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2 years ago

What are the solutions of the equation 4x2 + 3x = 24 – x?

Mathematics

2 answers:

prohojiy [21]2 years ago

8 0

answer

x = 2

x = -3

step-by-step explanation

4x^2 + 3x = 24 – x move all terms to one side

4x^2 + 4x = 24

4x^2 + 4x - 24 = 0 divide each side by 4

x^2 + x - 6 = 0/4 = 0

factor x^2 + x - 6 by finding two number whose product is -6 and sum is x

(x-2)(x+3) set each term equal to 0 and solve for x

x-2 = 0, x = 2

x+3 = 0, x = -3

Rashid [163]2 years ago

6 0

Answer:

X+4

Step-by-step explanation:

8+3x=25-x

3x+x=24-8

4x+16

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21 less than a number, multiplied by 4, results in 108.Find the value of the unknown number.

Anni [7]

21 - 4x = 108

Subtract 21 from both sides

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Divide both sides by -4

x = -21.75

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2 years ago

A square picture on the front page of a newspaper occupies an area of 24 square inches. Find the length of each side of the squa

Hoochie [10]

Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

determine the point of intersection of the following pair of lines ............2x-3y-4=-13 and 5x=-2y+25. 3x+2y-7=0 and 2x=12-5y

grandymaker [24]

Answer:

(x, y) = (3, 5)
(x, y) = (1, 2)

Step-by-step explanation:

A nice graphing calculator app makes these trivially simple. (See the first two attachments.) It is available for phones, tablets, and as a web page.

The usual methods of solving a system of equations involve elimination or substitution.

There is another method that is relatively easy to use. It is a variation of "Cramer's Rule" and is fully equivalent to elimination. It makes use of a formula applied to the equation coefficients. The pattern of coefficients in the formula, and the formula itself are shown in the third attachment. I like this when the coefficient numbers are "too messy" for elimination or substitution to be used easily. It makes use of the equations in standard form.

_____

1. In standard form, your equations are ...

2x -3y = -9
5x +2y = 25

Then the solution is ...

$x=\dfrac{-3(25)-(2)(-9)}{-3(5)-(2)(2)}=\dfrac{-57}{-19}=3\\\\y=\dfrac{-9(5)-(25)(2)}{-19}=\dfrac{-95}{-19}=5\\\\(x,y)=(3,5)$

2. In standard form, your equations are ...

3x +2y = 7
2x +5y = 12

Then the solution is ...

$x=\dfrac{2(12)-5(7)}{2(2)-5(3)}=\dfrac{-11}{-11}=1\\\\y=\dfrac{7(2)-12(3)}{-11}=\dfrac{-22}{-11}=2\\\\(x,y)=(1,2)$

_____

Note on Cramer's Rule

The equation you will see for Cramer's Rule applied to a system of 2 equations in 2 unknowns will have the terms in numerator and denominator swapped: ec-bf, for example, instead of bf-ec. This effectively multiplies both numerator and denominator by -1, so has no effect on the result.

The reason for writing the formula in the fashion shown here is that it makes the pattern of multiplications and subtractions easier to remember. Often, you can do the math in your head. This is the method taught by "Vedic maths" and/or "Singapore math." Those teaching methods tend to place more emphasis on mental arithmetic than we do in the US.

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2 years ago

Let m and n be two positive integers greater than 1 . If

sammy [17]

<h2>SOLUTION :-</h2>

PLEASE CHECK THE ATTACHED FILE

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1 year ago

A survey of 542 consumers reveals that 301 favor the new design for a product. Construct a 90% confidence interval for the true

kodGreya [7K]

Answer:

The 90% confidence interval for the true proportion of all consumers who favor the design is (0.52, 0.59).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.