If the simple interest on ​$3,000 for 8 years is ​$1,200​, then what is the interest​ rate?

The correct answer is the inverse matrix: [ 1 -3 2]

                                                                      [ 2 -5 3]

                                                                      [-1 3 -2]

To find the inverse matrix that can be used to solve the given system of equations, we need to represent the system in matrix form as AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants.

The given system of equations can be written as:

[1 -1 -1] [x] [ 4]

[-1 2 3] * [y] = [-2]

[ 1 1 4] [z] [10]

To find the inverse matrix, we'll set up the augmented matrix [A | I], where I represents the identity matrix:

[1 -1 -1 | 1 0 0]

[-1 2 3 | 0 1 0]

[1 1 4 | 0 0 1]

Using Gaussian elimination, we'll perform row operations to transform the left side into the identity matrix, while applying the same operations to the right side. The resulting matrix on the right side will be the inverse matrix.

After performing the row operations, the augmented matrix becomes:

[1 0 0 | 1 -3 2]

[0 1 0 | 2 -5 3]

[0 0 1 | -1 3 -2]

Therefore, the inverse matrix is:

[ 1 -3 2]

[ 2 -5 3]

[-1 3 -2]

Hence, the correct answer is the inverse matrix:

[ 1 -3 2]

[ 2 -5 3]

[-1 3 -2]

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Answer:

A quadrilateral has 4 sides, 4 angles and 4 vertices.

Answer:

80,000

Step-by-step explanation:

20,000 x 2 = 40,000

40,000 x 2 = 80,000

(I'm pretty sure it's right if not let me know.)

Answer:

x=number1 and y=number2

product of the two numbers is 14 which translates to

xy=14

either x or y are 3.5 times big as the other one

so 3.5x=y

substituting in xy=14

x(3.5x)=14

[tex]3.5x^2=14\\x^2 =\frac{14}{3.5}=4[/tex]

then x must be equal to 2 or -2

x+y=

by substituting

x+3.5x=

if x =2 then 2+7=9 or if x=-2 then -2-7=-9

Answer:

x = -1, y = 1

Step-by-step explanation:

x + 2y = 1

Subtract 2y from both sides

x + 2y - 2y = 1 - 2y (simplify) -> x= 1 - 2y

----

-x + y = 2

Subtract y from both sides

-x + y - y + 2 - y (simplify) -> -x = 2 - y

Divide both sides by -1

[tex]\frac{-x}{-1}[/tex] = [tex]\frac{2}{-1}[/tex] - [tex]\frac{y}{-1}[/tex] (simplify) -> x = -2 + y

We are given with a function y =2/(2x) . So , if we cancel the 2 from both numerator and denominator we are left with y = 1/x . Now , here we need to find the domain , bur let's Recall that Domain is the set of all values for which the given function is defined .Now , here , if we put x = 0 , then y will be not defined , but as for domain we need only the set of values for which the function is defined , so domain willn't include 0 , and for all real numbers except 0 , the given function is defined . So Our domain is [tex]{\boxed{\bf{(-\infty,0)\cup (0,\infty)}}}[/tex] and as this interval contains all real numbers except 0 , so domain can be further written as [tex]{\boxed{\mathbb{R}-\bf \{0\}}}[/tex] . Now , Range is the set of all output values of the function when we put the values of domain as input . So , now here when we put values of domain as input like let's put x = -1 , -2 , -3 , -4 , 1 , 2 , 3 ,..... we will get y = -1 , -1/2 , -1/3 , -1/4 , 1 , 1/2 , 1/3 and so on , now , the input will give output as 0 , iff input is Infinite , but as input can never be infinite, so output will never comes to 0 as the intervals of real numbers is [tex]{\bf{(-\infty,\infty)}}[/tex] it's an open interval so Infinity and -ve infinity is not concluded in the above interval because whenever we think a number as large as much we can think , their exists infinitely large numbers greater than it , assume you're thinking 10¹⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰ as the largest number you can think , but if we add 1 in that i.e 10¹⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰ + 1 comes to be greater than it , Hence , we don't include Infinity and -ve Infinity in the interval which represents the set of all real numbers. So now the range is same as the Domain i.e [tex]{\boxed{\bf{(-\infty,0)\cup (0,\infty)}}}[/tex] or [tex]{\boxed{\mathbb{R}-\bf \{0\}}}[/tex]

Hence , we concluded that :

Answer:

Keep track of every 1, 2, 3, or 4. These represent the number of days the temperature is above 80 degrees F. repeat this 20 times.

Answer:

SO this equation is y={4-3x}

This is an absolute value so the domain is all real numbers

For this equation, we are shifting left 3 and up 4

The vertex is (1,1) Turning point

Points:
(-1,7)

(0,4)

(1,1)

(2,2)

(3,5)

(4,8)

It will make a v shape

(if u were too do this on the ti-84, hit y=, then hit 2nd catalog and hit abs, plug in the equation; then hit 2nd graph to get the table. You will need to find the vertex by finding the number at which they are not the same)

I hope this helps!

Step-by-step explanation:

Answer:

The midpoint formula

Step-by-step explanation:

(x,y)=(x1+x2)/2,(y1+y2)/2 ..(Take any two points that are opposite to each other in this case first and third points)

(x,y)=(1+2)/2,(-4+9)/2

(x,y)=3/2,5/2

As the diagonals of a square are equal, their intersection point will be the midpoint.

Answer:

Step-by-step explanation:

35

Answer:

3080

Step-by-step explanation:

Let us set up some variables:

Now let us set up some equations based on the facts:

Equations:

   L = 4W     -- equation 1

   2L + 2W = 80 -- equation 2

   Plug the value of L from equation 1 into equation 2

    2(4W) + 2W = 80

     8W + 2W = 80

        10W = 80

           W = 8 -- equation 3

   Plug the value of W from equation 3 into equation 1:

    L = 4W = 4 * 8 = 32

Therefore the length is 32 and the width is 8.

Hope that helps!

Answer:

3/4

Step-by-step explanation:

Given:

⇒ 1/4 are boys

To Solve/Find:

⇒ What fraction are girls

Solve:

well, We know that 4/4 = 1 Whole

Thus, We have to Subtract to find what fraction are girls

→ 4/4 - 1/4 = 3/4          

Hence, We can conclude that 3/4 are girls

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a square has four equal sides, and we know the perimeter or namely the sum of all those four sides is 1/7 yard, so

s = length of one side.

[tex]s + s + s + s = \cfrac{1}{7}\implies 4s=\cfrac{1}{7}\implies s=\cfrac{~~ \frac{1}{7}~~}{4}\implies s=\cfrac{~~ \frac{1}{7}~~}{\frac{4}{1}} \\\\\\ s=\cfrac{1}{7}\cdot \cfrac{1}{4}\implies s=\cfrac{1}{28}~yd\qquad \stackrel{\textit{how many feet is that?}}{s = \cfrac{1~yd}{28}\cdot \cfrac{3~ft}{yd}}\implies s=\cfrac{3}{28}~ft[/tex]

Answer:

x>

4

9

Step-by-step explanation:

|3x−4|<6x

Let's find the critical points of the inequality.

|3x−4|=6x

We know either3x−4=6xor3x−4=−6x

3x−4=6x(Possibility 1)

3x−4−6x=6x−6x(Subtract 6x from both sides)

−3x−4=0

−3x−4+4=0+4(Add 4 to both sides)

−3x=4

−3x

−3

=

4

−3

(Divide both sides by -3)

x=

−4

3

3x−4=−6x(Possibility 2)

3x−4+6x=−6x+6x(Add 6x to both sides)

9x−4=0

9x−4+4=0+4(Add 4 to both sides)

9x=4

9x

9

=

4

9

(Divide both sides by 9)

x=

4

9

Check possible critical points.

x=

−4

3

(Doesn't work in original equation)

x=

4

9

(Works in original equation)

Critical points:

x=

4

9

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<

4

9

(Doesn't work in original inequality)

x>

4

9

(Works in original inequality)

Answer:

x>

4

9

Answer:

300 [tex]m^{2}[/tex]

Step-by-step explanation:

The spread has a rate of 25 [tex]m^{2}[/tex] per every 1/6 hour.  That can be expressed as   25 [tex]m^{2}[/tex] per every 1/6 hour:

25 [tex]m^{2}[/tex]/ (1/6 hour), or

150 [tex]m^{2}[/tex]/hour

After 2 hours, the spread would be (150 [tex]m^{2}[/tex]/hour)*(2 hours) = 300 [tex]m^{2}[/tex]

Answer: pi (3.14)

Step-by-step explanation:

The circumference formula is pi*radius squared. Radius is half the diameter so radius is 1.

1 squared is still 1.

The answer is 3.14 or pi

Answer:A

Step-by-step explanation:

Because as you look around we notice line A. We can see that when we look at it there is symmetric. The line divide both of the parts equal

If the function is translated 4.5 units to the left to createe the graph of function g(x), hence the resuting function will be g(x) = (x + 4.5)^2

Given the function expressed as
f(x) = x^2

If the function is translated 4.5 units to the left to createe the graph of function g(x), hence the resuting function will be:

g(x) = (x + 4.5)^2

Note that translation to the left means addition of the factor

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Answer:39 hours

Step-by-step explanation:First, let's find the rate of money per hour:$554.30 / 23 hour= $24.1 / 1 hourDaniel earns $24.10 every hour he works.To find the hours that Daniel has to work to earn $939.90, divide it by 24.10:$939.90 / 24.10= 39Now, we can check:$24.10 * 39= $939.90

Answer:

[tex]12x^5-9x^2-6x[/tex]

Step-by-step explanation:

[tex]\left(4x^5+8x^5+3x\right)-\left(3x^2+6x^2+9x\right)[/tex]

[tex]4x^5+8x^5+3x-\left(3x^2+6x^2+9x\right)[/tex]

[tex](4x^5+8x^5):12x^5[/tex] ( Combine like terms)

[tex]12x^5+3x-\left(3x^2+6x^2+9x\right)[/tex] (Apply the distributive law)

[tex]12x^5+3x-9x^2-9x[/tex]

[tex](3x-9x):-6x[/tex]  ( Combine like terms)

[tex]12x^5-9x^2-6x[/tex]

~

Answer:

[tex]\sf 9x^2 - 12x^5 +6x[/tex]

solving steps:

[tex]\hookrightarrow \sf (3x^2 + 6x^2 + 9x )- (4x^5 + 8x^5 + 3x)[/tex]

remove parenthesis

[tex]\hookrightarrow \sf 3x^2 + 6x^2 + 9x - 4x^5 - 8x^5 - 3x[/tex]

group variables

[tex]\hookrightarrow \sf 3x^2 + 6x^2 - 4x^5 - 8x^5 - 3x+ 9x[/tex]

simplify

[tex]\hookrightarrow \sf 9x^2 - 12x^5 +6x[/tex]

Answer

It might be 88%

Step-by-step explanation:

Answer:

53 people

Step-by-step explanation:

[tex]\frac{2}{5}[/tex]  × 120 = = 48
48 + 5 = 53 people
____

You've made your grade level high school, lower it to Grade 4. Thank you!

Answer:

m∠A = 79°

m∠B = 112°

Step-by-step explanation:

A+C=180

A=180-C=180-101=79

B+D=180

B=180-D=180-68=112

Answer:

600 + 40 + 8 + .2 + .09 + .007 = 648.297

Answer:

[tex]55.7 feet[/tex]

Step-by-step explanation:

[tex]h=\sin{\left(23\right)\times135}[/tex]

[tex]\sin{23}\approx0.39[/tex]

[tex]h=0.39\times135=52.65\left(feet\right)\[/tex]

[tex]H=h+3[/tex]

[tex]=52.65+3[/tex]

[tex]=55.65\left(feet\right)[/tex]

[tex]55.65\ feet\approx55.7\ feet[/tex]

I hope this helps you

:)