*35 BRAINLY POINTS! BRAINLIEST TO THE FIRST CORRECT PERSON!*

Silas just bought a used car for $5000. It loses value at a rate of 30% per year. The value of the car in n years is modeled by

Fantom [35]

Answer:

$1200.50

plug 5 for n

5000(.7)^4

5000*.2401

=1200.5

8 0

3 years ago

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.

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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.

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

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

Then the solution is ...

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

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

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

Then the solution is ...

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

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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.

7 0

4 years ago

The slope of a line is -1/3, and the y-intercept is 10/3. What is the equation of the line written in general form?

Y_Kistochka [10]

The answer is: [B]: " x + 3y + 10 = 0 " .
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Explanation:
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Note the equation for a line; in 'slope-intercept form': "y = mx + b" ;

in which "y" is isolated alone, as a single variable, on the left-hand side of the equation;
"m" = the slope of the line; and is the co-efficient of "x" ;
b = the "y-intercept"; (or the "y-coordinate of the point of the "y-intercept").
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So, given the information in this very question/problem:
______________________________________________________
slope = m = (-1/3) ;
b = y-intercept = (10/3) ;
______________________________________________________
And we can write the equation of the line; in "slope-intercept form"; that is:
______________________________________________________
" y = mx + b " ; as:
______________________________________________________

" y = (-1/3)x + (10/3) " ;
______________________________________________________
Now, the problem asks for the equation of this line; in "general form"; or "standard format"; which is:
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"Ax + By + C = 0 " ;
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So; given:
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" y = (-1/3)x + (10/3) " ;
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We can multiply the ENTIRE EQUATION (both sides) by "3" ; to get rid of the "fractions" ;

→ 3* { y = (-1/3)x + (10/3) } ;

→ 3y = -1x + 10 ;

↔ -1x + 10 = 3y ;

Subtract "(3y)" from each side of the equation:
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-1x + 10 − 3y = 3y − 3y ;

to get:

-1x + 10 − 3y = 0 ;

↔ -1x − 3y − 10 = 0 ;

→ This is not one of the "3 (THREE) answer choices given" ;

→ So, multiply the ENTIRE EQUATION (both sides); by "-1" ; as follows:

-1 * {-1x − 3y − 10 = 0} ;

to get:
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→ " x + 3y + 10 = 0 " ; which is: "Answer choice: [B] ."
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Note that is equation is in the "standard format" ;
→ " Ax + By + C = 0 " .
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6 0

4 years ago

Read 2 more answers

An Equilateral Triangle has sides that all measure 10 inches. What is

densk [106]

Answer:

easy peasy lemon squeasy

Step-by-step explanation:

1. base of triangle: it is an equilateral triangle, so any side of the triangle you take is the base, (usually the largest side of the triangle is the base)

so that would be => 10 inches,

2. a property of an equilateral triangle is that , the median of the triangle coincides with the height of the triangle,

therefore, the height bisects the base and makes a right triangle with another side, therefore by using the Pythagoras theorem, we find it to be 8.66(approx)

now,

area of the triangle would be (putting the values we just found in the formula given)

=> [(10)(8.66)]/ 2

=>43.3 square inches

4 0

3 years ago

Radius of 0.75 centimeters is rational or irrational

ella [17]

A radius of 0.75 would be rational because the decimal ends and does not repeat itself.

6 0

4 years ago