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2 years ago

5,356+2,398

Mathematics

1 answer:

Anna11 [10]2 years ago

3 0

Answer:

No because she added 2 instead of 2398. She thought the 2 was separate because of the comma separating the 2 thousand. She also made a mistake by thinking she could add easily by adding 2 to 2398 to make 2400.

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What is an equation of the line that passes through the points (-2, 1) and (-8, 4)

telo118 [61]

Answer:

y= -1/2x

Step-by-step explanation:

y-y1/x-x1=y2-y1/x2-x1

y-1/x+2=-1/2

2y-2= -x-2

2y= -x-2+2

2y=-x

y=-1x/2„

5 0

2 years ago

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 pi feet cubed.

LenaWriter [7]

Answer:

C. V = two-thirds (27)

Step-by-step explanation:

Given

Solid Shapes: Cylinder and Sphere

Volume of Cylinder = 27π ft³

Required

Volume of the sphere.

From the question,

1. The volume of the sphere is the same as the volume of the cylinder

2. The height of the sphere is the same as the height of the cylinder.

From (2) above;

This means that the height of the cylinder equals the diameter of the sphere.

Let h represent the height of the sphere and d represent the diameter of sphere.

Mathematical, d = h

Recall that radius, r = $r = \frac{d}{2}$

Substitute h for d in the above expression

$r = \frac{h}{2}$ . ----- (take note of this)

Calculating the volume of a cylinder.

V = πr²h

Recall that V = 27; This gives us

27 = πr²h

Divide both sides by h

$\pi r^2 = \frac{27}{h}$

-------------------

Calculating the volume of a sphere

$V = \frac{4}{3}\pi r^3$

Expand the above expression

$V = \frac{4}{3}\pi r^2 * r$

Substitute $\pi r^2 = \frac{27}{h}$

$V = \frac{4}{3} * \frac{27}{h} * r$

Recall that $r = \frac{h}{2}$

So,

$V = \frac{4}{3} * \frac{27}{h} * \frac{h}{2}$

$V = \frac{4}{3} * \frac{27}{2}$

$V = \frac{2}{3} * 27$

$V = \frac{2}{3} (27)$

V = two-third (27)

4 0

3 years ago

How. Many 5s is in 200989

olga_2 [115]

Answer:

40197 these many 5s make up 200985 so 4 are left to make 200989

Step-by-step explanation:

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2 years ago

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Complete the square to re-write the quadratic function in vertex form:<br> y = x2+ 10x - 2

Blababa [14]

Answer:

Step-by-step explanation:

$y = x^2+ 10x - 2\\\\y = x^2+ 2\cdot x\cdot5+5^2-5^2 - 2\\\\y=(x+5)^2-25-2\\\\y=(x+5)^2-27$

8 0

3 years ago

f(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, [infinity]) and g(x) = 2x^2

iren2701 [21]

Answer with Step-by-step explanation:

We are given that function f(x) which is quadratic function.

x -intercept of function f(x) at (-1,0) and (-3,0)

x-Intercept of f means zeroes of f

x=-1 and x=-3

Range of f =[-4, $\infty$ )

g(x)= $2x^2+8x+6=2(x^2+4x+3)$

$g(x)=0$

$2(x^2+4x+3)=0$

$x^2+4x+3=0$

$x^2+3x+x+3=0$

$x(x+3)+1(x+3)=0$

$(x+1)(x+3)=0$

$x+1=0\implies x=-1$

$x+3=0\implies x=-3$

Therefore, x-intercept of g(x) at (-1,0) and (-3,0).

Substitute x=-2

$g(-2)=2(-2)^2+8(-2)+6=8-16+6=-2$

$g(x)=2(x^2+4x)+6$

$g(x)=2(x^2+2\times x\times 2+4-4)+6=2(x^2+2\times x\times 2+4)-8+6$

$g(x)=2(x+2)^2-2$

By comparing with the equation of parabola

$y=a(x-h)^2+k$

Where vertex=(h,k)

We get vertex of g(x)=(-2,-2)

Range of g(x)=[-2, $\infty$ )

Zeroes of f and g are same .

But range of f and g are different.

Range of f contains -3 and -4 but range of g does not contain -3 and -4.

f and g are both quadratic functions.

3 0

3 years ago