MATHEMATICS HIGH SCHOOL

The length of a side of an equilateral triangle is 40 centimeters.What is the length of the altitude of the triangle?

Answers

Answer 1
Answer:

Answer:

34.64 cm

Step-by-step explanation:

sin 60 = (x)/(40)

sin 60 (40) = x

34.64 = x

equilateral triangles have 60° angles.

sin Ф = (opposite)/(hypotenuse)

hypotenuse is 40. All sides are 40.

x = opposite or height of triangle.

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Determine the solution to f(x) = g(x) using the following system of equations:f(x) = 5.5x − 13
g(x) = −5x + 18.5

x = 1
x = 2
x = 3
x = 4

Answers

5.5x-13=-5x+18.5 so 10.5x=31.5 so x=3

Answer:

the answer is x = 3

Step-by-step explanation:

The quotient of 14t^5-10t^4-14t^3 divided by 2t^2

Answers

7t^3-5t^2-7t

Subtract the exponents when dividing.

Pex Algebra PLS HELP

simplify 3^5 x 3^4

Answers

3 x 3 x 3 x 3 x 3 = 243
3 x 3 x 3 x 3 = 81
243 x 81 = 19,683
You are welcome

How do u write 4,000,000+3,000+50+2 in standard form

Answers

The answer to that would be 4,003,052.
4,003,052 is the answer

Taryn bought 12.6 gallons of gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closest to the number of liters of gasoline Taryn bought?

Answers

Answer:

Amount in liters is 47.9 liters

Step-by-step explanation:

The Question is incomplete, it does not provide the measurements or options to choose from, but we can estimate the answer

Step one:

Given data

Taryn Bought 12.6gallons of gasoline

1 gallon of gasoline is  3.8 liters

We want to convert from gallons to liters

Step two:

----if 1 gallon has 3.8 liters

then 12.6 gallons will have x liters

cross multiply we have

x= 12.6*3.8

x=47.88 liters

Hence the estimated amount in liters is 47.9 liters

A boat travels at 15 km/hr in still water. In travelling 45 km downstream from town A to town Bit completes the journey in 75 minutes less than it takes for the return journey. At what speed does the river flow?

Answers

Let the speed of river be x   km/hr down stream.

Time = Distance / speed

Since river flows downstream,  speed of boat down stream = Speed of boat + speed of river =  (15 + x).

 Since river flows downstream,  speed of boat upstream = Speed of boat - speed of river =  (15 - x).

Time Upstream - Time Downstream = 75 minutes

Time Upstream =  45 / (15 - x)

Time Downstream =  45 / (15 + x)

75 minutes = 75/60  =  5/4 hours

Time Upstream - Time Downstream = 75 minutes = 5/4 hours

45 / (15 - x)    -    45 / (15 + x)  = 5/4          Divide both sides by 45

1 / (15 - x)    -    1 / (15 + x)  = (5/4)*(1/45)

 1 / (15 - x)    -    1 / (15 + x)  = 1/36

((15 + x) - (15 -x)) / (15-x)(15+x)  = 1/36

(15 +x - 15 +x) / (15-x)(15+x)  =  1/36

  2x / (15-x)(15+x)  = 1/36

 (15-x)(15+x) = 2x*36

(15-x)(15+x) = 72x

225 - x² = 72x

0 =  x² + 72x -225

x² + 72x -225 = 0            This is a quadratic function, use a calculator that can solve the function, by inputting the function.

x = 3, or -75.  Since we are solving for speed, we can not have negative values.

x = 3 is the only valid solution.

Speed of the river =  3 km/hr  downstream.

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