MATHEMATICS COLLEGE

In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, ifc=2b, a=12?

Answers

Answer 1
Answer:

b = 4√3

using Pythagoras' identity in the given triangle

c² = a² + b² ( substitute c = 2b and a = 12 into the equation )

(2b)² = 12² + b²

4b² = 144 + b² ( subtract b² from both sides )

4b² - b² = 144

3b² = 144 ( divide both sides by 3 )

b² = 48 ( take the square root of both sides )

b = √48 = √( 16 × 3 ) = √16 × √3 = 4√3 ' exact value '

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If ΔABC = ΔDEF, angle m∠A = 50, and angle m∠E = 30, what is angle m∠C?

Answers

100 degrees
Triangles add up to 180 degrees
30 + 50 = 80
180 - 80 = 100

When you indicate triangle congruency, the order of the letters matter. As you see these statements, look at how the side length names correspond to how the letters are written in its order, ΔABC ≅ ΔDEF. (By the way, triangles aren't equal with an = sign. It's a ≅ congruency sign.)

AB is congruent or the same length as DE.

BC is congruent or the same length as EF.

AC is congruent or the same length as DF.

In the same way, all of the angles in the corresponding order are ALSO congruent. By the way, we say that angles are congruent and angle MEASURES (like 30 degrees) are equal.

m∠A = m∠D

m∠B = m∠E

m∠C = m∠F

In the same way, we can try to find m∠C, or measure C!

1. Let's find the missing angle!

So, we know that m∠A is 50 degrees and m∠E is 30 degrees. Since we know that m∠E = m∠B because of the order of the triangles, now we know two of the angles in triangle ABC.

m∠A = 50 degrees

m∠B = 30 degrees

m∠C = 180 degrees - (50 + 30) = 100 degrees

(We minus from 180 degrees because 180 degrees is the sum of the angles in a triangle!)

And that's it! If you have any questions, please feel free to ask questions. I'm not here to judge, and I'm only here to help. Again, ask questions if you need help. It's crucial that you know the basics of geometry!

I need help plz and fast

Answers

Answer:

1

Step-by-step explanation:

1+19=20

so only 1 visit is available if they only have $20 to use.

Answer:

1

Step-by-step explanation:

19+1=20

The temperature, H, in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation. H = 70 + 120(1/4)t (a) What is the coffee's temperature initially (that is, at time t = 0)? 190 °F What is the coffee's temperature after 1 hour? 100 °F What is the coffee's temperature after 2 hours? (Round your answer to one decimal place.) 2 °F (b) How long does it take the coffee to cool down to 85°F? (Round your answer to three decimal places.) 5 hr How long does it take the coffee to cool down to 75°F? (Round your answer to three decimal places.) 5 hr

Answers

Answer:

The temperature a t = 0 is 190 °F

The temperature a t = 1 is 100 °F

The temperature a t = 2 is 77.5 °F

It takes 1.5 hours to take the coffee to cool down to 85°F

It takes 2.293 hours to take the coffee to cool down to 75°F

Step-by-step explanation:

We know that the temperature in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation:

H(t)=70+120((1)/(4))^t

a) To find the temperature a t = 0 you need to replace the time in the equation:

H(0)=70+120((1)/(4))^0\nH(0)=70+120\cdot 1\nH(0) = 70+120\nH(0)=190 \:\°F

b) To find the temperature after 1 hour you need to:

H(1)=70+120((1)/(4))^1\nH(1)=70+120((1)/(4))\nH(1) = 70+30\nH(1)=100 \:\°F

c) To find the temperature after 2 hours you need to:

H(2)=70+120((1)/(4))^2\nH(2)=70+120((1)/(16))\nH(2) = 70+(15)/(2) \nH(2)=77.5 \:\°F

d) To find the time to take the coffee to cool down 85 \:\°F, you need to:

85 = 70+120((1)/(4))^t\n70+120\left((1)/(4)\right)^t=85\n70+120\left((1)/(4)\right)^t-70=85-70\n120\left((1)/(4)\right)^t=15\n(120\left((1)/(4)\right)^t)/(120)=(15)/(120)\n\left((1)/(4)\right)^t=(1)/(8)

\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)

\ln \left(\left((1)/(4)\right)^t\right)=\ln \left((1)/(8)\right)

\mathrm{Apply\:log\:rule}=\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)

t\ln \left((1)/(4)\right)=\ln \left((1)/(8)\right)

t=(\ln \left((1)/(8)\right))/(\ln \left((1)/(4)\right))\nt=(3)/(2) = 1.5 \:hours

e) To find the time to take the coffee to cool down 75 \:\°F, you need to:

75=70+120\left((1)/(4)\right)^t\n70+120\left((1)/(4)\right)^t=75\n70+120\left((1)/(4)\right)^t-70=75-70\n120\left((1)/(4)\right)^t=5\n\left((1)/(4)\right)^t=(1)/(24)

\ln \left(\left((1)/(4)\right)^t\right)=\ln \left((1)/(24)\right)\nt\ln \left((1)/(4)\right)=\ln \left((1)/(24)\right)\nt=(\ln \left(24\right))/(2\ln \left(2\right)) \approx = 2.293 \:hours

Of the 250 sheep in a flock,
34% are spotted what is the total of spotted sheep

Answers

the answer is 85 sheep are spotted
34% = 0.34

0.34 * 250 = 85

34% of 250 would be 85

Which fractions convert into repeating decimals? Select ALL that apply. 4/40. 12/100. 3/18. 1/5. 9/27​

Answers

9/27 & 3/18 are repeating decimals

Answer:

3/18     = 1.6666

9/27​    = 0.3333

Step-by-step explanation:

4/40    = 0.1

12/100 = 0.12

3/18     = 1.6666

1/5       = 0.2

9/27​    = 0.3333

By what factor is z multiplied to get z1?

Answers

Answer:

The correct answer is -2.

Step-by-step explanation:

"z" = 3+2i, which is (3, 2i) on the graph. You must multiply -2 by 3 and 6, which will give you the plot points for z1, (-6, -4i).

A negative number multiplied into a positive number will result in a negative number.

Therefore, -2 is the correct answer.

Answer:

-2

Step-by-step explanation:

just did it
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Can someone answer this please!!! I only have 5 mins and u will get Brainly too :)