denominators common we get;

Number of hours she need to ride on third day = \frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}

Now denominators are common so we will solve the numerator we get;

Number of hours she need to ride on third day =\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.

Hence Rebecca and Dan need to ride 7\frac{9}{20}\ hrs. on the third day in order to achieve goal of biking.

8 0
2 years ago
A culture of bacteria has an initial population of 41000 bacteria and doubles every 5 hours. Using the formula P t = P 0 ⋅ 2 t d
Crazy boy [7]

Answer:

Population of bacteria in culture after 14 hours is 285541.

Step-by-step explanation:

We are given with P_{t} =P_{0}(2)^{\frac{d}{t}}

Here initial population is 41000 , t=5 and d=14

Plug in these values into the formula

P_{14} =41000(2)^{\frac{14}{5} }

Simplify

P_{14}= 41000(2)^{2.8}

     =41000(6.9644)

     =285540.5847...

To the nearest whole number is 285541.

3 0
3 years ago
Please awnser this correctly! I will make you Brainliest!
Andrews [41]
Volume of cone: pi * r^2 * h/3
Given volume, height

942in^3 = 3.14 * r^2 * 9/3
942in^2 = r^2 * 9.42
Divide by 9.42
r^2 = 100, r = -10, 10
Cannot be negative so...

Solution: radius is 10 in.
8 0
2 years ago
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What is the general form of the equation for the given circle?
Tom [10]
Hhhhhhhhahahahahahahahahahahaahabahahah 4.7
4 0
2 years ago
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