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Marianna [84]
3 years ago
12

Witch shows the expression ordered correctly from least value to greater value a b c or d

Mathematics
1 answer:
Goshia [24]3 years ago
6 0
I think the answer is D
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One step equations: integers <br> 3x=36
Scorpion4ik [409]

Answer:

12

Step-by-step explanation:

3 times 12 is 36

7 0
3 years ago
Read 2 more answers
The diagram below shows the measurements of two identical rectangular prisms joined together. Austin says the combined volume of
Ksivusya [100]

Answer:

450 cubic meters

Step-by-step explanation:

  1. ( 15 X 5 X 3) + ( 15 x 5 x 3)
  2. 225 + 225
  3. 450 cubic meters

Austin didn't add the 2 prisms, he multiplied the 1st prism and kept it as the answer.  

7 0
3 years ago
1) Let f(x)=ax2+bx+c for some value of a, b and c. f intersects the x-axis when x=−2 or x=3, and f( 1 3 )=−25. Find the values o
antiseptic1488 [7]

Answer:

1) a = -⅙, b = ⅙, c = 1

2) 6 units

Step-by-step explanation:

1) f(x) = ax² + bx + c

Given the roots, we can write this as:

f(x) = a (x + 2) (x − 3)

We know that f(13) = -25, so we can plug this in to find a:

-25 = a (13 + 2) (13 − 3)

-25 = 150a

a = -⅙

Therefore, the factored form is:

f(x) = -⅙ (x + 2) (x − 3)

Distributing:

f(x) = -⅙ (x² − x − 6)

f(x) = -⅙ x² + ⅙ x + 1

Graph: desmos.com/calculator/6m6tjoodvb

2) Volume of a right prism is area of the base times the height.

V = Ah

The base is an equilateral triangle.  Area of a triangle is one half the base times height.

V = ½ ab h

The height of the triangle is the same as the height of the prism.

V = ½ bh²

In an equilateral triangle, the height is equal to half the base times the square root of 3.

V = ½ b (½√3 b)²

V = ⅜ b³

Given that V = 81, solve for b.

81 = ⅜ b³

216 = b³

b = 6

5 0
3 years ago
Find the derivative by definition of the function 2x^3-x^2+4
nikklg [1K]
The answer is 6x^2-2x
6 0
3 years ago
Match each of the parametric equations 1-5 with the curve it represents from the list A through E below. 1. r=3 2. r=2sinθ 3. θ=
ira [324]

Answer:

Step-by-step explanation:

1. r=3

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

y=rSinθ

Sinθ=y/r

Also, r²=x²+y²

When r =3,

Then we have

r=3,

x²+y²=3

All points with r = 3 are at

distance 3 from the origin, so r = 3 describes the circle of radius 3, with center at the origin (0,0).

Option C

2. r=2sinθ

When r=2sinθ

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

y=rSinθ

Sinθ=y/r

Also, r²=x²+y²

Now, apply the given information

r=2sinθ

Since Sinθ=y/r

r=2y/r

Cross multiply

r²=2y

x²+y²=2y

x²+y²-2y =0

x²+ (y-1)² -1 =0

x²+(y-1)²=1²

Then,

It is a circle with center (0,1) and radius 1.

Because the sine is periodic, we know that we will get the entire curve for values of θ in [0, 2π). As θ runs from 0 to π/2, r increases

from 0 to 2. Then as θ continues to π, r decreases again to 0. When θ runs from π to

2π, r is negative, and it is not hard to see that the first part of the curve is simply traced

out again, so in fact we get the whole curve for values of θ in [0, π). Thus, check attachment for curve, Now, this suggests that the curve could possibly be a circle,

and if it is, it would have to be the circle x² + (y − 1)² = 1. Having made this guess, we can easily check it. First we substitute for x and y to get (r cos θ)² + (r sin θ − 1)² = 1;

expanding and simplifying does indeed turn this into r = 2 sin θ.

Option E

A circle of radius 1 with center on the x-axis

3. θ=π/4

This is a point on the circle

p=(r, θ)

So, r=0

x = rCosπ/4=rCos45

x=r√2 /2

and

y = rsin(π/4) = rSin45

y=r√2 /2

This makes it very

easy to convert equations from rectangular to polar coordinates.

x²+y²= (r√2/2)²+(r√2/2)²

x²+y²= 2r²/4 + 2r²/4

x²+y²= r²

Since r=0

x²+y²= 0

x²=y²

Therefore, x=y

Option D

The straight line y=x

4. r=4θ

Here the distance from the origin

exactly matches the angle, so a bit of thought makes it clear that when θ ≥ 0 we get the spiral of Archimedes ( check attachment ) When θ < 0, r is also negative, and so the full graph is the right hand picture in the figure. Check attachment

The correct option is B

None of the above

5. r=2Cosθ

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

y=rSinθ

Sinθ=y/r

Also, r²=x²+y²

Now, apply the given information

r=2cosθ

Since cosθ=x/r

r=2x/r

Cross multiply

r²=2x

x²+y²=2x

x²+y²-2x=0

(x-1)² + y² -1 =0

(x-1)² + y² = 1²

Then,

It is a circle with center (1,0) and radius 1.

A circle of radius 1 with center on the y-axis

Option A is correct

7 0
3 years ago
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