The parabola in the image has its focus at (4,3).Its directrix is the line y=1.The point (8,6) is on the parabola.

1. The equation in slope-intercept form is: y = -3/2x + 7/2

2. y = -3/2x - 18

3. Both lines have the same slope, they are therefore parallel.

Two lines that are parallel will have the same slope (m), and is represented by the equation in slope-intercept form as, y = mx + b.

1. Rewrite 3x + 2y = 4 in slope-intercept form:

2y = -3x + 4

y = -3x/2 + 4/2

y = -3/2x + 2

The slope is -3/2. Therefore, the slope (m) of the line that passes through (-1, 5) would be -3/2.

Substitute m = -3/2, and (a, b) = (-1, 5) into y - b = m(x - a):

y - 5 = -3/2(x - (-1))

y - 5 = -3/2(x + 1)

Rewrite in slope-intercept form:

2(y - 5) = -3(x + 1)

2y - 10 = -3x - 3

2y = -3x - 3 + 10

2y = -3x + 7

y = -3x/2 + 7/2

y = -3/2x + 7/2

2. The slopes of perpendicular lines are negative reciprocal to each other.

Rewrite 2x + 3y = 4

3y = -2x + 4

y = -2/3x + 4/3

The slope of the ine that passes (-2, 15) would be -3/2.

Substitute (a, b) = (-2, 15), and m = -3/2 into y - b = m(x - a):

y - 15 = -3/2(x - (-2))

y - 15 = -3/2x - 3

y = -3/2x - 3 - 15

y = -3/2x - 18

Therefore, the equation in slope-intercept form of the line that passes through (-2, 15) is: y = -3/2x - 18.

3. Given the equations, 2x – y = −1 and 4x – 2y = 6:

Rewrite in slope-intercept form and find their slope

2x - y = -1

-y = -2x - 1

y = 2x + 1 (slope if 2)

4x - 2y = 6

-2y = -4x + 6

y = -4x/-2 + 6/-2

y = 2x - 3 (slope is 2)

Both lines are therefore, parallel.

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Answer:

d. multiply the second equation by 4

Answer:

175,424.02

Step-by-step explanation:

multiply 145,117 by 106%

multiply 1800 by 12 (months in a year)

add 21600 to 153,824.02

[tex]~~~~x^2-6xy=z-9y^2\\\\\implies x^2- 2\cdot x\cdot 3y + (3y)^2 - (3y)^2 = z-9y^2\\ \\\implies (x-3y)^2 -9y^2 = z-9y^2\\\\\implies (x-3y)^2 = z\\\\\implies x - 3y =\pm\sqrt z\\\\\implies x = 3y\pm\sqrt z[/tex]

Answer:

1,001

Step-by-step explanation:

13ft X 11ft X 7ft = 1,001
Not sure if its correct but im glad to help atleast

Answer:

68 is the perimeter.

Step-by-step explanation:

You can find the perimeter by adding up all of the sides. 13 + 11 + 3 + 7 = 34. To find the other sides of the shape you do 11 + 7 and 13 + 3. 11 + 7 = 18. 13 + 3 = 16. 18 + 16 = 34. 34 + 34 = 68.

Answer:

65 - 80 = -15

7 - 5 = 2

which is -15/2

which is A

The points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on graph.

Table is a way to represent the data of the two or more variable. To read the data from the table, look for the value of one variable, and get the resultant value of other variable from the corresponding block.

Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005.

The table gives the number of tickets sold for each concert. Select the points that represent this data.

The graph which represent the data in the data is attached below year wise.

For the first point, select the value 10 on graph vertically at year 2000. Similarly, select all the points on the graph for the table.

Thus, the points which represent the data in the table for Jeremiah's band played concerts at XYZ Stadium every year from 2000 through 2005 are selected on the graph.

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Answer:

0.04

Step-by-step explanation:

3÷80.81= 0.037

to the nearest whole number = 0.04

Answer:

b

Step-by-step explanation:

Answer:

  $359.42

Step-by-step explanation:

The difference in the investment values can be computed by making use of the formulas for the account balance in each case.

  compound interest: A = P(1 +r)^t . . . . interest at rate r compounded annually

  simple interst: A = P(1 +rt) . . . . simple interest at rate r

__

The account earning simple interest will have a balance of ...

  A = $8000(1 +0.12×3) = $10,880

The account earning compound interest will have a balance of ...

  A = $8000(1 +0.12)^3 ≈ $11,239.42

The difference between the two investments is ...

  $11,239.42 -10,880 = $359.42

Answer:

y=x+12, add 12

Step-by-step explanation:

To get from each x to y you have to add 12

so the equation is:

y=x+12

The expression (3xy) is an algebraic expression

The equivalent expressions of (3xy) are (6xy)/2 and (9xy)/3

The expression is given as:

(3xy)

Multiply by 2/2

(3xy) = (6xy)/2

Multiply by 3/3

(3xy) = (9xy)/3

The above products means that, we multiply the expression by 1 (i.e. n/n) to get an equivalent expression

Hence, the equivalent expressions of (3xy) are (6xy)/2 and (9xy)/3

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#8

Vertex at (0,0)

#11

Same Vertex

#14

Vertex (0,2)

Step-by-step explanation:

by order

the 1st one y = 4x^2

vetex (0,0) and upward

the 2nd one y = -6x^2

vertex (0,0) and downward

the 3rd one y = -x^2 + 2

vertex (0,2) and downward

In the context of the least squares procedure, any data point that does not fall on the regression line is the result of multicollinearity.

A least square regression simply shows the linear relationship that exist between two variables.

Here, in the context of the least squares procedure, any data point that does not fall on the regression line is the result of multicollinearity.

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Answer:

See below ~

Step-by-step explanation:

The equation which represents 1/12 :

The division equation which represents 1/14 :

Answer:

Question 3:

C) 1 divided by 12 _

Question 4:

A) 1 divided by 14 _

Answer:

[tex]\sqrt{51[/tex]

Step-by-step explanation:

6^2 + 8^2 = y^2 (Pythag)

100 = y^2

10 = y

7^2 + x^2= 10^2

49+ x^2 = 10^2

x^2 = 51

Answer:

63√6 cm

Explanation:

Perimeter is the total measure of all sides.

Solve:

15√6 + 12√54 + 6√24

factorize

15√6 + 12√6(9) + 6√6(4)

apply radical rule: √ab = √a √b

15√6 + 12√6 √9 + 6√6 √4

simplify

15√6 + 12(3)√6 + 6(2)√6

multiply

15√6 + 36√6 + 12√6

add similar terms

63√6

Answer:

Step-by-step explanation:

Perimeter : Sum of the sides

Perimeter

Answer:

[tex]f(x)=1250*(\frac{4}{5})^x[/tex]

Step-by-step explanation:

Answer:

[tex]\dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}[/tex]

[tex]\textsf{or}\quad \dfrac{5\sqrt{3+\sqrt{5}}}{2}[/tex]

Step-by-step explanation:

[tex]\textsf{Given expression}:\dfrac{5}{\sqrt{3-\sqrt{5}}}[/tex]

Method 1

[tex]\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}:[/tex]

[tex]\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}=\dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}[/tex]

Simplify the denominator using the radical rule [tex]\sqrt{a} \sqrt{a} =a[/tex]:

[tex]\implies (\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})=3-\sqrt{5}[/tex]

Therefore:

[tex]\implies \dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}= \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}}[/tex]

[tex]\textsf{Multiply by the conjugate}\quad \dfrac{3+\sqrt{5}}{3+\sqrt{5}}:[/tex]

[tex]\implies \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}} \times \dfrac{3+\sqrt{5}}{3+\sqrt{5}}=\dfrac{5\sqrt{3-\sqrt{5}}(3+\sqrt{5})}{(3-\sqrt{5})(3+\sqrt{5})}[/tex]

Simplify the denominator:

[tex]\implies (3-\sqrt{5})(3+\sqrt{5})=9+3\sqrt{5}-3\sqrt{5}-5=4[/tex]

Therefore:

[tex]\implies \dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}[/tex]

Method 2

[tex]\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}:[/tex]

[tex]\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}=\dfrac{5\sqrt{3+\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})}[/tex]

Simplify the denominator using the radical rule [tex]\sqrt{a} \sqrt{b} =\sqrt{ab}[/tex]:

[tex]\implies (\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})=\sqrt{(3-\sqrt{5})(3+\sqrt{5})[/tex]

[tex]\implies\sqrt{(3-\sqrt{5})(3+\sqrt{5})}=\sqrt{9-5}=\sqrt{4}=2[/tex]

Therefore:

[tex]\implies \dfrac{5\sqrt{3+\sqrt{5}}}{2}[/tex]

[tex]\huge\color{pink}\boxed{\colorbox{Black}{♔︎Answer♔︎}}[/tex]

To rationalise:-

[tex] \frac{5}{ \sqrt{3 - \sqrt{5} } } [/tex]

There is a formula in math if there is root in denominator

for example

[tex] \frac{1}{ \sqrt{a - b} } [/tex]

we can say rationalize by multiplying √(a-b) in numerator and denominator both

[tex] \frac{1}{ \sqrt{a - b} } \times \frac{ \sqrt{a - b} }{ \sqrt{a - b} } \\ \frac{ \sqrt{a - b} }{a - b} [/tex]

In here

[tex] \frac{5}{ \sqrt{3 - \sqrt{5} } } \times \frac{ \sqrt{3 - \sqrt{5} } }{ \sqrt{3 - { \sqrt{5} } } } \\ \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } [/tex]

but still here is root to remove this we have to multiply

3 + √5 in numerator and denominator.

[tex] \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5} ) }{ {3}^{2} - { (\sqrt{5} )}^{2} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5}) }{9 - 5} \\ \frac{5( \sqrt{3 - \sqrt{5} } )(3 + \sqrt{5}) }{4} [/tex]

Answer:

3 oranges

Step-by-step explanation:

Helen has 5 pounds of oranges

2 pounds of oranges are brought to a party, so they are gone

5-2 = 3

Helen will only have 3 oranges left.

Answer:

12

Step-by-step explanation:

When you multiply 12 by itself its 144.

I hope it helps! Have a great day!

pan~

Answer:

12

Step-by-step explanation:

Divide 144 by 2 and it’s 12.

Or you could guess and check b dividing each number by itself until you get 144.

I hope it helps! Have a great day!

Muffin °-°

Answer:

the answer is A

Step-by-step explanation:

410 is the total amount paid

so 50 dollars was a base fee for the service charge

and 90 was per tire. Because we dont know how many tires she bought 90 x number of tires(t) = 90t

so 410 dollars = 50 dollars(service fee) + 90 dollars ( multilied by number of tires "t")

Answer:

[tex]\huge\boxed{\sf 350\ g\ salami = 5.565}[/tex]

Step-by-step explanation:

From the question:

100 g salami = 1.59

Divide 100 to both sides

1 g salami = 1.59/100

1 g salami = 0.0159

Multiply both sides by 350

350 g salami = 0.0159 × 350

350 g salami = 5.565

[tex]\rule[225]{225}{2}[/tex]

Answer:

A, 12ft, 16ft, 20ft.

Step-by-step explanation:

3,4,5 Triangles are right triangles, Answer A on the Paper says 12:16:20 which is proportinate to said ratio, hence the answer is A

Answer:

12 3/8

Step-by-step explanation:

6 1/2 + 5 7/8 =

= 6 4/8 + 5 7/8

= 11 11/8

= 11 + 8/8 + 3/8

= 11 + 1 + 3/8

= 12 3/8

Answer:

21600/a

Step-by-step explanation:

800/a *9

7200/a

21600/a

First, times 800 divided by a by 9.

Then, we get 7200/a.

Lastly, times it by 3.

The answer is 21600/a

Sussy mcsuser
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