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3 years ago

Solve the following: a. 4x^2 + 5x + 3 = 2x^2 − 3x b. c^2 − 14 = 5c

Mathematics

1 answer:

Jet001 [13]3 years ago

7 0

Answer:

(a) x = -0.418 , -3.581

(B) c = 6.855, -1.855

Step-by-step explanation:

(A) We have given equation $4x^2+5x+3=2x^2-3x$

$2x^2+8x+3=0$

On comparing with standard quadratic equation $ax^2+bx+c$

a = 2, b = 8 and c = 3

So roots of the equation will be $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-8\pm \sqrt{8^2-4\times 2\times 3}}{2\times 2}=\frac{-8\pm 6.324}{4}=-0.418,-3.581$

(b) $c^2-14=5c$

$c^2-5c-14=0$

a = 1, b = -5 and c= -14

So $c=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-(-5)\pm \sqrt{(-5)^2-4\times 1\times (-14)}}{2\times 1}=\frac{5\pm 8.71}{2}=6.855,-1.855$

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Suppose that $3000 is placed in an account that pays 16% interest compounded each year. Assume that no withdrawals are made from

Papessa [141]

Answer:

a) $3480

b) $4036.8

Step-by-step explanation:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Suppose that $3000 is placed in an account that pays 16% interest compounded each year.

This means, respectively, that $P = 3000, r = 0.16, n = 1$

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(t) = 3000(1 + \frac{0.16}{1})^{t}$

$A(t) = 3000(1.16)^{t}$

(a) Find the amount in the account at the end of 1 year.

This is A(1).

$A(t) = 3000(1.16)^{t}$

$A(1) = 3000(1.16)^{1} = 3480$

(b) Find the amount in the account at the end of 2 years.

This is A(2).

$A(2) = 3000(1.16)^{2} = 4036.8$

4 0

3 years ago

Two numbers multiply to be -7 and add to be -6. What are the numbers? Example; 2,3

rewona [7]

Given:

Let the two numbers be x and y.

Two numbers multiply to be -7 and add to be -6.

This can be written in equation as,

$xy=-7$ and

$x+y=-6$

Value of the two numbers:

Let us determine the value of the two numbers using substitution method.

Substituting $y=-6-x$ in the equation $xy=-7$ , we get;

$x(-6-x)=-7$

Simplifying, we get;

$-6x-x^2=-7$

$x^2+6x-7=0$

$(x+7)(x-1)=0$

$x=-7, 1$

Thus, the values of x are x = 1,-7

When x = 1 , the equation $x+y=-6$ becomes $y=-7$

When x = -7, the equation $x+y=-6$ becomes $y=1$

Therefore, the two numbers are 1 and -7

3 0

3 years ago

Examine the data below for a stalk of corn. Logarithmic regression Use logarithmic regression to find an equation of the form y

masya89 [10]

The value of a and b for the data values of stalk of corn using the logarithmic regression is -76.2038 and 37.6735 respectively.

<h3>What is logarithmic regression?</h3>

Logarithmic regression is a type of regression which is used to model the statement in which the growth or decay initially at rapid rate, and then slow down with respect to time.

The data of the table for the day and height of the stalk of corn is listed below.

Day (x) 9 12 22 40

Height (y) in 5 17 45 60

Mean of x values,

$m_x=\dfrac{9+12+22+40}{4}\\m_x=17.5581$

Mean of y values,

$m_y=\dfrac{5+17+45+60}{4}\\m_y=31.75$

For the above table, the value of correlation coefficient is 0.99133. For these values, the logarithmic regression can be given as,

$y = -76.2038+37.6735\ln(x)$

Compare it with the following logarithmic regression equation, we get

$y = a+b\ln(x)$

$a=-76.2038\\b=37.6735$

Hence, the value of a and b for the data values of stalk of corn using the logarithmic regression is -76.2038 and 37.6735 respectively.

Learn more about the logarithmic regression here;

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2 years ago

What do you think are some of the advantages and disadvantages of a capitalist economic system? Do you feel that the advantages

Tcecarenko [31]

Hello!

Advantages of a capitalist economic system:

• Economic growing and expansion.

• Consumer choice (The consumers get to choose what to consume, which leads to better products and services).

• Efficiency of economics (Goods and services based on demand)

Disadvantages of a capitalist economic system:

• Inequality (A small group of people hold most of the wealth)

• There can be a monopoly of power (a specific enterprise is the only supplier of particular commodity)

• Unemployment

• Social benefit ignored. A free market will ignore externalities.

No, I feel the disadvantages outweigh the advantages, because there are more of them.

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3 years ago

Count the possible combinations of 3 letters chosen from A, B, C, D. The possible combinations of 3 letters are __.

anygoal [31]

Answer:

Step-by-step explanation:

We are given the letters:

We write the possible permutations of 3 letters from the given list:

Because order is not important in a combination we cross out the duplicate pairs:

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2 years ago

Read 2 more answers