What method of matrixes would be used for this question? ( Inverse Matrices, Cramer's Rule, Gaussian Elimination, and Gauss-Jordan Elimination)

John had $24,500 to invest. He divided the money into three different accounts. At the end of the first year he had made a total of $1,300 in interest between the three accounts. If the first account earned 4% interest on its original amount for the year, the second account earned 5.5% interest on its original amount for the year, and the third account earned 6% interest on its original amount for the year. Also, the amount of money in the first account was 4 times the amount in the second account. How much had he originally placed in each account?

Answers

Answer 1

Answer:

The method of matrixes that would be used for this question is Gaussian Elimination.

Step-by-step explanation:

Gaussian Elimination is a method of solving linear equations by transforming them into upper triangular form. In this case, we want to solve for the original amount of money placed in each account, which can be represented by variables x, y, and z. We can set up the equations as follows:

4x + 5.5y + 6z = 1,300

x + y + z = 24,500

4x = y

We can then use Gaussian Elimination to solve for x, y, and z.


Related Questions

The amounts spent by 12 customers at a Burger King's restaurant were as follows:
11.01
10.50 5.70 14.67 9.50 12.54
8.90 13.56 11.23 6.80 3.00 10.55
Find the mean amount spent by these customers.

Answers

Answer:  9.83

Explanation:

The first step is to add up all the values given:

11.01 + 10.50 + 5.70 + 14.67 + 9.50 + 12.54 + 8.90 + 13.56 + 11.23 + 6.80 + 3.00 + 10.55 = 117.96

Then we divide this sum over n = 12 since this is the sample size given (i.e. the number of customers)

117.96/n = 117.96/12 = 9.83

The answer is $9.83.
I hope this helps!

PLEASEEE HELP!!!!!!!

Answers

It’s the number 4. Trust me

What is the value of the sum?
Drag and drop the answer into the box to match the sum with its value.
-7/9+2/3

Answers

The answer is -1/9. If you have any questions let me know

PLS ANSWER BOTH OF THESE QUESTIONS

WILL MARK BRAINLIEST

EXPLANATION IS NOT NEEDED

Answers

Here are the awnsers

1. D ⅔

2.C 60%

The number of registered users logged in to the new social media app varies with time. The table shows the average number of users logged in, y, on any given weekday, x hours after 6:00 a.m.

Answers

Answer:

1,483

Step-by-step explanation:

The equation that models this set of data is y=17.2x^2-226.3x+2184.5. Since x=0 represents 6:00 a.m, x=5 represents 11:00 a.m. Substitute 5 for x in the model, and solve for y.

Based on the number of registered users who log into the social media app during weekdays and weekends, the following are true:

1,483 users are logged in after 11 am. During the week, post at 8pm.During the weekends, post at 12 pm.

When should the marketing department post the update?

The given model for the users in the week is:

y = 17.2x² - 226.3x + 2,184.5

x is 5 because 11 am is 5 hours after 6 am:
= 17.2(5)² - 226.3(5) + 2,184.5

= 1,483 users

The company should post when there are the most people online and on weekdays that's 14 hours after 6 am which is:
=14 + 6

= 20:00

= 8 pm

On weekends this is 6 hours after 6 am:

= 6 + 6

= 12 pm

Missing information from question:

Model for calculating weekday users y = 17.2x² - 226.3x + 2,184.5.

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Write the equation for the quadratic function in the graph

Answers

Answer:

[tex] {x}^{2} - 16 = 0 \: is \: the \: equation[/tex]

Step-by-step explanation:

[tex]x = - 4 \\ or \: x = 4[/tex]

[tex](x + 4) = 0 \: or \: (x - 4) = 0 \\ (x + 4)(x - 4) = 0 \\ open \: the \: bracket[/tex]

[tex]x(x - 4) + 4(x - 4) = 0[/tex]

[tex] {x}^{2} - 4x + 4x - 16 = 0 \\ {x}^{2} - 16 = 0[/tex]

Simplify the expression.

Answers

Answer:

4x

Step-by-step explanation:

[tex]\frac{500x^{4} }{(5x)^{3} }[/tex] = [tex]\frac{500x^{4} }{125x^{3} }[/tex] = [tex]4x[/tex]

Which number completes the system of linear
inequalities represented by the graph?
y ≥2x - 2 and x + 4y

Answers

The number that completes the System of Linear Inequalities represented by the Graph y >= 2x – 2 and x + 4y > =  is -12. Hence, x + 4y [tex]\geq[/tex] -12

What is a System of Linear Inequalities?

A collection of linear inequalities in the same variables is referred to as a system of linear inequalities. Any ordered pair that fulfills all of the inequalities is the solution.

What is the calculation to prove the above assertion?

Recall that:

The linear equation with slope m and intercept c is given as follows.

y = mx + c

The formula for slope of line with points  and  can be expressed as

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

Given that

The orange line intersects y-axis at (0,-2), therefore the y-intercept is -2.

The orange line intersect the points that are (1,0)  and (0, -2).

The slope of the line can be obtained as follows:

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

= -2/-1

= 2

The slope of the line is m = 2.

Therefore, the orange line is y [tex]\geq[/tex] 2x -2

The blue line intersects y-axis at (0,-3), therefore the y-intercept is -3.

The blue line intersect the points that are (-4, -2) and  (0, -3)

The slope of the line can be obtained as follows.

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

= (-3 + 2)/4

= - (1/4)

The slope of the line is:
m = -(1/4)

The inequalities is x + 4y [tex]\geq[/tex] b passes through the point (0, -3)

(0) + 4 (-3) = b

-12 =b

Thus, -12 in is the number that completes the system. Hence, x + 4y [tex]\geq[/tex] -12

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which number best represents the slope of the graphed line -5,-1/5,1/5,5

Answers

The slope of the line will be – 1/5. Then the correct option is B.

What is the equation of line?

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

Take two point from the graph.

(0, 2) and (1, –3)

Then the slope will be

m = (2 – (–3)) / (0 – 1)

m = 5 / (–1)

m = – 1/5

Then the correct option is B.

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The function V(t) = 38000 (0.94)^t represents the value (in dollars) of a car "t" years after its purchase. Use this function to complete the statements below.

The value of this car is decreasing at a rate of ______
Describe how an exponential function model helped you answer this question.
*will give brainliest!

Answers

The value of this car is decreasing at a rate of 6% per year.

The function V(t) = 38000 (0.94)^t represents the value (in dollars) of a car "t" years after its purchase

What is rate of change?

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,

V(t) = 38000 (0.94)^t
Cleary, above function is an exponential function
while putting certain values in equation we have certain outcomes.
for,
V(1) = 35720;    V(2) =33576.8;      V(3) = 31562.192

Now, the rate of change is given by = [V(2)-V(1)/ V(1)] x 100
= [(33576.8-35720)/35720]*100
= 6%

now V(2) x 6% = V(3)
33576.8 x 6% = 31562.192 = V(3)

Thus, The required rate of decreasing care price is 6%.

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Pls help
Geometry
What is the volume?

Answers

Answer:

199.5 ft^3

Step-by-step explanation:

to find your answer you simply multiply all the measurements together

19 * 1.5 * 7 is your equation

19 * 1.5 * 7 = 199.5

it is 199.5 ft^3

Scarlett is designing a package for a candy her company makes. She has cut several cardboard equilateral triangles, squares, rectangles, and regular pentagons to try out her ideas for the package. Which 3-D figure and combination of shapes can Scarlett use?

Equilateral triangle prism with two equilateral triangles and three rectangles
Pentagonal prism with one pentagon and five rectangles
Rectangular prism with four rectangles
Square prism with four squares

Answers

The 3-D figure and combination of shapes that Scarlett can use is A. Equilateral triangle prism with two equilateral triangles and three rectangles

What is a 3-D Figure?

This refers to the solid figure or shape that has defined dimensions of length, width, and height.

Therefore, based on the fact that a 3-D figure is made up of six equal squares, option A is the best answer because it contains a total of six squares.

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someone please help omg

Answers

The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

This question is incomplete, the complete question is;

Which equation is correct for ∆FON?

Answers:

A.) cos F= 9/18

B.) sin F 9/18

C.) sin F=18/9

D.) cos F=18/9

Which equation is correct for ΔFON?

From the diagram, we have a right angle triangle.

Hypotenuse = 18Perpendicular height or opposite to ∠F = 9Equation of angle F = ?

Note that; sinθ = Opposite / Hypotenuse

Therefore, for angle F

sin F = Opposite / Hypotenuse

sin F = 9/18

The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

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Which polygon has an interior angle sum of 1260°?

Answers

Answer:

Step-by-step explanation:

Solution

Interesting question.

The formula for the sum of the interior angles is

(n - 2)*180 = x

In this case, x = 1260

(n - 2)*180 = 1260                            Divide both sides by 180

(n -2 )* 180/180 = 1260/180

( n - 2) = 7                                         Remove the brackets

n - 2 = 7                                            Add 2 to both sides

n - 2 + 2 = 7 +2                                 The 2s on the left cancel

n = 9

Answer: Nonagon

The polygon with an interior angle sum of 1260° is the nonagon as per the concept of interior angles.

To find the sum of the interior angles of a polygon, we can use the formula:

Sum of interior angles = (n - 2) × 180°

where "n" is the number of sides of the polygon.

To achieve an interior angle sum of 1260°, we would need to consider a polygon with fewer sides.

For example, a nonagon (9 sides) would have an interior angle sum of 1260°:

Sum of interior angles = (9 - 2) × 180°

Sum of interior angles = 7 × 180°

Sum of interior angles = 1260°

So, a nonagon (a polygon with nine sides) has an interior angle sum of 1260°.

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the polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and a root of multiplicity 1 at x=-4. the y-intercept . is y=-11.2
find a formula for P(x)=

Answers

The formula of P(x) = -0.7 (x-2)²(x+4)

What is a root of a polynomial ?

A root of a polynomial is defined as the point or value at which the overall value of the polynomial = 0

It is given that

for a polynomial of degree 3

root x=2, multiplicity 2:  (x-2)²

root x= - 4, multiplicity 1:  (x+4)                  ³ ²

P(x) = a(x-2)²(x+4)

here a is constant

y-intercept =  -11.2

P(0) = -11.2

a(0-2)²(0+4) = -11.2

a * 4 * 4  = -11.2

16a = -11.2

a = -11.2/(16)

a= -11.2/16

P(x) = -(11.2/16)(x-2)²(x+4)

P(x) = -0.7 (x-2)²(x+4)

Therefore the formula of P(x) = -0.7 (x-2)²(x+4)

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Completely simplify the rational expression 6-(x-1)/(x+1)

Answers

Answer:

-x + 7 / x + 1

Step-by-step explanation:

6 -(x - 1)/ x + 1

Apply distributive law: -(x - 1) = -x + 1

= 6 - x + 1 / x +1

Group like terms:

= -x + 7/ x + 1

Answer:  its 5x+7/x+1

Step-by-step explanation:

What is 0.6% as a fraction in simplest form

Answers

Answer:

3/500

Step-by-step explanation:

.6%   = .006   =    6/1000  = 3/500

You start your working career when you are 24 years oldEach month, you deposit $144 into a pension planYou continue making deposits into the plan un you are 68 years oldWhat is the balance, in dollars, when the plan earns 6%, compounded monthly? Round your answer to the nearest cent

Answers

Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.

What is the monthly payment formula?

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

A is the monthly payment.P is the total amount.r is the interest rate.n is the number of payments.

The parameters for this problem are given as follows:

A = 144, r = 0.06, n = (68 - 24) x 12 = 528.

Then:

r/12 = 0.06/12 = 0.005.

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}[/tex]

[tex]P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}[/tex]

P = $26,731.23.

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help please! thanks so much!

Answers

Answer: D

Step-by-step explanation:

Answer: Choice D

Open hole at -3 with shading to the left.

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

Explanation:

The inequality [tex]-3 > \text{x}[/tex] is the same as [tex]\text{x} < -3[/tex]

When swapping both sides, the inequality sign flips as well.

Since we're looking for numbers smaller than -3, this includes things like -4, -5, -6, -7, and so on. Therefore we shade to the left of -3 on the number line.

We have an open hole at -3 to indicate it's not included as part of the solution set. We would include it if there as an "or equal to" as part of the inequality sign.

Directions: Name the coefficient (s) in the following expressions: 1. 12s + 4t 2. 46rs + 10x 3. 12q + 14x 4. 10x + 10y 5. 17rs + 32x 6. 5x + 7y - 12z 7. 36ab + 70m 8. 3r + 19a + 10m 9. 7k + 16m 10. 8r + 5s 11. 9h + 120m 12. 12k + m 13. 7g + 15h + w 14. 4c - 8d + 12f 15. 6t + 17r - 35j

Answers

The coefficient are as follows:

What is Algebra?

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

1. 12s + 4t

Variables: s, t

Coefficient: 12, 4

2. 46rs + 10x

Variables: r, s, x

Coefficient: 46, 10

3. 12q + 14x

Variables: q, x

Coefficient: 12, 14

4. 10x + 10y

Variables: x, y

Coefficient: 10, 10

5. 17rs + 32x

Variables: r, s, x

Coefficient: 17, 32

6. 5x + 7y - 12z

Variables: x, y, z

Coefficient: 5, 7, -12

7. 36ab + 70m

Variables: a, b, m

Coefficient: 36, 70

8. 3r + 19a + 10m

Variables: r, a, m

Coefficient: 3, 19, 10

9. 7k + 16m

Variables: k, m

Coefficient: 7, 16

10. 8r + 5s

Variables: r, s

Coefficient: 8, 5

11. 9h + 120m

Variables: h, m

Coefficient: 9, 120

12. 12k + m

Variables: k, m

Coefficient: 12, 1

13. 7g + 15h + w

Variables: g, h, w

Coefficient: 7, 15 , 1

14. 4c - 8d + 12f

Variables: c, d, f

Coefficient: 4, -8, 12

15. 6t + 17r - 35j

Variables: t, r, j

Coefficient: 6, 17, -35

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barbara works at a law office as an entry level lawyer. She spends 2/5 of her time at the law office doing paperwork. How many hours does she have to work to spend 10 hours doing paperwork.

Answers

Answer:

25 hours.

Step-by-step explanation:

Let the hours worked be x

2/5x = 10

2x = 50

x = 25

She has to work 25 hours to spend 10 hours doing paperwork.

When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. results. What is the value of ?

–1
–negative StartFraction one-half EndFraction
0
StartFraction one-half EndFraction.

Answers

The value of x in the equation 1/2x = -1/2x when 4 is subtracted from both sides is 0(not defined)

Subtraction of fraction

Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction

1/2x = -1/2x

Subtract 4 from both sides

1/2x - 4 = -1/2x - 4

(x-8) / 2 = (-x-8) / 2

(x - 8) / 2 = (-x-8) / 2

cross product

2(x - 8) = 2(-x - 8)

2x - 16 = -2x - 16

2x + 2x = -16 + 16

4x = 0

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Answer:c

is the answer

Step-by-step explanation:

Given: Triangle ABC, mmBC=24 cm, line segment AL- < bisector
Find: AL

AL= __cm
Please answer in detail ASAP thank you so much it would help a lot <3

Answers

The value of line AL is 21. 51cm

How to determine the length

Let's start by finding line AB using

Sin α = opposite/ hypotenuse

Sin 90 = x/ 24

1 = x/24

Then, cross multiply

We have line AB = 24cm

Now, let's find line AC

Sin angle B = line AC/24

Let's find angle B

We know that angle A + angle B + angle C = 180

But angle B = 2 Angle A

x + 2x + 90 = 180

3x + 90 = 180

3x = 180-90

x = 30°

Then Angle B = 2 × x = 2 × 30 = 60°

Sin 60 = x/ 24

0. 8660 = x/24

Cross multiply

x = 24 × 0. 8660

x = 20. 78cm

From the diagram, we have the angle of A  in the given triangle to be divide into two by the bisector, angle A = 15°

To find line AL, let's use

Cos α = adjacent/ line AL

Cos 15 = 20. 78/ line AL

Line AL = 20. 78/ cos 15

Line AL = 20. 78 / 0. 9659

Line AL = 21. 51 cm

Thus, the value of line AL is 21. 51cm

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Round
8724 to the nearest whole number ​

Answers

Round

8724 to the nearest whole number is 8720

points X, Y, and Z are colinear.
X
What is the slope of YZ in simplest form?

Answers

Based on the calculations, the slope of line YZ in simplest form is equal to 2.

How to determine the slope of YZ?

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Since points X, Y, and Z are collinear, we can deduce that the line passes through line Z at 6 units form the origin and 3 units for Y from the origin.

Substituting the parameters into the formula, we have;

[tex]Slope, m = \frac{6\;-\;0}{3\;-\;0}[/tex]

Slope, m = 6/3

Slope, m = 2.

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please help me asap...

Answers

Answer:

( x-7) ( x-5)

Step-by-step explanation:

x^2 -12x + 35

To factor this problem, we want to know that two numbers multiply to 35 and add to -12

-7 * -5 = 35

-7 + -5 = -12

( x-7) ( x-5)

Answer:

The answer is (x-7)( x-5)

Step-by-step explanation:

We need to find two numbers that add up to −12 and those same two numbers should have a product of 35

Here the common factors are -7 and -5 because when added they give -12 and when multiplied they give 35.

Therefore we write the answer as (x-7)(x-5)

Select the three equations that pass through the points (–4, –16) and (5, 2):

y + 4 = 2(x – 16)

y – 2 = 2(x – 5)

y = 2x – 8

y + 16 = 2(x + 4)

Answers

Answer:

y-2=2(x-5), y=2x-8, y+16=2(x+4)

Step-by-step explanation

find x and y

please help ! tyyyy

Answers

Answer:

x = 41* & y = 90.

Step-by-step explanation:

Since we know that the figure is a right triangle, we can solve for y easily, as 90+y = 180

y = 90

to solve for x, we have 49+90+x, since the angle that makes up the left side is perpendicular to the triangle,

so 139+x = 180

x = 180-139

x = 41

How could you correctly rewrite the equation 4(5 + 3) = 2(22-6) using the distributive property ?

Answers

Answer 20 + 12 = 44 - 12
32 = 32
Step by step
The number outside the ( ) is multiplied by the numbers inside the ( )
So 4 x 5 and 4 x 3
And 2 x 22 and 2 x -6

find x and y

helppppp !!

Answers

3x + 6 = 48 (alternate angles are equal)

- 6

3x. = 42

÷3

x = 14 degrees

180-48 - 2y + 5y-9 =180

123 + 3y = 180

-123

3y = 57

÷3

y = 19 degrees

Explanation:

To find the last angle on the top straight line, do:

180 - (the 2 given angles).

So, 180 - (3x + 16, which is 48 due to alternate angles being equal). Then, minus the 2y.

(180 - 48 - 2y) & simplify => 132 - 2y

This gives you the equation for the missing angle on our top straight line.

Thus, co-interior angles add to 180. So, we add the new equation (132 - 2y) to 5y - 9.

Simplify

=> 123 + 3y (because - 2+5 =3)

and put it equal to 180. Solve for y

Hope this helps!

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