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3 years ago

Calculate the simple interest paid on a loan of $544 at 3% for three months.

Mathematics

1 answer:

exis [7]3 years ago

5 0

Answer:

Step-by-step explanation:

Answer: interest at the end of 3 months is $4.08

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 3 months = 3/12 = 0.25 years

P = $544

R = 3%

Therefore

I = (544 × 3 × 0.25)/100

I = 408/100

I = 4.08

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What is the value of z in the equation 4×2-z=7?

sladkih [1.3K]

4×2-z=7
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⇒ 8 - 7 = z
⇒ 1 = z

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3 years ago

Help math look at pic

Sloan [31]

Answer: $\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}$

Step-by-step explanation:

Given the system of equation

$1)~y=-(x+2)^2+1$

$2)~y=2x+5$

Expand the parenthesis of the 1) equation

$y=-(x+2)^2+1$

$y=-(x^2+4x+4)+1$

$y=-x^2-4x-4+1$

$y=-x^2-4x-3$

Current System

$1)~y=-x^2-4x-3$

$2)~y=2x+5$

Substitute the y value of the 1) equation with the 2) equation

$2x+5=-x^2-4x-3$

Add ( x² + 4x + 3) on both sides

$2x+5+(x^2+4x+3)=-x^2-4x-3+(x^2+4x+3)$

$2x+5+x^2+4x+3=0$

Combine like terms

$x^2+2x+4x+5+3=0$

$x^2+6x+8=0$

Factorize the quadratic equation

$(x+4)(x+2)=0$

$x=-4~\text{or}~x=-2$

Substitute the x values into one of the equations to find the y value

$y=2x+5$

$y=2(-4)+5=-8+5=-3$

$y=2(-2)+5=-4+5=1$

Therefore, the two solutions are:

$\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}$

Hope this helps!! :)

Please let me know if you have any questions

8 0

2 years ago

A box has a total surface area of $100.$ The length of the box is equal to twice its width, as well as equal to $3$ less than it

CaHeK987 [17]

Answer:

Formula: width x depth x height

Step-by-step explanation:

times 100 and 3. As we know that the formula for a box is width x depth x height.

We need to measure the box from all side so 4 sides. so times the 2 number by 2 cause there is 4 sides each.

Hope this helps

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3 years ago

How to determine if the columns of a matrix are linearly independent?

astra-53 [7]

Let's consider an arbitrary 2x2 matrix as an example,

$\mathbf A=\begin{bmatrix}\mathbf x&\mathbf y\end{bmatrix}=\begin{bmatrix}x_1&y_1\\x_2&y_2\end{bmatrix}$

The columns of $\mathbf A$ are linearly independent if and only if the column vectors $\mathbf x,\mathbf y$ are linearly independent.

This is the case if the only way we can make a linear combination of $\mathbf x,\mathbf y$ reduce to the zero vector is to multiply the vectors by 0; that is,

$c_1\mathbf x+c_2\mathbf y=\mathbf 0$

only by letting $c_1=c_2=0$ .

A more concrete example: suppose

$\mathbf A=\begin{bmatrix}1&2\\4&8\end{bmatrix}$

Here, $\mathbf x=\begin{bmatrix}1\\4\end{bmatrix}$ and $\amthbf y=\begin{bmatrix}2\\8\end{bmatrix}$ . Notice that we can get the zero vector by taking $c_1=-2$ and $c_2=1$ :

$-2\begin{bmatrix}1\\4\end{bmatrix}+\begin{bmatrix}2\\8\end{bmatrix}=\begin{bmatrix}-2+2\\-8+8\end{bmatrix}=\mathbf 0$

so the columns of $\mathbf A$ are not linearly independent, or linearly dependent.

8 0

3 years ago

2x = x +3 Help pls I can’t do this one

Fudgin [204]

Answer:

x=3

Step-by-step explanation:

Subract the x from the left side and add it to the right side and then you got your answer

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3 years ago