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Veseljchak [2.6K]
2 years ago
13

What is the surface area of the rectangular prism below?

Mathematics
1 answer:
sveta [45]2 years ago
3 0
Where is the picture
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How to find the probability of exactly one event happening?
Vlad [161]


probability \: of \: an \: event \: happening =  \: number \: of \: ways \: it \: can \: happen \div total \: number \: of \: outcomes
6 0
3 years ago
What is an equation of the line that passes through the point (2,−6) and is parallel to the line x-2y=8
lana [24]

Answer:

y=\frac{1}{2}x-7, or x-2y=14

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the point (2, -6) and is parallel to the line x-2y=8

First, we need to find the slope of x-2y=8, since parallel lines have the same slopes

We can convert the equation from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept), in order to help us find the slope of the line

Start by subtracting x from both sides

-2y=-x+8

Divide both sides by -2

y=\frac{1}{2}x-4

The slope of the line x-2y=8 is 1/2

It's also the slope of the line parallel to it.

Since we know the slope of the line, we can plug it into the equation for slope intercept form:

y=\frac{1}{2}x+b

Now we need to find b.

As the equation of the line passes through (2, -6), we can use it to help solve for b

Substitute -6 as y and 2 as x:

-6=\frac{1}{2}(2)+b

Multiply

-6=1+b

Subtract 1 from both sides

-7=b

Substitute -7 as b into the equation:

y=\frac{1}{2}x-7

The equation can be left as that, or you can convert it into standard form if you wish.

In that case, you will need to move 1/2x to the other side:

-\frac{1}{2}x+y=-7

A rule about the coefficients a, b, and c in standard form is that a (coefficient in front of x) CANNOT be negative, and every coefficient must be an integer (a whole number, not a fraction or decimal).

So multiply both sides by -2 in order to clear the fraction, as well as change the sign of a

x-2y=14

Hope this helps!

8 0
2 years ago
Given that x^2+y^2=9 and xy=5, find the value of (x - y)^2. ​
Ede4ka [16]

Answer:

(x -y)^2 = -1

Step-by-step explanation:

(x - y)^2 = x^2 + y^2 - 2xy

           = (x^2 + y^2 ) - 2(xy)\\\\=(9) - 2( 5)\\\\= 9 - 10 \\\\ = -1

4 0
3 years ago
Read 2 more answers
What expression is equivalent to x + x + 4y?
Elenna [48]
I’m pretty sure an equivalent expression would be 2x + 4y
7 0
2 years ago
(a) Show that the volume of a metal sphere of radius 15 cm is 14140 cm”, correct to 4 significant
Sladkaya [172]

Answer:

a) The volume of the sphere is approximately 14,137.16694 which is 14,140 cm³ correct to 4 significant figures

b) The volume of water required to fill the tank is approximately 103,670 cm³

Step-by-step explanation:

a) In the question, the radius of the sphere, r = 15 cm

The formula for the volume, 'V', of a sphere is given as follows;

V = \dfrac{4}{3} \times \pi \times r^3

Where;

r = The radius of the the sphere

V = The volume of the sphere

Plugging in the value for the radius, 'r', of the sphere, in the equation for, 'V', we get;

V = \dfrac{4}{3} \times \pi \times 15^3 \approx = 14,137.16694

Therefore;

The volume of the sphere to 4 significant figures is V ≈ 14,140 cm³

b) The parameters of the cylindrical tank are;

The height of the cylindrical tank, h = 60 cm

The radius of the cylindrical tank, r = 25 cm

The volume of a cylinder, V = π·r²·h

∴ The volume of the cylindrical tank without water, 'V_t', is given as follows;

V_t = π × (25 cm)² × 60 cm ≈ 117809.72451 cm³

The volume of water, V_{water}, required to fill the tank with the sphere of volume 'V' placed inside is given as follows

V_t = V + V_{water}

∴ V_{water} = V_t - V

From which we get;

V_{water} ≈ 117809.72451 cm³ - 14,140 cm³ = 103,669.72451 cm³ ≈ 103,670 cm³

The volume of water required to fill the tank, V_{water} ≈ 103,670 cm³.

8 0
3 years ago
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