Simplify the expression.
8-17 / 12-(-3)

The equation of the circle with radius 10 and center located at (1 , -3) is (x - 1)^2 + (y + 3)^2 = 100.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (1 , -3)

r = 10

(x - 1)^2 + (y - -3)^2 = 10^2

(x - 1)^2 + (y + 3)^2 = 100

Learn more about equation of a circle here: https://brainly.com/question/14150470

#SPJ4

The expression that represents the sum of the number of blue bikes and the 9 red bikes is B + 9. Option D

Algebraic expressions are expressions that consists of terms, variables, coefficients, and constants.

They are also made up of arithmetic operations such as division, addition, multiplication, subtraction, etc

From the information given, we have that;

B is the number of blue bikes

And there are 9 red bikes

The expression for the sum of blue and red bikes is written as;

B + 9

Thus, the expression that represents the sum of the number of blue bikes and the 9 red bikes is B + 9. Option D

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

By combining the like terms, the simplified form of the expression -5a-4a+b is -9a+b

Given,

The algebraic expression = -5a-4a+b

Combine the like terms

-5a-4a+b=(-5-4)a+b

=-9a+b

simplified form is -9a+b

Hence, By combining the like terms, the simplified form of the expression -5a-4a+b is -9a+b

Learn more about algebraic expression here

brainly.com/question/953809

#SPJ4

The simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12)  is (b + 12)/12.

According to the given question.

We have an expression

(1/3)(b + 12) - (1/4)(b + 12)

As we know that, simplification of an expression means to write an equivalent expression which contains no similar terms.

Therefore, the simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12)  is given by

(1/3)(b + 12) - (1/4)(b + 12)

= (b + 12)[(1/3) -(1/4)]             (taking (b + 12) common from each expression)

= (b + 12)[ (4-3)/12 ]

= (b + 12)[1/12]

= (b + 12)/12

Hence,the simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12)  is (b + 12)/12.

Find out more information about expression here:

https://brainly.com/question/25201049

#SPJ4

By elimination, the solution of the system of equations, 2r + s = 3 and 4r - s = 9, is (r , s) = (2 , -1).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in r and s, a variable should be eliminated by adding/subtracting the two equations.

Adding the two equations will eliminate the variable s.

2r + s = 3     (equation 1)

4r  - s = 9     (equation 2)

6r       = 12

r = 2

Substitute the value of r to any of the two equations and solve for s.

2r + s = 3     (equation 1)

2(2) + s = 3

s = 3 - 4

s = -1

Hence, the solution of the system of equations is (r , s) = (2 , -1).

Learn more about solving systems of equations by elimination here: https://brainly.com/question/28405823

#SPJ4

The first five terms of the sequence (geometric) are: 2, 6, 18, 54, 162.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Now, given formula: [tex]a_n=3a_{n-1}[/tex], a₁ = 2.

For n = 2, a₂ = 3 (a₁) = 3 (2) = 6

For n = 3, a₃ = 3 (a₂) = 3 (6) = 18

For n = 4, a₄ = 3 (a₃) = 3 (18) = 54

For n = 5, a₅ = 3 (a₄) = 3 (54) = 162.

Hence, The first five terms of the sequence (geometric) are: 2, 6, 18, 54, 162.

To learn more about geometric progression, refer to the link: https://brainly.com/question/15978376

#SPJ4

-3 < x < 3

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

8!

Step-by-step explanation:

8!=8*7*6*5*4*3*2*1

The midpoint is at  ( -8 , 9/2 , 4)

In the given statement is

To find the midpoint of the line segment joining the pair of points

W(-12,8,10) and Z(-4,1,-2)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} , \frac{z_{1} +z_{2} }{2}[/tex] )

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points W(-12,8,10) and Z(-4,1,-2)

Solving for the midpoint , we have,

m = ([tex]\frac{-12+(-4)}{2} , \frac{8+1}{2} ,\frac{10+(-2)}{2}[/tex])

m =( [tex](\frac{-16}{2} ) ,\frac{9}{2} , \frac{8}{2}[/tex])

m = ( -8 , 9/2 , 4)

Therefore, the midpoint is at  ( -8 , 9/2 , 4)

Learn more about Midpoint at :

https://brainly.com/question/28563066

#SPJ4

The function y= |x+1| is increasing for the domain -1 < x < ∞ and decreasing for the domain -∞ < x < -1.

As given in the question, for what domain intervals is the function y= |x+1| increasing and/or decreasing is to be determined.

Here,
Given function,
f(x) = |x + 1|
Given functions absolute function,
Whose domain is all real numbers from -∞ to ∞.
And when we plot the graph of the function, we see that its decreasing from -∞ to -1 and increases from -1 to ∞.

Thus, The function y= |x+1| is increasing for the domain -1 < x < ∞ and decreasing for the domain -∞ < x < -1.

Learn more about inequality here:

brainly.com/question/14098842

#SPJ1

The correct option is B. 1/11.

The probability of choosing 2 white marbles is 1/11.

A combination is an arithmetical technique for determining the number of different arrangements in a set of items in which the sequence of the selection is irrelevant.

You can choose the objects in any order in combinations. Permutations and combinations are often confused.

Now, as pet the stated question.

The total number of red marble in the bag are 5.

The total number of blue marble in the bag are 2.

The total number of white marble in the bag are 4.

The total number of yellow marble in the bag are 1.

The combination for selecting the 2 white marbles out of 4 are;

⁴C₂ = 4!/(4-2)!2!

⁴C₂ = 6

Ans, the combination for selecting the 2 marbles out of total 12 are;

¹²C₂ = 12!/(12-2)!2!

¹²C₂ = 66

Thus, the combination for selecting the 2 white marbles out of total 12 is;

= ⁴C₂ / ¹²C₂

= 6/66

= 1/11

Therefore, the the probability of outcome of the 2 white marbles out of total 12 marbles is 1/11.

To know more about the combination, here

https://brainly.com/question/26852614

#SPJ4

Using linear functions, it is found that until $77,000 in sales, Job B pays more, and for more than than, Job A pays more.

A linear function is modeled according to the following rule:

y = mx + b

In which:

For this problem, the earnings are modeled by linear functions, in which:

Hence the earnings for sales of x are given as follows:

Due to the higher intercept, until they are equal, A(x) is greater, and after that B(x) is greater, hence we have to find when they are equal as follows:

A(x) = B(x)

45050 + 0.065x = 46975 + 0.045x

0.025x = 1925ntil $77,000 in sales, Job B pays more, and for more than than, Job A pays more.

x = 1925/0.025

x = 77000.

Hence:

Until $77,000 in sales, Job B pays more, and for more than than, Job A pays more.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

1. 4

2. [tex]5\frac{9}{11}[/tex]

3. [tex]7\frac{6}{16} = 7\frac{3}{8}[/tex]

4. [tex]1\frac{8}{7} = 2\frac{1}{7}[/tex]

Answer:

-7x³+ 4x²+x+9

Step-by-step explanation:

The figure have 4 pairs of parallel sides after the 90 degree rotation.

What is 90° rotation of an object ?

For every point in the plane (x, y), a 90° rotation can be described by the transformation P(x, y) → P'(-y, x). We can achieve this same transformation by performing two reflections.

It is given that figure has 4 sets parallel sides is graphed on a grid and is then rotated 90 degrees clockwise.

The figures with 4 sets parallel sides are : square, rectangle, rhombus  

Let us consider square as our figured graphed in grid :

Now, Transformation involves moving a shape from one position to another, 90 degrees clockwise transformation that carries the square onto itself that is after rotation there will be 4 pairs of parallel sides.

Therefore, the figure have 4 pairs of parallel sides after the 90 degree rotation.

Read more about transformations at:

brainly.com/question/11709244

#SPJ1

The expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.

Option (A) is correct.

It is required to choose the expressions.

Index laws are the rules for simplifying expressions involving powers of the same base number. Index (indices) is the exponent which is raised to a number.

Given:

It follows from the task content that the equivalent expression as in the task content can be determined by the laws of Indices.

Now, according to laws of indices;

[tex]3^{2x} =( 3^{2}) ^{x}[/tex]

Thus, we now have;

[tex]= (3^{2} )^{x} )/3^{3} \\= (9^{x} )/3^{3} \\= (9^{x} )/27[/tex]

Therefore, the expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.

Learn more details about laws of indices  here:

https://brainly.com/question/27432311

#SPJ1

The vakues based on the function f(x) = -x² + x + 6 will be:

12

0

12

When x = -2, the value will be:

f(x) = -x² + x + 6

= -2² + 2 + 6

= 4 + 2 + 6

= 12

When x = 0

f(x) = -x² + x + 6

= 0² + 0 + 6

= 0

When x = 2

f(x) = -x² + x + 6

= 2² + 2 + 6

= 12

Learn more about functions on:

brainly.com/question/25638609

#SPJ1

Answer:

2000.18

Step-by-step explanation:

Volume=V=(3.14)r^2h=3.14·7^2·13=2000.18.

Hope this helps.

Answer:

RM350

Step-by-step explanation:

calculate 30% of RM500

= [tex]\frac{30}{100}[/tex] × 500 = 0.3 × 500 = 150

RM150 is left in the bank

and 500 - 150 = RM350 is the money he has with him

Answer:

The answer is 10n-8

Step-by-step explanation:

Hope this helps!!

Answer:

  (x, y, z) = (1, 1, 0)

Step-by-step explanation:

You want to solve the given system of equations by elimination.

There are a couple of nice choices for variables to eliminate.

The last equation has an x-coefficient that is the opposite of the x-coefficient in the other two equations. Adding that equation to those will eliminate the x-variable:

  (-2x +2y +3z) +(2x +3y +3z) = (0) +(5)   ⇒   5y +6z = 5 . . . . add eqns 1, 3

  (-2x -y +z) +(2x +3y +3z) = (-3) +(5)   ⇒   2y +4z = 2 . . . . add eqns 2, 3

The second of these equations can be divided by 2 to give ...

  y +2z = 1

Three times this equation can be subtracted from the first of the reduced equations to eliminate z:

  (5y +6z) -3(y +2z) = (5) -3(1)   ⇒   2y = 2

  y = 1 . . . . divide by 2

Now, we can substitute this value into the previous equation to find the other variables.

  y +2z = 1 = 1 +2z   ⇒   0 = 2z   ⇒   z = 0

  -2x -y +z = -3 = -2x -(1) +(0)   ⇒   -2 = -2x   ⇒   x = 1

The solution is (x, y, z) = (1, 1, 0).

__

Additional comment

The attachment shows a calculator solution to the system of equations by reducing the augmented matrix to "reduced row-echelon form." In general, that is a process of elimination. Each equation ends up with one variable having a coefficient of 1, so we have x = 1, y = 1, z = 0.

You could also start by eliminating the y-variables. Adding twice the second equation to the first will do that, as will adding 3 times the second equation to the third. The result of these operations is two equations in x and z.

Answer:

x=82.7

Step-by-step explanation:

3x+6-6=248

3x=248

x=82.7

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: 3x + 6 - 6 = 248[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x = 248[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \dfrac{248}{3} [/tex]

The approximate value will be :

[tex]\qquad \sf  \dashrightarrow \: x \approx82.67[/tex]

Answer:

after 5 hours: 14.5 inches

after t hours: 2 + 2.5t

Step-by-step explanation:

2 + 2.5t

2 + 2.5(5) = 2 + 12.5 = 14.5

The value of x is 1.5 units

Given that a quadrilateral RSTU is circumscribed about [tex]\odot J[/tex].

Also given that the perimeter of the quadrilateral is 18 units.

Then the the sides ST, TU, UV and RS are tangents to the circle at points A, B, C and D respectively.

Then we have,

 AT = BT

 BU = UC

 RC = RD

 SD = SA

Given that AT = UC = x and RC = RD = SD = SA = 3 units

Therefore, BT = BU = x

We need to find 'x'.

Perimeter = 18 units

i.e., ST + TU + UV + RS = 18 units

⇒   AT + BT + BU + UC + RC + RD + SD + SA = 18 units

⇒ x + x + x + x + 3 + 3 + 3 + 3 = 18

⇒ 4x + 12 = 18

⇒4x = 6

⇒ x = 6/4 = 3/2

⇒ x = 1.5 units

Learn more about circumscribed quadrilaterals at https://brainly.com/question/15988303

#SPJ4

Using the graph, the value of r(-2) is 8

From the question, we are to determine the value of r(-2)

The given graph is the graph of the function r(x), and we have that

y = r(x)

To determine the value of r(-2), we will trace from the point where x = -2 on the graph to the parabola (the curve of a quadratic function), and then read the corresponding value on the y-axis by tracing this point to the y-axis.

On the graph, if we trace from the point x = -2, to the curve, we will find out that the value of y is 8.

Thus,

From y = r(x), we can write that

8 = r(-2)

∴ r(-2) = 8

hence, the value of r(-2) is 8

Learn more on Graph of functions here: https://brainly.com/question/14212952

#SPJ1

According to the given statement the thermal conductivity is :

0.0003(W/(m* c))

Thermal conductivity is defined as the rate at which heat is transported by conduction through a unit cross-section surface of a material that whenever a temperature gradient exists perpendicular to the area.

The material's thermal conductivity is defined as the ratio of the rate of heat flow per unit area to the negative of the temperature gradient: dQdt=KAdTdx.

0.03 watts (W) per meter (m) per degree Celsius as a result, thermal conductivity is:

= 0.03(W/(m* c))

while we want the heat conductivity of the batting in w/cm•c

The only distinction is between metre and cm.

As a result, we must convert meter's to centimeters.

we are aware

1m =100cm

As a result, thermal conductivity may be written as.

= 0.03(W/(m* c))

we can replace 1m as 100cm.

= 0.03(W/(100m* c))

No simplifying the equation we get:

=  0.0003(W/(m* c))

According to the given statement the thermal conductivity is :

0.0003(W/(m* c)).

To know more about  thermal conductivity visit:

https://brainly.com/question/7643131

#SPJ9

Answer:

X = 3 and -7

Step-by-step explanation:

area of a triangle is = ½ ×base × height

Answer:

B= 67

Step-by-step explanation:

Being vertically opposite angle