Find f(4) if f(x) = 3x + 13

The focus is the point inside a parabola that helps determine the shape of the curve.

A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.

The equation of a parabola:

y = a(x - h)² + k

We have,

A parabola is a type of curve that is formed when a plane intersects a cone at an angle that is parallel to one of the cone's sides.

One of the key defining features of a parabola is that all points on the curve are equidistant from a fixed point, known as the focus, and a fixed line, known as the directrix.

The focus is located inside the parabola, and its distance from the directrix is equal to the distance from any point on the parabola to the directrix.

This property allows us to use the focus and directrix to determine the shape and location of the parabola.

Thus,

The focus is the point inside a parabola that helps determine the shape of the curve.

Learn more about parabola here:

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Answer:

R6.775

Step-by-step explanation:

Given that :

The transaction fee charged is calculated using the relation :

Transaction fee = R2.50 + 0.95%(amount deposited)

If amount to deposit is R450 ; the bank charge will be:

R2.50 + 0.95%(Amount deposited)

R2.50 + 0.0095(450)

R2.50 + R4.275

R(2.50 + 4.275)

R6.775

Answer:21.99

Step-by-step explanation: Given diameter of a circle is(d)=7cm.

Now, we know that circumference of circle is =πd, where d is diameter of circle.

So, here circumference is = π×7cm

= 22/7 x 7 cm

Circumference = 22cm

[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]

Diameter of the circle "d" = 7 cm

[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]

The circumference of the circle.

[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\: 22\:cm.}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]

[tex] = \frac{22}{7} \times 7 \: cm[/tex]

[tex] = 22 \: cm[/tex]

Therefore, the circumference of the circle is 22 cm.

[tex]\large\mathfrak{{\pmb{\underline{\pink{Mystique35 }}{\pink{❦}}}}}[/tex]

Answer:

7x+5=180

7x=175

x=25

Hope This Helps!!!

Answer:

Part A:

[tex]x\in \mathbb{R}[/tex] ([tex]x[/tex] is equal to all real numbers)

Part B:

[tex]5+(-4)-12=-4-7,\\-11=-11\:\checkmark,\\\\5+0-12=0-7,\\-7=-7\:\checkmark,\\\\5+5-12=5-7,\\-2=-2\:\checkmark[/tex]

Step-by-step explanation:

Part A:

Given [tex]5+x-12=x-7[/tex], combine like terms:

[tex]x-7=x-7[/tex]

Add 7 to both sides:

[tex]x=x[/tex]

Since this is merely a true statement for all real numbers (reflexive property), this equation is true for any real value of [tex]x[/tex].

Therefore,

[tex]x\in \mathbb{R}[/tex] ([tex]x[/tex] is equal to all real numbers).

Part B:

Using arbitrary values [tex]x=-4, x=0, x=5[/tex] as requested in part B, verify:

[tex]5+(-4)-12=-4-7,\\-11=-11\:\checkmark,\\\\5+0-12=0-7,\\-7=-7\:\checkmark,\\\\5+5-12=5-7,\\-2=-2\:\checkmark[/tex]

Answer:

honestly for division of fractions the only sentence you need to know is...

"mine is not to question why, but to invert and multiply"...

fractional division can be done with "an inverse multiplication:

5/6 ÷ 1/6 can be changed to 5/6 * 6/1 = 30/6 = 5

3/5 ÷1/10 can be changed to 3/5 * 10/1 = 30/5 = 6

Step-by-step explanation:

Answer:

5/3π or 5.2

Step-by-step explanation:

30 / 360 = x / 20π

then x = 5/3π or 5.2

Answer:

5/3 [tex]\pi[/tex]

Step-by-step explanation:

30/360 * 2 [tex]\pi 10[/tex]

1/12 * 2 [tex]\pi 10[/tex]

20/12 [tex]\pi[/tex]

5/3 [tex]\pi[/tex]

Step-by-step explanation:

Cog, KY tj, kyzkysiyso6doydi6wkyx co70 kysu5, 5i

Given:

The vertices of a triangle are [tex](1,1),(-1,-1),(-\sqrt{3},\sqrt{3})[/tex].

To prove:

The given vertices are the vertices of an equilateral triangle.

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let the vertices of the triangle are [tex]A(1,1),B(-1,-1),C(-\sqrt{3},\sqrt{3})[/tex]. Then, by using the distance formula, we get

[tex]AB=\sqrt{(-1-1)^2+(-1-1)^2}[/tex]

[tex]AB=\sqrt{(-2)^2+(-2)^2}[/tex]

[tex]AB=\sqrt{4+4}[/tex]

[tex]AB=\sqrt{8}[/tex]

Similarly,

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

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

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

[tex]BC=\sqrt{1+3+1+3}[/tex]

[tex]BC=\sqrt{8}[/tex]

And,

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

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

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

[tex]CA=\sqrt{1+3+1+3}[/tex]

[tex]CA=\sqrt{8}[/tex]

Clearly, [tex]AB=BC=CA[/tex].

Since all sides of the given triangle are equal, therefore the given vertices are the vertices of an equilateral triangle.

Hence proved.

Answer:

x = 14000

Step-by-step explanation:

Function representing the cost to the company,

C(x) = -27x² + 51000x + 20433

Function defining the revenue generated,

R(x) = -36x²+ 303000x

Since, Profit to the company = Revenue - Cost

                                                = R(x) - C(x)

P(x) = -36x² + 303000x - (-27x² + 51000x + 20433)

      = -36x² + 27x² + 303000x - 51000x - 20433

P(x) = -9x² + 252000x - 20433

To maximize the profit,

P'(x) = -18x + 252000 [Derivative of the function P(x)]

P'(x) = 0

-18x + 252000 = 0

18x = 252000

x = 14000

Therefore, for the maximum profit company has to produce and sell 14000 phones.

Answer:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Step-by-step explanation:

Answer:

y = -5x - 9

Step-by-step explanation:

y = -5x + b

6 = -5(-3) + b

6 = 15 + b

b = -9

Answer:

x=8

Step-by-step explanation:

assuming this is what you mean:

(5x+2)=42

try to

isolate the variable by subtracting 2 from both sides

5x=40

continue to isolate the variable

divide by 5 on both sides

5x/5=40/5

x=8

Answer:

The new slope is 1 and the line is shifted flatter.

Step-by-step explanation:

Line A slope is 4.

Line B slope is 1.

The y-intercept rose up 3

As far as slope, it became flatter because the line only rises 1 'square' for every 1 'square' it travels to the right. It was rising 4 'squares' for every 1 to the right.  

Answer:

if you wanna do long division you have to simply just follow a procedure that is nice and easy so long division method is mainly need to find the square of a number with out using the prime factorization method the procedure is consisting of these of two steps

Hope it helps

Answer:

yards

Step-by-step explanation:

Answer:

Which is greater, 2 miles

1 mile = 1760 yards

2 miles = 2 * 1760

2 miles = 3,520 yards

How much greater?

3,520 - 1000 = 2520 yards

Answer:

[tex]\displaystyle w=\frac{9}{2}=4.5[/tex]

Step-by-step explanation:

We can use slope formula:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So:

[tex]\displaystyle m=\frac{4-w}{-10-(-6)}=\frac{4-w}{-10+6}=\frac{4-w}{-4}[/tex]

We are given that this equals 1/8. Therefore:

[tex]\displaystyle \frac{4-w}{-4}=\frac{1}{8}[/tex]

Solve for w. Cross-multiply:

[tex]-4(1)=8(4-w)[/tex]

Distribute:

[tex]-4=32-8w[/tex]

Isolate:

[tex]-8w=-36[/tex]

So:

[tex]\displaystyle w=\frac{-36}{-8}=\frac{9}{2}=4.5[/tex]

Answer:

Almost...

The correct answer would be

To find the area of the base, multiply 15 times 16 then divide by 2

Then multiply by 19 to find the volume of the shape

Step-by-step explanation:

The base is a triangle

The area of a triangle = base length times height divided by 2

The triangle has a base length of 16 and a height of 15

So to find the area of the base we multiply 15 times 16 and divide that by 2

The volume of a prism is equal to the area of the base times the length of the prism

The length of the prism is 19 so we would then multiply by 19

Answer:

67

Step-by-step explanation:

we are given adjacent and opposite sides. thus tan^-1 would be used to determine the angle

opposite side = 665 - 5 = 660

adjacent side = 280

tan = opposite / adjacent

[tex]tan^{-1}[/tex] (660/280) = 67

Answer:

67

Step-by-step explanation:

I took it on EDG

Answer:

volumn= l*b*h

4x*2x*1x= 8000 cm3

8x= 8000 cm3

x= 1000cm3

length = 4000

breadth= 2000

height = 1000

Answer:

Step-by-step explanation:     6  29  7  42

6)  a number x increased by -18

             x + (-18)    

   or       x -  18

7)    x subtracted from its reciprocal

              1/x  - x  

8)   two numbers have the sum of 11, one number is q find the other

             x + q = 11

             x + q - q = 11 - q       q - q = 0

              x + 0  = 11 - q

              x = 11 - q

9)    six is added to 4 times a number equals 42, find the number

      ( I don't know the six steps discussed in class.  This is how I would do it)

             6 + 4x = 42

             6 - 6 + 4x = 42 - 6              isolate the variable,  - 6 from both sides

             0 + 4x = 36                            6 - 6 = 0,  43 - 6 = 36, solve for x

                4x/4 = 36/4                      divide both sides by 4

                  1x  =  36 /4                        4/4 = 1

                  x  =   9                            

Answer:

600[tex]e^{10*.04}[/tex]

$895.09

Step-by-step explanation:

Answer:

You multiply length by width.

Step-by-step explanation:

To find the area of a rectangle you multiply length and width together.

For example if a rectangle has length 2 and width 3 the area of the rectangle would be 6, since 2 * 3 is 6.

Answer:area =length x width

Step-by-step explanation:

Answer:

rv = 18

Step-by-step explanation:

if rt is 36, rv is half of that so you take 36 and divide by 2 and get 18,

have a great day!!

Answer:

18

Step-by-step explanation:

Because i have parallegram RSTU

=> RT = 2*RV = 2*VT

SU = 2* SV = 2*VU

Answer:

[tex]= \frac{2x-3\sqrt{x} }{x-1}[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}[/tex]

Expand

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

This gives the simplified form

Answer:

B 63 units

Step-by-step explanation:

Dilatation is an increase of shape , a larger imagine , the dilatation is 3 so times each side by three and add them all up

Answer:

C)48 pi square units

Step-by-step explanation:

The lateral area is  the area around the sides  ( does not include the top or bottom)

LSA = 2pirh

      = 2 pi(4) (6)

    = 48 pi