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ivolga24 [154]
3 years ago
12

Use the Pythagorean theorem to find b. b, 13, 12 b =

Mathematics
2 answers:
Nana76 [90]3 years ago
4 0

\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{12}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{13^2-12^2}=b\implies \sqrt{25}=b\implies 5=b

liubo4ka [24]3 years ago
4 0

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

13 is the hypotenuse because it is the longest side.

12^2 + b^2 = 13^2

144 + b^2 = 169

subtract the 144 from both sides to isolate the variable you are solving for

b^2 = 25

Square root both sides to solve

b = 5

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What is the area of the floor of a room that is 12 feet wide and 18 feet long
BabaBlast [244]

area of floor = length * width

length =18 feet

width =12 feet

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7 0
2 years ago
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Two airplanes are flying in the air at the same height. Airplane A is flying east at 300mi/h and airplane B is flying north at 2
Ipatiy [6.2K]

Answer:

\frac{dAB}{dt}=340 mil/h

Step-by-step explanation:

The change of distance over time of the plain A is 300 mi/hour and 200 mi/hour for plane B. O is the point of the airport.

So, the distance from A to O AO = 90 miles and BO = 120 miles.

Now, we have a right triangle here.  We can use the Pythagorean theorem, so the distance between the planes will be:

AB^{2} =AO^{2}+BO^{2} (1)

AB =\sqrt{AO^{2}+BO^{2}}=

AB =\sqrt{90^{2}+120^{2}}=150 miles

If we take the derivative of the equation (1) we could find the change of the distance between planes.

2AB\frac{dAB}{dt}=2AO\frac{dAO}{dt}+2BO\frac{dBO}{dt}

2*150\frac{dAB}{dt}=2*90*300+2*120*200=102000 mil/h

\frac{dAB}{dt}=\frac{102000}{150*2}

Finally,

\frac{dAB}{dt}=340 mil/h

I hope it helps you!

6 0
2 years ago
Ms. Hernandez is taking her children and their friends to the movies. She will pay $10 for adult ticket and $7 for each child ti
arlik [135]

Answer: 10 + 7x \leq \\ 40

We can use exclusion method:

A and C  is not correct because Ms Hernandez doesn't want to spend more than 40 dollars --> so it must be less than or equal to 40

3 0
2 years ago
Factorising quadratics<br><br> X squared + 5x -6<br> X squared - 2x15<br> X squared -7x +12
34kurt

Answer:

  • (x -1)(x +6)
  • (x -5)(x +3)
  • (x -4)(x -3)

Step-by-step explanation:

In each case, you're looking for divisors of the constant that have a sum equal to the x-coefficient. Those divisors are the constants in the binomial factors.

1) -6 = -1·6 = -2·3 . . . . . (-1)+(6) = 5, so these are the constants of interest.

  x^2 +5x -6 = (x -1)(x +6)

__

2) -15 = -1·15 = -3·5 = -5·3 . . . . . (-5)+(3) = -2, so these are the constants of interest

  x^2 -2x -15 = (x -5)(x +3)

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3) 12 = -1·-12 = -2·-6 = -3·-4 . . . . . (-3) +(-4) = -7, so these are the constants of interest

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5 0
3 years ago
How do you find a side length of a cube with the surface area of one face (64cm)
jasenka [17]
Fact #1:
A cube has six faces.

Fact #2:
Every one of them has the same area.

Fact #3:
The surface area of each face is (the length of the cube's side)²

Now that I look at this one more carefully, the only thing you need to know
to solve it is Fact #3.  (But you can keep the others and save them for later.)

The surface area of each face is (the length of the cube's side)²

64 is the (length of the cube's side)²

Can you find a number that gives you 64 when you multiply it by itself ?
That's the length of the cube's side.

Hint: If you don't get ' 8 ', work on it a little more.

7 0
2 years ago
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