Using basic geometry, solve sin 105°​

well, tis noteworthy that the equation of the parabola above is already in vertex form, which means its vertex is at (3 , 6) and its focus point is at (3 , 1).

now, the focus point is below the vertex, meaning is a vertical parabola opening downwards, like a hump.

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]y=-\cfrac{1}{20}(x-3)^2+6\implies y-6=-\cfrac{1}{20}(x-3)^2\implies \stackrel{4p}{-20}(y-\stackrel{k}{6})=(x-\stackrel{h}{3})^2 \\\\\\ 4p=-20\implies p=-\cfrac{20}{4}\implies p=-5[/tex]

the focus point must be a negative distance since the parabola is opening downwards, and the directrix is across the vertex at "p" distance, Check the picture below.

0.10100100010000 and 0.110100100010000 are two irrational numbers between 0.1 and 0.12.

Step-by-step explanation:

=> greater than 0.1 and smaller than 0.12

You can also choose any other numbers too.

Irrational Number :

Answer:

1)  N/A

2) ( -0.714, 3.857)

Step-by-step explanation:

for question 1 since the slope is the same, they will never intersect

for question 2 they intersect at (-0.714, 3.857)

1) as for the coordinates, for y=3x+2 it is (0,2) (-2/3, 0) it's an upward slope

y=3x-5 coordinates are (0, -5) (1.667, 0) it's an upward slope

2) 4x+y=1 coordinates are (0,1) (1/2, 0) it's a downwards slope

y=3x+6 coordinates are (-2, 0) (0,6) it's a upward slope

Answer:

1st choice : 706.5 square inches

Step-by-step explanation:

circumference is pi times diameter

divide 94.2 by pi to get diameter = 29.9847912785

diameter 29.9847912785 divided by 2 is

14.9923956393 which is the radius

area is pi times radius times radius again

pi times 14.9923956393 times 14.9923956393 =

706.141834613

The statement third “the difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour” is correct.

It is defined as the difference between the maximum value in the data set to the minimum value in the data set.

As we know, the difference between the greatest and lowest values, called the range.

According to this response, the range is 1 hour, which is the difference between the most and least amount of time spent surfing the Internet. This is based on the term “Range.”

Thus, the statement third “the difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour” is correct.

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Answer:

The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 1 hour!

Step-by-step explanation:

Answer:

4 385 000 000 000 000 000 000 000 000 000.

Step-by-step explanation:

Wellllll.....e +30 means  10^30

Step-by-step explanation:

Area: Length X width

Perimeter: Add all sides

The function represented by the table of values is an exponential function

The table is given as:

x 0 1 2 3 4

y 5 10 20 40 80

On the table, we have the following highlights:

This means that the function has a common ratio

Only exponential functions have a common ratio

Hence, the function is an exponential function

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Answer:

2.33 x  10^24  kilograms

Step-by-step explanation:

hope this helps!!

=2.33 × [tex]10{^{21}[/tex]

scientific notation

= 2.33e21

scientific e notation

= 2.33 × [tex]10{^{21}[/tex]

engineering notation

= 2.33 × [tex]10{^{21}[/tex]

21

Order of Magnitude

for scientific and standard forms

two setillion three hundred thirty quintillion

Answer:

H - 5 hours

Step-by-step explanation:

We can setup an equation to solve the question.

Let [tex]h[/tex] be the number of hours Mary must work.

[tex]250 = 160 + 3(6h)[/tex]

250 - the amount of money Mary needs

160 - the amount of money Mary has saved already

3 - How many days she works

6h - How much she gets paid per day

[tex]250 = 160 + 3(6h)\\90 = 3(6h)\\90=18h\\5=h[/tex]

This means Mary must work 5 hours each day to pay her rent.

Answer:

( 18.4, 4.6 )

Step-by-step explanation:

2x - 6y  = 14

Add 6y to both sides

2x = 6y + 14

divide both sides by 2

             x = (3y + 7)

Substitute this ^ for x in the othe equation

4 (3y + y) - y = 9

distribute the 4

12y + 4y - y = 9

combine like terms

15y = 9

divide both sides by 15

y = 4.6

Now substitute this value for y in the equation we previously substituted .to find the value of x

x = 3 (4.6) + 4.6

x = 13.8 + 4.6

x = 18.4

Hope this makes sense and was helpful!

The area of the walkway that is painted with the 12 arrows will be 840 cm². Then the correct option is C.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

This figure represents an arrow painted on a walkway 12 times.

The figure is given below.

The figure is the combination of a triangle and a rectangle. Then the area of the figure will be

Area = 1/2 x 8 x 5 + 10 x 5

Area = 20 + 50

Area = 70 cm²

Then the area of the walkway that is painted with the 12 arrows will be

Area of the walkway = 70 x 12

Area of the walkway = 840 cm²

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Answer:

A) 70%

B) 95%

Step-by-step explanation:

A) $200 to $340

Increase = $340 - $200 = $140

Percentage of increase = $140/$200 * 100% = 70%

B) Additional $50

Increase = $140 + $50 = $190

Percentage of increase = $190/$200 * 100% = 95%

So

a_2

a_3

a_4

a_5

Based on the price he purchased the stock and the amount he sold them for, Jeff's annualized HPR on the investment is 2,395%.

First find the net profit:

= (1,000 x 9.26) - (1,000 x 1.89) - 10

= $7,360

The HPR is:

= 7,360 / (1,000 x 1.89)

= 389.4%

The annualized HPR is:

= (1 + 389.4%)² - 1

= 2,395%

Note: Taken to the power of 2 because there are two six-month periods in a year.

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Check the picture below.

[tex]sin(\theta )=\cfrac{\stackrel{opposite}{30\cdot sin(24^o)}}{\underset{hypotenuse}{50}}\implies sin^{-1}[sin(\theta )]=sin^{-1}\left[ \cfrac{30\cdot sin(24^o)}{50} \right] \\\\\\ \theta =sin^{-1}\left[ \cfrac{30\cdot sin(24^o)}{50} \right]\implies \theta \approx 14.1^o[/tex]

The value of angle does this replacement ramp make with the horizontal is,

⇒ θ = 14.1°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

A 30-foot ramp is used to move product to a loading dock.

The ramp makes a 24° angle with the horizontal.

And, The ramp is to be replaced with a ramp that is 50 feet long.

Hence, By given figure;

We have;

⇒ sin θ = 30 × sin 24° / 50

⇒ θ = sin ⁻¹ (30 × sin 24° / 50)

⇒ θ = 14.1°

Thus, The value of angle does this replacement ramp make with the horizontal is,

⇒ θ = 14.1°

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Answer:

= 25√3/3

Step-by-step explanation:

x/25 = tan 30o

x = 25/√3

= 25√3/3

Answer:

1 x 10^-7

Step-by-step explanation:

[H+] = 10^-pH

[H+] = 10^-7

Answer:

[tex] a = \boxed{1},\: b=\boxed{0}\\\\c=\boxed{0},\: d=\boxed{1}[/tex]

Step-by-step explanation:

Answer:

Hope this helps. Credit to the other user.

Step-by-step explanation:

Answer:

decreasing and linear

Step-by-step explanation:

it just is

Answer:

Decreasing,  linear

Step-by-step explanation:

you are going -4 every time

The missing parts of the given table are

∠1 ≅ ∠4                  → Alternate interior angles Theorem

DB ≅ DB                 → Reflexive property

ΔDAB ≅ ΔBCD       → SAS (Side Angle Side)

From the question, we are to complete the table to prove that ABCD is a parallelogram

The missing parts in the table can be completed as shown below

∠1 ≅ ∠4                  → Alternate interior angles Theorem

DB ≅ DB                 → Reflexive property

ΔDAB ≅ ΔBCD       → SAS (Side Angle Side)

Hence, the missing parts of the given table are

∠1 ≅ ∠4                  → Alternate interior angles Theorem

DB ≅ DB                 → Reflexive property

ΔDAB ≅ ΔBCD       → SAS (Side Angle Side)

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.

The sum of the expression (x - 2) and (x+6) is 2x + 8

The sum of numbers simply means to add up the numbers.

Therefore,

(x  -2) + (x + 6)

Hence,

(x - 2) + (x + 6)

open the brackets

Therefore,

x - 2 + x + 6

combine like terms

x + x + 2 + 6

add or subtract the like terms

2x + 8

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The length of the half chord is given as 21. The length of the perpendicular drawn from the center to the chord is 20. The radius would be 29 units.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]  

where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).

The length of the half chord is given as 21.

The length of the perpendicular drawn from the center to the chord is 20.

By Pythagoras' Theorem

[tex]|r|^2 = |21|^2 + |20|^2\\\\|r|^2 = 441 + 400\\\\|r|^2 = 841\\\\|r| = \sqrt{841} \\\\r = 29[/tex]

The radius of the circle would be 29 units.

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Answer:

i. No, Maurice statement is wrong

ii. Stephan does not have sufficient pieces of wood to make the tray because the square inches required is more than what he has.

Step-by-step explanation:

Stephan's piece of wood measures; 18 inches in length and 12 inches in width. Since the piece of wood has a shape of a rectangle,the area of the piece of wood = length × width                                                 = 18 × 12                                                = 216 square inchesAccording to Maurice's statement, he could make a tray that has a base of 1012 inches by 1012 inches. The base has the shape of a square, so that;     the area of the base = length × width =                                        = 1012 ×1012                                      = 1024144 squared inchesThis shows that Stephan does not have sufficient wood to make the tray because the square inches required is more than what he has.

If  he is single and claims 3 allowances. The amount deducted for federal taxes is $39.8

Federal tax withheld:

Federal tax withheld =6.2% social security + 1.45% Medicare

Federal tax withheld = 7.65%

Deduction:

Deduction= 0.0765 × $520.75

Deduction=$39.8

Therefore the amount deducted for federal taxes is $39.8

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Caroline, Colin & Sarah share some money.Caroline will get [tex]\dfrac{2}{3}[/tex]  when Caroline, Colin & Sarah share some money.

The ratio defined as the sharing of the two or three things or it represent that one thing or number is how many times to the other.

One part is excluded in the problem. That part is:

"Caroline gets [tex]\dfrac{1}{9}[/tex] of the money."

If Caroline gets 1/9th, then remaining is:

[tex]1-\dfrac{1}{9}=\dfrac{8}{9}[/tex]

Colin and Sarah share in ratio 3 is to 1, that means 3 + 1 = 4 parts...

8/9th in 4 parts means, each part is:

[tex]\dfrac{\dfrac{8}{9}}{4}=\dfrac{2}{9}[/tex]

We know Colin gets "3" parts of the total, each part is (2/9)th, so 3 parts would be:

[tex]3\times \dfrac{2}{9}=\dfrac{6}{9}=\dfrac{2}{3}[/tex]

Colin gets  [tex]\dfrac{2}{3}[/tex] money when three of them share money.

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Answer:

z° = 68°

x = 2

Step-by-step explanation:

[tex](14x+84)^{0} =\frac{360-2(68)}{2} =112[/tex]

[tex]14x=112-84=28[/tex]

[tex]x=\frac{28}{14} =2[/tex]

Hope this helps