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3 years ago

What equation would represent the graph of the parabola y = 3x^2 - 4x - 1

Mathematics

1 answer:

jekas [21]3 years ago

3 0

This is the equations of a parabola

y = 3x^2 - 4x - 1 graphed is a parabolic arc

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CAn you help me with ratios? Mrs. Sturkie mixed 3 quarts of blue paint and 2 quarts of red paint to make purple paint to her cla

fredd [130]

So as we already know the ratio is 3 quarts blue paint to 2 quarts red paint, also written as 3:2. if she only has 1 quart blue paint she will need half of a quart of red paint because the ratio has to remain the same amount. if you multiply one side then you must multiply the other. same goes with division. If she only has 1 quart of red paint then that shows she divided the 2 red by 2. There fore you would have to divided the 3 by 2 in order to get 1.5 which would then make the ratio 1.5:1

3 0

3 years ago

The 13th term of a geometric sequence is 16, 384 and the first term is 4. What is the common ratio?

AleksAgata [21]

Answer:

$\large \boxed{2}$

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

In your geometric sequence, a₁ = 4 and a₁₃ = 16 384.

$\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}$

Check:

$\begin{array}{rcl}16384 & = & 4(2)^{12}\\16384 & = & 4(4096)\\16384 & = & 16384\\\end{array}$

It checks.

7 0

3 years ago

10) A wheelchair ramp is getting built at the entrance of a building. The ramp will be 25 feet long from front

mezya [45]

Answer:

The angle complies with the state regulations.

Step-by-step explanation:

The angle of elevation is the angle $\theta$ in the figure, and from trigonometry we find that

$sin(\theta) = \dfrac{1.5ft}{25ft}$

taking the inverse sine of both sides we get

$\theta = sin^{-1}(\dfrac{1.5ft}{25ft})$

which gives

$\theta = 3.44^o$

which is less than 5°, and therefore is well within the state regulations.

3 0

3 years ago

Find the slope of the line. y=6

Sedaia [141]

Answer:

slope: 0

Step-by-step explanation:

y=6

no matter what x is, y is always going to equal 6

7 0

3 years ago

Please help me :)))))

svetoff [14.1K]

Part a)

Answer: 5*sqrt(2pi)/pi

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

Work Shown:

r = sqrt(A/pi)
r = sqrt(50/pi)
r = sqrt(50)/sqrt(pi)
r = (sqrt(50)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(50pi)/pi
r = sqrt(25*2pi)/pi
r = sqrt(25)*sqrt(2pi)/pi
r = 5*sqrt(2pi)/pi

Note: the denominator is technically not able to be rationalized because of the pi there. There is no value we can multiply pi by so that we end up with a rational value. We could try 1/pi, but that will eventually lead back to having pi in the denominator. I think your teacher may have made a typo when s/he wrote "rationalize all denominators"

============================================================

Part b)

Answer: 3*sqrt(3pi)/pi

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

Work Shown:

r = sqrt(A/pi)
r = sqrt(27/pi)
r = sqrt(27)/sqrt(pi)
r = (sqrt(27)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(27pi)/pi
r = sqrt(9*3pi)/pi
r = sqrt(9)*sqrt(3pi)/pi
r = 3*sqrt(3pi)/pi

Note: the same issue comes up as before in part a)

============================================================

Part c)

Answer: sqrt(19pi)/pi

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

Work Shown:

r = sqrt(A/pi)
r = sqrt(19/pi)
r = sqrt(19)/sqrt(pi)
r = (sqrt(19)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(19pi)/pi

8 0

3 years ago

Read 2 more answers