Write an equation of a parabola with the given vertex and focus. Vertex (3,-2); focus (3,-3). Y=

Answer:

C = [tex]\frac{963}{92}[/tex]

Step-by-step explanation:

given A varies directly as B and inversely as C then the equation relating them is

A = [tex]\frac{kB}{C}[/tex] ← k is the constant of variation

to find k use the condition A = 6 , B = 10 , C = 15 , then

6 = [tex]\frac{x10k}{15}[/tex] ( multiply both sides by 15 )

90 = 10k ( divide both sides by 10 )

9 = k

A = [tex]\frac{9B}{C}[/tex] ← equation of variation

when A = 92 and B = 107 , then

92 = [tex]\frac{9(107)}{C}[/tex] ( multiply both sides by C )

92C = 963 ( divide both sides by 92 )

C = [tex]\frac{963}{92}[/tex]

Answer:

C = 963/92

Step-by-step explanation:

Given :

Finding the constant of variation, k

Finding C

Answer:

624

Step-by-step explanation:

Answer: Its 28.

Step-by-step explanation:

The missing number in the card s 28

Represent the missing number with x.

So, we have:

x, 19, 22 and 31

The mean of a dataset is:

Mean = Sum/Count

So, we have:

25 = (x + 19 + 22 + 31)/4

Multiply both sides by 4

100 = x + 19 + 22 + 31

Evaluate the sum

100 = x + 72

Subtract 72 from both sides

x = 28

Hence, the missing number is 28

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Answer:

B and E

Step-by-step explanation:

0.5 ÷ 0.25 = 2

A. NO because it's 20

B. Yes

C. NO because it's 0.2

D. NO because it's 1.1 repeating

E. Yes

Answer:

Step-by-step explanation:

assume that [tex]y=\sqrt{x}[/tex] is [tex]f(x)=\sqrt{x}[/tex] and [tex]y=\sqrt{-2x+6}+3[/tex] is

[tex]g(x)=\sqrt{-2x+6}+3\\ f(x)=\sqrt{x} \\g(x)=\sqrt{-2x+6}+3[/tex]

The transformation from the first equation to the second equation can be found by finding a,h and k for each equation.

[tex]y=a\sqrt{x-h}+k[/tex]

factor a 1 out of the absolute value to make the coefficient of x equal to 1

[tex]y=\sqrt{x}[/tex]

factor a 2 out of the absolute value to make the coefficient of x equal to 1

[tex]y=\sqrt{2}\sqrt{x-3}+3[/tex]

find a, h and k for [tex]y=\sqrt{2}\sqrt{x-3}+3[/tex]

[tex]a=1.41421356\\ h=3\\k=3[/tex]

the horizontal shift depends on the value of h when [tex]h > 0[/tex], the horizontal shift is described as:

[tex]g(x)=f(x+h)[/tex] - the graph is shifted to the left h units

[tex]g(x)=f(x-h)\\[/tex] - the graph is shifted to the right h units

the vertical shift depends on the value of k

area of trapezoid: 153 units²

Here given information:

trapezium area = [tex]\sf \frac{1}{2}[/tex] * ( side 1 + side 2 ) * height

[tex]\hookrightarrow \sf \dfrac{1}{2} * ( 10 + 24) * 9[/tex]

[tex]\hookrightarrow \sf 153 \ units^2[/tex]

Answer:

15500

Step-by-step explanation:

Solution

here

price of tv after discount: 13950

discount : 10%

now,

Answer:

  [tex]\left[\begin{array}{ccc}0&3&-5\\0&-1&-2\end{array}\right][/tex]

Step-by-step explanation:

Rotation 180° (in either direction) about the origin causes each coordinate to have its sign changed. Effectively, the coordinate matrix is multiplied by -1.

__

Additional comment

This is equivalent to reflection across the origin.

The value of x in the special right triangle is 39.60 ft.

Right angle triangle has one of its angles as 90 degrees. The side and angles can be found using trigonometric ratios.

Therefore, let's find the base of the triangle with 30 degrees.

sin 30° = opposite / hypotenuse

1 / 2 = 7 / b

b = 14 ft

Let's use the value(14 ft) to find the height of the biggest triangle.

sin 30 = opposite / hypotenuse

sin 30 = 14 / h

0.5h = 14

h = 14 / 0.5

h = 28 ft

Therefore, let's find the value of x .

sin 45° = 28 / x

x = 28 / 0.70710678118

x = 39.5979797464

x = 39.60 ft

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Answer:

6 3 5 6 8 8

Step-by-step explanation:

farthest apart than any other number

Answer:

Your correct answer is 90 :)

Step-by-step explanation:

90 is the biggest number in the number set so therefore it is an outlier. 

Have an amazing day!!

Please rate and mark brainliest!!

well, let's assume a year has 365 days, so 75 days is simply 75/365 of a year.  We also know that your loan was $650 and you paid back $680 or namely 30 bucks extra, so the interest on those $650 is really 30 bucks.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill &\$30\\ P=\textit{original amount deposited}\dotfill & \$650\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{75}{365}\dotfill &\frac{15}{73} \end{cases} \\\\\\ 30 = (650)(\frac{r}{100})(\frac{15}{73})\implies 30=\cfrac{9750r}{7300}\implies 30=\cfrac{195r}{146}\implies 4380=195r \\\\\\ \cfrac{4380}{195}=r\implies \stackrel{\%}{22.46}\approx r[/tex]

Answer:

3cm

Step-by-step explanation:

V = L * W * H

V = 10 * W * 4

10 * 4 = 40

120 / 40 = 3

W = 3

Answer:

1,511 cm²

Step-by-step explanation:

      We will find the surface area, but not include the top.

      This means we will have five sides to calculate for, see attached.     Please note that the area of a rectangle can be found with A = L * W

[1] 19 cm * 10 cm = 190 cm²

[2] 19 cm * 10 cm = 190 cm²

[3] 29 cm * 10 cm = 290 cm²

[4] 29 cm * 10 cm = 290 cm²

[5] 19 cm * 29 cm = 551 cm²

    Add them all together:

190 cm² + 190 cm² + 290 cm² + 290 cm² + 551 cm² = 1,511 cm²

Answer:

Step-by-step explanation:

he paid a 3 dollar fee so we can remove that 23.79-3 = 20,79

now we devide 20,79 by 11 or 189 minutes.

Answer:2 squared +3 squared and the square root of that number

Step-by-step explanation:

Step-by-step explanation:

Step 1: Take the First Derivative This means only differentiate once.

Disclaimer: Since absolute value only take positve outputs and quadratics only take positve outputs, we can get rid of the absolute value signs so we now have

[tex]e {}^{ {x}^{2} - 1 } [/tex]

We have the function x^2-1 composed into the function e^x.

So we use chain rule

Which states the derivative of a function composed is the

derivative of the main function times the derivative of the inside function.

So the derivative of the main function is

[tex] \frac{d}{dx} (e {}^{x} ) = e {}^{x} [/tex]

Then we replace x with x^2-1

[tex]e {}^{ {x}^{2} - 1} [/tex]

Then we take the derivative of the second function which is 2x so qe multiply them

[tex]e { }^{ {x}^{2} - 1 } 2x[/tex]

Step 2: Set the equation equal to zero.

[tex]e {}^{x {}^{2} - 1} 2x = 0[/tex]

Since e doesn't reach zero. We can just set 2x=0.

[tex]2x = 0 = x = 0[/tex]

So the critical point is 0.

Since e^x will never reach zero

Since 0 is the only critical point, this where the max or min will occur at.

Next we pick any numbergreater than zero, and plug them in the derivative function which gives us a positve number.

Any pick less than zero will give us a negative number.

Since the function is decreasing then increasing, we have a minimum.

Since 0 is the only critical point, we have a absolute minimum at 0.

To find the y coordinate, plug 0 in the orginal function.

Which gives us

[tex]e {}^{ {0}^{2} - 1 } = e {}^{ - 1} = \frac{1}{e} [/tex]

So the minimum occurs at

(0,1/e).

Answer:

y=x-5

Step-by-step explanation:

try that my good sir

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Consider the number as x

let's solve ~

[tex]\qquad \sf  \dashrightarrow \:6(x + 20) = 26[/tex]

[tex]\qquad \sf  \dashrightarrow \:6x + 120 = 26[/tex]

[tex]\qquad \sf  \dashrightarrow \:6x = - 120 + 26[/tex]

[tex]\qquad \sf  \dashrightarrow \:6x = -94[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = - 94 \div 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{ - 47}{3} [/tex]

・ ．━━━━━━━†━━━━━━━━━．・

Answer:

[tex](x + 20) 6 = 26[/tex]

[tex]6x + 120 = 26[/tex]

[tex]6x = 26 - 120[/tex]

[tex]6x = - 94[/tex]

[tex] \displaystyle \: x = \frac{ - 94}{6} [/tex]

[tex] \displaystyle{x = \frac{ - 47}{3} }[/tex]

[tex]\red {\rule{35pt}{2pt}} \green{ \rule{35pt}{2pt}}\orange{ \rule{35pt}{2pt}}\pink{ \rule{35pt}{2pt}}\blue{ \rule{35pt}{2pt}}\purple{ \rule{35pt}{2pt}}\red{ \rule{35pt}{2pt}}[/tex]

[tex] \bold{ \displaystyle{x = - \frac{47}{3} }}[/tex]

Answer: 1250 square feet!

Step-by-step explanation:

A (25)=25•(100-2•25)=25•50=1250 Sq Ft

If you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall.

Any rectangle's length and width differences must be as small as possible for the area to be maximized.

The largest area you can enclose

A =25×(100-2•25)

A=25•50

A=1250 Sq Ft

Thus, if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.

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Answer:

As Per Provided Information

Area of given square slice of cheese is 25 square inches .

We have been asked to determine the perimeter of the slice of cheese .

First we will find the side of square slice of cheese .

Let us assume the side of square slice of cheese be s .

Now Let's Solve

[tex] \boxed{\bf \:Area_{(Square)} = {Side}^{2}}[/tex]

Substituting the value and we obtain

[tex] \sf \longrightarrow \: 25 = {s}^{2} \\ \\ \\ \sf \longrightarrow \: \sqrt{25} = s \\ \\ \\ \sf \longrightarrow \: s \: = 5 \: inch[/tex]

So, the side of square slice cheese is 5 inch

Now let's calculate the Perimeter of cheese

[tex] \boxed{\bf \: Perimeter_{(Square)} = 4 \times side}[/tex]

Substituting the value we obtain

[tex] \longrightarrow \sf \: Perimeter_{(Square)} = 4 \times 5 \\ \\ \\ \longrightarrow \sf \: Perimeter_{(Square)} =20 \: inches[/tex]

Therefore,

Apply Pythagorean theorem

Answer:

Distance between point P and Q = 5m

Step-by-step explanation:

Given

Using Pythagorean Theorem (applicable for only right triangles)

Hope it helped~

Answer:

y=-41

Step-by-step explanation:

[tex]\frac{y+31}{2} =-5\\y+31=-5 \times 2\\y+31=-10\\y=-10-31\\y=-41[/tex]

Check the picture below.

Answer:

W = 5

L = 15

Step-by-step explanation:

Formula for Area of Rectangle is L × W

Since stated triple;

L = 3W

Area = L×W = 3W² = 75

It'll be:

3W² = 75

Divide both sides with 3:

3W² = 75

3 3

W² = 25

Then square root both sides:

w = 5

Again stated that length is triple the width:

L = 5 × 3

L = 15

Therefore;

W = 5

L = 15

Recall the well-known series

[tex]\displaystyle 2 \arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}[/tex]

Replace x with √x :

[tex]\displaystyle 2 \arcsin^2(\sqrt x) = \sum_{n=1}^\infty \frac{(4x)^n}{n^2 \binom{2n}n}[/tex]

Differentiate both sides:

[tex]\displaystyle -\frac{\arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^n}{n \binom{2n}n}[/tex]

Multiply by 4x :

[tex]\displaystyle -\frac{4x \arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^{n+1}}{n \binom{2n}n}[/tex]

All the series I've mentioned converge for |x| < 1, so we can take x = -1/4 to find the value of the sum we want.

[tex]\displaystyle \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n \binom{2n}n} = -\frac{4 \times \left(-\frac14\right) \arcsin\left(\sqrt{-\frac14}\right)}{2\sqrt{-\frac14-\left(-\frac14\right)^2}} = -\frac{\arcsin\left(\frac i2\right)}{\frac{\sqrt5\,i}2}} = \boxed{\frac2{\sqrt5} \mathrm{arsinh}\left(\frac12\right)}[/tex]

where

[tex]\arcsin\left(\frac i2\right) = z \iff 2\sin(z) = -2i\sinh(iz) = i \implies z = i \, \mathrm{arsinh}\left(\frac12\right)[/tex]