What is 24 − 6 × 3 + 5x^{2} − (16 ÷ 2)?

Contains the point (-1, 2) and is parallel to<br> x – 2y = -3

ivanzaharov [21]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange x - 2y = - 3 into this form

Subtract x from both sides

- 2y = - x - 3 ( divide all terms by - 2 )

y = $\frac{1}{2}$ x + $\frac{3}{2}$ ← in slope- intercept form

with m = $\frac{1}{2}$

• Parallel lines have equal slopes, thus

y = $\frac{1}{2}$ x + c ← is the partial equation

To find c substitute (- 1, 2) into the partial equation

2 = - $\frac{1}{2}$ + c ⇒ c = 2 + $\frac{1}{2}$ = $\frac{5}{2}$

y = $\frac{1}{2}$ x + $\frac{5}{2}$ ← in slope- intercept form

Multiply through by 2

2y = x + 5 ( subtract 2y from both sides )

0 = x - 2y + 5 ( subtract 5 from both sides )

- 5 = x - 2y, thus

x - 2y = - 5 ← in standard form

4 0

3 years ago

A field is a rectangle with a perimeter of 960 feet. The length is 100 feet more than the width. Find the width and length of th

marta [7]

To start, let x represent the width and x+100 represent the length.

Since the perimeter of a figure is the sum of all the measurements of the side which can be represented by (x+100)+(x+100)+x+x and since you know your perimeter is 960 feet, you can set the expression equal to 960. This would look like this:
(x+100)+(x+100)+x+x=960

Once you have done that, combine any like terms (combine terms with the same variables and raised to the same power together) which would simplify to this:
4x+200=960

Now that you have your like terms simplified, subtract 200 from both sides to get 4x=760 and finally, to solve for x, or find the width, divide both sides by 4 to get x=190.

Now that you have your width, now you must find your length as the question asks to find the dimensions of the rectangular field. To find the length, add 100 to the width of (190) since according to the information given, the length is 100 more than the width. When you add 100 to 190, you should get that your length is 290.

Now that you have your length and width, you can conclude that the dimensions of the field is 190 by 290 feet, which is your answer :)

4 0

1 year ago

Michelle is building a rectangular landing strip for airplanes .She has material to cover 1/1,500 of a square mile. The landing

ANEK [815]

I think that the missing word here is:
"with the amount of the material that Michelle has"

Let's say that her landing strip is x miles long, then its area would be:

$\frac{1}{6} *x$

We also know how big it is:

$\frac{1}{6} *x= \frac{1}{1 500}$

now, let's multiply both sides by 6:
$\frac{6}{6} *x= \frac{6}{1 500}$
$1 *x= \frac{3}{750}$
$x= \frac{1}{250}$

So the answer is that it would be $x= \frac{1}{250}$ miles wide

3 0

3 years ago

Solve for x in the equation

Viktor [21]

Answer:

${x}^{2} + 2x + 1 = 17 \\ {x}^{2} + 2x - 16 = 0 \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} \\ x = \frac{ - 2± \sqrt{68} }{2} \\ x = \frac{ - 2±2 \sqrt{17} }{2 } \\ x = - 1± \sqrt{17}$

5 0

3 years ago

Jason is mikes older brother. the sum of their ages is 25. the differnece in their ages is 7 write the system of equation that r

Jet001 [13]

Answer:

Equation 1: m+j=25

Equation 2: j=m+5

I hope this helps! Good luck! <3

-YAND3R3

5 0

2 years ago