6) Which of the following equations is of a parabola with a vertex at (3, 0)?
a) y = x2 + 3
b) y = x2-3
c) y = ( x + 3) 2
d) y = ( x - 3)2

Answer:rectangle

Step-by-step explanation:

Answer:

a) 52.0 cm

b) 62.8 cm

c) 114.8 cm

Conversion:

120° = 2π/3 radians

(a) Find Length of chord PR;

⇒ 2(radius)sin(θ/2)

⇒ 2(30)sin((2π/3)/2)

⇒ 2(30)sin((2(3.142)/3)/2)

⇒ 30√3

⇒ 52.0 cm

(b) Find Length of arc PQR;

⇒ radius(θ)

⇒ 30(2π/3)

⇒ 30(2(3.142)/3)

⇒ 62.8 cm

(c) The perimeter of shaded region;

⇒ Length of chord + Length of arc

⇒ 62.84 + 51.965

⇒ 114.8 cm

Answer:

(a)  52.0 cm

(b)  62.8 cm

(c)  115 cm

Step-by-step explanation:

Part (a)

[tex]\textsf{Chord length}=2r \sin \left(\dfrac{\theta}{2}\right)[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies PR & =2(30)\sin \left(\dfrac{120^{\circ}}{2}\right)\\\\& = 30\sqrt{3}\\\\ & = 52.0\:\sf cm\:(3\:sf)\end{aligned}[/tex]

Part (b)

[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies PQR & =2 (3.142)(30)\left(\dfrac{120^{\circ}}{360^{\circ}}\right) \quad\\\\ & = \dfrac{1571}{25}\\\\ & = 62.8 \sf \:\:cm \:(3 \:sf)\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}\textsf{Perimeter of shaded portion} & = \textsf{chord length} + \textsf{arc length}\\\\ & = 30\sqrt{3}+\dfrac{1571}{25}\\\\ & = 114.80152...\\\\ & = 115\:\: \sf cm\:(3\:sf)\end{aligned}[/tex]

Answer: The domain wouldn’t include negative because it’s not possible to backward in time. The studio might limit the domain to numbers less than or equal to 10 because for x > 10 the number of views is unrealistically big. Also, viral marking slow after a while so the functions may not fit the data as well after 10 days.

Answer:

The answer above is the exact same as on edmentum that the teacher put, just so you know.

[tex]\left[\begin{array}{cc}1&3\\0&-2& \end{array}\right] \begin{bmatrix} 3& 1&-1& 0 \\ -1& 0&3&-1\end{bmatrix}\\\\\\=\begin{bmatrix} 3-3& 1+0&-1+9&0-3\\ 0+2&0-0&0-6&0+2\end{bmatrix}\\\\\\=\begin{bmatrix} 0&1&8&-3\\2&0&-6&2\end{bmatrix}[/tex]

Answer:

Yes.

Step-by-step explanation:

Let's first convert his speed to km/h.

[tex]\frac{105km}{1.5h} = 70\frac{km}{h}[/tex] > [tex]80\frac{km}{h}[/tex]. Therefore, Rob is traveling within the speed limit.

Answer:

for the first answer the second option is correct and 8 will go in the box and for the second question the second option is correct and 40 will go in the box.

Answer:

area: 1.9×0.75÷2

0.7125

perimeter: 2+0.75+2.25

5

Answer:

iii) R2

Step-by-step explanation:

Answer:

36 38 40 42

and

38 40 42 44.

Step-by-step explanation:

160 / 4 = 40  so the numbers are close to 40.

38 + 40 + 42 + 44 = 164

36 + 38 + 40 + 42 = 156.

Answer:

122.7 cm³

Step-by-step explanation:

    Square pyramid:

          a = 4 cm ; h = 4 cm

       [tex]\boxed{\text{Volume of square pyramid = $\dfrac{1}{3}$*base area * height}}[/tex]

                                                   [tex]\sf = \dfrac{1}{3}*a^{2}*h\\\\ =\dfrac{1}{3}*4*4*4\\\\ = 21.3 \ cm^3[/tex]

Rectangular prism:

        l = 6 cm ; w = 6 cm  ; h = 4 cm

        [tex]\boxed{\text{Volume of rectangular prism = l*w*h}}[/tex]

                                                       = 6 * 6 * 4

                                                       = 144 cm³

                       = 144 - 21.3

                       = 122.7 cm³

The change that would increase Susie’s limits is C. increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.

It should be noted that an insurance simply means a form of risk reduction that is taken regarding an asset.

In this case, the change that would increase Susie’s limits is to increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.

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Answer:

hope this will help you ( ◜‿◝ )♡

Step-by-step explanation:

[tex] \frac{ \sin(theta) }{ \sqrt{1 - \sin {}^{2} ( theta) } } \\ \frac{ \sin(theta) }{ \cos(theta) } \\ \tan(theta) [/tex]

Answer:

Angle HEF

105*

Step-by-step explanation:

Considering the amount they raised and the amount they spent, it is found that the art club had $358 after the show.

The net amount is found by the subtraction of the amount raised by the amount spent.

In this problem:

Then:

A = 564 - 206 = $358.

The art club had $358 after the show.

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Answer:

im gonna say it would be around 9 inches, because the actual answer, a decimal, isnt an option so the closest would be around 9 in.

Answer:

x = -5

Step-by-step explanation:

-3+x = -8

Add 3 to each side to isolate x

-3+x+3 = -8+3

x = -5

Answer:

I think the volume is 538.51 in^3.

Step-by-step explanation:

I have tried my hardest sorry if i am wrong

Answer:

26^2 meters

Step-by-step explanation:

l + b

16 + 10

= 26m×2

Answer:

Part A: 12.5 cm

Part B: 0.8 km

Step-by-step explanation:

Map scale problems can be solved with proportions.

Part A

5 cm / 2 km = x cm / 5 km

5/2 = x/5

2x = 25

x = 12.5

Answer: 12.5 cm

Part B

5 cm / 2 km = 2 cm / x km

5/2 = 2/x

5x = 4

x = 4/5

x = 0.8

Answer: 0.8 km

Your question is Incomplete. Please read below for the missing content.

Total cards = 8 + 5 = 13

The selections are being made with replacement. Hence,

a) P(G1 and G2) = P(G1)*P(G2) = (8/13)*(8/13) = 0.3787

b) P(Atleast 1 green) = 1 - P(No green) = 1 - (5/13)*(5/13) = 0.8521

c) P(G2 | G1) = P(G2) = 8/13 = 0.6154

Probability with replacement is used for questions where the outcomes are back again to the sample space again. which means that when the object is selected, then its miles changed and returned to the sample space, so the range of elements of the sample space remains unchanged.

Conclusion: The chance of two consecutive attracts without a replacement from a deck of playing cards is calculated because the range of viable successes over the variety of viable results, is expanded together for each case. accordingly, for the primary ace, there may be a 4/52 possibility and for the second there is a 3/51 probability.

Suppose that you have 8 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacements. Round your answers to four decimal places.

G1 = the first card drawn is green

G2 = the second card drawn is green

a. P(G1 and G2) =

b. P(At least 1 green) =

c. P(G2|G1) =

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Answer:

20

Step-by-step explanation:

2/3(30)

=20

Answer:

300

Step-by-step explanation:

[tex]5\% \: of \: x = 15 \\ x = 1500 \div 5 = 300[/tex]

0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

In the last 10 presidential elections, the democratic candidate has won six times in Michigan and four times in Ohio

We need to  find the probability of  that the democratic candidate wins both Michigan and Ohio in the next presidential election

As 6 wons from Michigan out of 10, so it 6/10

4 wons from Ohio out of 10, so it 4/10

The probability is 6/10/×4/10

24/100=0.24

In the next year also democratic candidate wons then the probabiltiy will be same 0.24

Hence 0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election

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Answer:

[tex]27cm^{2}[/tex]

Step-by-step explanation:

Area of compound shapes = Area of shape A + Area of shape B

Area of this shape = (L x B) + (L x B)
                               = (5 x 3) + (6 x 2)
                               = 15 + 12
                               = [tex]27cm^{2}[/tex]

Answer:

A = 27 cm²

Step-by-step explanation:

the figure consists of 2 rectangles

the one on the right with dimensions 2 cm by 6 cm and

the one on the left with dimensions 5 cm by 3 cm

the total area (A) is then calculated as

A = (2 × 6) + (5 × 3) = 12 + 15 = 27 cm²

Answer:

5/9.

Step-by-step explanation:

Theoretical probability = number of outcomes with1 or 2 blues

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

                                             number of all possible outcomes

= 5/9

All vertical lines intersected the curve at exactly 1 point.

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

Explanation:

If there is a case when a single vertical line crosses 2 or more points on the  curve, then it will not be a function. In this situation, it is said that the curve fails the vertical line test.

Passing the vertical line test means that every vertical line passes through exactly one point on the curve. Each x input leads to exactly one output. If such a situation happens, then we have a function.

Since Kelly concluded that the curve is a function, this means the curve passed the vertical line test, and it points us to choice D as the answer.

To find side given angle and two sides:

a² = b² + c² − 2bc cos(A)

Here given:

Solve for AC (a):

Answer:

AC = 14.8 cm (1 dp)

Step-by-step explanation:

Cosine rule

[tex]\sf b^2=a^2+c^2-2ac \cos B[/tex]

(where a, b and c are the sides, and B is the angle opposite side b)

Given:

Substituting the given values into the formula and solving for b:

[tex]\implies \sf AC^2=10^2+7^2-2(10)(7) \cos 120^{\circ}[/tex]

[tex]\implies \sf AC^2=100+49+70[/tex]

[tex]\implies \sf AC^2=219[/tex]

[tex]\implies \sf AC=\pm\sqrt{219}[/tex]

As length is positive,

[tex]\implies \sf AC=\sqrt{219}\:cm[/tex]

[tex]\implies \sf AC=14.8\:cm\:(1\:dp)[/tex]

Answer:

Question seven is 14, Question 8 is 16

Step-by-step explanation:

hoped this helped

Answer:

30

Step-by-step explanation: