What is the equation of the parabola with focus (3,0) and directrix x= -3?

Answer:

x = 3

Step-by-step explanation:

the midsegment XW is half the sum of the parallel bases , that is

7x + 10 = [tex]\frac{1}{2}[/tex] (46 + 16 ) = [tex]\frac{1}{2}[/tex] × 62 = 31 ( subtract 10 from both sides )

7x = 21 ( divide both sides by 7 )

x = 3

Answer:

5.7 and 4.2

Step-by-step explanation:

Outside diagonal = √a² + a² = √4² + 4² = 4√2

= 5.7

Inside diagonal = √b² + b² = √3² + 3² = 3√2

= 4.2

Answer:

10

Step-by-step explanation:

Using the distance formula,

[tex] \sqrt{ {( - 2 - ( - 8))}^{2} + { (- 4 - 4)}^{2} } = 10[/tex]

Answer:

[tex]x = 2, y = -1[/tex]

Step-by-step explanation:

We can add the 2 equations together to solve for y.

[tex](-3x + 5y) + (3x + 7y) = (-11) + (-1)\\-3x + 3x + 5y + 7y = -11 -1\\12y = -12\\y = -1[/tex]

Now we can solve for x by substituting y in one of the original equations.

[tex]3x + 7y = -1\\3x + 7(-1) = -1\\3x - 7 = -1\\3x = 6\\x = 2[/tex]

Those are the answers

- Kan Academy Advanced

Answer:

[tex]\underline{\boxed{\sf{2(x - 11)(x + 11)}}}[/tex]

Step-by-step explanation:

[tex]\sf{2x^2 - 242}[/tex]

Common factor :

[tex]\sf{2x^2 - 242}[/tex]

[tex]\sf{2(x^2 - 121)}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Use the sum-product pattern :

[tex]\sf{2(x^2-121)}[/tex]

[tex]\sf{2(x^2 + 11x-11x - 121)}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Common factor from the two pairs :

[tex]\sf{2(x^2 + 11x-11x - 121)}[/tex]

[tex]\sf{2(x(x+11) -11(x + 11))}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Rewrite in factored form :

[tex]\sf{2(x(x+11)- 11(x + 11))}[/tex]

[tex]\sf{2(x - 11)(x + 11)}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Solution :

[tex]\sf{2(x - 11)(x + 11)}[/tex]

To increase sales, an online clothing store began giving a 50% off coupon to random customers Six customers each made purchases from the website the binomial random variable and  mean and standard deviation of X  is mathematically given as

[tex]X ~ Bin(n = 6, p = 0.2)[/tex]

x= 0.9798

Generally, the equation for is mathematically given as

P(coupon) = 1/5

P(coupon)= 0.2

the binomial distribution

[tex]X ~ Bin(n = 6, p = 0.2)[/tex]

Therefore, The mean and standard deviation of X

[tex]пВ = np \\np= 6* 0.2 = 1.2\\[/tex]

[tex]x=\sqrt{ np(1 - p)} \\ x=\sqrt{ 6 * 0.2 + (1 -0.2)} \\[/tex]

x= 0.9798

In conclusion, mean and standard deviation of X

x= 0.9798

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Step-by-step explanation:

oksosjaoqkqeand

[tex]66 \sqrt[3x9 \frac{ \sqrt[xx. \sqrt[36 \sqrt[3136(2 > kaki \: kwl{]{?} ]{?} ]{?} }{?} ]{?} [/tex]

Answer:

-4.25

Step-by-step explanation:

The amount that Theresa was charged in interest for the billing cycle is $5.30

By using the average daily balance, the amount will be:

= (350 × 12) + (520 × 19) / (12 + 19)

= (4200 + 9880)/31

= 454.19

Therefore, the interest will be:

= (454 × 0.14)/12

= $5.30

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Answer:

2

Step-by-step explanation:

Start by simplifying the expression:

[tex]4(x-3)+5x-x^2[/tex]

Use distribution:

[tex]4x-4(3)+5x-x^2\\4x-12+5x-x^2[/tex]

Add like terms:

[tex]9x-12-x^2[/tex]

Now, substitute the given value of x into the expression:

[tex]9(2)-12-2^2\\18-12-4\\6-4\\2[/tex]

Answer:

2

Step-by-step explanation:

Given: 4(x − 3) + 5x − x²

Substitute 2 for the value of x in the expression and simplify:

➜ 4(2 − 3) + 5(2) − (2)²

➜ 4(−1) + 10 − 4

➜ -4 + 10 - 4

➜ 2

Therefore, the value of the expression when x equals 2 is 2.

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Answer:

.35 < 38% < 3/5

Step-by-step explanation:

.35 is the same as 35 percent which is less than 38, and 3/5 when divides is .60 turned into percent is 60 percent

Answer:

option c

Step-by-step explanation:

a) NOT TRUE

A composite number is a positive integer that can be formed by multiplying two smaller positive integers.

3 and 7 are not composite numbers because each of them can only be divided by one and itself

b) NOT TRUE

2 is also a prime number so 3 and 7 are not the only numbers

c) TRUE

All the number listed are prime numbers hence why they are all at the bottom of the tree (only have 1 and itself as factors)

d) NOT TRUE

21 is not a prime number. The number 21 is divisible by 1, 3, 7, 21. For a number to be classified as a prime number, it should have exactly two factors. Since 21 has more than two factors, i.e. 1, 3, 7, 21, it is not a prime number.

The equations of the graphed line and function can be written as:

f(x) = 1/2x + 2

y - 3 = 1/2(x - 2)

y - 1 = 0.5(x + 2)

Equation of a graphed line can be expressed in:

Slope-intercept form as y = mx + b, where m = slope, b = y-intercept; or

Point-slope form as y - b = m(x - a), where (a, b) is a point and m = slope.

Find the slope (m) of the line:

Slope (m) = change in y / change in x = 1/2 = 0.5

y-intercept (b) = 2

To express the graphed line in slope-intercept form, substitute m = 1/2 and b = 2 into f(x) = mx + b:

f(x) = 1/2x + 2.

Using the point-slope form, write the equation by substituting m = 1/2 and (a, b) = (2, 3) into y - b = m(x - a):

y - 3 = 1/2(x - 2)

Or substitute m = 0.5 and (a, b) = (-2, 1) into y - b = m(x - a):

y - 1 = 0.5(x - (-2))

y - 1 = 0.5(x + 2)

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Answer:

Step-by-step explanation:

Answer: 123 boxes

Step-by-step explanation:

Find how many nails she used.

692-200=492

she used 492 nails

we know that 4 nails are needed to set up a box

so we divide.

492/4=123

Sally set up 123 boxes

Step-by-step explanation:

= 5 • ( 4• x )

= 5 ( 4x )

= 20x

[tex]...[/tex]

Answer:

E 150

Step-by-step explanation:

The coordinates of the mid - point of the line AB is (-1, -5).

A midpoint is a point that divides a given line into two equal parts.

Given is that AB has endpoints at A(4, -8) and B(-6, -2). It is asked to find the coordinates of the midpoint of AB.

We can write the coordinates of the midpoint of AB as -

{x} = (x₁ + x₂)/2

{x} = (4 - 6)/2

{x} = - 2/2

{x} = -1

{y} = (y₁ + y₂)/2

{y} = (-8 - 2)/2

{y} = - 10/2

{y} = - 5

Therefore, the coordinates of the mid - point of the line AB is (-1, -5).

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Answer:

Step-by-step explanation:

(2,1) and (4,2) are on the line.

slope

[tex]=\frac{2-1}{4-2} =\frac{1}{2} \\[/tex]

eq. of line is

[tex]y-1=\frac{1}{2} (x-2)\\2y-2=x-2\\2y=x\\or \\x-2y=0\\[/tex]

in slope intercept form

[tex]y=\frac{1}{2} x[/tex]

Answer:

the unit cost per rubber tile is $$$$$$$$$$$$$6

Step-by-step explanation:

..

Answer:

38% is your answer boss. hope that helps :)

The percentage of people who supported the home team is 38 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The total number of people attending the baseball game = 3500 people

The number of people supporting the home team = 1300 people

The number of people supporting the visiting team is = 2170

Now , the equation will be

The percentage of people supporting the home team is = number of people supporting the home team / total number of people attending the baseball game

Now , the equation will be

The percentage of people supporting the home team is A = ( 1300 / 3500 ) x 100

The percentage of people supporting the home team is A = 0.38 x 100

The percentage of people supporting the home team is A = 38 %

Therefore , the value of A is 38 %

Hence , The percentage of people who supported the home team is 38 %

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Answer:

V = 3053.63 mm^3

Step-by-step explanation:

radius : 9mm

V = 4/3 * pi * r^3

V = 4/3 * (3.1415926535898...) * 9^3

V = 3053.63 mm^3

Check the picture below.  so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}[/tex]

[tex](\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}[/tex]

Answer:

GCF=3[tex]x^{2}y[/tex]

Step-by-step explanation:

First, take a look at the numbers.

GCF of 15 and -18 = 3

Then, look at the variables.

GCF of (x^2)(y^3) and (x^3)(y)(z) = (x^2)(y)

Lastly, combine the two expressions

GCF = 3(x^2)(y)

Answer: 3(x^2)(y)

Hope this helps!

Answer:

132.84 is the answer as volume is area times length

Answer:

0.267

Step-by-step explanation:

4/15 as a decimal is 0.26 repeating so rounded to the nearest thousandth would be 0.267

Answer:

Kelly has read more of the book

Well, let's use the Euclidean algorithm:

164 = 4×37 + 16

37 = 2×16 + 5

16 = 3×5 + 1

Then working backwards,

1 = 16 - 3×5

1 = 16 - 3×(37 - 2×16) = 7×16 - 3×37

1 = 7×(164 - 4×37) - 3×37 = 7×164 - 31×37

so that x = 7 and y = -31.

Answer:

Alice

Step-by-step explanation:

14$ the amount he had - X the amount he lost (the unknown) is what is described by Alice

The products of the polynomials are:

To do this, we multiply each pair of polynomial as follows:

Pair 1: (xy + 9y + 2) and (xy – 3)

(xy + 9y + 2) * (xy - 3)

Expand

(xy + 9y + 2) * (xy - 3) = x²y² - 3xy + 9xy² - 27y + 2xy - 6

Evaluate the like terms

(xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6

Pair 2: (2xy + x + y) and (3xy² - y)

(2xy + x + y) * (3xy² - y)

Expand

(2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²

Pair 3: (x – y) and (x + 3y)

(x - y) * (x + 3y)

Expand

(x - y) * (x + 3y) = x² + 3xy - yx + 3y²

Evaluate the like terms

(x - y) * (x + 3y) = x² + 2xy + 3y²

Pair 4: (xy + 3x + 2) and (xy – 9)

(xy + 3x + 2) * (xy – 9)

Expand

(xy + 3x + 2) * (xy – 9)  = x²y² - 9xy + 3x²y - 27x + 2xy - 18

Evaluate the like terms

(xy + 3x + 2) * (xy – 9)  = x²y² - 7xy + 3x²y - 27x  - 18

Pair 5: (x² + 3xy - 2) and (xy + 3)

(x² + 3xy - 2) * (xy + 3)

Expand

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 9xy - 2xy - 6

Evaluate the like terms

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 7xy - 6

Pair 6: (x + 3y) and (x – 3y)

(x + 3y) * (x – 3y)

Apply the difference of two squares

(x + 3y) * (x – 3y) = x² - 9y²

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