What’s the standard form of a circle?

Answer:

radius = 5

Step-by-step explanation:

Given

Using completing the square method

Standard form for equation of a circle

On comparison to our equation in the question :

Answer:

radius = 5

Step-by-step explanation:

[tex]x^2+y^2-10x+8y+16=0[/tex]

The equation of a circle is shown. What is the radius?

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Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Given equation:

[tex]x^2+y^2-10x+8y+16=0[/tex]

Collect like terms:

[tex]\implies x^2-10x+y^2+8y+16=0[/tex]

Subtract 16 from both sides:

[tex]\implies x^2-10x+y^2+8y=-16[/tex]

Complete the square for both variables.

Add 25 to both sides for x.  Add 16 to both sides for y.

[tex]\implies x^2-10x+25+y^2+8y+16=-16+25+16[/tex]

[tex]\implies (x^2-10x+25)+(y^2+8y+16)=25[/tex]

Factor the two variables:

[tex]\implies (x-5)^2+(y+4)^2=25[/tex]

Therefore:

Answer:

d

Step-by-step explanation:

The answer is A.thus, this is a linear model. To check,you can see visually that the points are more fitted to the line than the curve.

Linear regression is the most basic and commonly used predictive analysis. Regression estimates are used to describe data and to explain the relationship.

The difference between the linear model and the exponential model is the degree of difference of consecutive points. If their difference is constant, then it is more appropriate for the linear model. If their difference is increasing at a very fast rate, then that follows an exponential model. With that being said, let's look at the differences at every 6 month-intervals.

2700-2110 = 590

2110-1500 = 610

1500-870 = 630

870-220 = 650

Their differences are about the same having a mean of 620. Thus, this is a linear model. To check,you can see visually that the points are more fitted to the line than the curve. The answer is A.

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Answer:

A is the correct answer

Step-by-step explanation:

Answer:

i think this is the answer

Answer:

see below

Step-by-step explanation:

Area = pi r^2     r = radius

  diamter = 94    then radius = 94/2 = 47 cm

area = pi (47)^2 = 2209 pi    or 6939.78  cm^2

Answer:

A ≈ 6,939.8 cm²

Step-by-step explanation:

Given : " the diameter is 94cm "

d = 94

Radius is r = d/2 = 94/2 = 47 cm

Area of a circle is

A= π·r²

A = π·47² ≈ 6,939.8 cm²

To find the straight time pay for two weeks,

we'll multiply the amount per hour to the number of working hours

hence,

___________________________________

The Straight time pay of one week would be ,

___________________________________

Straight time pay of a month would be,

___________________________________

Weeks no is not of any use here

Straight time pay:-

Step-by-step explanation:

-2 -0.5b + 12 = 0.3b + 6.2

-2 + 12 - 6.2 = 0.3b + 0.5b

3.8 = 0.8b

b = 3.8/0.8

= 4.75

Answer:

4.75

Step-by-step explanation:

-2-0.5b + 12 = 0.3b + 6.2

Move all terms to the left:

-2-0.5b + 12 - (0.3b + 6.2) = 0

Add all the numbers together, and all the variables

-0.5b - (0.3b + 6.2) + 10 = 0

Get rid of parentheses

-0.5b - 0.3b - 6.2 + 10 = 0

Add all the numbers together, and all the variables

-0.8b + 3.8 = 0

Move all terms containing b to the left, all other terms to the right

-0.8b = -3.8

b= -3.8/-0.8

b= 4+0.6/0.8

b= 4.75

Answer:

Asnwer is in explanation

Step-by-step explanation:

f' (x) = 2x

Hope this helps!

Answer:

$ 2779.88

Step-by-step explanation:

185 325  x  1.5 % =

185 325 x  .015 = 2779.88

Answer:

flipping a quarter

Step-by-step explanation:

a quarter has two sides so the chance of getting one is 1/2

a dice has 6 sides so the chance of getting a certain number is 1/6

Answer:

17*12 area of triangle is base*height

Answer:

Use the formula for the area of a triangle:

A = BH x 1/2

Where 'B' represents the base, 'H' the height, and multiplying by 1/2 just means dividing the product of those two lengths by 2.

What we know:

Which is all we need to know, so plug these values into our formula;

A = BH x 1/2

A = 12(17) x 1/2

Now just solve:-

A = 204 x 1/2

A = 204/2

A = 102, the area of this triangle is 102 ft²!

Answer:

9x^4 [ x^3 + 5x^2 - 2 ]

Step-by-step explanation:

9x^7 - 36x^4 + 45x^6

=9x^7 + 45x^6 - 36x^4

=9x^4 [ x^3 + 5x^2 - 2 ]

//

I hope this is the answer that you are looking for

Answer:

3/4

Step-by-step explanation:

If Ty and his brothers share a pizza equally, then the pizza is split into four parts because there are four people sharing it. That means that each person has 1/4 of the pizza.

Since Ty has 3 brothers, they share 3/4 of the pizza since 1/4 * 3 = 3/4.

The Brelynn can cut 9 pieces from the piece of ribbon that is 3/4 yard long of 1/12 yard.

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

Let's assume Brelynn can cut x pieces from the piece of ribbon that is 3/4 yard long.

So from the problem:

[tex]\rm \frac{\frac{3}{4} }{x} = \frac{1}{12}[/tex]

[tex]\rm \dfrac{3}{4} = \dfrac{x}{12}[/tex]

x = 9 pieces

Thus, the Brelynn can cut 9 pieces from the piece of ribbon that is 3/4 yard long of 1/12 yard.

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Answer:

It is False

Step-by-step explanation:

The answer is not the same.

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given with three sides of a triangle that are as follows ,

And we are asked to :

We know that for finding perimeter of any shape we must have to add all the sides of the shape or ,

[tex] \qquad \: \underline{\boxed{\frak{Perimeter = Sum \: of \: all \: sides}}}[/tex]

Solution : -

( a )

Now adding all the three sides of triangle to find the perimeter .

[tex] \hookrightarrow \quad \: ( x + 5 ) + ( 2 x + 4 ) + ( 2x - 3 ) [/tex]

[tex] \hookrightarrow \quad \: \: x + 5 + 2x + 4 + 2x - 3[/tex]

Combining like terms :

[tex] \hookrightarrow \quad \:x + 2x + 2x + 5 + 4 - 3[/tex]

Now , solving :

[tex] \hookrightarrow \quad \: \red{\underline{ \boxed{ \frak{(5x + 6) \: cm}}}}[/tex]

( b )

Now , we are finding perimeter of triangle when value of x is 10 . So substituting value of x in given sides of triangle ,

First Side :

Second Side :

Third Side :

So , all the sides are 15 cm , 24 cm and 17 cm .

Now , adding all these to find perimeter .

[tex] \hookrightarrow \qquad \: 15 + 24 + 17[/tex]

[tex]\hookrightarrow \qquad \: 39 + 17[/tex]

[tex]\hookrightarrow \qquad \: \red{\underline{\boxed{\frak{56 \: cm}}}}[/tex]

Alternative Solution : -

As above we have find the perimeter of triangle in term of x that is ( 5x + 6 ) cm. So we can put value of x as 10 in this to get perimeter. So ,

Therefore, perimeter of triangle is 56 cm .

To find the perimeter of a shape, we should add all sides , like so :

x+5+2x+4+2x-3

Combine the x's :

x+2x+2x+5+4-3

x+4x+9-3

5x+6

5x+6 cm

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b.

Find the perimeter of the triangle if x = 10

Just write 10 instead of x :

5(10)+6

5(10) simplifies to 50 ↓

50+6

56

hope helpful ~

#1

D:-

D<0 so unequal and un real roots

#2

D>0 so unequal and real roots

#3

Equal and real roots

Answer:

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}[/tex]

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Question 5

Given function:  [tex]f(x)=3x^2-3x+2[/tex]

[tex]\implies a=3, \quad b=-3, \quad c=2[/tex]

Inputting these values into the discriminant:

[tex]\implies \textsf{discriminant}= (-3)^2-4(3)(2)=-15[/tex]

As -15 < 0 there are no real solutions

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Question 6

Given function:  [tex]f(x)=x^2-10x+1[/tex]

[tex]\implies a=1, \quad b=-10, \quad c=1[/tex]

Inputting these values into the discriminant:

[tex]\implies \textsf{discriminant}= (-10)^2-4(1)(1)=96[/tex]

As 96 > 0 there are two real solutions

at [tex]x=5 \pm 2\sqrt{6}[/tex]

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Question 7

Given function:  [tex]f(x)=x^2-4x+4[/tex]

[tex]\implies a=1, \quad b=-4, \quad c=4[/tex]

Inputting these values into the discriminant:

[tex]\implies \textsf{discriminant}= (-4)^2-4(1)(4)=0[/tex]

As 0 = 0 there is one real solution

at [tex]x=2[/tex]

Answer:

380

Step-by-step explanation:

760 divide 2= 380

Answer:

x=16

Step-by-step explanation:

12 is three fourths of x, there are three 1/4s that make up 12.

Divide 12 by three to find out 1/4 is.

Then simply multiply that by four.

Answer:

She would need 6/4 or 1 1/2 cups juice

Step-by-step explanation:

Answer:

1.5 cups of juice.

Step-by-step explanation:

1 / 0.5 = 2

0.75 x 2 = 1.5

Using the mean concept, it is found that the value of the number that was removed was of 4.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

The mean of five numbers is 8, hence, the sum of the numbers is given by:

S = 5 x 8 = 40.

If one of the five numbers is removed, the mean becomes 9, hence, the sum of the four numbers is given by:

S = 4 x 9 = 36.

The difference is:

40 - 36 = 4.

Hence, the value of the number that was removed was of 4.

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Using a t-distribution calculator and finding the p-value, the correct option regarding the conclusion is given by:

a) the p-value is 0.02. We reject h0 at the 5% significance level because the p-value 0.02 is less than 0.05.

It also involves the significance level, as follows.

In this problem, a t-distribution calculator for a right-tailed  with t = 2.15 and 25 - 1 = 24 df is used to find a p-value of 0.02.

It is less than 0.05, hence option a is correct.

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