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2 years ago

X2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is

Mathematics

1 answer:

erastova [34]2 years ago

7 0

The Standard form of the equation of circle is (x+21)² + (y+19)² = 849

<h3>What is Standard form of circle?</h3>

To transform general form to a standard form, you can use completing the square method or you can convert this equation

x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0

Here, Given: x² + y² + 42x + 38y − 47 = 0

Required: Find the values of h, k, and r using this formula

x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0

On comparing we get,

-2h = 42

h = 21

-2k = 38

k = 19

-47 = h² + k² - r²

-47 = 21² + 19² - r²

r² = 849

r = √849

Thus, the Standard form of the equation of circle is (x+21)² + (y+19)² = 849

Learn more about Circle from:

brainly.com/question/11833983

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In one area, the cable company marked up the

butalik [34]

Cable company marked up monthly cost by 6% .New cost = $63.6

cost before increase = 63.6 × 100/106

= $60

7 0

3 years ago

The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has under

Ann [662]

Answer:

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$

Step-by-step explanation:

Data given and notation

$\bar X=1.20$ represent the sample mean given

$\sigma = 0.14$ represent the population standard deviation

$n=49$ sample size

$\mu_o =1.25$ represent the value that we want to test

t would represent the statistic (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean for the gasoline prices is lower than 1.25, the system of hypothesis would be:

Null hypothesis: $\mu \geq 1.25$

Alternative hypothesis: $\mu < 1.25$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$

5 0

3 years ago

A small explanation would be really appreciated

shutvik [7]

Step-by-step explanation:

the 2 angles marked with orange and green are equal becos the question said that the indicated angles are congruent meaning same deg. so 180 - that given angle = the 2 marked angles (based on the rule known as angles on a str line are supplementary)

since the 2 marked angles are same, you can say that d and k are parallel due to the rule of alternate angles

Topic: angle properties

If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!

7 0

3 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Gemiola [76]

Answer: (D) <em>bottom right graph</em>

<u>Step-by-step explanation:</u>

The vertex form of a quadratic equation is: f(x) = a(x - h)² + k, where

(h, k) is the vertex
|a| is the vertical stretch
sign of "a" determines the direction of the parabola

Given g(x) = (x - 3)² - 5

vertex (h, k) = (3, -5)
vertical stretch |a| = 1
sign of "a" is positive so parabola points up

The only graph that satisfies all of these conditions is the bottom right.

7 0

3 years ago

Marco's mom has measured his height in centimeters every few months between the ages of 4.5 and 7.5. The recorded values are bes

Contact [7]

Answer:

Extrapolation

Step-by-step explanation:

Extrapolation is a type of estimation, beyond the original observation range. In this case, the observation range is from 4.5 to 7.5 years. Marco's mom is extrapolating the regression line to estimate Marco's height at 14 years old. This sort of estimation assumes that Marco's height will continue changing at the same rate until he is 14 years old.

7 0

3 years ago