does the point (3,-1) lie on the circle (x+1)^2 + (y-1)^2=16

Answer:

858 sq. units

Step-by-step explanation:

Area of a rhombus is found by A=ab/2 where a and b are the diagonals of the rhombus and A is the area.

AC is a and BD is b

A= (AC.BD)/2

=(66×26)/2

=858 Sq units

The area of the rhombus is therefore 858 sq. units.

Answer:

Angelo is 66 Brandon is 26 Carl is 31

Step-by-step explanation:

Variables a=Angelo b=Brandon c=Carl

Equation (1/3)(a+b+c) = 41

The age of each man is Carl (31), Angelo (66), and Brandon (26).

Part A: Let's use the variable x to represent Carl's age.

Part B: Angelo's age is 4 years more than twice Carl's age, so we can write his age as 2x + 4. Brandon is 5 years younger than Carl, so his age is x - 5.

Part C: The average of the three ages is given as 41, so we can write the equation (x + 2x + 4 + x - 5) / 3 = 41.

Part D: To find the age of each man, we solve the equation:
(x + 2x + 4 + x - 5) = 3 * 41
4x - 1 = 123
4x = 124
x = 31

Carl's age is 31, Angelo's age is 2(31) + 4 = 66, and Brandon's age is 31 - 5 = 26.

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Answer:

D

Step-by-step explanation:

The Rational root theorem states that the possible roots ( zeros) of a polynomial are of the form

( plus or minus ) factors of the constant term divided by the factors of the leading coefficient.

For x³ - 3x² + 27x - 8

The factors of constant term (- 8) are ± 1, 2, 4, 8

The coefficient of the leading term x³ is 1

Hence possible zeros are

± ([tex]\frac{1,2,4,8}{1}[/tex]) = ± 1, ± 2, ± 4, ± 8 → D

Answer:  The required value of y is 22.

Step-by-step explanation:  We are given the following function of a and b :

[tex]y=3ab+2b^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to find the value of y when a = 1 and b = 2.

To find the required value of y, we need to substitute the values of a and b in equation (i).

From (i), we get

[tex]y=3\times1\times2+2\times2^3=6+16=22.[/tex]

Thus, the required value of y is 22.

The solution to the given algebraic Expression is; y = 22

We are given the algebraic expression;

y = 3ab + 2b³

We want to find y when a = 1 and b = 2.

Plugging in the relevant values gives;

y = 3(1*2) + 2(2³)

y = 6 + 16

y = 22

In conclusion, the solution to the expression is y = 22

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Answer:

The total surface area of a rectangular prism is 310 inches

Step-by-step explanation:

The surface area of rectangular prism can be found using formula

Surface Area = 2(lw+hl+hw)

Where l = length

h = height

w = width

We are given:

l = 4

h = 5

w = 15

Putting values in the formula:

Surface Area = 2(lw+hl+hw)

Surface Area = 2((4*15)+(5*4)+(5*15))

Surface Area = 2(60+20+75)

Surface Area = 2(155)

Surface Area = 310 inches

So, The total surface area of a rectangular prism is 310 inches

Answer:

The total surface area of a rectangular prism is 310 inches

Step-by-step explanation:

The surface area of rectangular prism can be found using formula

Surface Area = 2(lw+hl+hw)

Where l = length

h = height

w = width

We are given:

l = 4

h = 5

w = 15

Putting values in the formula:

Surface Area = 2(lw+hl+hw)

Surface Area = 2((4*15)+(5*4)+(5*15))

Surface Area = 2(60+20+75)

Surface Area = 2(155)

Surface Area = 310 inches

So, The total surface area of a rectangular prism is 310 inches

Answer:

The distance between 2 points is √97 or 9.84

Step-by-step explanation:

The distance between two points can be found using distance formula:

[tex]d(x_{1},x_{2})=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

x₁ = -4, y₁ = -2 x₂ =5 and y₂ = 2

Putting values:

[tex]d(x_{1},x_{2})=\sqrt{(5-(-4))^2+(2-(-2))^2}\\d(x_{1},x_{2})=\sqrt{(5+4)^2+(2+2)^2}\\d(x_{1},x_{2})=\sqrt{(9)^2+(4)^2} \\d(x_{1},x_{2})=\sqrt{81+16}\\d(x_{1},x_{2})=\sqrt{97}[/tex]

So, the distance between 2 points is √97 or 9.84

Answer:

  =sqrt(97)

Step-by-step explanation:

The distance between the two points is found by

d = sqrt(( x2-x1)^2 + (y2-y1)^2)

   = sqrt( ( 5--4)^2 + (2--2)^2)

   = sqrt( ( 5+4)^2 + (2+2)^2)

   = sqrt( ( 9)^2 + (4)^2)

  = sqrt( 81 + 16)

  =sqrt(97)

Answer:

x = 8

Step-by-step explanation:

Since m and n are parallel lines, then

6x - 2 = 46 ← alternate angles

Add 2 to both sides

6x = 48 ( divide both sides by 6 )

x = 8

Answer:

x=8

Step-by-step explanation:

The value of the angles are the same due to them being alternate interior angles and opposite angles. This means we can set 6x-2=46. Add 2 to each side to isolate the 6x. This leaves you with 6x=48. Divide by 6 to isolate x. 48/6= 8. X=8. Hope this helps :).

Answer:

2xy is the greatest common factor of the three monomials.

Step-by-step explanation:

There are three monomials such that greatest common factor of first and third monomial is 2xy and greatest common factor of second and third monomial is 2x²y.

As we know greatest common factor means, common prime factors of two numbers or expressions.

Greatest common factors of 1st and second and greatest common factors of 2nd and third monomials have been given.

So, common prime factors of these two greatest common factors will be greatest common factor of all three monomials.

Prime factors of 2xy = (2)(x)(y)

Prime factors of 2x²y = (2)(x)(x)(y)

So common factors are (2)(x)(y) which is the greatest common factors of all three monomials.

ANSWER

[tex] \sum _{n = 1} ^{18} (6n - 15)[/tex]

EXPLANATION

The given series

[tex] - 9 - 3 + 3 + 9 + ... + 81[/tex]

This is an arithmetic series with a common difference of

[tex]d = - 3 - - 9 = 6[/tex]

The first term of the series is:

[tex]a_1 = - 9[/tex]

The general term is given by:

[tex]a_n =a_1 + d(n - 1)[/tex]

[tex]a_n = - 9+ 6(n - 1)[/tex]

[tex]a_n = - 9+ 6n - 6[/tex]

[tex]a_n =6n - 15[/tex]

The last term is 81

We can use this to determine the number of terms in the series.

[tex]81=6n - 15[/tex]

[tex]81 + 15=6n [/tex]

[tex]6n = 96[/tex]

[tex]n = \frac{96}{6} = 16[/tex]

The summation notation is:

[tex] \sum _{n = 1} ^{18} (6n - 15)[/tex]

A diameter is a special type of chord that passes through the center of a circle. It has its endpoints on the circle's circumference, with the center of the circle as its midpoint.

In the field of mathematics, a diameter is indeed a special type of chord. The unique characteristic of a diameter, differentiating it from other chords, is that it must contain the center of the circle - that is the definition finds its completion. As a line segment, a diameter has its endpoints on the circumference of the circle and its middle point is the center of the circle. So, when referring to a diameter, you are essentially talking about the largest chord in a circle that passes through the center.

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Answer:

5y^2−4y−14

Step-by-step explanation:

Equation:2(3y−7)−5y(2−y)

First Distribute:

(2)(3y)+(2)(−7)+5y2+−10y

6y+−14+5y2+−10y

Then Combine Like Terms:

6y+−14+5y2+−10y

(5y2)+(6y+−10y)+(−14)

5y2+−4y+−14

Answer:

5y^2 -4y -14

Step-by-step explanation:

2(3y-7)-5y(2-y)

Distribute

2*3y -2*7  -5y *2 -5y*(-y)

6y -14 -10y +5y^2

Combine like terms and put in decreasing order

5y^2 -4y -14

Answer:

6 3/5 , 3 4/5, 4/5

Step-by-step explanation:

1) -8 2/5 + 9 1/5 =

-42/5 + 46/5 = 4/5

2) 9 2/5 + (-5 3/5) =

47/5 + -28/5 = 19/5 = 3 4/5

3). 2 1/5 + 2 2/5 =

11/5 + 22/5 = 33/5 = 6 3/5

answer is tile 3 then tile 2 then tile 1

6 3/5 , 3 4/5, 4/5

The expression are arranged in the descending order, that is from largest to smallest as follows:

33/5 > 19/5 > 4/5

The expressions are the combination of various constants numbers and mathematical symbols. They form a meaningful context that is in accordance to the mathematical rules and theories.

The expressions are computed as follows:

Given:

-8 2/5 + 9 1/5

Computation:

={(-8*5)+2}/5 + {(-9*5)+1}/5

=-42/5 + 46/5

= 4/5

Given:

9 2/5 + (-5 3/5)

Computation:

={(9*5)+2}/5 + {(-5*5)+3}/5

=47/5 + -28/5

= 19/5

Given:

2 1/5 + 2 2/5

Computation:

={(2*5)+1}/5 + {(2*5)+2}/5

=11/5 + 22/5

= 33/5

Therefore, the expressions will be arranged in the order; largest to smallest: 33/5 > 19/5 > 4/5

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Answer:

5 to 13

Step-by-step explanation:

There are 5 girls in the class

To find the amount of kids in the class you have to add the girls and boys together.

There are 5 girls and 8 boys.

So 8 + 5 = 13

So there are 5 girls out of 13 students.

Answer:

5 to 13

Step-by-step explanation:

The ratio of girls to all the students in the class is 5 to 13.

8 + 5 = 13

5 girls out of 13 students

Answer:

she will have saved a total of $600.00

Step-by-step explanation:

$50.00 x 12=$600.00

Answer:

A) 6x2-2x-10

B) 2m+1n-6

C) 170c-68

Step-by-step explanation:

4x2 + 2x2 = 6x2     5x -7x = -2x     -7 + -3 = -10

8m - 6m = 2m     -2n + 3n = 1n     -4 - 2 = -6

34 x 5c = 170     34 x -2 = -68

Answer:

Step-by-step explanation:

a) (4x2 + 5x - 7) + (2x2 - 7x - 3)

This is an addition question. We have to perform addition

The first step is open the parenthesis/brackets.

4x^2+5x-7 + 2x^2 -7x-3

Arrange the terms according to the exponents:

4x^2+2x^2-7x+5x-7-3

Combine the like terms:

6x^2-2x-10

Thus the answer is 6x^2-2x-10

b)  (8m - 2n - 4) - (6m - 3n + 2)

We have to perform subtraction:

There is a rule in the subtraction that when you open the brackets then the signs of 2nd bracket will be multiplied by the negative sign:

Open the brackets:

8m - 2n - 4 - 6m+3n-2

Arrange the terms:

8m-6m+3n-2n-4-2

Combine the like terms:

2m+n-6

Thus the answer is 2m+n-6

c) (30+4) (5c-2)

This expression shows the operation of multiplication:

Solve the first parenthesis.

(34)(5c-2)

Now multiply 34 by each term of 2nd bracket:

=170c-68

Thus the answer is 170c-68....

Answer:

C

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

(x+1) + (x-3) = 180

2x-2=180

2x=182

x=91

(x+1) = 92

(x+1) and y are equal angles

y = 92

edge 2023

Answer:

Horizontal and it's slope is 0.

Step-by-step explanation:

y=a number is horizontal while x=a number is vertical.

The slope of horizontal lines are 0 because there is no rise.

The slope of vertical lines are undefined because there run is 0.

Slope is equal to rise over run.

y=-8 is horizontal because it represents all the points in the form (x,-8) where x is any real number.

Graph as many points as you want in the form (x,-8), you should see a horizontal line formed.  The slope of y=-8 is 0.

Example of points in the form of (x,-8):

(-10,-8)

(-5,-8)

(-1,-8)

(0,-8)

(1,-8)

(5,-8)

(10,-8)

All of these go down 8 units after going left or right however many.

This is a horizontal line 8 units below the x-axis.

Answer:

Horizontal

0

Step-by-step explanation:

No matter what the x value is, the y value is - 8. Make a small table to see what that means.

x        y

2       -8

0       -8

- 2     -8

See what's happening?

Look at the y intercept. The y value is - 8 when x = 0.  It is also - 8 when x = 2.

Make a rough drawing on a scrap piece of paper. Plot just those 2 points. Roughly. You don't even need a ruler.

What do you see? The line must be going horizontally.

The next question is a little harder. It is not obvious, but you do know that this line either goes horizontally or vertically. So the slope can either be 0 or undefined. There is no third choice.

The general equation is y = mx + b

There is no x in y = - 8

Therefore the slope is 0. That's the only way you could get rid of the x.

Answer:

C

Step-by-step explanation:

Try to plug in the first pair of numbers to eliminate some equations, all but C fail to satisfy the equation. So C is the answer.

Answer:

Step-by-step explanation:

Notice that the table doesn't have an exponential behaviour. Because an exponential function has the point (0,1), because all powers with a null exponent are equal to 1.

Also, notice that the table doesn't show a linear relation, because y-variable has all values positive.

Therefore, the only relation that follows the values of the table is

[tex]y=2.5x^{2}[/tex]

Let's evalue each x-value

[tex]y=2.5(-2)^{2} =2.5(4)=10\\y=2.5(-1)^{2}=2.5(1)=2.5\\ y=2.5(0)^{2}=2.5(0)=0\\y=2.5(1)^{2}=2.5\\y=2.5(2)^{2}=10[/tex]

Therefore, the right answer is C. The given values show a quadratic relation.

A faster way to deduct the quadratic pattern is observing that y-values are symmetric no matter if x-values are positive or negative, that meanst he function is pair, or quadratic.

Answer: 6,050,000

Step-by-step explanation:

5%=0.05

302500/0.05=6,050,000

Answer:

x = 6050000

Step-by-step explanation:

Set up a proportion

5%  = 302500 people

100%  = x

5/100 = 302500

100/100 = x            Cross multiply

5x / 100 = 302500 * 100/100                        Multiply both sides by 100

5x / 100 * 100 = 302500 * 100 / 100 *100    Do the multiplication

5x = 302500 * 100                                         Combine the right.

5x = 30250000                                              Divide by 5

5x/5 = 30250000/5

x = 6050000

1/100 of a million is the 5. It is already rounded to what it should be. So the answer is what we have.

Answer:

[tex]\frac{17}{7}[/tex]

Step-by-step explanation:

51 males to 21 females is equivalent to the following:

51 to 21

51:21

51/21

[tex]\frac{51}{21}[/tex]

We could simplify this ratio. Both 51 and 21 have factors of 3 so I'm going to divide both parts of our ratio be 3.

So 51 divided by 3 is 17 and 21 divided by 3 is 7.

The simplified version of the answers above:

17 to 7

17:7

17/7

[tex]\frac{17}{7}[/tex]

The ratio of males to females is written in the form of fraction as 17/7.

When a number is divisible by another number, then it can be written in the

form of p:q, this is called Ratio.

The number of total males = 51

The total females = 21

The ratio of males: females = 51 : 21

As fraction, in terms of p/q it can be written as 51/21

It can be simplified as

17/ 7

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[tex]\huge{\boxed{y+5=2(x-4)}}[/tex]

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope of the line and [tex](x_1, y_1)[/tex] is a known point on the line.

Substitute the values. [tex]y-(-5)=2(x-4)[/tex]

Simplify the negative subtraction. [tex]\boxed{y+5=2(x-4)}[/tex]

Note: This equation is in point-slope form. If you require or prefer another form, please let me know in a comment below.

Answer:

y = 2x - 13

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2, hence

y = 2x + c ← is the partial equation

To find c substitute (4, - 5) into the partial equation

- 5 = 8 + c ⇒ c = - 5 - 8 = - 13

y = 2x - 13 ← equation of line

Answer:

$26.45

Step-by-step explanation:

If Chris lost $5.29 playing poker in one week, in five weeks he would lose $26.45.

$5.29 lost per week.

5 weeks.

$5.29 x 5 = $26.45.

The net loss of Chris after five weeks will be $26.45.

Average value per week: -$5.29
Net loss after five weeks: -$5.29 x 5 = -$26.45

Both chords are the same distance from the center of the circle ( the 12 inch lines are the same length).

This means that both chords are the same length. The bottom chord has a dimension of 22.5.

B id half the top chord so would be equal to half of 22.5

b = 22.5 / 2 = 11.25

Answer:

Option C Geometric space

Step-by-step explanation:

Which of the following is three-dimensional and infinitely large?

Verify each case

case A) A plane is two-dimensional and infinitely large.

case B) A line is infinitely large but is only one-dimensional

case C) Geometric space is three-dimensional and infinitely large

case D) A solid is three-dimensional, but not infinite

therefore

The answer is Geometric space

Answer:

Geometric Space

Step-by-step explanation:

Which of the following is three-dimensional and infinitely large?

Verify each case

case A) A plane is two-dimensional and infinitely large.

case B) A line is infinitely large but is only one-dimensional

case C) Geometric space is three-dimensional and infinitely large

case D) A solid is three-dimensional, but not infinite

therefore

The answer is Geometric space

Answer:

2d=m

Step-by-step explanation:

2xd=m

The variable expression that represents the money Robin earned this week, if 'd' is the money she earned last week, is '2d'. This is because Robin earned twice as much this week as she did the previous week.

In the context of this question, Robin earned twice as much money this week as she did last week. Because last week's earnings are represented by the variable, the expression to represent this week's earning becomes 2d. The number 2 is multiplied by d because Robin earned double this week of what she earned last week. Therefore, 2d accurately represents Robin's earnings for this week, if d is the amount she earned last week.

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Answer:

the length is 40 ft

Step-by-step explanation:

perimeter is length+length+height+height.

If the height is 19 ft then the first equation would be 118-(19+19)=80

Then you would do 80/2= 40

The length is 40 ft.

The length of the billboard with a perimeter of 118 feet and a height of 19 feet is 40 feet.

To find the length of the billboard when the perimeter is 118 feet and the height is 19 feet, you can use the formula for the perimeter of a rectangle: Perimeter = 2(length + height). Given that the height is 19 feet, you set up the equation 118 = 2(l + 19) and solve for the length (l).

First, divide both sides of the equation by 2:

59 = l + 19

Next, subtract 19 from both sides:

l = 59 - 19

l = 40

Answer:

[tex]\large\boxed{C.\ \left|-\dfrac{1}{4}-\dfrac{3}{4}\right|}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a distance between x and y on a number line:}\\\\d=|b-a|=|a-b|\\\\\text{We have}\ a=-\dfrac{1}{4}\ \text{and}\ b=\dfrac{3}{4}.\ \text{The distance:}\\\\d=\left|-\dfrac{1}{4}-\dfrac{3}{4}\right|=\left|\dfrac{3}{4}-\left(-\dfrac{1}{4}\right)\right|[/tex]

Answer:

The correct answer is C none of the above

Step-by-step explanation:

Answer:

7. (4x - 3xy^2 - 2y) / (3x^2y + 2x).

Step-by-step explanation:

Implicit differentiation:

7.  3x^2 y^2 = 4x^2 - 4xy

6x * y^2  +  3x^2 * 2y y' =  8x - 4(x y' + y)

6xy^2 + 6x^2y y' = 8x - 4x y' - 4y

6x^2y y'  + 4x y' = 8x - 6xy^2 - 4y

y' =   (8x - 6xy^2- 4y) / (6x^2y + 4x)

y' =  2(4x - 3xy^2- 2y) / 2(3x^2y + 2x)

= (4x - 3xy^2 - 2y) / (3x^2y + 2x).

Numbers 8 and 9 are done in the same way.

We use the Chain, Product  and Quotient rules where applicable.

Answer: False

Step-by-step explanation: A net is when a 3 dimensional shape is unwrapped. For example, a cube’s net is 6 squares when unwrapped.

Answer:

2

Step-by-step explanation:

Varies directly means we multiply to the constant, where as inversely means we divide the constant.

So we have

"y varies directly with the square of x and inversely with z".

This means x^2 will be on top and z will be on bottom.

Like this:

[tex]y=k\frac{x^2}{z}[/tex]

We are given x=9,z=27, and y=6.  This will allow us to find k.

k is constant no matter what (x,y,z) we have.

[tex]6=k\frac{9^2}{27}[/tex]

[tex]6=k\frac{81}{27}[/tex]

[tex]6=k(3)[/tex]

Divide both sides by 3:

[tex]2=k[/tex]

So the constant of variation is 2.

Answer:

The constant of variation is 2.

Step-by-step explanation:

If y is directly influenced by x², it means that the function of y will be multiplied with x². with y being inversely influenced by z, it means that the function will be divided by z. The entire function can be written as being multiplied by an unknown factor, a:

[tex]y=a\frac{x^{2} }{z}[/tex]

Replacing the known values of x, y and z, the unknown factor, a can be calculated:

[tex]6=a*\frac{9^{2}}{27}\\6=a*\frac{81}{27}\\6=a*3\\a=2[/tex]

The constant of variation is 2.