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Lunna [17]
2 years ago
7

Consider y+2=14x.

Mathematics
1 answer:
liraira [26]2 years ago
3 0

Answer:

Step-by-step explanation:

y + 2 = 14x

     y = 14x - 2

When x = 0 , y = 14*0 - 2 = 0-2 = -2

When x= 4  , y = 14*4 - 2 = 56 - 2 = 54

When x = 8 , y = 14*8 - 2 = 112-2 = 110

x             y

0            -2

4            54

8            110

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Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP​
-Dominant- [34]

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$\Rightarrow \frac{h}{2}=r

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

  $\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3 (formula)

$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3

$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3

Hence it is true.

Option A, option C and option E are true.

6 0
3 years ago
Read 2 more answers
4n+1=25<br>Please help with an explanation ​
dlinn [17]

Answer:

n = 6

Step-by-step explanation:

To isolate n, subtract 1 from both sides:

4n + 1 = 25

4n = 24

Then divide by 4 on both sides:

4n = 24

n = 6

Hope this helped :)

4 0
2 years ago
Read 2 more answers
Este curso nuestro instituto tiene 473 alumnos. Si nos dicen que respecto al curso anterior se ha producido un aumento de inscri
tester [92]

Answer:

En el curso anterior había 430 alumnos.

Step-by-step explanation:

El curso tiene 473 alumnos. Nos dicen que respecto al curso anterior se ha producido un aumento de inscripciones del 10 %. Entonces, siendo x la cantidad de alumnos que había en el curso anterior, se puede plantear la ecuación:

x + 0.1*x= 473

Resolviendo se obtiene:

1.1*x=473

x= 473 ÷1.1

x= 430

<u><em>En el curso anterior había 430 alumnos.</em></u>

7 0
3 years ago
Please answer. Will mark the brainliest and will give 20 points.
Dimas [21]

Answer: it is C

Step-by-step explanation:

5 0
3 years ago
Which of the following
Ronch [10]

Answer:

Option A

Step-by-step explanation:

<u>Given equation is</u>

=> 3y = 6x + 3

<u>In slope-intercept form, it becomes</u>

=> 3y = 3(2x+1)

=> y = 2x+1

So, Slope = m = 2

<u><em>Parallel lines have equal slope, So any line parallel to the above line would have its slope equal to 2</em></u>

=> Line parallel to 3y = 6x + 3 is y = 2x + 10

3 0
3 years ago
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