Mathematics High School

Which conic section does the equation below describe?
x^2+y^2- 8x+ 10y+15 = 0
O A. Hyperbola
O B. Parabola
OC. Circle
OD. Elipse

Answers

Answer 1

Answer:

[tex]\large\boxed{\boxed{\pink {\bf \leadsto The \ equation \ represents \ a \ circle. }}}[/tex]

Step-by-step explanation:

Given equation to us is ,

[tex]\green{\implies x^2 + y^2 - 8x + 10y + 15 = 0 }[/tex]

And we need to find which conic section does the equation below describe . So for that let's simpify the Equation .

[tex]\implies x^2 + y^2 - 8x + 10y + 15 = 0 \\\\\implies x^2 - 8x + y^2 + 10y = (-15) \\\\ \implies x^2 -8x + 4^2 - 4^2 + y^2 + 10y + 5^2-5^2 + 15 = 0\\\\ \implies (x -4)^2 + (y+5)^2 - 16 - 25 + 15 = 0 \\\\ \implies (x -4)^2 + (y+5)^2 - 26 = 0 \\\\\implies (x-4)^2 + (y+5)^2 = 26 \\\\\implies (x-4)^2+(y+5)^2=(\sqrt26)^2 [/tex]

And this is similar to the standard equation for a circle is ( x - h )² + ( y - k )²= r² , where ( h, k ) is the center and r is the radius.

Hence the given equation represents a circle with center ( 4 , -5) and radius √26 units.

Related Questions

The following rectangle has an area of 3x^2-5x-12. What are the possible side lengths, in terms of x? Explain your answer and justify how you know that the sides you found are possible lengths

Answers

Answer:

the possible side lengths:

3x+4 and x-3

Step-by-step explanation:

factorize the the expression and you will get two expressions in terms of x. those expressions are the lengths of the rectangle

[tex]3 {x}^{2} - 5x - 12[/tex]

1) write -5x as a difference

[tex]3 {x}^{2} + 4x - 9x - 12[/tex]

2) factor out x from the expression 3x²+4x

[tex]x(3x + 4) - 9x - 12[/tex]

3) factor out -3 from the expression -9x-12

[tex]x(3x + 4) - 3(3x + 4)[/tex]

4) factor out 3x+4 from the expression

[tex](3x + 4)( x - 3)[/tex]

the possible lengths are 3x+4 and x-3

to check whether the answer is correct, you can just multiply the both lengths using the area of rectangle formulae

area of rectangle formulae

[tex]length \times height[/tex]

(3x+4)(x-3)

= 3x²-9x+4x-12

= 3x²-5x-12 ( proven )

On Saturday, a souvenir shop had 125 customers. Sixty-four percent of the customers paid with a credit card. The other customers paid with cash. How many customers paid with cash?

Answers

Answer:

45 customers

Step-by-step explanation:

Given

Total number of customers = 125

percent that paid with credit card = 64%

Customers that paid with credit card = 64% * 125

Customers that paid with credit card = 0.64 * 125 = 80

Number of customers that paid with cash = 125 - 80

Number of customers that paid with cash = 45 customers

All 7 crawfish in Gumbo's family love hot dogs. Gumbo's mom made 20 hot dogs for
supper one night. Is that enough for each of them to have 3 hot dogs?
No
Yes

Answers

Answer:

Step-by-step explanation:

if there is 7 of them and each have 3 that would call for 21 hot dogs

I have a question on Khan Academy and it says super salad dressing is made with 8 mL of oil for every 3 ml of vinegar which of the following mixtures will take the same as super salad dressing
then it says choose 3 answers there's 5 choices a b c and d a is 80 ml of oil with 30 ml of vinegar

B is 3 ml oil with 8 ml of vinegar
C is 56 mL of oil with 21 mL of vinegar
d 40 mL of oil with 25 mL of vinegar
e is 48 mL of oil with 18 mL of vinegar

Answers

Answer:

Step-by-step explanation:

8ml x 6= 48ml of oil

3ml x 6= 18ml of vineger

Given the student is a "Moderate" what is the probability that the student is male? Round your answer to three decimal places if necessary.
a. 0.454
c. 0.47
b. 0.614
d. 0.386

Answers

Answer: B

Step-by-step explanation:

How do you use substitution to solve a system of linear equations?

Answers

Answer:

Step 1 : First, solve one linear equation for y in terms of x .

Step 2 : Then substitute that expression for y in the other linear equation. ...

Step 3 : Solve this, and you have the x -coordinate of the intersection.

Step 4 : Then plug in x to either equation to find the corresponding y -coordinate.

(hope this helps :) )

Approximately 10% of the population is left-
handed. If a school had a student population
of 1200 students, how many of them could
you expect to be right-handed?

Answers

Answer:

1080

Step-by-step explanation:

if 10 percent are left handed that means that 90 percent are right handed

number of people that are right handed = 0.9 × 1200number of people that are right handed = 1080

Answer:

120

Step-by-step explanation:

10%=0.1

1200*0.1=120

Find the rate of change
Pls help thx

Answers

Answer:3

Step-by-step explanation:

Go up from one point to the other and whatever the number comes is the answer.

Write an equation that will satisfy the x and y values in the table below.

Answers

Answer:

The equation that will satisfy x and y values in the table is y = 2x + 3

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

m is the slope of the line that represents the equation b is the y-intercept, value y at x = 0

The rule of the slope of the line is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where

(x1, y1) and (x2, y2) are two points on the line

From the given table

∵ x = 0 and y = 3, x = 1 and y = 5

∴ x1 = 0 and x2 = 1

∴ y1 = 3 and y2 = 5

→ Substitute them in the rule of the slope above

∵ m = [tex]\frac{5-3}{1-0}[/tex] = [tex]\frac{2}{1}[/tex]

∴ m = 2

∵ b is the value of y at x = 0

∵ y = 3 at x = 0

∴ b = 3

→ Substitute the values of m, b in the form of the equation above

∴ y = 2x + 3

∴ The equation that will satisfy x and y values in the table is y = 2x + 3

Which of the following is equivalent to 5x - x + 3x = 30? A 8x = 30 o 7x = 30 с 3x + 5= 30 x = 30

Answers

Answer:

Step-by-step explanation:

5x -x + 3x =30, first you combine like terms 5x + 3x-x=30

8x-x =30

8-1=7

7x=30

Answer:

7x=30

Step-by-step explanation:

7x=30

Simplify: (5x2 - 9x + 3) + (4x2 + 4x - 12)
(1) 9x2 + 5x - 9
2) 9x2 - 5x + 15
3) 9x² - 5x-9
4) 9x2 - 13x - 9

Answers

Answer:

3) 9x² - 5x - 9

Step-by-step explanation:

Combine like terms

5x² - 9x + 3 + 4x² + 4x - 12 = 5x² + 4x² - 9x + 4x + 3 - 12

= 9x² - 5x - 9

Which point on the graph best represents the location of left parenthesis minus 4.5 comma space minus 7 right parenthesis ?

Answers

Answer:

The answer would be A which is L

Answer:

so its A?

Step-by-step explanation:

Graph y < x and y ≥ 4x + 2

Answers

Answer:

Image is attached.

Step-by-step explanation:

Remember since the blue line is greater than, instead of being dashed like the red line, it's solid.

Kristine and her friends are raising money for charity. They hope to raise $900 to reach their goal. So far, they have $780. How much more do they need to collect in order to reach their goal?

Answers

Answer:

$120

Step-by-step explanation:

They have raised $780 and need to raise $900.

(Total amount they need to raise) - (total amount they raised) = (how much more they need to collect)

$900 - $780 = $120

On a test, Jim answered 28 problems correctly. He answered 80% of the questions correctly.
How many questions were on the test?

Answers

Answer:

Step-by-step explanation:

I need help wit this

Answers

Answer:

Step-by-step explanation:

\+_+/

Find the value of x.
3x-10
25
X+15

Answers

Value of x is 3x-10 25 x * 15

The answer should be 25

Identify the parent function. 5 --5
a absolute
b reciprocal
c cube root
d square root

Answers

Step-by-step explanation:

For an absolute value function, the graph will look like an arrow with a sharp inflection point.

Reciprocal function will tend towards a limit when stretched to infinity.

Cube root and square root functions do not tend towards infinity at x = 0, because it is either 0 or the constant value.

The best answer here is Reciprocal. (B)

Answer:

b reciprocal

Step-by-step explanation:

The graphed is the function y = 1/x, it is an odd function and the graph is hyperbola

The function is reciprocal

Correct option is B

Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!

Answers

p = √24

Step-by-step explanation:

5² = 1² + p²

25 - 1 = p²

p² = 24

p = √24

could somebody help me on the 2 question please

Answers

-20 because after the the thermometer hits zero the more negative the temperature gets the colder it is

Answer:

on question 2 the one which you need to write is -20 degrees bcz it's colder than -10 degrees

Step-by-step explanation:

where is the question 1

+this sentence :" is -20 degrees bcz it's colder than -10 degrees "is a 2answer sentence

hope this helps

What is electrical energy converted to inside a toaster?
A. thermal energy and light
B. nuclear energy
C. chemical energy
D. kinetic energy

Answers

I believe it is C :)

The electric energy converted in a toaster is A thermal and light

a factor of all even numbers other than 1? pls answer quick

Answers

Answer: 2

Explanation: 2 is a prime number that is a factor for all even numbers.

Please help!

Sin A =

Sin C =

Cos A =

Cos C =

I’ll give brainliest!!

Answers

Answer:

sin A= 3/5

sin C= 4/5

cos A= 4/5

cos C= 3/5

Step-by-step explanation:

Please see the attached picture for the full solution.

if an object has a density of 3.6g/ml and you put it into water, will it sink or float?

Answers

Answer:

Sink

Step-by-step explanation:

We need to find if an object with a certain density will float or sink in water.

The object will sink in water.

The density of the object is 3.6 g/mL

The density of water is generally [tex]1000\ \text{kg/m}^3[/tex]

An object which has a density more than the liquid it is in then the object will sink.

Let us convert the density of the object to [tex]\text{kg/m}^3[/tex]

[tex]1\ \text{g}=10^{-3}\ \text{kg}[/tex]

[tex]1\ \text{mL}=10^{-6}\ \text{m}^3[/tex]

[tex]1\ \text{g/mL}=\dfrac{10^{-3}}{10^{-6}}=10^3\ \text{kg/m}^3[/tex]

[tex]3.6\ \text{g/mL}=3.6\times 10^3=3600\ \text{kg/m}^3[/tex]

The density of the object [tex](3600\ \text{kg/m}^3)[/tex] is greater than that of water [tex](1000\ \text{kg/m}^3)[/tex].

Hence, the object will sink.

Learn more:

https://brainly.com/question/18950364

https://brainly.com/question/2200299

Is someone kind and available enough to do this work for me
I need it really

Answers

Answer:

D. 40.0km

Step-by-step explanation:

When rounding to 3 significant figures, we will have to look at the 4th significant figure. If that figure is 1-4, you round the 3rd figure down. If that figure is 5-9, you round the 3rd figure up.

In this case, the 3rd figure is the tenth 9 and the 4th figure is the hundredth 7.

Since 7 is from 5-9, you round the tenth 9 up. This adds one whole to 39, which makes it 40. You also need to keep 3 significant figures so the decimal zeros are significant. Thus, the answer is 40.0km

P(x) = 2x3 – x2 + 4x + 5 is divided by x + 2. Choose the correct option from each drop-down menu.

When P(x) is divided by x + 2, the remainder is [ ] P(–2) = [ ]. The Remainder Theorem is [verfied/not verified] ]

Answers

The remainder of the division of polynomial, P(x) = 2x3 – x2 + 4x + 5 by (x + 2) is; -23

The remainder of the division of the polynomial, P(x) = 2x3 – x2 + 4x + 5 by (x + 2) can be evaluated by the remainder theorem.

This involves adding evaluating the value of the polynomial at, x = -2.

Since, (x +2) is the Divisor, we evaluate, P(x) at x = -2

Therefore, we have;

P(-2) = 2 ×(-2)³ -(-2)² + 4(-2) + 5

P(-2) = -16 -4 -8 +5

P(-2) = -23.

Therefore, the remainder when P(x) = 2x3 – x2 + 4x + 5 is divided by (x + 2) is; -23

https://brainly.com/question/11456067

Transitive Property of Congruence
If MN = LK and LK = OP, then

Answers

Answer:

If MN=LK and LK=OP, then MN= OP

Answer:

MN = OP

Step-by-step explanation:

Jason purchased 3 popcorns and 2 soft drinks for a total of $15.50.

Ann purchased 4 popcorns and 3 soft drinks for a total of $22.00.

how much does a single soft drink cost?

Answers

A single soft drink costs $4 and a single popcorn costs $2.50

Solve the equation
3/2x - 2 > 7

Answers

X > 6

You can multiply each side of equation by the denominator to eliminate the fraction.

Work:

Why do 25 ÷ 10 and 250 ÷ 100 give the same answer?

Answers

Answer:

One zero can be cancel out from both the numerator and denominator of [tex]250[/tex] ÷ [tex]100[/tex]

Step-by-step explanation:

[tex]25[/tex] ÷ [tex]10[/tex] [tex]=\frac{25}{10}=\frac{5}{2}[/tex]

[tex]250[/tex] ÷ [tex]100[/tex] [tex]=\frac{250}{100}=\frac{5}{2}[/tex]

Therefore,

[tex]25[/tex] ÷ [tex]10[/tex] [tex]=[/tex] [tex]250[/tex] ÷ [tex]100[/tex]

Here, 25 ÷ 10 and 250 ÷ 100 give the same answer.

Here, one zero can be cancel out from both the numerator and denominator of [tex]250[/tex] ÷ [tex]100[/tex]

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Which conic section does the equation below describe? x^2+y^2- 8x+ 10y+15 = 0 O A. Hyperbola O B. Parabola OC. Circle OD. Elipse

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Which conic section does the equation below describe?
x^2+y^2- 8x+ 10y+15 = 0
O A. Hyperbola
O B. Parabola
OC. Circle
OD. Elipse