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Tcecarenko [31]
2 years ago
13

Which of the following equations is written in standard form ? A. 2.5x+3=12 B. -10x-3=1 C. 2x+3=12 D. 5x+5y=10

Mathematics
1 answer:
muminat2 years ago
8 0
D. 5x+5y=10

The other 3 could be simplified further and have no y value.

Hope that helps
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What is the measure of ZBAC?
IceJOKER [234]

Answer:

80 degrees

Step-by-step explanation:

Sum of the interior angles of a triangle = 180

a + 50 + 50 = 180

a = 80

6 0
2 years ago
A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the
Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0
2 years ago
Why does 0.25 x 0.4 have a one decimal place in the product
Dafna11 [192]
The product of these numbers are 0.100
since 0.100 is same as 0.1
so there is only one decimal place
COMMON SENSE
4 0
3 years ago
MZRSK = x + 53, m KST = x + 109,<br> and mZRST = 156º<br><br><br> Find x.
Dahasolnce [82]

Answer:

-3 = x

Step-by-step explanation:

Since we are not given a midpoint, we use the Angle Addition Postulate:

156 = [x + 109] + [x + 53]

156 = 162 + 2x

-162 - 162

_______________

−6 = 2x

___ ___

2 2

−3 = x

[−3 + 53] + [−3 + 109] = 156

50 106

156 = 156 ☑

Therefore, -3 = xis a genuine statement.

I am joyous to assist you anytime.

4 0
3 years ago
A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using a
givi [52]

Answer:

8 is the side length of the greater square.  100=x^2+(x-2)^2

Step-by-step explanation:

64+36=100

8 squared plus 6 squared equals 10 squared

8 is 2 more than 6

100=x^2 +y^2

x-y=2

100=x^2+(x-2)^2

7 0
3 years ago
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