Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.

For a system of linear equations to have a solution, it means that they would cross over at some point, thus if we are looking for a system of linear equations that do not have a solution (ie. they do not cross over), we are looking for two parallel lines.

Now for two lines to be parallel, they must have the same gradient. Thus, we must find the value of a for which both the equations have the same gradient. In order to do this, we should first write both equations in the form y = mx + c, where m is the gradient and c the y-intercept.

1) Equation 1:

(1/2)x - (2/3)y = 7

(3/4)x - y = 21/2 (Multiply both sides by 3/2)

(3/4)x = 21/2 + y (Add y to both sides)

(3/4)x - 21/2 = y (Subtract 21/2 from both sides)

Thus, the first equation may be written as y = (3/4)x - 21/2

2) Equation 2:

ax - 8y = -1

(a/8)x - y = -1/8 (Divide both sides by 8)

(a/8)x = -1/8 + y (Add y to both sides)

(a/8)x + 1/8 = y (Add 1/8 to both sides)

Thus, the second equation may be written as y = (a/8)x + 1/8

Now that we know the equations of the two lines, we can compare their gradients.

Equation 1: m = 3/4

Equation 2: m = a/8

Remember, for the two lines to be parallel, their gradients must be the same. Thus, we must equate the two gradients above to find the value of a:

3/4 = a/8

24/4 = a (Multiply both sides by 8)

6 = a

Therefor, if the system of linear equations has no solution, and a is a constant, the value of a is 6 (answer D).

Answer:

A

Step-by-step explanation:

Degree: that's the power on the x term. 2

Coefficient on the x term. That is             3

Constant term. That has no x                   -4

The minus is included.

The answer is A

Answer:

  (B) only I and II

Step-by-step explanation:

An odd relation is symmetrical about the origin. All of the relations are odd.

An even relation is symmetrical about the y-axis. Only the first two relations are even.

_____

The graph shows the first relation is that of a circle. It is symmetrical about its center at the origin and about any diameter, including the y-axis.

The second relation is a degenerate hyperbola. It graphs as the pair of lines y=x and y=-x. It is symmetrical about both the origin and the y-axis. (It also has other lines of symmetry.)

The third relation is a line with slope -1 (represented by dots). It is symmetrical about the origin, but not the y-axis. It is only an odd relation.

The length of first side is 5 feet, the length of second side is 7 feet, the length of third side is 3 feet.

The perimeter is the sum of measurement of all sides of a triangle. It is done by a ruler.

let the second side be x

according to question first side will be (x-2) feet and the third side will be (x-4) feet.

We know that  the perimeter is equal to the sum of all sides of a triangle.

so

x+x-2+x-4=15

3x=6=15

3x=21

x=7

The length of first side=7-2=5 feet

The length of second side=7 feet

The length of third side=3 feet

Hence the sides of the triangle is 5 feet, 7 feet, and 3 feet.

Learn more about perimeter at https://brainly.com/question/19819849

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Answer:

Part 21) The distance from Football Field to the Park is [tex]10.95\ miles[/tex]

Part 22)

a) The value of a is [tex]20\ units[/tex]

b) The value of b is [tex]20.10\ units[/tex]

Step-by-step explanation:

Part 21)

Let

A -----> Football Field

B -----> Park

C -----> Home

D -----> Library

x -----> the distance from Football Field to the Park

In the right triangle ABD

[tex]cos(A)=10/x[/tex] -----> equation A

In the right triangle ABC

[tex]cos(A)=x/12[/tex] ----> equation B

equate equation A and equation B

[tex]10/x=x/12[/tex]

solve for x

[tex]x^{2}=120\\ \\x=10.95\ miles[/tex]

Part 22)

see the attached figure with letter to better understand the problem

step 1

Find the value of a

In the right triangle ABD

[tex]tan(ABD)=a/200[/tex] ----> equation A

In the right triangle ADC

[tex]tan(DAC)=2/a[/tex] ----> equation B

remember that angle ABD is congruent with angle DAC

therefore

equate equation A and equation B

[tex]a/200=2/a[/tex]

solve for a

[tex]a^{2}=400\\ \\a=20\ units[/tex]

step 2

Find the value of b

In the right triangle ADC

Applying the Pythagoras Theorem

[tex]b^{2}=a^{2}+2^{2}[/tex]

substitute the value of a

[tex]b^{2}=20^{2}+2^{2}[/tex]

[tex]b^{2}=404[/tex]

[tex]b=20.10\ units[/tex]

Answer:

59

Step-by-step explanation:

Let c and b represent the scores of Colin and Brian respectively.  Then

c + b = 59.  Since brian scored 59 more points than Colin, that means c = 0 and b = 59.  Their combined score is 0 + 59 = 59.

Answer:

112/125

Step-by-step explanation:

If we know all 25 are in at least one foreign language class then we can assume that exactly 4 of the 18 kids in French only take French to add up to 25 and this means that the 14 left take both classes. Now we can create three fractions for each case which are 7/25 (Spanish only) 4/25 (French only) and 14/25 (Both) and we can know say that if he goes down the route of getting a Spanish only as his first he needs one of the 18 other students the chances of this happening are 7/25 * 18/25 = 126/625 the same thing is done with the French only and we get 4/25 * 21/25 = 84/625 and then we have the possibility of just getting a student that does both which is 14/25 or 350/625. now we add them all together to get 560/625 which is simplified to 112/125.

Hope this helps please mark brainliest :)

This would be the symmetric property!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The property illustrated here is symmetric property .

Explanation:

Symmetric Property of Equality. The following property: If if a = b then b = a. This is one of the equivalence properties of equality. See also. Reflexive property of equality, transitive property of equality, transitive property of inequalities.

For this case we have that the area of the kite is given by the area of two triangles, the triangles share the same base of 3 + 3 = 6 meters and one has height of 2m and the other height of 4m.

So, the total area is given by:

[tex]A = \frac {1} {2} * 6 * 2 + \frac {1} {2} * 6 * 4\\A = \frac {1} {2} 12+ \frac {1} {2} *24\\A = 6 + 12\\A = 18[/tex]

Thus, the area of the kite is [tex]18m ^ 2[/tex]

ANswer:

[tex]18m ^ 2[/tex]

Answer:

24 units cubed

Step-by-step explanation:

Volume is just length x width x height

so the width is 2 units and the height is 2 units and the length is 6 units: 2 x 2 = 4

4 x 6 = 24 units cubed

One unit cube = 1 by 1 by 1.

In the long picture, we have 2 by 2 by 6.

Volume = 2 x 2 x 6

Volume = 4 x 6

Volume = 24 units^3

Answer:

Solution to pair of linear equations

Step-by-step explanation:

Subtract second equation from the first

[tex]3x-8y=29\\3x+ y=-2\\[/tex]

subtraction eqn 2 from 1 we get

[tex](3x-3x)+(-8y-y) = (29-(-2))\\-9y=31\\y=-\frac{31}{9} \\y= - 3.44[/tex]

In order to find the value of x we will put this value of y in anyof the above equation and solve it for x

[tex]3x-\frac{31}{9} = -2\\3x=-2+\frac{31}{9} \\3x=\frac{-18+31}{9} \\3x=\frac{13}{9} \\x=\frac{13}{9*3} \\x=\frac{13}{27} \\x=0.4814[/tex]

The Correct answer which is solution two the above linear pair of equations is

x=0.4814

y=-0.344

Answer:

see below

Step-by-step explanation:

The first equation is in slope-intercept form, so you can see that the boundary line has a slope of -2 and goes through the point (x, y) = (0, -4). Since the comparison is "<", the line is dashed and shading is below it.

The second equation is that of a vertical boundary line at x=-3. It is solid, because the comparison includes the "equal" case. Shading is to the right of it, where x values are greater than -3.

Answer: 3.6 hours

Step-by-step explanation:

Given : The time taken by Blake to paint the room : [tex]t_1=9\text{ hours}[/tex]

The time taken by Ned to paint the room : [tex]t_2=6\text{ hours}[/tex]

Then , the time taken (T) by both of them to paint the room if they work together is given by :-

[tex]\dfrac{1}{T}=\dfrac{1}{t_1}+\dfrac{1}{t_2}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{1}{9}+\dfrac{1}{6}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{5}{18}\\\\\Rightarrow\ T=\dfrac{18}{5}=3.6\text{ hours}[/tex]

Hence, it will take 3.6 hours to the two companies if they working together .

Answer:

Graph D last graph

Step-by-step explanation:

Answer: The answer is B.

Step-by-step explanation:

Area of parallelogram = B*H (base times height)

Here, the base is 32 inches and the height is 33 inches.

32*33=1,056in^2

Answer:b

Step-by-step explanation:

We multiply base and height

Answer:

Perimeter = 20 units

x = 120°

Step-by-step explanation:

We are given a triangle ABC with known side lengths for all three sides and an inscribed circle.

We are to find the perimeter of triangle ABC and the value of x.

Perimeter of triangle ABC = 2 + 2 + 5 + 5 + 3 + 3 = 20 units

The kite shape at the end is a quadrilateral which has a sum of angles of 360 degrees.

Two out of four angles are right angles and one is 60 so we can find the value of x.

x = 360 - (90 + 90 + 60) = 120°

Answer:

6.  20                      8.  120

Step-by-step explanation:

add the side measurements up of the triangle:

2+5+2+3+3+5=7+5+8=20

That shape where the x is a quadrilateral so is't interior angles must add to 360 so you have 90+90+60+x=360

Solving:  230+x=360

So x=360-240=120

Answer:

right towards positive x axis

Step-by-step explanation:

In order to find the orientation of the parabolas we can follow following steps.

1. if in the equation x is squared , the parabola opens up. Also if its coefficient is negative it opens down.

2. If y is squared , the parabola opens right , and its coefficient is negative , it opens left

but before that we have to convert our function in standard form of the parabola. Our equation is

[tex]y=\sqrt{x-4}[/tex]

hence we square on both sides

[tex]y^2=x-4[/tex]

which is now into one of the standard form of a parabola. here y is squared and its coefficient is not negative hence it opens towards right.

Answer:

A. -19

Step-by-step explanation:

There are lots of ways to get there. One of them is to realize that the average rate of change between two adjacent numbers is the negative of their sum. -(9+10) = -19.

__

Another is to extend the table:

6 to 7 : -13

7 to 8 : -15

8 10 9 : -17

9 to 10 : -19

__

Yet another is to write an equation for the function, and compute the average rate of change:

f(x) = -x^2 -1

average rate of change from 9 to 10 = (f(10) -f(9))/(10 -9) = (-101 -(-82))/(10 -9) = -19

Answer:

A. -19

Step-by-step explanation:

Answer:

Two

Step-by-step explanation:

x² + x = 11

The degree of a polynomial will always tell us the maximum number of solutions

You have a second degree polynomial, so there are two possible solutions.

They are

[tex]x = \dfrac{1}{2} \left (-1 - 3\sqrt{5} \right )[/tex]

and

[tex]x = \dfrac{1}{2} \left (-1 + 3\sqrt{5} \right )[/tex]

The diagram below shows that the zeros are at (-3.854,0) and (2,854, 0), which are the decimal equivalents of the roots.

Answer:

  (n/24)^3

Step-by-step explanation:

If "n" represents "a number," then "the quotient of a number and 24" means ...

  (n/24)

The cube of that is ...

  (n/24)^3

Answer:

12 in

Step-by-step explanation:

the arc length formula is s = rФ, where Ф is the central angle in radians.

Here, the arc length is s = (4 in)(3 radians) = 12 in

Answer:

D on edge

Step-by-step explanation:

Step-by-step explanation:

You need to look for where f(x) and g(x) have the same value.  That's at x=0 and x=2.

Answer: If you want to see in what value of x there is true that f(x) = g(x), you need to see in the table when f(x) and g(x) has the same value, this is lock in in table when the second and third values are the same.

This is true for x = 2, where f(2) = 0 and g(0) = 2, and for x = 0, wher f(0) = -3 and g(0) = -3.

Answer:

A. (1,2)

B. (3,1)

C.(4,4)

D. (6,6)

E. (8,4)

Step-by-step explanation:

Answer:

Answer:

A. (1,2)

B. (3,1)

C.(4,4)

D. (6,6)

E. (8,4)

Step-by-step explanation:

Answer: [tex]a_n=-50+(n-1)17[/tex]

Step-by-step explanation:

The Arithmetic Sequence Formula is:

[tex]a_n=a_1+(n-1)d[/tex]

Where:

[tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the sequence.

[tex]a_1[/tex] {a_1} is the first term of the sequence.

[tex]n[/tex] is the term position.

[tex]d[/tex] is the common difference of any pair of consecutive numbers.

We can observe that the first term is:

[tex]a_1=-50[/tex]

Now, we need to find "d". This is:

[tex]d=-16-(-33)\\d=-16+33\\d=17[/tex]

Then, substituting, we get the following equation:

[tex]a_n=-50+(n-1)17[/tex]

Answer:

6π ft

Step-by-step explanation:

I believe you meant CIRCUMFERENCE, the distance around the outer edge of this circle.  The appropriate formula for the circumference is C = 2πr, where r is the radius.  In the illustration we see that line segment PA has length 3 ft.  Thus, the circumference of this circle is C = 2π(3 ft) = 6π ft (the next to last answer choice).

Answer:

=6π ft

Step-by-step explanation:

The circumference of a circle is calculated using the formula C=2πr where r is the radius and C the circumference of the circle.

In the circle provided r= 3ft

C= 2π × (3ft)

=6π ft

We do not use the approximate value of pi as the question demands us to leave pi unsolved.

Answer:

The initial position was 35.1 m

Step-by-step explanation:

Let

x -----> the initial position

we know that

The linear equation that represent this problem is equal to

x+18.4=53.5

Solve for x

Subtract 18.4 both sides

x=53.5-18.4

x=35.1 m

Answer:

1) 2x-5                 2)  -10/x^2

Step-by-step explanation:

Use power rule and constant rule for the first one:

1) f(x)=x^2-5x^1+1                                (x^n)'=nx^(n-1) and (c)'=0

f'(x)=2x^1-5(1)x^0+0                        

f'(x)=2x-5(1)                                        x^0=1

f'(x)=2x-5

Use just power rule for last one after a rewrite

2) f(x)=10/x

f(x)=10x^(-1) now use power rule

f'(x)=-10x^(-2) =-10/x^2

Answer: se necesitan 4 medidas de B para obtener una de D

Step-by-step explanation:

Las medidas serán entendidas como unidades de.. (A , B o C)

Entonces, de esta manera

1A + 1C = 5B

1A + 1B = 1 C

1B + 1C = 1D

Para lograr el cometido debo combinar las 3 relaciones de cambio de tal manera que se cancelen totalmente las partes A y C utilizando los multiplicadores adecuados

Entonces,

Uso 5 unidades de B para conseguir una de A y una de C

5B = 1A + 1C

Con esa A y otra de B obtengo otra C

1A + 1B = 1C

Por último con esas dos unidades de C y dos unidades mas de B consigo 2 de D

2B+ 2C = 2D

En total utilicé 5 + 1 + 2 = 8 unidades de B para obtener 2 de D

Entonces para obtener una de D necesitaría 4 unidades de B

Answer:

  Altogether, they had ?28

Step-by-step explanation:

Had Obi spent only ?12, they would have been even. Thus ?12 is the same as 5-2 = 3 "ratio units". So, each "ratio unit" is worth ?12/3 = ?4.

Then Obi started the day with 5·4 = 20, and Obi started the day with 2·4 = 8. Obi ended with 0, which is 8 less than Rudy.

Altogether, they started with 20 + 8 = 28 of whatever a ? is.

Answer:

Money they have  initially altogether = 28

Step-by-step explanation:

The ratio of money in Obi's wallet to Rudy's wallet one day was 5:2.

Money Obi has = 5 r

Money Rudy has = 2 r

Obi spent 20 that day and bi now had 8 less than Rudy

               5r -20 = 2r - 8

               3r = 12

                 r = 4

Initial money they have

                Obi = 5r = 5 x 4 = 20

                 Rudy = 2 x 4 = 8

Altogether they have 20+8 = 28

Money they have  initially altogether = 28