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GarryVolchara [31]
2 years ago
7

Sam puts $10,000 in an account earning 4% interest, compounded monthly. If he adds 5100 to the account each month, how much

Mathematics
2 answers:
Zielflug [23.3K]2 years ago
6 0
The answer is d for Daniel
alexandr1967 [171]2 years ago
6 0
The correct answer is D
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Create a matrix for this system of linear equations, The determinant of the coefficient matrix is
marin [14]

Answer:  The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

Step-by-step explanation:  The given system of linear equations is :

2x+y+3z=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x+z=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.

The determinant of the co-efficient matrix is given by

D=\begin{vmatrix}2 & 1 & 3\\ 1 & 2 & 0\\ 3 & 0 & 1\end{vmatrix}=2(2-0)+1(0-1)+3(0-6)=4-1-18=-15.

Now, from equations (ii) and (iii), we have

x+2y=11~~~~~\Rightarrow y=\dfrac{11-x}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\\\\\\3x+z=10~~~~~~\Rightarrow z=10-3x~~~~~~~~~~~~~~~~~~~~~~~~~(v)

Substituting the value of y and z from equations (iv) and (v) in equation (i), we get

2x+y+3z=13\\\\\Rightarrow 2x+\dfrac{11-x}{2}+3(10-3x)=13\\\\\Rightarrow 4x+11-x+60-18x=26\\\\\Rightarrow -15x+71=26\\\\\Rightarrow -15x=26-71\\\\\Rightarrow -15x=-45\\\\\Rightarrow x=3.

From equations (iv) and (v), we get

y=\dfrac{11-3}{2}=4,\\\\z=10-3\times3=1.

Thus, the determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

3 0
3 years ago
Maria must choose a number between 61 and 107 that is a multiple of 5, 6, and 10. Write all the numbers that she could choose. I
RSB [31]
Multiples of 5 : 65,70,75,80,85,90,95,100,105
multiples of 6 : 66,72,78,84,90,96,102
multiples of 10 : 70,80,90,100

she could choose : 90...and thats it
4 0
3 years ago
Spaceship Earth, a spherical attraction at Walt Disney worlds epcot center, has a diameter of 50 meters. Find the surface area o
gladu [14]

Answer:

The surface area of the structure is SA=2,500\pi\ m^{2}

Step-by-step explanation:

we know that

The surface area of a sphere is equal to

SA=4\pi r^{2}

In this problem we have

r=50/2=25\ m -----The radius is half the diameter

substitute

SA=4\pi (25)^{2}

SA=2,500\pi\ m^{2}

5 0
3 years ago
During dance practice, Sasha drank 21⁄2 pints of water, and on the way home she drank 1⁄2 cup of water. How much water did she d
Flura [38]
Try adding the two and think of it mentally as if you were drinking the amount of cups of water that's what I do when I have questions like these :))
5 0
3 years ago
The diameter of the base of the cone measures 8 units. The height measures 6 units
daser333 [38]

For this case we can find the volume and area of the cone:

V = \frac {\pi * r ^ 2 * h} {3}

Where:

V: It's the volume

A: It's the radius of the base

h: It's the height

We have to:

r = \frac {8} {2} = 4 \ units\\h = 6 \ units

Substituting:

V = \frac {\pi * 4 ^ 2 * 6} {3}\\V = \frac {96 * \pi} {3}\\V = 32 \pi \ units ^ 3

On the other hand, the area of the cone is given by:

A = \pi * r * g +  \pi * r ^ 2

Where:

A: It's the radio

g: It is the generator of the cone.

g = \sqrt {h ^ 2 + r ^ 2} = \sqrt {6 ^ 2 + 4 ^ 2} = \sqrt {36 + 16} = \sqrt {52} = 7.2

SW:

A = \pi * 4 * 7.2 + \pi * 4 ^ 2\\A = 28.8 \pi + 16 \pi\\A = 44.8 \pi \ units ^ 2

Answer:

V = 32 \pi \ units ^ 3\\A = 44.8 \pi \ units ^ 2

7 0
3 years ago
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