Find the vertex and focus of the
parabola:
x² + 14x-8y + 65 = 0

I can’t figure this out!!!

Answers

Answer 1

Answer:

[tex]\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}[/tex]

Step-by-step explanation:

Completing the square :

x² + 14x - 8y + 65 = 0

x² + 14x + 49 - 49 - 8y + 65 = 0

(x + 7)² - 8y + 16

(x + 7)² = 8y - 16

⇒ x = -7, y = 2 (Vertex)

Finding a :

⇒ x² = 4ay

⇒ (-7)² = 4(2)a

⇒ a = 49/8

Finding the focus :

⇒ (0, a)

⇒ (0, 49/8) (Focus)


Related Questions

Which graph shows the greatest integer function?

Answers

a) because since it is a greatest integer function, it includes the highest integer, but excludes the lowest since it is the highest integer when x is less than or equal to an integer but greater than x-1.

The graph of the greatest integer function is graph A.

What is graph?

A graph is a diagram or a pictorial representation of data or values that show the relationship between quantities or objects.

Given are graphs we need to find the graph of the greatest integer function,

The graph of the greatest integer function is graph A because since it is a greatest integer function, it includes the highest integer, but excludes the lowest since it is the highest integer when x is less than or equal to an integer but greater than x-1.

Hence the graph of the greatest integer function is graph A.

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Estimate
12.4 × 18
—————-
0.012

Answers

Answer: 12.4 x 18

-------------- = 18600

0.012

30 point!!!! Help me fast!!!PLS!!Question is attached!!!

Answers

Answer:

This is an extremely easy question bro!

1.

2. 3 (Base) ² (Exponent)

3. Expanded form: (9 * 1)

   Standard form: 9

Step-by-step explanation:

Well, there's none.

Please mark me as Brainliest! Thanks! :)
Detailed Answers:

1) 5^3

2) Base = 5; Exponent = 2

3) Expanded Form = 5 * 5
Standard Form = 25

Find (f • g) (x) Assume x>0

Answers

Answer:

[tex]\textsf{B.} \quad (f \cdot g)(x)=10x[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}f(x)=\sqrt{50x}\\g(x)=\sqrt{2x}\end{cases}[/tex]

[tex]\begin{aligned}\textsf{As }(f \cdot g)(x) & = f(x) \cdot g(x)\\\implies (f \cdot g)(x)& = \sqrt{50x} \cdot \sqrt{2x}\end{aligned}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]

[tex]\begin{aligned}\implies (f \cdot g)(x) &= \sqrt{50x2x}\\& = \sqrt{100x^2}\end{aligned}[/tex]

Rewrite 100 as 10²:

[tex]\implies (f \cdot g)(x)=\sqrt{10^2x^2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^bc^b=(ac)^b:[/tex]

[tex]\implies (f \cdot g)(x)= \sqrt{(10x)^2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies (f \cdot g)(x)=10x[/tex]

HELP ANGJHHGG plssssssssssssssssssfghgg

Answers

Answer:

5377

Step-by-step explanation:

this is a vector question where how far is the Resultant. that is, it is determined by the magnitude of the Hypotenuse.

using Pythagoras theorem

Hypotenuse ²= Opposite ²+Adjacent²

Hypotenuse ²= 2865²+4550²

Hypotenuse ²= 8208225+20702500

Hypotenuse ²=28910725

Hypotenuse=√28910725

Hypotenuse=5376.86944234282

Hypotenuse= 5377 approximated

I NEED HELP PLEASE OMGOGMOMOG

Answers

Answer

c 

I'm not sure how to explain my bad

Multiplying a fraction by a repeating decimal will give you a rational answer.

Fractions are rational and repeating decimals are rational.

Rational + rational = rational

Use the formula to solve the equation x^2 + 9x + 8 = 0.

Answers

Answer:

[tex]x=-8, -1[/tex]

Step-by-step explanation:

Given the equation [tex]x^{2} +9x+8=0\\[/tex],

By the quadratic formula,

[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex],

[tex]x=\frac{-(9)+-\sqrt{(9)^{2}-4(1)(8) } }{2(1)}=\frac{-9+-\sqrt{49 } }{2}=\frac{-9+-7 }{2}[/tex]

We have two different solutions for x where [tex]x=\frac{-9-7 }{2}[/tex] and [tex]x=\frac{-9+7 }{2}[/tex]

So, x = [tex]-16/2=-8[/tex] and [tex]x=-2/2=-1[/tex]

Therefore, the solutions to this quadratic equation is x = -8, -1, by the quadratic formula.

Which expression is equivalent to?

Answers

The expression obtained is 2g³-5g² +6 , Option C is the correct answer.

What is an Expression ?

An expression is a mathematical statement that consists of constant , variable and mathematical operators.

The expression given is

[tex]\rm \dfrac{(5g^4 +5g^3 -17g^2 +6g) -(3g^4 +6g^3-7g^2 -12)}{g+2}[/tex]

On subtracting the numerator

2g⁴-g³-10g²+6g+12

Now dividing the numerator by denominator

The expression obtained is 2g³-5g² +6

Therefore Option C is the correct answer.

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18.
(05.06 LC)

A librarian measured the number of young adult books in a library. The number of books in the library as a function of time (in years since 2008) is shown in the scatterplot. Choose the linear function that best describes the scatterplot relating the number of books in the library, y, to time, x. (1 point)
y = 8 − 10x

y = 8 + 10x

y = 10 − 8x

y = 10 + 8x

Answers

Answer:

y=8+10x that then answer I guess

Quick
Check
Match each power of a power expression with its simplified expression.

Answers

(4^-3)^-3 =4^9 (4^6)^-3 =1/4^18. (4^0)^-9 =4^0. (-4^9)^2 =4^18

It takes 6 hours for 2 people to build a swing set. Can you use the proportion 2 - 6 = 5 - h to determine the number of hours h it will take 5 people to build the swing set? Explain.

Answers

The number of hours, h it will take 5 people to build the swing set is; 2.4 hours

What is the number of hours it will take 5 people to build the swing set?

From the task content, it follows that it took 6 hours for 2 people to build the swing set, hence, it follows that it'd take 12 hours for 1 person to build the swing.

However, when the work is divided between 5 People, the time taken is therefore; 12/5 = 2.4hours.

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Which describes the graph of y= -(x + 6)² + 6?
O A. Maximum at (-6, 6)
OB. Maximum at (6, 6)
OC. Minimum at (-6, 6)
OD. Minimum at (6, 6)

Answers

Answer:

A

Step-by-step explanation:

Since x has a negative coefficient, the graph opens downwards meaning that it has a maximum.

The vertex formula is y = a(x - h)^2 + k so the coordinate must be (-6, 6).

The correct answer would be A.Maximum (-6,6)

evaluate the expression below when x is 4

3x^2 +5 =​

Answers

Answer:

[tex]\fbox {53}[/tex]

Step-by-step explanation:

⇒ 3x² + 5

Substitute x = 4 :

⇒ 3(4)² + 5

⇒ 3(16) + 5

⇒ 48 + 5

53

3x^2+5
3(4)^2+5
*note*
(4)^2= 4•4=16
3(16)+5
48+5= 53

In a family the ages of children arranged from youngest to oldest are 2,6,y,14 and z if the square of ages is in an a.p what is the ratio of z and y

Answers

Answer:

y=10

z=18

Step-by-step explanation:

2,6,y,14,z

there are 4 years different between the childrens.

2-6-10-14-18

can someone please help mee (20 points and i will give brainliest!!!)

Answers

Answer:

Step-by-step explanation:

Four students are trying to determine what number must replace the question (x^2)^?=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? In words explain why.

Answers

Joe is correct as the unknown number is 6.

What are exponents?

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

Given :

[tex](x^2)^?=x^4\times x^8[/tex]

Let the question mark exponent outside the bracket be y, which needs to be determined

[tex](x^2)^y=x^4\times x^8[/tex]

Simplify the equation by applying exponent rules to either side of the equation:

Apply the rule [tex](a^b)^c = a^{b \times c}[/tex]

[tex](x^2)^y=x^4\times x^8[/tex]

[tex](x)^{2y}=x^4\times x^8[/tex]

Now apply [tex]a^b \times a^c = a^{b+c}[/tex]

[tex](x)^{2y}=x^{4+8}\\\\(x)^{2y}=x^{12}[/tex]

So, the base is the same the exponent will be the same also,

2y = 12

y = 6

Hence, Joe is correct as the unknown number is 6.

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What is sin and cos ​

Answers

    Sin and cos are trigonometry functions used to find measurements in a right triangle.

         [tex]\displaystyle sin=\frac{\text{opposite side}}{hypotenuse}[/tex]

         [tex]\displaystyle cos=\frac{\text{adjacent side}}{hypotenuse}[/tex]

Work out (6 × 10²) ÷ (3 × 105)
Give your answer in standard form.

Answers

Answer: 40/21

Step-by-step explanation:

[tex]3 \times 105=315\\\\6 \times 10^{2}=600\\\\\implies \frac{6 \times 10^{2}}{3 \times 105}=\frac{600}{305}=\boxed{\frac{40}{21}}[/tex]

Plsss helppppp I neeed this

Answers

Based on the calculations on the bisector of ST, the value of ST are equal to 38 and 30 respectively.

How to find the bisector of ST?

In order to determine the bisector of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

For exercise 1, we have:

ST = SM + MT

ST = 19 + 19

ST = 38.

For exercise 2, we have:

First of all, we would determine the value of x as follows;

3x - 6 = x + 8

3x - x = 8 + 6

2x = 14

x = 14/2

x = 7.

ST = SM + MT

ST = 3x - 6 + x + 8

ST = 3(7) - 6 + 7 + 8

ST = 30.

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The frequency table shows the results asking people how many hours they spend online per week

Answers

The histogram is attached with the answer.

What is a Histogram ?

It is a mathematical representation of data in a bar shaped graph , the range is user defined.

The histogram is drawn and the shape of the histogram is left skewed as the peak of the graph lies to the left of the centre.

The histogram is attached with the answer.

The complete question is

the frequency table shows the results of a survey that asked people how many hours they spend working in the yard per month. display the data in a histogram. describe the shape of the distribution

The data is attached with the answer.

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In a school, the number of girls is 70 more than boys. the total number of students is 1280. find the number of girls and boys simple equations

Answers

Answer:

Boys = 605

Girls = 675

Step-by-step explanation:

Let x be the number of boys in school.

So, girls = (x+70)

Total no. of students = 1280

x + x + 70 = 1280

2x + 70 = 1280

2x = 1280 - 70

2x = 1210

x = 1210/2

x = 605

Hence, no. of boys = 605

no. of girls = 605 + 70 = 675

What is the quotient of 0.8449 ÷ 0.71?

Answers

Answer:

1.19

Step-by-step explanation:

1) Shift the decimals of both 0.8449 and 0.71 to the right by 2 decimal places. (This is needed to convert 0.71 to 71, since long division must divide by a whole number.)

84.49 ÷ 71

2)  Use the algorithm method.

1 . 1 9

7 1 | 8 4 . 4 9

7     1 .  

1 3 . 4

7 . 1

6 . 3 9

6 . 3 9

3) Therefore,  0.8449 ÷ 0.71 = 1.19.

1.19

Venn diagram ( attached image )

Answers

Assessing the given Venn diagram and the data related to it, we can answer the required question:

Q1. How many people were surveyed = 86.

Q2. What is the probability that a customer chosen at random:

a) takes salt P(S) = 46/85.

b) takes both salt and vinegar P(S ∩ V) = 13/85.

c) takes salt or vinegar or both P(S ∪ V) = 66/85.

The number of people who take salt chips n(S) = 46.

The number of people who take vinegar chips n(V) = 33.

The number of people who takes both n(S ∩ V) = 13.

The number of people who take neither n((S ∪ V)') = 19.

Therefore, the total number of people surveyed n(U) = n(S) + n(V) - n(S ∩ V) + n((S ∪ V)') = 46 + 33 - 13 + 19 = 85.

The number of people who takes salt or vinegar or both n(S ∪ V) = n(U) - n((S ∪ V)') = 85 - 19 = 66.

The probability that a customer chosen at random takes salt P(S) = n(S)/n(U) = 46/85.

The probability that a customer chosen at random takes both salt and vinegar P(S ∩ V) = n(S ∩ V)/n(U) = 13/85.

The probability that a customer chosen at random takes salt or vinegar or both P(S ∪ V) = n(S ∪ V)/n(U) = 66/85.

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How many solutions does the system have?
x + y = 5
x + y = 6
Onone
O one
O two
O infinite

Answers

Answer:

none

Step-by-step explanation:

please mark me as brainlest

None because the interfere

Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?

Answers

Hello, wheres the statement? Please provide full questions

1kg of sugar costs ₹25.30 . Find the cost of 13.5kg of sugar

Answers

Answer:

₹ 341.55

Step-by-step explanation:

Cost of 1 kg sugar = ₹ 25.30

Cost of 13.5 kg sugar = 25.30 × 13.5 = 341.55

Hence, the cost of 13.5 kg is ₹ 341.55

If you are writing, write statements too as in my school they give extra marks.

Thankyou and have a great day ahead.

Answer:341.55

Step-by-step explanation:

If one KG of sugar does cost  ₹25.3 and if you want to know how much 13.5 kg costs you just would have to multiply/times  ₹25.3 by 13.5 and what is 25.3 x 13.5.  ₹341.55 and that's your answer!

What is the area of triangle ABC?

Answers

Answer:

3 square units

Step-by-step explanation:

Use BC as the base   =   2

   Use y -axis to C   (or B) as the height =  3

Area of triangle = 1/2  * base * height = 1/2 * 2 * 3 = 3 units^2

What is the result of adding the system of equations? Equation 1: 2x + y = 4 Equation 2: 3x - y = 6 A) 5x = 10 B) x = 5 C) x = 10

Answers

An equation is formed of two equal expressions. The correct option is A, the sum will be equal to 5x = 10.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the two systems of equations Equation1: 2x+y=4 and Equation 2: 3x-y=6. Now if the two of the given equations are added the result will be,

2x + y + 3x - y = 4 + 6

5x  = 10

Hence, the correct option is A, the sum will be equal to 5x = 10.

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* GEOMETRY

please help me show the work for 9, 10, and 11!!

Answers

9) Diagonals of a parallelogram bisect each other, so KN=NM. Thus, KM=13.5+13.5=27 cm

10) Opposite sides of a parallelogram are congruent, so LM=KJ=17 cm

11) Based on Question 9, MN=13.5 cm

HELPPPPPPPPPPPPPPPPP PLEASE

Answers

Y=-4
X=2
Yeah that’s all I got to say lol
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