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3 years ago

Question 5

Mathematics

1 answer:

nadezda [96]3 years ago

4 0

When you distribute you should get
$12 {x}^{2} + 8x - 3x - 2$
Simplify to get
$12 {x}^{2} + 5x - 2$
Answer 2 is correct

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You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00.

Misha Larkins [42]

Answer:

$167.2

Step-by-step explanation:

It has been given that the price of a new computer is $800.00 and refurbished computer with the same equipment has a price of $640.00.

Let us find the amount that we will save with a refurbished computer if we put the difference into the savings account for a year using simple interest formula.

$A=P(1+rt)$ , where A= Amount after t years, P=principal amount, r = interest rate (decimal form) and t=time.

Our principal amount will be the difference of prices of new computer and refurbished computer.

$\text{Principal amount}=800-640=160$

$\text{Interest rate}=\frac{4.5}{100}=0.045$

Upon substituting our given values in above formula we will get,

$\text{Amount we will save with a refurbished computer}=160(1+0.045\times 1)$

$\text{Amount we will save with a refurbished computer}=160(1+0.045)$

$\text{Amount we will save with a refurbished computer}=160(1.045)$

$\text{Amount we will save with a refurbished computer}=167.2$

Therefore, we will save $167.2 with refurbished computer when we put the difference into the savings account for a year.

5 0

3 years ago

A model rocket is launch from a platform 17 feet high in the initial velocity is 40 ft The path of the rocket is modeled by the

Katarina [22]

Answer:

It will be in the air until P(x) is zero.

P(x) = -16x2 + 32x = -16x(x - 2)

P(x) = 0 ⇒ x = 0 or x = 2

It starts on the ground at x = 0, so the total time in the air must be x = 2 seconds.

6 0

2 years ago

let a = (a1, a2) and b = (b1, b2) and c = (c1,c2) be three non zero vectors. if a1b2 - a2b1 is not equal to 0. then show three a

Ksenya-84 [330]

Consider the contrapositive of the statement you want to prove.

The contrapositive of the logical statement

p ⇒ q

¬q ⇒ ¬p

In this case, the contrapositive claims that

"If there are no scalars α and β such that c = αa + βb, then a₁b₂ - a₂b₁ = 0."

The first equation is captured by a system of linear equations,

$\begin{cases}c_1 = \alpha a_1 + \beta b_1\\ c_2 = \alpha a_2 + \beta b_2\end{cases}$

or in matrix form,

$\begin{pmatrix}c_1\\c_2\end{pmatrix} = \begin{pmatrix}a_1&b_1\\a_2&b_2\end{pmatrix}\begin{pmatrix}\alpha\\\beta\end{pmatrix}$

If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be

$\begin{vmatrix}a_1&b_1\\a_2&b_2\end{vmatrix} = a_1b_2-a_2b_1 = 0$

and this is what we wanted to prove. QED

3 0

3 years ago

An angle measures 36° more than the measure of a complementary angle. what is the measure of each angle?

nexus9112 [7]

An acite becaues it lowers than the others

6 0

3 years ago

What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Rufina [12.5K]

Answer:

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

$Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, the average rate of change of:

$f(x)=-x^2+3x+6$

Over the interval $-3$

Is:

$f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12$

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Therefore, the average rate of change of this function over that interval is 3.

3 0

3 years ago