Write an equation of a parabola with vertex at the origin and the given focus. (0,6)

Answer:

7th term = (-1)

rule for the nth term = an = a+(n-1)d

Step-by-step explanation:

a = 5, d = a2-a1 = 4-5 = -1, n = 7

an = a+(n-1)d

a7 = 5+(7-1)(-1)

a7 = 5-6

a7 = (-1)

The missing term is 6.

Here the sequence is -1,__, 11...

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Here the sequence is in an arithmetic sequence, as there is a common difference between the two numbers.

To find the nth term of the sequence we have a formula:

[tex]a_{n}[/tex] = a + (n-1)d

From this we can find a common difference, as we know the 3rd term of the sequence.

[tex]a_{3}[/tex] = -1 + (3-1) d

11 = -1 + 2d

2d = 12

d = 6

Now we have to the 2nd term of the series we have

[tex]a_{2}[/tex] = -1 + (2-1) 6

   = -1 + 6

   = 5

Therefore the 2nd i.e., the missing term of the sequence is 5

To know more about the arithmetic sequence refer to the link given below:

https://brainly.com/question/22972770

#SPJ4

The division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3

In this question,

we have been given a complex rational expression [tex]\frac{3x^{2} -9x}{x-2}\div \frac{x^2-9}{4x-8}[/tex]

We need to find the division of given rational expression.

We rewrite given rational expression as,

3x²-9 x / x-2 ÷ x² - 9 / 4 x-8

= 3x²-9 x / x-2 / x² - 9 / 4 x-8

= (3x²-9 x / x-2) × (4 x-8 / x² - 9 )

= [tex]\frac{3x(x-3)}{x-2}\times \frac{4(x-2)} {(x+3)(x-3)}[/tex]

= 12x / x + 3     .........(provided x ≠ -3)

Therefore, the division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3

Learn more about the rational expression here:

brainly.com/question/13015660

#SPJ4

Answer:

Step-by-step explanation:

change = dollar_amount - spent_amount

change = 50 - 36.85

change = 13.15

Answer:

1) 15

Step-by-step explanation:

The smallest integer is 15 because,

There are 7 consecutive integers with n + 6 being the largest, therefore:

7n + 21 = 6(6 + n)

7n + 21 = 36 + 6n

7n - 6n + 21 = 36

n + 21 = 36 ⇒ n = 36 - 21 = 15

Hope this helps!

2) -3  

2/5 = .4

The least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is  (x-6)(x+1)(x-6).

In the given question

[tex]=\frac{1}{x^{2} -5x-6} , \frac{1}{x^{2} -12x+36}[/tex]  ...(i)

First we will factor each denominator

So,

x²-5x-6

On splitting the factors of the above expression , we get

(x+1)(x-6)   ....(ii)

x²-12x+36

On splitting the factors of the above expression , we get

(x-6)(x-6)    ...(iii)

Substituting the value of (ii) and (iii) in (i) ,we get ;

[tex]=\frac{1}{(x+1)(x-6)} , \frac{1}{(x-6)(x-6)}[/tex]

As the LCM of denominator is the Least common denominator , we have

LCM of (x+1)(x-6) and (x-6)(x-6)

LCM=(x-6)(x+1)(x-6)

Hence the LCD is (x-6)(x+1)(x-6).

Therefore , the least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is  (x-6)(x+1)(x-6).

Learn more about Least Common Denominator here https://brainly.com/question/11879136

#SPJ4

Answer:

14 to 8

Step-by-step explanation:

8 roses+6 daisies=14 is all the flowers in the vase

The Simplified value is [tex]\frac{-3}{4} a^{2} +2b^{2}[/tex].

Like terms are defined as terms that have same variable and and same power.

For Example ; 2a² , 6a² are like terms.

In the given question ,

[tex]=-a^{2} +2b^{2} +\frac{1}{4} a^{2} \\ \\ =-a^{2} +\frac{1}{4} a^{2} +2b^{2}[/tex]

[tex]=a^{2}(-1+\frac{1}{4} )+2b^{2}[/tex]  ( taking a² common )

taking LCM and solving further we get

[tex]=a^{2} (\frac{-4+1}{4} )+2b^{2}[/tex]

[tex]=\frac{-3}{4} a^{2} +2b^{2}[/tex]

Therefore , The value by combining Like terms in -a² + 2b² + (1/4) a² is [tex]\frac{-3}{4} a^{2} +2b^{2}[/tex].

Learn more about Like terms here https://brainly.com/question/16286623

#SPJ4

Answer:

26 miles

Step-by-step explanation:

add 9 miles to 17 miles= 26 miles

Answer:

[tex] \sf \large \: p = 8[/tex]

Step-by-step explanation:

Let's solve the equation step by step,

p – 6 = 2

Add +6 to both sides

p - 6 + 6 = + 6

p = 8

Answer:

8

Step-by-step explanation:

A triangle is a shape whose all three angles have a sum of 180 degrees. So from the above definition we know that:

P + Q + R = 180

Q=3P

T=P + 20

Therefore:

P + 3P + P + 20 = 180

5P + 20 = 180

5P = 160

P = 32

Q = 3(32) = 96

R = 32 + 20 = 52

To Additional Control P + Q + R = 32 + 96 + 52 = 180 °Degree

More similar problems are solved in the given link below.

https://brainly.com/question/27682397?referrer=searchResults

#SPJ4

Answer:

< 5 gigabytes

Step-by-step explanation:

Let the number of gigabytes be represented as: g

Under her cell phone plan, Nicole pays a flat cost of $35 per month and $5 per gigabyte. She wants to keep her bill under $60 per month.

Under $60 = less than (<) $60

Hence, our inequality equation is given as:

$35 + $5 × g < 60

35 + 5g < 60

Collect like terms

5g < 60 - 35

5g < 25

g < 25/5

g < 5 gigabytes

Therefore, the number of gigabytes she can use while staying within her budget less than 5 gigabytes

Based on the information, it should be noted that the inequality to solve for m will be D. m + 6 < 8; m < 2.

It should be noted that in Mathematics, an inequality is used to show the expressions that are hot the same or equal.

Based on the information given about the triangle, it should be noted that the hypothenuse which is given as 8 is the longest side of the triangle.

Therefore, the inequality to solve for m will be:

m + 6 < 8.

Collect like term

m < 8 - 6

m < 2

Therefore, based on the information, it should be noted that the inequality to solve for m will be m + 6 < 8; m < 2.

Learn more about inequalities on:

https://brainly.com/question/24372553

#SPJ1

===========================================

Work Shown:

x = first integer

x+1 = second integer right after x

The two consecutive integers add to -207

(first) + (second) = -207

(x)+(x+1) = -207

2x+1 = -207

2x = -207-1

2x = -208

x = -208/2

x = -104 is the first integer

x+1 = -104+1 = -103 is the second integer

Check:

-104 + (-103) = -207

The answers are confirmed.

Answer:

= 0.377 liters

= 377 mililiters

Step-by-step explanation:

Volume of a regular cylindrical container = л r ² h

л = 3.1416   (aprox,)

r = radius

h = height = 15cm (half filled) = 15/2 = 7.5cm

then:

Volume = 3.1416 * (4cm)² * 7.5cm

volume = 3.1416 * 16cm² * 7.5cm

volume =  377 cm³      (aproximadly)

1 cm³ = 0.001 liters

377 cm³ = 0.001*377 = 0.377 liters = 377 mililiters

Answer:

3500cm3

Step-by-step explanation: since A and B are equal, and B has a volume of 3500 cm3 then A will have the same.

Extra: The horizontal measure of A is 1500 and the verticle is 1500

Given the question, <11 and <14 are supplementary because they sum up to give 180 degrees. Detail below

These are angles that sum up to give 180 degrees. On the other hand, angles on a straight line sum up to give 180 degrees.

Considering the question given above, we can prove that <11 and <14 are supplementary as follow:

<11 + <12 = 180 (angle on straight line)

But

<12 = <14 (corresponding angles)

Thus,

<11 + <14 = 180

Recall

Angle that sum up to give 180 are called supplementary angles

Therefore,

<11 + <14 = 180 => supplementary

From the illustrations given above, we can see clearly that <11 and <14 are supplementary angles

Learn more about supplementary angles:

https://brainly.com/question/13038686

#SPJ1

The fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.

So, (A) The fraction of the animals is chickens: 52/80

Simplest form: 13/20

(B) In decimal form: 0.65

Therefore, the fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.

Know more about fractions here:

https://brainly.com/question/17220365

#SPJ9

The coordinates of E in Quadrant lll is (3 - [tex]2\sqrt{3}[/tex], -4)

Given,

m < F = 90°

E (x, y) in quadrant lll

F(-3, 4), G(-3, 2)

FG = The longer leg.

FG = [tex]\sqrt{(-3-(-3)^{2} )+(2-(-4)^{2} }[/tex] = [tex]\sqrt{36}[/tex] = 6

FE = [tex]\frac{FG}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }[/tex] = 2[tex]\sqrt{3}[/tex]

GE = 2FE = 2 × 2√3 = 4√3

ΔEFG is a 30° - 60° - 90° triangle with the longest leg FG = 6.

We apply the 30° - 60° - 90° triangle theorem to determine the short side FE and the hypotenuse GE.

l = 4√3

h = 2√3

[tex]\sqrt{(x-(-3))^{2} +(y-(-4))^{2} }[/tex] = (2√3)²

[tex]\sqrt{(x-(-3))^{2} +(y-2)^{2} }[/tex] = (4√3)²

∴ (x + 3)² + ( y + 4)² = 12

   (x + 3)² + (y - 2)² = 48

Solving this, we get:

Coordinates of E as (3 - 2√3, -4)

Learn more about coordinates here: https://brainly.com/question/13516953

#SPJ4

The joules are in 12.1 g of parsley is 24.806936 Joules of energy

10g has 4.9 cal

1g has 4.9/10 cal

Energy in 12.1 g = 4.9 x 12.1 / 10 = 5.929 Cal = 5.929 x 4.18400 = 24.806936 Joules of energy [1 calorie = 4.18400]

In the International System of Units (SI), a joule is a unit of work or energy equal to the work done by a force of one newton acting through one meter. It is named after the English scientist James Prescott Joule and equals 107 ergs, or about 0.7377 foot-pounds. The joule is equivalent to one watt-second in electrical terms, which is the amount of energy released in one second by a current of one ampere through a resistance of one ohm.

To  learn more about joule from the given link:

https://brainly.com/question/25982371

#SPJ9

The solutions of the rational equation x-1 / x+2 = x² + 2 x-3/x+2 are x = -2 and x = 1

In this question,

We have been given a rational equation.

x-1 / x+2 = x² + 2 x-3/x+2

We need to find the solution of given rational equation.

Here, the denominator is same on the both sides.

x-1 / x+2 = x² + 2 x-3/x+2

⇒ x - 1 = x² + 2 x-3

⇒ x² + 2x - 3 - x + 1 = 0

⇒ x² + x -2 = 0

We solve above quadratic equation.

⇒ x² + 2x - x - 2 = 0

⇒ x(x + 2) - (x + 2) = 0

⇒ (x + 2)(x - 1) = 0

⇒ x + 2 = 0                or          x - 1 = 0

⇒ x = -2        or         x = 1

Therefore, the solutions of the rational equation x-1 / x+2 = x² + 2 x-3/x+2 are x = -2 and x = 1

Learn more about the rational equation here:

https://brainly.com/question/20850120

#SPJ4

Answer: A. 4w+(-75)

B. 925

Step-by-step explanation:

Answer:

3, 9% more people have green as their favorite color over yellow. 4. Picture is cut off so I can't see sorry 5. science and social studies 6. Mike spends 40% more time studying math then he does science

Step-by-step explanation:

Each function's vertex, axis of symmetry, maximum or lowest value, domain, and range are all described as follows: Vertex: (125,125); range: (125,125); minimum: at y=125;  x=125; maximum: no., axis of symmetry is x=125.

The domain of a function is the set of values that we are allowed to enter into our function.

The set of values that a function can accept as input is known as its range.

            y=(x-125)²-125

we know that;

y=(x-h)²+k

Vertex: In this form, the vertex (or, in other words, the "pointy bit") is given to us in the (h ,k);here we have (125,125).

Axis of symmetry : Two equal segments of the parabola. It moves straight up and down via the vertex.

Thus, we may formulate an equation for the vertical line that passes through the vertex. It is x=125 in this query..

Maximum and lowest values: Here, we're concerned in examining the vertex to determine whether it is at the maximum or lowest of the parabola's range (i.e., when a negative sign is placed in front of the (x-h) = 0 term, respectively).

Range: The value of range is (125,∞ )

To know more about Domain and Range visit;

brainly.com/question/28393663

#SPJ1

By using the fact that the two angles whose measures are expressed in terms of x are vertical angles, we will see that x = 8.

Then using that we will see that the measure of angle BAC is 63 degrees.

On the given diagram, we can see that the two angles whose measures are expressed in terms of x are vertical angles, thus, these two angles have the same measure, then we can write a linear equation that helps us to find the value of x, which is:

(2x + 3) = (4x - 5)

Solving the linear equation for x we get:

2x + 3 = 4x - 5

3 + 5 = 4x - 2x

8 = 2x

8/2 = x = 4

So we can see that the value of x is 4.

Now we want to find the measure of angle BAC.

We can see that the measure of angle BAC plus the measure of the angle to its right will be a right angle, then we can write:

m∠BAC + (4x - 5)° = 90°

Replacing the value of x we get:

m∠BAC + (4*8 - 5)° = 90°

m∠BAC + 27° = 90°

m∠BAC = 90° - 27° = 63°

We conclude that the measure of angle BAC is 63 degrees.

If you want to learn more about vertical angles:

https://brainly.com/question/14362353

#SPJ1

Answer:

Step-by-step explanation:

we cant see the question :)

Answer: If you have to fill in the chart I think you just add them together so aluminum would be +3, phosphide -3, iodide -1, and tin 0

Step-by-step explanation:

The slope of the line with points (0,-1/2) and (7/5, 10) is 7.5

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We know that slope, slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the pairs of points (0,-1/2) and (7/5, 10)

⇒ m = [tex]\frac{10 - (-1/2)}{(7/5) - 0}[/tex]

⇒ m = [tex]\frac{21/2}{(7/5) }[/tex]

⇒ m = 15/2

⇒ m = 7.5

Hence, the slope of the line with points (0,-1/2) and (7/5, 10) is 7.5

Learn more about slope

brainly.com/question/16949303

#SPJ4

Answer:

[tex]\displaystyle 25 = GQ[/tex]

Step-by-step explanation:

If point Q is the centre of GH, then QH and GQ are equivalent segments. So, double the length of GQ, set it equal to the length of GH, then solve for x:

[tex]\displaystyle \boxed{4x + 6} = 2[2x + 3] \\ \\ 5x - 5 = 4x + 6 \hookrightarrow -11 = -x \hookrightarrow \boxed{\boxed{11 = x}}[/tex]

Plug the result into the expression for the length of GQ to get twenty-five units.

I am joyous to assist you at any time.

Answer:

I believe the answer is 30.

Step-by-step explanation:

-

Answer:

8xh h=hours

Step-by-step explanation:

8 times how ever much hour than that's all if there's tips well just add it to your answer