What Is The Center Of The Circle With The Equation (x-1)^2 + (y+3)^2= 9? A (1,3) B (-1,3) C (-1,-3) D (2024)

Answer:

-2

Step-by-step explanation:

The slope formula is

m = ( y-2-y1)/(x2-x1)

Using two points on the line (0,4) and (2,0)

m = ( 0-4)/(2-0)

= -4/2

=-2

Answer:

-2

Step-by-step explanation:

Slope is change in y over change in x

the change in y is -2 and the change in x is 1 so you do -2/1 and that as a whole number is -2.

Answer:

a 1 : 5

Step-by-step explanation:

Blue mables: 3

green and red marbles: 8 + 7 = 15

then, the radio blue:(green+red) is:

3 : 15

simplified unit rate is:

3/3 = 1

15/3 = 5

then:

3:15

is equal to:

1:5

Answer:

a 1 : 5

Answer: 6.5

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Explanation:

This is a visual example of the pythagorean theorem. We add the areas of the two squares to get

13+29.25 = 42.25

Then we apply the square root to this to get the value of x, which is the hypotenuse of the right triangle

x = sqrt(42.25) = 6.5

---------

Side note: if you're curious about finding the other lengths of the triangle, apply the square root to those areas. The blue area 29.25 will lead to a side length of approximately sqrt(29.25) = 5.4083269; the red square will follow the same idea.

Answer:

Step-by-step explanation:

area of a square=a²

A=29.25

a=side=√29.25 first square

second square =a=√13

find x(c)

right triangle: a²+b²=c²

(√29.25 )²+(√13)²=c²

29.25+13=c²

c=√(29.25+13)=6.5 unit

Answer:

B

Step-by-step explanation:

B is the correct answer

2+i/5= i=5 +=-

have a nice day

Answer:

[tex]\boxed{\sf B) \ 2-i}[/tex]

Step-by-step explanation:

[tex]\sf \frac{2+i}{5}[/tex]

Reciprocal the fraction.

Switch the denominator with the numerator.

[tex]\sf \frac{5}{2+i }[/tex]

Multiply the numerator and the denominator with the conjugate [tex]\sf 2-i[/tex].

[tex]\sf \frac{5(2-i)}{(2+i)(2-i)}[/tex]

[tex]\sf \frac{10-5i}{(2+i)(2-i)}[/tex]

Apply rule to solve for the denominator:

[tex]\sf (a+bi)(a-bi)=a^2 +b^2[/tex]

[tex]\sf a=2\\b=1[/tex]

[tex]\sf \frac{10-5i}{2^2 +1^2 }[/tex]

[tex]\sf \frac{10-5i}{4+1}[/tex]

[tex]\sf \frac{10-5i}{5}[/tex]

Simplify the fraction.

[tex]\sf \frac{10}{5}-\frac{5i}{5}[/tex]

[tex]\sf 2-i[/tex]

Answer:

Classes studied for, Classes he did not study for Total

Classes Passed, 23 4 27

Classes Failed, 3 2 5

Total, 26, 6 32

Please find attached the two way frequency table formatted on Excel spreadsheet

Step-by-step explanation:

The given information are;

The total number of classes Romain took in high school = 32

The number of classes he studied for but did not pass = 3

The total number of classes Romain passed = 27

The number of classes Romain studied for = 26

Therefore;

The number of classes Romain studied for and passed = 26 - 3 = 23

The total number of classes Romain failed = 32 - 27 = 5

The total number of classes Romain passed but did not study for = 27 - (26 - 3) = 4

The number of classes Romain did not study for and failed = 5 - 3 = 2

The total number of classes Romain did not study for = 4 + 2 = 6

Answer:

17,725/14.

Step-by-step explanation:

Let's say that the blank is represented by x.

Since the question asks what is 16.8% of x, we can set up a proportion where 16.8 out of 100 is equivalent to 212.7 out of x. The 100 represents the "whole" number, which corresponds to x. The 212.7 IS the 16.8 of x.

[tex]\frac{16.8}{100} =\frac{212.7}{x}[/tex]

16.8 * x = 212.7 * 100

16.8x = 21,270

x = 21,270 / 16.8

x = 212,700 / 168

x = 17,725 / 14 = 1,266.071429

To check our work, 1,266.071429 * 0.168 = 212.7.

Hope this helps!

Answer: The value of b= 15.6

Step-by-step explanation:

The given equation: [tex]4\dfrac{1}{3}b+b=6b-10.4[/tex]

To find : Value of b.

Since, we can write [tex]4\dfrac{1}{3}=\dfrac{13}{3}[/tex]

So, the given equation becomes [tex]\dfrac{13}{3}b+b=6b-10.4[/tex]

[tex]\Rightarrow\dfrac{13b+3b}{3}=6b-10.4\Rightarrow\dfrac{16b}{3}=6b-10.4[/tex]

Subtract 6b from both sides , we get

[tex]\Rightarrow\dfrac{16b}{3}=6b-10.4\\\\\Rightarrow\dfrac{16b-18b}{3}=-10.4\\\\\Rightarrow\dfrac{-2b}{3}=-10.4\\\\\Rightarrow b=-10.4\times\dfrac{-3}{2}\\\\\Rightarrow\ b= 15.6[/tex]

hence, the value of b= 15.6

The rectangle they give you is 12 units tall. This is the result of scaling by a factor of 1.5, ie it is 1.5 times taller than what the answer will be. Let the answer rectangle have a height of h. This means h*1.5 = 12, or 1.5h = 12

Divide both sides by 1.5 to find that h = 8. The answer rectangle's height is 8 units.

The width's will be treated in a similar manner. I picked on the height since it's easier to see that the height lines up with 12 (the width seems to be between 2 and 4, but its not clear if its at the midpoint).

Answer:

Copy this onto a piece of graph paper

Step-by-step explanation:

when graphing you want to make sure that the slope is correct and the y-intercept is the same

Answer:

$20, 533.33

Step-by-step explanation:

From the question, we are given the following values

Principal = $20000

Rate = 8% = 0.08

Time( in years) = 120days = 4 months = 4/12 years = 1/3 years

Interest = Principal × Rate × Time

Interest = 20,000 × 0.08× (1/4)

Interest = $533.33

Hence, the proceeds to Aster Corporation are

$20000 + $533.33

= $20,533.33

Answer:

D.

A. x ≤ 1

Step-by-step explanation:

Well for the first question we need to simplify the inequality.

4x + 3 < x - 6

-x to both sides

3x + 3 < -6

-3 to both sides

3x < -9

Divide 3

x < -3

So if x is less than -3 than it goes to the left starting at -3.

So D. is the answer.

So to solve the floowing inequality we simplify, distribute, and combine like terms.

3(2x - 5) + 3 ≤ -2(x + 2)

6x - 15 + 3 ≤ -2x -4

6x -12 ≤ -2x - 4

8x - 12 ≤ -4

+12

8x ≤ 8

8/8

x ≤ 1

Hence the answer is A. x ≤ 1

Answer:

(a) y = 3x + 2; (b) (0,2); (c) y = 3x - 8; (d) (2,-2)

(e) Area of ∆ABC = 30; (f) Area of ABCD = 40

Step-by-step explanation:

(a) Equation of AD

(i) Slope of AB

m₁ = (y₂ - y₁)/(x₂ - x₁) = (6 - 8)/(8 - 2)= -2/6 = -⅓

(ii) Slope of AD

m₂ = 3

(ii) y-intercept

y = 3x + b

8 = 3(2) + b= 6 + b

b = 2

The equation of AD is y = 3x + 2.

(b) Coordinates of D

The coordinates of D are (0,2).

(c) Equation of perpendicular bisector of AB

(i) Mid-points of AB

x = ½(x₂ + x₁) = ½(8 + 2) = ½(14) = 5

y = ½(y₂ + y₁) = ½(6 + 8) = ½(14) = 7

The coordinates of the mid-point are (5,7).

Slope = 3

y = mx + b

7 = 3(5) + b = 15 + b

b = 7 - 15 = -8

The equation of the perpendicular bisector is y = 3x - 8.

(d) Coordinates of C

C is at the intersection of BC and the perpendicular bisector of AD.

y = 3x - 8

3y = 4x - 14

3y = 9x - 24

0 = 5x - 10

5x = 10

x = 2

y = 3(2) - 8 = 6 - 8 = -2

The coordinates of C are (2,-2).

(e) Area of ∆ABC

A = ½bh = ½ × 10 × 6 = 30

(f) Area of ABCD

Area of ∆ACD = ½bh = ½ × 10 × 2 = 10

Area of ABCD = ∆ACD + ∆ABC =10 + 30 = 40

Answer:

False

Step-by-step explanation:

Given

A = [tex]\frac{1}{2}[/tex] bh ( multiply both sides by 2 to clear the fraction )

2A = bh ( divide both sides by b )

[tex]\frac{2A}{b}[/tex] = h

Answer:

x = 30

(30, 0)

Step-by-step explanation:

The x-intercept is when the graph crosses the x-axis when y = 0. In that case, simply plug in 0 for y:

x + 6(0) = 30

x + 0 = 30

x = 30

Answer: (30,0)

Step-by-step explanation:

x-intercept can be found in the form x = my + b, where b is the x-intercept. Thus, simply turn x+6y=30 into x-6y+30, to find that the x-intercept is (30,0)

Hope it helps <3

Answer: [tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Step-by-step explanation:

When you subtract b/2a from both sides, you end up with the Quadratic Formula.

Answer:

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

Step-by-step explanation:

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

Subtract [tex]\frac{b}{2a}[/tex] from both sides.

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

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

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

This is a quadratic formula.

Answer:

HL and SAS

which agrees with the third option listed among your options

Step-by-step explanation:

Notice that you have two triangles (see attached image) which have a common side (marked in blue), sides YW and YZ (marked in green) congruent, and the angle in between also congruent.

Therefore we have two postulates than can be applied to prove that the triangles YWX and YXZ are congruent:

HL postulate : "congruent hypotenuse and a corresponding congruent leg " that corresponds to hypotenuses YW and YZ, and congruent leg which is the common segment YX.

and:

SAS postulate: "two sides and the included angle" which corresponds to sides YW, YX, and angle WYX on one triangle, and sides YX, YZ, and angle XYZ in the other triangle

Answer:

49453757

Step-by-step explanation:

Answer:

49453757

Step-by-step explanation:

Dont forget to rate and thanks!

Answer:

11

Step-by-step explanation:

6.7 / .6

Multiply top and bottom by 10

67/6

66/6 = 11 so this is close to 11

the answer i believe is C which is 11

Step by step just divide man shouldnt be hard

Answer:

[tex] g(x) =\sqrt{x-4}[/tex]

[tex] h(x) =2x-8[/tex]

And we want to find:

[tex] g o h(x)[/tex]

Replacing we got:

[tex] go h(x)= \sqrt{2x-8 -4}= \sqrt{2x-12}[/tex]

And the restriction for this case would be:

[tex] 2x-12 \geq 0[/tex]

[tex] 2x \geq 12[/tex]

[tex] x \geq 6[/tex]

Step-by-step explanation:

Assumign that we have the following two functions:

[tex] g(x) =\sqrt{x-4}[/tex]

[tex] h(x) =2x-8[/tex]

And we want to find:

[tex] g o h(x)[/tex]

Replacing we got:

[tex] go h(x)= \sqrt{2x-8 -4}= \sqrt{2x-12}[/tex]

And the restriction for this case would be:

[tex] 2x-12 \geq 0[/tex]

[tex] 2x \geq 12[/tex]

[tex] x \geq 6[/tex]

Answer:

You have to shade 6 pieces.

Step-by-step explanation:

Hope it helps!

Answer: 0.0046

Step-by-step explanation:

First, let's calculate the total number of outcomes that you can see from a pair of dice.

Each dice has 6 options, so the total number of combinations is:

6*6 = 36.

Now, the combinations that are equal to 3 are:

3 and 1

1 and 3

2 combinations.

So the probability is equal to the quotient between the number of combinations that are equal to 3, and the total number of combinations:

P = 2/36 = 0.055

Now, the combinations that are equal to 10 are:

5 and 5

4 and 6

6 and 4.

3 combinations.

Then the probability is:

P = 3/36 = 0.0833

Now, the probability of both events happening is equal to the product of the probabilities for each event, so the total probability is equal to:

P = ( 0.0833)*( 0.055) = 0.0046

Answer:

Hey there!

To solve this problem, you want to divide 22 by 3, which is about 7.33 feet.

We can check this by seeing 7.33 times 3=22

Hope this helps :)

I'm assuming your teacher wants you to distribute. If so, then you multiply the outer term 8 by each term inside (3a and 5). After that you add.

8 times 3a = 24a

8 times 5 = 40

So 8(3a+5) becomes 24a+40

We do not combine 24a and 40 as they are not like terms. So we leave 24a+40 as it is.

Step-by-step explanation:

-2x + 3 – (5 – 6x)

=-2x + 3 - 5 + 6x

= 4x - 2

Answer:

4x - 2

Step-by-step explanation:

We have to combine the like terms which are -2x and 6x. We will get 4x. Next, we have to subtract 3 - 5 and we get -2. This brings us to the conclusion of 4x - 2.

Answer:

5/216

Step-by-step explanation:

There are 5 possibilities that Annie will roll a 6 out of 36 possible outcomes and there 6 possible outcomes of Jose rolling doubles out of 36 if you multiply these possibilities 5/36 x 6/36 you get 5/216. Sorry if wrong that's what I put for my test.

Answer: Choice A) [tex]y \ge 2x-2[/tex]

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

Explanation:

The boundary line is y = 2x-2. This line goes through (0,-2) and (2,2). Use the slope formula to find the slope to be m = 2, and use the y intercept b = -2 to help form the equation.

Since the boundary line is solid, we will have "or equal to" as part of the inequality sign. This indicates points on the boundary are part of the solution set. Furthermore, we will have a greater than sign because the shaded region is above the boundary. Therefore, we change the equal sign to a "greater than or equal to" sign, going from y = 2x-2 to [tex]y \ge 2x-2[/tex]

If we simply did [tex]y > 2x-2[/tex] without the "or equal to" portion, then the boundary line would be dotted or dashed to tell the reader "points on the boundary are not part of the solution set".

cos (x - π/3) = cos (π/2)

Then we need x - π/3 = π/2

Solving the equation:

x - π/3 = π/2

x = π/2 + π/3

x = 5π/6

Answer:

158.73 yd

Step-by-step explanation:

A picture of the situation is needed, investigating I could find a related one, in the same way the important thing is the solution, the data can be exchanged. I attach the drawing.

Let use the formula of the law of cosine:

c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos C, to solve the problem

Let the third side be c, we replace:

c ^ 2 = 375 ^ 2 + 240 ^ 2 - 2 * 375 * 240 * cos 16 °

c ^ 2 = 198225 - 173027.10

c ^ 2 = 25197.9

c = 158.73

So the distance is 158.73 yd

Answer: the right answer is 195.4

Step-by-step explanation: this guy does not what's happening

Answer:

12 / 37 (or:=0.324324324...)

Step-by-step explanation:

Sinθ = opposite / hypotenuse

Hence

sinA = 12 / 37

(=0.324324324...)

Answer:

A = 19

Step-by-step explanation:

sin A = opp/hyp

sin A = 12/37

A = sin- ¹ 12/37

A= 18.92 or 19

Answer:

AC = 20°

Step-by-step explanation:

180° (total angle amount of a triangle) - 70° + 90° (right angle) = ac

AC = 20°

Hope this helps!