The directrix and vertex of a parabola are shown on the graph. What is the vertex form of the equation for the associated parabola?

Answer:

Step-by-step explanation:

Comment

The one you can pick out that is true is D. The others you have to be careful with. C is a line and it has two arrowheads in the symbol above the two letters which makes it correct as well. A is not correctly marked, so it is not there the way it is marked. One would think ZX is a ray the way it is marked.

Answer: C and D

Answer:

4.96 dollars

Step-by-step explanation:

20-5.12=14.88

14.88/3= 4.96 dollars

so each pair of socks costs 4.96$

Answer:

$0.16

Step-by-step explanation:

unit price = price of carton / number of eggs

unit price = $1.92/12

unit price = $0.16

Answer:

A)  144 feet

[tex]\textsf{B)} \quad h(t)=16t(6-t)[/tex]

Step-by-step explanation:

Part A

Given polynomial:

   [tex]h(t)=96t-16t^2[/tex]

where:

To find the height of the debris 3 seconds after the explosion, substitute t = 3 into the polynomial and solve:

[tex]\begin{aligned}\implies h(3)& = 96(3)-16(3)^2\\ & = 288 - 16(9)\\ & =288-144\\ & =144 \sf \:\: ft\end{aligned}[/tex]

Part B

To factor the polynomial, rewrite 96 as 6 × 16:

[tex]\implies h(t)=6 \cdot 16t-16t^2[/tex]

Rewrite t² as t × t:

[tex]\implies h(t)=6 \cdot 16t-16t \cdot t[/tex]

Factor out the common term 16t:

[tex]\implies h(t)=16t(6-t)[/tex]

Check

Substitute t = 3 into the factored expression:

[tex]\begin{aligned}h(3) & = 16(3)(6-3)\\& = 16(3)(3)\\& = 48(3)\\& = 144\:\: \sf ft \end{aligned}[/tex]

As the height is 144 ft when t = 3 is substituted into the original polynomial and the factored polynomial, this confirms that the factorization is correct.

The secant of circle is SU and RT.

A straight line that intersects a circle in two points is called a secant line.

From the given diagram,

The line which intersects the circle at two points or an extended chord is SU and RT.

Hence, secant is SU and RT.

Learn more about secant here:

https://brainly.com/question/23026602

#SPJ1

Answer:

4cos(θ)

{4cospheta}

Answer:

4cos(θ)

{4cospheta}

Step-by-step explanation:

[note, brainly doesn't allow pheta to be entered as a symbol when writing an equation, so I had to write it out, my apologies]

[tex]\frac{\sin \left(2pheta \right)}{\sin \left(pheta\right)}+\frac{1+\cos \left(2pheta\right)}{\cos \left(pheta\right)}\\[/tex]

[tex]\frac{1+\cos \left(2pheta\right)}{\cos \left(pheta\right)}\ = 2\cos \left(pheta\right)[/tex]

[tex]\frac{\sin \left(2pheta \right)}{\sin \left(pheta\right)}=2\cos \left(pheta\right)[/tex]

2cos(θ) + 2cos(θ) = 4cos(θ)

so, 4cos(θ) is your answer

(4cospheta)

hope this helps!! :)

Answer:

x = 4 or x = -3/2

Step-by-step explanation:

To simplify and solve this, let's use the quadratic formula.

So the format of a quadratic equation is supposed look like this:

[tex]ax^2+bx+c=0[/tex]

Let's find a, b, c:

Now let's solve the equation.

Let's solve your equation step-by-step.

2x^2−5x−12=0

For this equation: a=2, b=-5, c=-12

2x^2+−5x+−12=0

Step 1: Use quadratic formula with a=2, b=-5, c=-12.

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-12)} }{2(2)}[/tex]

[tex]x=\frac{5\pm\sqrt{121} }{4}[/tex]

[tex]x=4[/tex] or [tex]x=\frac{-3}{2}[/tex]

Answer:

x = 4 or x = -3/2

Answer:

The second table

Step-by-step explanation:

A proportional relationship is a relationship in which the ratio of two variables is equivalent.

2:10, 4:20, and 6:30 are all equivalent ratios that can all be simplified and written as 1:5, thus the second table is the correct answer

The measure of the largest angle of the triangular patch of grass is 81 degrees

In order to determine the measure of the largest angle, we will use the expression below;

[tex]\frac{60}{sin26^0} =\frac{135}{sinx^0}[/tex]

Cross multiply

135sin26 = 60sinx

sinx = 135sin26/60

sinx = 59.18/60
sinx = 0.986

x = 80.5 degrees

Hence the measure of the largest angle of the triangular patch of grass is 81 degrees

Learn more sine rule here; https://brainly.com/question/27174058

#SPJ1

Friday =11

Saturday =?

But, we know that the pictures he took on Saturday are eight times fewer than those he took on Friday.

Saturday = 11-8

               = 3

∴ He took 3 pictures on Saturday.

       Hope this helps >3

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

Answer:  [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]

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

Given:  [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]

Find:  [tex]\textsf{The equation in point-slope form}[/tex]

Solution: We need to take the values that were given to us and plug them into the point-slope form.  It doesn't seem like the problem is asking for anything more than that so we will leave it at that.

Plug in the values

Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).

Answer:

[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

Step-by-step explanation:

[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]

We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).

Then, we substitute these values into the Point-Slope Form to find the equation.

Here are both forms for future reference:

⇒ Slope-Intercept Form: y = mx + b

[ Where: m is the slope, and b is the y-intercept (when x = 0). ]

⇒ Point-Slope Form: y - y₁ = m(x - x₁)

[ Where: m is the slope, and (x₁, y₁) is a given point. ]

Substitute the values into the Point-Slope Form:

[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

Learn more here:

https://brainly.com/question/27971495

The complete sentence is as follows:

The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.

The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.

Given, An amusement park prices tickets at $55 and sells an average of 500 tickets daily. The management finds, over multiple increases in ticket pricing that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day.

Management uses the combined function P to model the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.

[tex]P(x) = -40x^2- 100x + 27,500[/tex].

In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

We need to use the given information to complete the sentences.

The complete sentence is as follows:

The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.

The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.

To learn more about combined function visit:

https://brainly.com/question/14996966.

#SPJ1

The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

An amusement park prices tickets at $55 and sells an average if 500 tickets daily.

The function P(x) represents the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.

Plug x = 0

P(0) = 27500

The above value is the constant of the polynomial function.

The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increases in the price of a ticket.

As the x is the number of $2 increases in the price of a ticket.

Then,

= (500 - 20x) is the binomial that represents the number of tickets sold after x increases by $2

Thus, the constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

By looking at the graph of the piecewise function, we can see that:

On the graph, we have a piecewise function, which we want to evaluate in some different values.

First we have x  = -0.0001

This value belongs to the interval (-5, 0), and by looking at the graph, you can see that the function on that interval is equal to -9, then:

G(-0.0001) = -9

x = 0

x = 0 belongs to the interval [0, 9). On that interval the function values -1. (x = 0 belongs to that interval because we have a closed dot). Then we conclude

G(0) = -1

x = 0.0001

This value also belongs to the interval  [0, 9)

Then G(0.0001) = -1

Finally, x = 9.

If you look at the domain of the function, you can see that there is an open dot at x = 9.

This means that x = 9 does not belong to that domain, so:

G(9) is not defined.

If you want to learn more about piecewise functions:

https://brainly.com/question/3628123

#SPJ1

The value of the equation a + b is 12

The system of equations is given as:

3a + 6b = 45

2a - 2b = 12

Multiply the second equation by 1.5

3a - 3b = 18

Subtract this equation from the first equation to eliminate a

9b = 27

Divide by 9

b = 3

Substitute b = 3 in 2a - 2b = 12

2a - 2*3 = 12

Divide through by 2

a - 3 = 6

Add 3 to both sides

a = 9

So, we have:

a + b = 9 + 3

Evaluate

a + b = 12

Hence, the value of the equation a + b is 12

Read more about system of equations at:

https://brainly.com/question/14323743

#SPJ1

Answer:

T = 15 + 0.75c

T = $19.5

Step-by-step explanation:

Assume that T stands for total cost and c stands for number of single cookies purchased, the equation would be:

T = 15 + 0.75c

Therefore, a dozen cookies plus six single cookies would cost:

T = 15 + 0.75(6)

T = 15 + 4.5

T = $19.5

Answer: [tex]k \parallel l[/tex]

Step-by-step explanation:

Lines that are parallel to the same line are parallel.

Answer:

x = 55°

Step-by-step explanation:

Hello!

The sum of angles in a triangle is 180°.

To solve for x, we have to subtract the given angles from 180°.

The value of x is 55°.

Angle sum property of a triangle

∠A + ∠B + ∠C = 180°

We need to find the value of ∠A

According to the angle sum property of a triangle

⇢∠A + ∠B + ∠C = 180°

⇢∠A + 75° + 50° = 180°

⇢∠A + 125° = 180°

⇢∠A = 180° - 125°

⇢∠A = 55°

Answer:

(-4, -3)

(-4,3)

(4,3)

The clock wise rotation of the coordinate will be

(3,4)

(3,-4)

(-3,-4)

(-3,4)

Answer:

(-4,3)

Step-by-step explanation:

starting at  -3 , 4

   rotate clockwise 90°    this will change (x,y ) to   (y ,-x)

   doing this 3 times   results in

      4,3      then     3, -4      then    -4,-3       so the answer is (-4,3)

The expression that represents the product of negative three-fourths x and –8x is 6x^2

The statement is given as:

the product of negative three-fourths x and –8x

Rewrite properly as:

-3x/4 * -8x

Divide 4 and 8 by 4

-3x * -2x

Multiply -3 and -2

6x * x

Multiply x and x

6x^2

Hence, the expression that represents the product of negative three-fourths x and –8x is 6x^2

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

Answer:

answer is 6x2 or D

Step-by-step explanation:

Answer:

Every ordered pair within this region will satisfy the inequality y ≥ x. Incorrect. The boundary line here is y = x, and the correct region is shaded, but remember that a dotted line is used for < and >. The inequality you are graphing is y ≥ x, so the boundary line should be solid.

Using it's concept, it is found that the probability that the first three balls are drawn out of the box alternated in colour is of 0.1541 = 15.41%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering the situation described, the ways that alternate colored balls can be taken, and their probabilities, are given as follows:

Hence the probability is given by:

[tex]p = \frac{5}{11} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex]

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

the scale factor of a drawing=1:4

The graph of the function:

[tex]f(x) = \sqrt{x + 2} - 3[/tex]

Is the last graph (bottom graph of the second image).  

Here we have the function:

[tex]f(x) = \sqrt{x + 2} - 3[/tex]

Remember that the argument of a square root must be zero or larger, then the minimum of the domain is the value of x such that:

x + 2 = 0

x = -2

Then the function starts at:

[tex]f(-2) = \sqrt{-2 + 2} - 3 = -3[/tex]

Then the graph should start at (-3, 2).

We can also identify another point by evaluating in x = 2.

[tex]f(2) = \sqrt{2 + 2} - 3 =2 - 3 = -1[/tex]

So the function also passes through (2, - 1).

Notice that the only graph that contains these two points is the last graph (the bottom graph on the second image), so that is the correct option.

If you want to learn more about square roots:

https://brainly.com/question/98314

#SPJ1

Answer:

D

Step-by-step explanation:

 did the test got it right

The description of the correlation in terms of strength (weak or strong) and direction positive or negative) is as explained below.

A correlation coefficient, is expressed as r and it indicates a measure of the direction and strength of a relationship between two variables.

Now, in terms of strength, Correlation strength ranges from -1 to +1. Thus, The closer the correlation is to 0, the weaker it is while the closer it is to ±1, the stronger it is.

Now, in terms of direction;

Read more about Correlation at; https://brainly.com/question/4219149

#SPJ1

Answer:

c = 37 mi

Step-by-step explanation:

   To find 'c' use Pythagorean theorem.

 [tex]\sf \boxed{\bf hypotenuse^2 = base^2 + altitude^2}[/tex]

                     c² = 35² + 12²

                         =1225 + 144

                        = 1369

                    [tex]\sf c = \sqrt{1369}\\\\ c = \sqrt{37*37}\\\\ \boxed{\bf c = 37 \ mi}[/tex]

Answer:

  a) 182.90 m

  b) 203.85 m

Step-by-step explanation:

The relations between trig functions and measures in a right triangle are summarized in the mnemonic SOH CAH TOA. Here, we are given an angle and the side opposite, and we are asked to find the adjacent side and the hypotenuse.

__

The foot of the cliff to the boat is the adjacent side of the angle in our model. So, we can use the relation ...

  Tan = Opposite/Adjacent

Solving for the adjacent side, we have ...

  BF = (90 m)/tan(26.2°) ≈ 182.90 m

The boat is about 182.90 meters from the foot of the cliff.

__

The top of the cliff to the boat is the hypotenuse of the triangle we're using to model the situation. This means the applicable relation is ...

  Sin = Opposite/Hypotenuse

  BC = (90 m)/sin(26.2°) ≈ 203.85 m

The boat is about 203.85 meters from the top of the cliff.

The elimination method is valid for the system of equation because the y term cancels.

The system of equation can be solved using elimination methods.

Therefore,

x - 2y = 3

3x + 2y = 17

Hence,

x + 3x  = 4x

-2y + 2y = 0

3 + 17 = 20

Therefore,

4x = 20

The y term cancels. Therefore, we can solve for x and later solve for y.

learn more on equation here: https://brainly.com/question/17746153

#SPJ1

Answer:

Adding a quantity like x – 2y to one side of an equation and another quantity like 3 to the other side maintains the equality if the two quantities are equal.

Answer:8.8 pounds a day

Step-by-step explanation:

7 days in a week

28/7=4 kg a day

2.2*4=8.8

8.8 pounds

The correct answer is option D which is the volume of the square pyramid will be  [tex]V = \dfrac{1}{2}x^2y\ cm^3[/tex].

A solid made up of a square base and four triangles connected side by side and meet at the same edge is called a square pyramid.

Given that:-

The volume of the pyramid will be calculated as:-

Volume = [tex]\dfrac{1}{2}[/tex] x Length of square pyramid x Height

Volume = [tex]\dfrac{1}{2}[/tex]  x (x)² x y

Volume = [tex]\dfrac{1}{2}[/tex] x²y

Therefore the correct answer is option D which is the volume of the square pyramid will be  [tex]V = \dfrac{1}{2}x^2y\ cm^3[/tex].

To know more about the square pyramid follow

https://brainly.com/question/3688277

#SPJ1