What shape is generated when AABC is rotated around the vertical line
through B and C?

Answer:

x² = -2y

Step-by-step explanation:

The focus is p away from the vertex, and so is the directrix.

To find the equation of the parabola, we must first determine if the parabola is horizontal or vertical.

If the parabola is vertical, the directrix, and focus will have the same x value but different y value compared to the vertex (h, k). You can also tell if the directrix in in the form y = k – p, and if the focus is in the form (h, k + p).

Likewise, if the parabola is horizontal, the directrix, and focus will have the same y value but different x value compared to the vertex (h,k) . You can also tell if the directrix is in the form x = h – p, and if the focus is in the form (h + p, k).

For this problem, given that the vertex is at the origin (0,0), and that the focus is at the point (0, -½).

You can tell that the x value is the same for the vertex, and focus so this must be a vertical parabola. Because this is a vertical parabola, we can use the form mentioned as earlier (x – h)² = 4p(y – k).

If h = 0, and k = 0, the p value must be the difference between the k of the vertex, and the k of the focus: -½ - 0 → -½.

Now we can just plug in our known information to derive the equation!

h = 0, k = 0, p = -½ → (x - h)² = 4p(y - k) →

(x - 0)² = 4(-½)(y - 0) → x² = -2(y - 0) →

x² = -2y.

Also p = 1/4a, if you are wondering.

So because this is a vertical parabola, x² = -2y is generally the same as y = -1/2x² in standard quadratic form. I just like to think of the horizontal parabola as an inverse quadratic because it is like reflecting over the line y = x.

Answer:

[tex]\boxed {\boxed {\sf x^2=-2y}}[/tex]

Step-by-step explanation:

First, plot the two points. We can see the focus is below the vertex. The result will be a vertical parabola. Since the parabola must contain the focus, it will have to open downward.

From this information, we know that the following equation must be used:

[tex](x-h)^2=-4p(y-k)[/tex]

where (h,k) is the vertex and p is the distance from the focus to the vertex.

Next, find p, the distance between the focus and vertex. We can use the distance formula.

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

The vertex is (0,0) and the focus is (0, -1/2). Therefore:

[tex]x_1=0\\y_1=0\\x_2=0\\y_2= -1/2[/tex]

[tex]d=\sqrt{(0-0)^2+(0--1/2)^2}[/tex]

[tex]d=\sqrt{(0)^2+(0+1/2)^2}[/tex]

[tex]d=\sqrt{0+(1/2)^2}[/tex]

[tex]d=\sqrt{0+1/4}[/tex]

[tex]d=\sqrt{1/4}[/tex]

[tex]d=1/2[/tex]

Now we know the distance and vertex. We can plug the values into the equation.

d=1/2 and (h,k)= (0,0)

[tex](x-0)^2=-4(1/2)(y-0)[/tex]

[tex](x)^2=-2(y)[/tex]

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

The equation of the parabola is x²= -2y

Answer:

5

Step-by-step explanation:

55$-17.50=37.5

37.5/7.5=5

Answer:

x=3/12 or 1/4

Step-by-step explanation:

x + 1/6 = 5/12

x + 2/12 = 5/12

x = 3/12

converts to 1/4

Answer:

x= 1/4

Step-by-step explanation:

5/12- 1/6 = 1/4

Answer:

Step-by-step explanation:

30/50= 3/5= 0.6

Answer:

4. CDB+DBE= CBE (55+35=90)

5. Definition of a right angle (90 degrees)

6. Linear pair postulate ( i think)

7. ABC and CBE are both 90 degrees

Step-by-step explanation:

Note: You missed to add the diagram. After a little research, I found the diagram.

Hence, I am solving the question based on the attached diagram.

Answer:

option C is the right graph that represents the point P(0, 8) on the coordinate plane.

Step-by-step explanation:

The assumed diagram is attached below.

From the diagram, it is clear that:

But, if we closely observe the graph C  on the diagram below, we can validate that graph C is clearly indicating that the point P is located at the location (0, 8).

Hence, option C is the right graph that represents the point P(0, 8) on the coordinate plane.

Answer:

First collect like terms

4x-2x=7+3

6x=10

x=10/6

x=1.66666666667

x=1.67

Step-by-step explanation:

Please give me brainliest

Answer:

Step-by-step explanation:

Neither are a function because they do not pass the vertical line test.

Answer:

D. y = 45x + 55

Step-by-step explanation:

If a computer technician charges $190 for a 3-hour appointment and $370 for a 7-hour appointment, we can say that;

when c1 = $190, t1 = 3

when c2 = $370, t2 = 7

c is the amount charged

t is the time taken

First thug is to get the slope;

slope = c2-c1/t2-t1

slope = 370-190/7-3

slope = 180/4

slope = 45

Next is to get the intercept by substituting m = 45 and (190, 3) into the standard form of the equation y = mx+c as shown;

190 = 45(3)+c

190 = 135+c

c = 190-135

c = 55

Substitute into the standard form of the equation;

y = mx+c

y = 45x + 55

Hence option D is correct

Answer:

Actually, I didn't get your question, is it -3/8÷ -1/3 or -1/3÷ -3/8?

If it is -3/8÷ -1/3, the answer will be 9/8

But if is -1/3÷ -3/8, the answer will be 8/9

Step-by-step explanation:

-3/8÷ -1/3

= -3/8× 3/-1

= -9/-8

= 9/8

If your question is -1/3÷ -3/8, the answer is 8/9 in the same way.

9514 1404 393

Answer:

Step-by-step explanation:

A terminating decimal has an equivalent denominator that is a power of 10. That is, it is the product of a power of 2 and a power of 5.

Any fraction that has a denominator that is a power of 2 can be expressed as an equivalent fraction with a power of 10 as the denominator.

Example:

  [tex]\dfrac{7}{2048}=\dfrac{7}{2^{11}}=\dfrac{7\cdot5^{11}}{2^{11}\cdot5^{11}}=\dfrac{7\cdot5^{11}}{10^{11}}=0.00341796875[/tex]

hope this helps.enjoy!!!!!!

Answer:

Ok, the domain is the set of values that we can input in a function.

In this case, we have:

y = Ix - 6I + 3.

Notice that there is no restriction here, x can actually take any value, then the domain will be the set of all real numbers.

The correct domain is x, x ∈ R

Now, if we had (for example) something like:

y = Ix - 6I < 3

Now we have a restriction in the domain because we can not have y equal or larger than 3.

To find the domain, we can break the absolute value:

Ix - 6I < 3

is equivalent to:

-3 < x - 6 < 3

now let's add 6 in each side.

-3 + 6 < x - 6 + 6 < 3 + 6

3 < x < 9

That will be the domain in that case.

Answer:

hi

Step-by-step explanation:

Answer:

please forgive me I have no clue

Step-by-step explanation:

Answer:

9 3/4 in a percent is 975%.

If you change 9 3/4 into a decimal, it will be 9.75, and 9.75 converted into a percent is 975%

Step-by-step explanation:

h= 55/12 if thats what u askin for

5h – 15 + 7h = 40

value of h

[tex]:\implies \bold{5h – 15 + 7h = 40}[/tex]

[tex] :\implies \bold{5h + 7h = 40 + 15}[/tex]

[tex] :\implies \bold{12h= 55}[/tex]

[tex]:\implies \bold{h = \dfrac{55}{12} }[/tex]

[tex]:\implies\underline{\boxed{ \bold{h = 4.583}}}[/tex]

[tex]:\implies \bold{5h – 15 + 7h = 40}[/tex]

[tex]:\implies \bold{(5 \times 4.583) – 15 +( 7 \times 4.583)= 40}[/tex]

[tex]:\implies \bold{ 30– 15 + 32= 40}[/tex]

[tex]:\implies \bold{ 30– 15 + 32= 40}[/tex]

[tex]:\implies\underline{\boxed{ \bold{ 40= 40}}}[/tex]

Answer: ab =6

have:

[tex]\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}=1\\\\=>\frac{b}{ab}+\frac{a}{ab}+\frac{1}{ab}=1\\\\<=>\frac{a+b+1}{ab}=1[/tex]

=> a + b + 1 = ab

⇔ a + b + 1 - ab = 0

⇔ b - 1 - a(b - 1) + 2 = 0

⇔ (b - 1)(1 - a) = -2

because a and b are postive integers => (b - 1) and (1 - a) also are integers

=> (b - 1) ∈ {-1; 1; 2; -2;}

(1 -a) ∈  {-1; 1; 2; -2;}

because (b -1).(1-a) = -2 => we have the table:

b - 1        -1             1              2             -2

1 - a         2            -2            -1              1

a              -1            3             2              0

b              0            2             3              -1

a.b            0           6             6               0

because a and b  are postive integers

=> (a;b) = (3;2) or (a;b) = (2;3)

=> ab = 6

Step-by-step explanation:

Answer:

The first one is x=45

The second one is w=14

The third one is x=6

Step-by-step explanation:

Answer:

you need to shade 4/6

Step-by-step explanation:

9514 1404 393

Answer:

  B.  (4, 28)

Step-by-step explanation:

Substitute the value of x into the first equation. This gives you the value of y.

After substitution, we have ...

  y = 8(4) -4

  y = 28

Then the point is (x, y) = (4, 28).

Answer:

330,750 people

Step-by-step explanation:

If the population increases by 5% every year, in 2 years the population of the city will be 330,750 people. D is also the correct answer as shown in the file.

Population after 2 year is 330,750

Given that;

Growth rate = 5% = 0.05

Current population = 300,000

Find:

Population after 2 year

Computation:

Population after 2 year = 300,000(1 + 0.05)²

Population after 2 year = 300,000(1.05)²

Population after 2 year = 330,750

Find out more information about 'Growth rate'.

https://brainly.com/question/13870574?referrer=searchResults

Answer:

orientation is preserved (stays the same)

Step-by-step explanation:

Answer: 400 calories per hour

Step-by-step explanation:

Q: Tina recorded the number of calories she burned during a bike ride. The graph shows Tina’s calories burned, y, after x hours. If Tina rode her bike at a constant rate for the first three hours, what was Tina’s average calories burned, in calories per hour, between hour 0 and hour 3?

Expalanation: It is seen from the graph that her rate of burning calories increased to 1200 in the first three hours of riding and then remained constant for the rest of the period (2 extra hours).

Her rate of calorie use therefore would be given as: (total calorie used up) / (total hours spent riding for the period of usage)

This is given as: 1200 calories / 3 hours = 400 calories per hour.

Answer:

y = 30 - 5.30x

Step-by-step explanation:

y-intercept: 30

slope: 5.30x

Just plug in the amount of weeks on x, and then subtract from 30.

Answer:

Luis tiene 30 años de edad y su amiga tiene 20 años edad.

Step-by-step explanation:

Cuando Luis tenia 20 años de edad (hace 10 años), su amiga tenia solamente 10 años de edad. Si multiplicamos 10 x 3 nos da como resultado 30, que es la edad actual de Luis.

L + A = 50

3(A - x) = L

L = 50 - A

3A - 3x = 50 - A

4A = 50 + 3x

en este punto podemos probar diferentes alternativas para x:

x = 5, entonces 4A = 50 + 15

A = 16.25 no es factible porque estamos buscando numeros enteros

x = 6, entonces 4A = 50 + 18

A = 17

al reemplazar, nos da una edad de 3(17 - 5) = 36 para Luis, pero 36 + 17 = 53

x = 8, entonces 4A = 50 + 24

A = 18.5 no es factible porque estamos buscando numeros enteros

x = 10, entocnes 4A = 50 + 30

A = 20

al reemplazar, nos da una edad de 3(20 - 10) = 30 para Luis, y 30 + 20 = 50