3y - 15 =y + 1 solve for y

A rectangular auditorium seats 1302 people. The number of seats in each row exceeds the number of rows by 11. Find the number of

sveticcg [70]

Number of seats = 42

Seats per row x row = 1302
s x r = 1302

rows + 11 = seats per row
r + 11 = s

s x r = 1302
(r + 11) x r = 1302
r^2 + 11r = 1302
r^2 + 11r - 1302 = 0
(r + 42) x (r - 31) = 0
r = -43 or 31

Cannot have negative rows so the number of rows is 31, and the number of seats per row is 31 + 11 = 42

Check: 31 x 42 = 1302 :)

8 0

3 years ago

4. Which graph represents the solution to<br> -2<3x+1 ?<br>

dalvyx [7]

Hey there!

-2<3x+1

= 3x + 1 < -2

SUBTRACT 1 to BOTH SIDES

3x + 1 - 1 < -2 + 1

CANCEL out: 1 - 1 because that gives you 0

KEEP: -2 + 1 because that helps you solve for x

-2 + 1 = -3

New EQUATION: 3x > -3

DIVIDE 3 to BOTH SIDES

3x/3 > -3/3

CANCEL out: 3/3 because that gives you 1

KEE3 -3/3 because that helps us compare for x

-3/3 = -1

Answer to the equation: x > -1

OVERALL Answer: x > -1; It is an OPENED circle shaded to the right starting at -1 (Option A.)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

8 0

2 years ago

Which of the following is a solution of x2 + 2x + 4?

RideAnS [48]

Answer:

option-D

Step-by-step explanation:

we are given

$x^2+2x+4$

Let's assume it is equal to 0

$x^2+2x+4=0$

We can use quadratic formula

Suppose, we are given quadratic equations as

$ax^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

we can compare and find a,b and c

a=1 , b=2 , c=4

now, we can plug values

and we get

$x=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \:4}}{2\cdot \:1}$

now, we can simplify it

and we get

$x=-1+\sqrt{3}i,\:x=-1-\sqrt{3}i$

6 0

3 years ago

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What is the slope of the line that passes through these two points? (-3, 2) (4, 2)

Alik [6]

Answer: 0

Step-by-step explanation:

To find slope, I found that an easy way is the equation y2 - y1 over (divided by) x2 - x1

so for this, it would be:

$\frac{2 - 2}{4-(-3)}$

which is 0/7

0 divided by 7 is 0, so there is your answer

6 0

3 years ago

1. What is an equation for the line with slope 2/3 and y-intercept 9?

Monica [59]

Question 1:

The generic equation of the line is given by:
$y = mx + b
$
Where,
m: slope of the line
b: cutting point with the y axis
Substituting values we have:
$y = \frac{2}3}x + 9
$
Answer:
an equation for the line with slope 2/3 and y-intercept is:
$y = \frac{2}3}x + 9$

Question 2:

The standard equation of the line is given by:
$y-yo = m (x-xo)
$
Where,
m: slope of the line
(xo, yo): ordered pair that belongs to the line
The slope of the line is:
$m = \frac{y2-y1}{x2-x1}$
Substituting values:
$m = \frac{1-(-3)}{3-1}$
$m = \frac{1+3}{3-1}$
$m = \frac{4}{2}$
$m = 2
$
We choose an ordered pair:
$(xo, yo) = (3, 1)
$
Substituting values:
$y-1 = 2 (x-3)
$
Rewriting:
$y = 2x - 6 + 1

y = 2x - 5$
Answer:
An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
$y = 2x - 5
$

Question 3:

For this case, since the variation is direct, then we have an equation of the form:
$y = kx
$ Where,
k: constant of variation.
We then have the following equation:
$-4y = 8x
$ Rewriting we have:
$y = \frac{8}{-4}x
$
$y = -2x
$ Therefore, the constate of variation is given by:
$k = -2
$
Answer:
the constant of variation is:
$k = -2$

Question 4:

For this case, since the variation is direct, then we have an equation of the form:
$y = kx
$ Where,
k: constant of variation.
We must find the constant k, for this we use the following data:
y = 24 when x = 8
Substituting values:
$24 = k8
$ Clearing k we have:
$k = \frac{24}{8} 
$
$k = 3
$
Therefore, the equation is:
$y = 3x
$ Thus, substituting x = 10 we have that the value of y is given by:
$y = 3 (10)

y = 30$ Answer:
the value of y when x = 10 is:
$y = 30$

6 0

3 years ago

Read 2 more answers