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4 years ago

What is the slope intercept form of 5x-y=9

Mathematics

2 answers:

Korolek [52]4 years ago

7 0

Slope-intercept:
y=mx+b

5x-y=9
5x=y+9
y+9=5x
y=5x-9

Slope-int: y=5x-9

ArbitrLikvidat [17]4 years ago

6 0

The answer: " y = 5x − 9 " .
___________________________________________
Explanation:
___________________________________________
Given: " 5x − y = 9 " ;
___________________________________________
Write in slope intercept form:
___________________________________________
" y = mx + b " ;
___________________________________________
in which "y" is on the left-hand side of the equation, "on its own" (that is, with no "written coefficient")—other than the "implied coefficient of 1 " ;
"m" is the number, or fraction (positive or negative) representing the slope, if there is one—and "m" is the coefficient of "x" and "b" is the "y-intercept", if there is one—and may be positive or negative.
_____________________________________________
Given:
__________________
5x − y = 9 ;
 __________________
Multiply the entire equation by "-1" ; to get rid of the "− y " ;
____________________________________________________ 
-1 * {5x − y = 9 } ;
____________________________________________________
-5x + y = -9 ;

↔ Rewrite as: y + (-5x) = -9 ;

↔ Rewrite as: y − 5x = -9 ;
___________________________________________
Add "5x" to both sides of the equation; to isolation "y" on the left-hand side of the equation:
___________________________________________
y − 5x + 5x = -9 + 5x ;

to get: y = -9 + 5x ;

↔ Rewrite as: y = 5x + (-9) ;

↔ Rewrite as: y = 5x − 9 ;
_____________________________
This equation is written is "slope-intercept form"; that is:
___________________________
" y = mx + b " ; in which;
m = the slope = 5 ;
b = the y-intercept = -9 ;
_______________________________________________

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An open box is to be made from a square piece of cardboard measuring 15 inches on a side by cutting a square from each corner an

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Answer:

Dimensions are;

2.5 inches height

Base: 10 inches by 10 inches

Max volume; 250 Sq.in

Step-by-step explanation:

Let each side of the square that's cut-off from each corner be represented by x.

This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.

Thus;

Volume of box is:

V = (15 − 2x)(15 − 2x)x

V = (15 − 2x)²x

V = (4x² - 60x + 225)x

V = 4x³ - 60x² + 225x

Let's differentiate with respect to x to get;

dV/dx = 12x² - 120x + 225

Maximum value of x is at dV/dx = 0

12x² - 120x + 225 = 0

Using quadratic formula, we arrive at;

x = 2.5 or 7.5

Now, let's find the second derivative of the volume;

d²V/dx² = 24x - 120

Putting x = 2.5 gives;

d²V/dx² = 24(2.5) - 120

d²V/dx² = -60

Thus, V is maximum at x = 2.5, since d²V/dx² is negative

At x = 7.5;

d²V/dx² = 24(7.5) - 120

d²V/dx² = 60

Thus, V is minimum at x = 7.5, since d²V/dx² is negative

Thus,we will use x = 2.5

Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)

V = 10 × 10 × 2.5

V = 250 Sq.inches

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3 years ago

Mrs. Nevin is making a costume for a school play. She needs a piece of fabric that is greater than 1/2 of a yard but less than 5

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Answer:

4/7 yards

Step-by-step explanation:

Given that :

Required fabric is > 1/2 but < 5/8

Let required fabric = x

Then ;

Converting the fractions to decimal :

1/2 = 0.5 ; 5/8 = 0.625

0.5 < x < 0.625

3/8 yards = 0.375 ;

4/7 yards = 0.571

3/7 yards = 0.429

2/4 yards = 0.5

0.5 < 0.571 < 0.625

From the options, only 4/7 yards satisfies the condition :

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3 years ago

The local hardware store has blue buckets that hold 2 gallons of water and white buckets that hold 5 gallons of water. You bough

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Answer:

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5×4=20

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3 years ago

Read 2 more answers

Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the oppor

stepan [7]

Answer:

Step-by-step explanation:

Answer:

a. The amount that is saved at the expiration of the 5 year period is $22,769.20¢

b. The amount of interest is $2,769.20¢

Step-by-step explanation:

Since the amount that is deposited every year for a period of five years is $4,000 and the rate of the interest is 6.5%. We can always calculate the amount that is saved at the expiration of the five years.

We will first state the formula for calculating the future value of annuity:-

Future value of annuity =

$P[\frac{(1 + r)^{t}-1 }{r}]$

Where P is the amount deposited per year.

r is the rate of interest

t is the time or period

and in this case, the actual value of P = $4,000

rate of interest, r is 6.5% = 0.065

time, t is 5 years.

Substituting e, we have:

Fv of annuity =

$4,000[\frac{(1 + 0.065)^{5}-1 }{0.065 }]$

= 4,000 × [((1.065)^5)- 1/0.065]

= 4,000 × [(1.37 - 1)/0.065]

= 4,000 × (0.37/0.065)

= 4,000 × 5.6923

= $22,769.20¢

a. Therefore the amount that is saved at the end of the five (5) years is $22,769.20¢

b. To find the interest, we will calculate the amount of deposit made during the period of five years and subtract the sum from the current amount that is saved ($22,769.29¢).

Since I deposited 4,000 every year for five years, the total amount of deposit I made at the period =

4,000 × 5 = $20,000

The amount of interest is then = $22,769.20¢ - $20,000 = $2,769.20¢

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3 years ago