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4 years ago

Solve the rational equation quantity 2 times x plus 6 end quantity divided by 3 equals quantity 5 times x minus 1 divided by 7.

Mathematics

1 answer:

fomenos4 years ago

5 0

Answer:

x = 45

Step-by-step explanation:

(2x + 6)/3 = (5x - 1)/7

Cross multiply

7(2x + 6) = 3(5x - 1)

Expand both expressions

14x + 42 = 15x - 3

Collect like terms

42 + 3 = 15x - 14x

45 = x

x= 45

Check:

7(2*45 + 6) = 3(5*45 - 1)

7(90 + 6) = 3(225 - 1)

7 * 96 = 3 * 224

672 = 672

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Dos motos, A y B, toman la salida en una carrera de 90 km. La moto A realiza el recorrido con una velocidad media inferior en 20

aleksandr82 [10.1K]

Answer:

motorcycle A: 180 km/h

motorcycle B: 200 km/h

Step-by-step explanation:

To solve this question we need to write a system of equations for A and B, using the equation:

distance = speed * time

The speed of A is 20 less than the speed of B, so:

speedA = speedB - 20

And the time A traveled is 3 minutes (0.05 hours) more than B's time, so:

timeA = timeB + 0.05

Then, using the distance equation, we have that:

distanceB = speedB * timeB

90 = speedB * timeB

distanceA = speedA * timeA

90 = (speedB - 20) * (timeB + 0.05)

90 = speedB * timeB + 0.05 * speedB - 20*timeB - 1

90 = 90 + 0.05 * speedB - 20*timeB - 1

20*timeB = 0.05 * speedB - 1

timeB = (speedB - 20)/400

using this timeB in the distance equation, we have:

90 = speedB * (speedB - 20)/400

90 * 400 = speedB^2 - 20*speedB

speedB^2 - 20*speedB - 36000 = 0

Solving this quadratic equation, we have speedB = 200 km/h

And the speedA is:

speedA = speedB - 20 = 200 - 20 = 180 km/h

6 0

3 years ago

Please I need help fast

Leya [2.2K]

Answer:

45 sq cm

Explanation:

3 0

3 years ago

For the following right triangle, find the side length of x. round your answer to the nearest hundredth.

tatyana61 [14]

Answer:

14.87 units

Step-by-step explanation:

The sides of all right triangles share the same relationship known as the Pythagorean Theorem a² + b² = c². Substitute the lengths of the triangle into the theorem and solve for the unknown side. Since the problem does have an attached a picture, assume that a = 10, b = 11, and c = x.

10² + 11² = x²

100 + 121 = 221²

221 = x²

√221 = √x²

14.87 = x

6 0

3 years ago

An angle, θ, is in standard position. The terminal side of the angle passes through the point (4, 5).

lara31 [8.8K]

Answer:

cos Θ = $\frac{4}{\sqrt{41} }$

Step-by-step explanation:

Given the angle passes through (4, 5 ) then the right triangle with sides 4 and 5 has hypotenuse h given by

h² = 4² + 5² = 16 + 25 = 41 ( take the square root of both sides )

h = $\sqrt{41}$

In relation to Θ, 4 is adjacent and 5 is opposite, thus

cos Θ = $\frac{adjacent}{hypotenuse}$ = $\frac{4}{\sqrt{41} }$

5 0

3 years ago

Find the sum of the interior angle measure of a regular polygon with 20 sides

AleksAgata [21]

Answer:

3240°

Step-by-step explanation:

For a regular icosagon,

sum of interior angles measure=180(n-2)°

180(20-2)

180(18)=3240°

8 0

3 years ago