50 points help me please

Answer:

a) The axis of symmetry is the line, y = 2

b)  The vertex  of a parabola is (-3, 2)

c) The focus of the parabola is (0, 2)

d) The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola

Step-by-step explanation:

a) The function for the parabola can be expressed as follows;

12·(x + 3) = (y - 2)²

The general form of the equation of the parabola is x = a·(y - k)² + h

The axis of symmetry is the line, y = k

By comparison, with the given equation of the parabola, we have;

12·(x + 3) = (y - 2)²

x = (1/12)·(y - 2)² - 3

Therefore;

a = (1/12), k = 2, h = -3

The axis of symmetry is y = k

∴ The axis of symmetry is the line, y = 2

b) The vertex  of a parabola = (h, k)

∴ The vertex  of a parabola = (-3, 2)

c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]

Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)

The focus of the parabola = (0, 2)

d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]

[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]

The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel

The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

It is given that the parabola equation is  [tex]\rm 12(x+3)=(y-2)^2[/tex]

It is defined as the graph of a quadratic function that has something bowl-shaped.

We know the standard form of a parabola is:

[tex]\rm x= a(y-k)^2+h[/tex]  .........(1)

We have the equation of parabola:

[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)

a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.

By comparing the equation (1) and (2), we get:

Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.

b) Vertex of the parabola = (h,k): (-3, 2)

c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],

[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]

∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]

The focus of the parabola is (0, 2)

d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]

[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]

The directrix of a is x = -6

e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry

Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

Know more about the parabola here:

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Answer:

1 1/6 ton

Step-by-step explanation:

Allison ran 3/8 km (0.375 km) in 3 minutes.

Set up a proportion to find how long it takes for her to run 1 km

[tex]\frac{0.375\textrm{km}}{3 \textrm{min}} = \frac{1\textrm{km}}{x \textrm{min}}[/tex]

Cross multiply to get:

[tex]3 = 0.375x[/tex]

Solve:

[tex]x = \frac{3}{0.375}[/tex]

x = 8 minutes

The easiest way is to transform this equation to intercept form of straight line.

[tex]\\[/tex]

Intercept form of straight line:

where [tex]a[/tex] is the x intercept - where the graph intersects the x axis, and [tex]b[/tex] is the y intercept - where the graph intersects the y axis.

[tex]\\[/tex]

Given that,

[tex]2y + x = 20[/tex]

[tex] \longrightarrow \: \dfrac{2}{20}y + \dfrac{x}{20} = 1[/tex]

[tex] \longrightarrow \: \dfrac{x}{20} + \dfrac{y}{10} = 1[/tex]

On comparing with [tex]\dfrac{x}{a}+\dfrac{y}{b}=1,[/tex] we get,

Hence, the graph shall cut the x axis and y axis at 20 and 10 respectively. This information is enough to plot the graph.

[tex]\\[/tex]

Graph: Refer to the attachment.

Answer:

a) 5 cm b) 12in c) 7yd

I think it's so simple. Anyways

This is your answer. If I'm right so,

Please mark me as brainliest. thanks!!!

Answer:

5 cm, 12in, 3.5 yrds

Step-by-step explanation:

to find the radius you divide the diamenter by 2.

Answer:

uh i dont know lol im new how do i use this thing bahahaha

Step-by-step explanation:

Answer:

A=30  B=90  C=60

Step-by-step explanation:

A=30 C=60  B=90

Answer:

Choice 1 is correct: 8/3 x 1/4 = 2/3

Step-by-step explanation:

Answer:

8^(7), which is 2097152

Step-by-step explanation:

8^(4) × 8^(3)

= 8^(4+3)

= 8^(7)

= 2097152

Answer:

The answer is 2097152.

Step-by-step explanation:

1) Use the product rule: x^a x^b = x^ a + b.

[tex] {8}^{7} [/tex]

2) Simplify.

[tex]2097152[/tex]

Thus, the answer will be 2097152.

Answer:

1.25 since all prices are sam e

Step-by-step explanation:

Answer:

1.75 x 1.75

fillerfillerfiller

Answer:  12 possible outcomes in total

Step-by-step explanation:

Answer:

A' (-2,-4) B' (-3,-7) C' (-1,-8) D' (1,-6)

Step-by-step explanation:

Just take it one point at a time and move each point down 3 and 4 left. Prime notation just means to put this little sign ' so it indicates that this is the new coordinate. So A was (2,-1) and A' (the new one) is (-2,-4)

Answer:

|2x+1|=0 has one solutions

2|x+1|=-2 has no solution

|x+21|=2 has two solution

Step-by-step explanation:

Answer:

Center... Mean

Step-by-step explanation:

The mean of a data set is the sum of the values divided by the number of values. The median of a data set is the middle value when the values are written in numerical order.

Answer:

Step-by-step explanation:

1. 6.96 in

2. 2.6 in

3. 8.1 in

4. 5.6 m

5. 1.89 cm

6. 6 in

area=1/2(AB+0A)Ac=4cm

Answer:

28cm²

Step-by-step explanation:

Area of trapezium = 1/2×(6+8)×4

= 28cm²

Answer:

24 because hsbs. hwhvw w Whelan has w hahaha

Answer:

Open circle going right. <-- graphed

Step-by-step explanation:

1billion is the correct answerStep-by-step explanation:

Answer:

D

Step-by-step explanation:

edge

D. approximately 4.3 in. to the right of the center

Problem-solving is the act of defining a problem; figuring out the purpose of the problem; determining, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a teacher may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Learn more about problem-solving here

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#SPJ2

Answer:

A sample size of 385 should be used.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

What sample size should be used (round the number up)

A sample of n should be used.

n is found when M = 5.

We have that [tex]\sigma = 50[/tex]

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5 = 1.96\frac{50}{\sqrt{n}}[/tex]

[tex]5\sqrt{n} = 1.96*50[/tex]

Simplifying by 10

[tex]\sqrt{n} = 1.96*10[/tex]

[tex]\sqrt{n} = 19.6[/tex]

[tex](\sqrt{n})^2 = (19.6)^2[/tex]

[tex]n = 384.16[/tex]

Rounding up

A sample size of 385 should be used.

Answer:

Tiger shows you, step by step, how to solve YOUR Quadratic Equations 3x^2-x-11=0 by Completing the Square, Quadratic formula or, ...

Answer:

151

Step-by-step explanation:

114+131= 272 376-272=104

9514 1404 393

Answer:

  6/5

Step-by-step explanation:

The slope formula is useful for finding the slope.

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -11)/(-5 -5) = -12/-10

  m = 6/5

The slope of the line through the given points is 6/5.

Answer:

Step-by-step explanation:

[tex]\text{Maximize p = 5X1 + 4X2 + 3X3 subject to;} \\ \\ 1X1 + 7X2 + 4X3 <= 90[/tex]

[tex]2X1 + 1X2 + 7X3 <= 96[/tex]

[tex]8X1 + 4X2 + 1X3 <= 90[/tex]

[tex]X1 > = 0[/tex]

[tex]X2 >= 0[/tex]

[tex]X3 >=0[/tex]

[tex]\text{USing LP software, The Optimal Solution: Maximum Contribution} = 90.547;}\\ \\ x1 = 7.07692, \\ \\ x2 = 5.62393, \\ \\ x3 = 10.8889[/tex]