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3 years ago

Solve the equation for y. 5x – 7y = 10 A. y=-7/5x-7/10 B.y=7/5x 10/5 C. 5/7x-10/7 D. -5x-7

Mathematics

2 answers:

Free_Kalibri [48]3 years ago

7 0

<h2>Answer:</h2>

Option: C is the correct answer.

$y=\dfrac{5x}{7}-\dfrac{10}{7}$

<h2>Step-by-step explanation:</h2>

We are given a linear equation in terms of variable x and y as:

$5x-7y=10$

Now, we are asked to solve the equation for y i.e. we are asked to find the value of y in terms of the variable x.

Now, we add 7y on both the sides of the equation to get:

$5x=10+7y\\\\i.e.\\\\10+7y=5x$

Now, we subtract 10 from both the sides of the equation to get:

$7y=5x-10$

Now, we divide both side of the equation by 7 to get:

$y=\dfrac{5x-10}{7}\\\\\\i.e.\\\\\\y=\dfrac{5x}{7}-\dfrac{10}{7}$

DanielleElmas [232]3 years ago

4 0

5x-7y=10
-7y=10-5x
y=(10-5x)/-7
y=10/-7-5x/-7
y=5x/7-10/7
hence C is correct option

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Find the m please it’s due today . (-11,5) & (2,-4)

d1i1m1o1n [39]

Answer:

m = $\frac{-9}{13}$

Step-by-step explanation:

I'm assuming by m, you mean the slope.

You have two points. (-11, 5) and (2, -4)

m = change in y-value ÷ change in x-value

1) Substitute in the points.

m = $\frac{(-4)- 5}{2 - (-11)}$

2) Solve.

-4 - 5 = -9

2 - (-11) = 13

So, the slope would equal $\frac{-9}{13}$ .

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3 years ago

When studying radioactive material, a nuclear engineer found that over 365 days,

Gnom [1K]

Answer:

a) The mean number of radioactive atoms that decay per day is 81.485.

b) 0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\lambda$ is the mean in the given interval.

a. Find the mean number of radioactive atoms that decayed in a day.

29,742 atoms decayed during 365 days, which means that:

$\lambda = \frac{29742}{365} = 81.485$

The mean number of radioactive atoms that decay per day is 81.485.

b. Find the probability that on a given day, 50 radioactive atoms decayed.

This is P(X = 50). So

$P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0$

0% probability that on a given day, 50 radioactive atoms decayed.

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3 years ago

Can you please help me solve this equation

Pavlova-9 [17]

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3 years ago

A bus with kids and a truck with their bags started moving from the school to the camp at the same time. The speed of the bus wa

lyudmila [28]

The kids have to wait for 1 hour to get their bags.

<u>Step-by-step explanation:</u>

Given that,

A bus with kids and a truck with their bags started moving from the school to the camp at the same time.

The speed of the bus was 60 mph.
It took kids 3 hours to reach the camp.

<u>To find the distance traveled by the bus :</u>

⇒ Distance = Speed × Time

⇒ 60 × 3

⇒ 180 m

∴ The distance is 180 m.

<u>To find the time taken by the truck to reach the camp :</u>

The speed of the truck was 45 mph.
We found the distance as 180 m.

Time taken = distance / speed.

⇒ 180 / 45

⇒ 4 hours.

∴ The time taken by the truck to reach the camp is 4 hours.

<u>To find how long the kids have to wait for their bags :</u>

The time taken by the truck to reach the camp - the time it took for the kids to arrive.

⇒ 4 hours - 3 hours

⇒ 1 hour.

∴ The kids have to wait for 1 hour to get their bags.

7 0

3 years ago

Classwork 12.1 surface area

s344n2d4d5 [400]

Answer:

6) LA = 90 units² and SA = 202 units²

7) LA = 377 units² and SA = 477.5 units²

8) LA = 208 units² and SA = 232 units²

9) LA = 455 units² and SA = 591 units²

Step-by-step explanation:

* Lets revise the rules of lateral area and surface area

- Lateral area of the solid = perimeter of its base × its height

- Surface area = lateral area + 2 × area of its base

* Now lets solve the problems

6) The solid is a rectangular prism

- Its base is a rectangle with dimensions 8 units and 7 units

- Its height is 3 units

∵ Perimeter of the rectangle = 2(L + W)

∴ Perimeter of the base = 2(8 + 7) = 2(15) = 30 units

∴ LA = 30 × 3 = 90 units²

∵ Area of the rectangle = L × W

∴ Area of the base = 8 × 7 = 56 units²

∴ SA = 90 + 2 × 56 = 90 + 112 = 202 units²

7) The solid is a cylinder

- Its base is a circle with diameter 8 units

∴ Its radius = 8 ÷ 2 = 4 units

- Its height is 15 units

∵ The perimeter of the circle is 2πr

∴ The perimeter of the base = 2π(4) = 8π

∴ LA = 8π(15) = 120π = 376.99 ≅ 377 units²

∵ The area of the circle = πr²

∴ The area of the base = π(4)² = 16π

∴ SA = 120π + 2 × 16π = 120π + 32π = 152π = 477.5 units²

6) The solid is a triangular prism

- Its base is a triangle with sides 5 , 5 , 6 units and height 4 units

- Its height is 13 units

∵ Perimeter of the triangle is the sum of the 3 sides

∴ Perimeter of the base = 5 + 5 + 6 = 16 units

∴ LA = 16 × 13 = 208 units²

∵ Area of the triangle = 1/2 × base × height

∴ Area of the base = 1/2 × 6 × 4 = 12 units²

∴ SA = 208 + 2 × 12 = 208 + 24 = 232 units²

9) The solid is a prism

- Its base is an isosceles trapezium with parallel bases 7 units and 10

units, 2 non-parallel bases 9 units and height 8 units

- Its height is 13 units

∵ Perimeter of the trapezium is the sum of its sides

∴ Perimeter of the base = 7 + 10 + 9 + 9 = 35 units

∴ LA = 35 × 13 = 455 units²

∵ Area of the trapezium = 1/2(b1 + b2) × h

∴ Area of the base = 1/2(7 + 10) × 8 = 68 units²

∴ SA = 455 + 2 × 68 = 455 + 136 = 591 units²

6 0

3 years ago