What is the equation of a circle with center (-7, -3) and radius 2?

Answer:

  (x, y, z) = (1, 12, 15)

Step-by-step explanation:

As with any set of linear equations, there are many possible routes to a solution. We might simplify the notation a bit by writing the coefficients in an augmented matrix. The columns, left to right, represent the coefficients of x, y, and z, in order, and the constant term.

The row operations we'll use are multiplying a row by a value and adding that result to another row, replacing the other row by the sum.

We can make things a little simpler by writing the second equation first. Then the augmented matrix we're starting with is ...

  [tex]\left[\begin{array}{ccc|c}4&-1&1&7\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]

Adding the second row to the first, we get ...

  [tex]\left[\begin{array}{ccc|c}5&0&0&5\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]

Dividing the first row by 5 gives ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]

Subtracting this from the second row, and again from the third row, we are left with ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&-3&2&-6\end{array}\right][/tex]

Multiplying the second row by 3 and adding that to the third row, we get ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&0&-1&-15\end{array}\right][/tex]

Subtracting the third row from the second gives ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&-1&-15\end{array}\right][/tex]

Finally, multiplying the last row by -1, we have the solution:

  [tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&1&15\end{array}\right][/tex]

This matrix corresponds to the equations ...

_____

The purpose of our choice of row operations is to make the diagonal elements 1 and the off-diagonal elements 0. That is how we end up with the final equations shown.

As we said, there are many ways to go about this. In general, one can ...

Answer:15

Step-by-step explanation:9+6=15

Answer: 15

Step-by-step explanation:

9+6

Ans 11ft

Step-by-step explanation:

Sq Area= length * length

Length=√area=√121=11

Answer:

x=8

Step-by-step explanation:

we know that

The diagonals of a parallelogram bisect each other. That means, each diagonal cuts the other into two equal parts.

so

[tex]5x=6x-8[/tex]

Solve for x

[tex]6x-5x=8\\x=8[/tex]

Step-by-step explanation:

We have,

[tex]\log _{a}x[/tex]

To find, the value of [tex]\log _{a}x[/tex] = ?

∴ [tex]\log _{a}x[/tex] , where a, b  and x are positive

a ≠ 1 and b ≠ 1

We know that,

The logarithm identity,

[tex]\log_{p}m=\dfrac{\log_{y}m}{\log_{y}p}[/tex]

∴ [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]

Where, b is the common base of logarithm

∴ The value of [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]

Thus, the required option A) [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex] is correct.

Answer:

Step-by-step explanation:

9

Final answer:

Multiplying the dimensions of a rectangle by 3 increases its area by a factor of 9, which is the square of 3. The area of the rectangle goes from 14 cm^2 to 126 cm^2.

Explanation:

When the dimensions of a rectangle are multiplied by a certain factor, the area of the rectangle is affected by the square of that factor. Initially, the area of a 7-cm by 2-cm rectangle is 14 cm2. When the dimensions are each multiplied by 3, the new dimensions become 21 cm by 6 cm. Therefore, the new area is 21 cm  imes 6 cm = 126 cm2. The area scales in proportion to the square of the linear dimensions. If we compare the new area to the old area, we see that 126 cm2 / 14 cm2 equals 9, meaning the area has increased by a factor of 9, which is 32, since we multiplied the dimensions by 3. This principle applies generally: when a rectangle's dimensions are scaled by a factor, its area is scaled by the square of that factor.

To determine how many ways to paint the buildings, we consider the choices for each building sequentially, considering the constraints. There are either 36 or 24 combinations, depending on the colors chosen for the first and last buildings. A step-by-step count confirms this range of possibilities.

A systematic approach gives us the general formula: 4 choices for the first building × 3 choices for the second building × 3 choices for the third building × (2 or 3) choices for the fourth building, depending on the first color chosen. This results in a total of 36 or 24 possible combinations, depending on the first and last color's relationship. A careful count avoiding the restrictions on the colors confirms this.

Answer: 9%

Step-by-step explanation:

You can just divide 200 in half which gives you 100. And divide 18 in half which gives you 9. 9/100, and since 100 is the percent’s denominator (if percent were viewed in fraction), it would be 9.

Answer:

see explanation

Step-by-step explanation:

Using the Cosine rule

a² = b² + c² - 2abcosA ← Rearranging for cosA gives

cosA = [tex]\frac{b^2+c^2-a^2}{2ab}[/tex]

(a)

let a = 10, b = 7, c = 8 and A = α, then

cosα = [tex]\frac{7^2+8^2-10^2}{2(7)(8)}[/tex] = [tex]\frac{49+64-100}{112}[/tex] = [tex]\frac{13}{112}[/tex], thus

α = [tex]cos^{-1}[/tex]( [tex]\frac{13}{112}[/tex] ) ≈ 83° ( to the nearest degree )

(b)

let the angle opposite side 7 be x

Using the Sine rule

[tex]\frac{10}{sin83}[/tex] = [tex]\frac{7}{sinx}[/tex] ( cross- multiply )

10sinx = 7sin83 ( divide both sides by 10 )

sinx = [tex]\frac{7sin83}{10}[/tex] , thus

x = [tex]sin^{-1}[/tex] ( [tex]\frac{7sin83}{10}[/tex] ) = 44°

The third angle can be found using the sum of angles in a triangle

third angle = 180° - (83 + 44)° = 180° - 127° = 53°

The 3 angles are 83°, 44°, 53°

So, the given statement is false.

Step-by-step explanation:

Given , Mr. Flores has 100 pictures in a photo album. Of these picture , 20 show his friends , 50 show his family and 30 show his pet dachshund.

Probability formula:

[tex]P(A)=\frac{\textrm{Number of favorable outcomes to A}}{\textrm {Total number of out comes}}[/tex]

Total number of out come = 100

Number of photo of his family = 50

Therefore the probability of Mr. Flores selecting a picture of his family is

[tex]=\frac{50}{100}[/tex] [tex]=\frac{1}{2}[/tex] [tex]= \frac{5}{10}[/tex]

The probability of Mr. Flores selecting a picture of his friend is [tex]=\frac{20}{100}[/tex] [tex]=\frac{1}{5} = \frac{2}{10}[/tex]

The probability of Mr. Flores selecting a picture of his pet dachshund [tex]=\frac{30}{100}[/tex] [tex]=\frac{3}{10}[/tex]

Since [tex]\frac{5}{10}>\frac{3}{10}>\frac{2}{10}[/tex]

Therefore the probability of Mr. Flores randomly selecting a picture of his family is greater than the probability of randomly selecting a picture Frou -Frou.

So, the given statement is false.

Answer:

-1.5

Step-by-step explanation:

The value of x is -3/2 or -1.5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

4x²+12x+9 =0

Now, the solution for the expression is

4x²+12x+9 =0

4x²+6x+ 6x +9 =0

2x( 2x + 3)+ 3 (2x+ 3)= 0

(2x+ 3) (2x+ 3) = 0

x= -3/2, x= -3/2

Hence, the value of x is -3/2 or -1.5.

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Answer:

f(x).f(x) [tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]

Step-by-step explanation:

Given f(x) is a linear function.

Let f(x)= ax+c

given,f(-2)=0

∴a(-2)+c=0

⇔-2a +c=0

⇔c=2a ..........(1)

Again f(4) = -5

∴a.4+c=-5

⇔4a+c=5

⇔4a +2a=5    [∵ c= 2a]

⇔6a=5

⇔[tex]a=\frac{5}{6}[/tex]

Putting the value of a in equation (1)

[tex]c=2 \times \frac{5}{6}[/tex]

[tex]\Leftrightarrow c= \frac{5}{3}[/tex]

Therefore f(x)  [tex]=\frac{5}{6} x+\frac{5}{3}[/tex]

f(x).f(x)

[tex]=(\frac{5}{6} x+\frac{5}{3})(\frac{5}{6} x+\frac{5}{3})[/tex]

[tex]=(\frac{5}{6} x+\frac{5}{3})^2[/tex]

[tex]=\frac{25}{36} x^2 +\frac{25}{9}x+\frac{25}{9}[/tex]

Answer:

The answer is true.

I took the quiz! :)

Answer:

n>12

Step-by-step explanation:

n/6>2

n>2*6

n>12

The Graph of the inequality is shown below.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have the inequality,

n÷6>2

Multiply both side by 6 we get

(n ÷ 6 ) 6 > 2 x 6

n > 12.

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Answer:1. 3 inches

Step-by-step explanation:1 inch =2ft 2x3=6

To find the length of the garden in Micah's model, we need to set up a proportion using the given scale. The scale for the figure on the left to the figure on the right can be determined by comparing corresponding lengths.

1.) To find the length of the garden in Micah's model, we need to use the scale 1 inch: 2 feet. Since the garden has a length of 6 feet, we can set up a proportion:

1 inch / 2 feet = x inches / 6 feet

Cross-multiplying, we get 2 feet * x inches = 1 inch * 6 feet

Simplifying, we have 2x inches = 6 inches, so x = 3 inches.

Therefore, the length of the garden in Micah's model is 3 inches.

2.) The scale of the figure on the left to the figure on the right can be determined by comparing the corresponding lengths. If we measure the lengths of a certain side of the left figure and the right figure, we can find the scale. For example, if the length of a side of the left figure is 2 cm, and the corresponding side on the right figure is 4 cm, the scale is 1 cm: 2 cm.

Therefore, the scale is 1 cm: 2 cm.

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The circumference of the circle is 23.89 ft

The circumference of a circle is the distance around it and it can be calculated by the formula:

Circumference = π x diameter

The circumference is therefore:

= 22/7 x 7.6

= 167.2 / 7

= 23.89 feet

The option given that is closest to 23.89 ft is the right answer.

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Answer: n since that number depends on s, the songs he already had.

Final answer:

The dependent variable in Steve's music player scenario is the total number of songs after buying new songs, represented by T = s + n. As the number of new songs purchased (n) changes, the total (T) changes, demonstrating a linear relationship between n and T.

Explanation:

In the scenario where Steve had s songs on his music player and he bought n new songs, the dependent variable is the total number of songs Steve has after the purchase. To define this in terms of a mathematical relationship, we can express the total number of songs (T) as an equation:

T = s + n

Here, s is the original number of songs, and n is the number of new songs purchased. The dependent variable is T (the total number of songs), which depends on the value of n (the number of songs bought). If we change the independent variable n, the total number of songs T will also change.

To illustrate this with a dataset, suppose Steve originally had 5 songs (s = 5). If he buys:

The relationship between the number of new songs purchased (n) and the total number of songs (T) is linear, as T increases by the same amount that n does.

Answer:

it is B. -11 and 47

Step-by-step explanation:

you have to take away 47 and 11 and it equals 36.

would be a 25% decrease or .25

Answer:

Divide it all by 3, then put it outside the parentheses.

3(2x+5)

Step-by-step explanation:

The requried factors of the given expression are given as 3[x + 5].

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

here,
The distributive property is given as,
a[b + c] = ab + bc

Now,
the given expression performing the distributive property in a way given as,
ab + bc = a[b + c]

Given expression,
= 6x + 15
= 3 × 2x + 3 × 5
= 3 [2x + 5]

Thus, the requried factors of the given expression are given as 3[x + 5].

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Answer:

Option 3

Step-by-step explanation:

y is less than the y values on the red line and greater than the y values on the blue line.

Equation of the red line:

y-intercept is clearly 3

using (0,3) & (-2,2)

Slope = (y2-y1)/(x2-x1)

= (3-2)/(0-(-2)) = 1/2

y = (1/2)x + 3

Equation of the blue line:

y-intercept is clearly -2

Using (0,-2) & (1,1)

Slope = (1-(-2))/(1-0) = 3/1 = 3

y = 3x - 2

y < (1/2)x + 3 & y > 3x - 2

The graph shows the solution for the following inequalities; C. y ≥ 3x - 2 and y ≤ -1/2(x) + 3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

[tex]y - y_1 = m(x - x_1)[/tex]

Where:

First of all, we would determine the slope for the red line by using these points (2, 4) and (0, 3);

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope (m) = (3 - 4)/(0 - 2)

Slope (m) = 1/2

At point (0, 3) and a slope of 1/2, an inequality for this line can be calculated by using the point-slope form as follows:

y - 3= 1/2(x - 0)  

y = 1/2(x) + 3

y ≤ 1/2(x) + 3 (since the solid line is shaded below).

At point (0, -2) and a slope of 3, an inequality for this line can be calculated by using the point-slope form as follows:

y + 2= 1/2(x - 0)  

y = 3(x) - 2

y ≥ 3x - 2 (since the solid line is shaded below).

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15/k

15/3

5

Hope this helps! ;)

Answer:

5

Step-by-step explanation:

Since k=3 you would put 3 under 15. Now the equation would look like this: 15/3 instead of 15/k. Then you would divide 15 by 3 which is 5.

Answer:

ideas and conflict and maybe elements depending on the story

Answer:

Notebook = $2.75

Pencil = $1.25

Markers = $ 0.50

Step-by-step explanation:

Stan:

n + 3p + 2m = 7.5

Jan:

2n  + 6p + 5m = 15.50

Fran:

n + 2p + 2m = 6.25

Stan - Fran:

p = 1.25

Lets replace p with 1.25

n + 3(1.25)  + 2m  = 7.5

2n + 6(1.25) + 5m = 15.50

n + 2(1.25) + 2m = 6.25

Simplify

n + 3.75 + 2m = 7.5

2n + 7.5  + 5m = 15.50

n + 2.50 + 2m = 6.25

n + 2m = 3.75     stan

2n + 5m = 8       jan

n + 2m = 3.75     fran

stan = fran

jan - 2(stan)

m = 0.5

n = 2.75

Answer:

The volume of the actual house is 1,324.94 cubic meters

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Height of the scale model = 53 cm

Height of the actual house = 624 cm

Scale of the model = 642/53 = 11.77

Volume of the scale model = 0.8125 cubic meters

2. What is the volume of the house?

For answering the question we have to find the width and the length of the model, then use the scale of the model for calculating the volume of the actual house, this way:

Volume of the scale model = 0.8125 cubic meters

Area of the scale model = Volume of the model/Height of the model

Area of the scale model = 0.8125/0.53

Area of the scale model = 1.533 square meters

Area of the scale model = Length * Width

Area of the scale model = 1.533 * 1

Now, we can calculate, the measurements of the house to calculate its volume:

Height of the actual house = 6.24 meters

Length of the actual house = 1.533 * 11.77 = 18.04 meters

Width of the actual house = 1 * 11.77 = 11.77 meters

Volume of the actual house = 6.24 * 18.04 * 11.77

Volume of the actual house = 1,324.94 cubic meters

Answer:

The volume of the plastic pipe  is 141 cubic centimetre

Step-by-step explanation:

Given:

The Length of the plastic water pipe = 12 cm

The inner Diameter of the  plastic water pipe = 12 cm

The outer Diameter of the  plastic water pipe = 15 cm

To Find:

the volume of the plastic pipe not the hollow interior to the nearest hundredth = ?

Solution:

The volume of the plastic water pipe can be found by using the volume of the cylinder formula

The Volume of the cylinder  = [tex]\pi r^2 h[/tex]

Where

r is the radius

h is the height

Radius r  [tex]= \frac{diameter}{2} = \frac{15}{2} = 7.5 cm[/tex]

On substituting the values

The Volume of the cylinder  

= [tex]\pi (7.5) (6)[/tex]

= [tex]45 \pi[/tex]

=  141.37   cubic centimetre

= 141  cubic centimetre