A plane is a set of blank on a flat surface that extends forever

The student council wants to rent a chocolate fountain for an overnight dance-a-thon. Their budget allows them to spend a maximu

vekshin1

$125 is a "must budget" so it will be the constant in the inequality

The fountain is $30 per hour. If they spend x hours, then their budget for fountain will be
fountain = 30x

The inequality
Their budget is maximum $250, that means they are able to spend less than or equal to $250
constant + fountain ≤ 250
125 + 30x ≤ 250
This is the inequality expression

6 0

3 years ago

Read 2 more answers

If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f

nikklg [1K]

The quadratic function given by:

$f(x)=a(x-h)^2+k, \ \ \ a\neq 0$

is in vertex form. The graph of $f$ is a parabola whose axis is the vertical line $x=h$ and whose vertex is the point $(h, k)$ . So:

To translate the graph of a function to the right, left, upward or downward we have:

$For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)$

By knowing this things, we can solve our problem as follows:

FIRST.

Translating 11 units to the left:

$g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2$

Then translating 5 units down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5$

Since the new function is fatter, the factor we need to multiply the term $(x+11)^2$ must be less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

Therefore, the right answer is b. f(x) = 1/2(x + 11)^2 - 5

SECOND.

Translating 8 units to the right:

$g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2$

Then translating 1 unit down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1$

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

Therefore, the right answer is a. g(x) = 1/3(x - 8)^2 - 1

7 0

2 years ago

Triangles and algebra

Elanso [62]

Hello from MrBillDoesMath!

Answer:

x = 10

Discussion:

A plane triangle contains 180 degrees. Adding the angles in the triangle shown in #8 gives

(4x + 7) + (3x + 13) + 90 = 180

Note the "right angle" shown in the triangle has been replaced by its 90 degree equivalent in the above equation.

Combining like terms gives

( 4x + 3x) + (7 + 13) + 90 = 180

7x + 20 + 90 = 180 => (subtract 90 from each side)

7x + 20 + 90 - 90 = 180 - 90 = 90 =>

7x +20 = 90 => (subtract 20 from each side)

7x + 20 -20 = 90 -20 =>

7x = 70 =>

x 70/7 =10.

Thank you,

MrB

3 0

3 years ago

PLEASE ITS ALREADY LATE AND I NEED TO TURN IT TODAY

Troyanec [42]

Answer:

4800

Step-by-step explanation:

I attached a picture of the work.

We need to made a function that will help us solve this

f(x)=dx; d = $ per hour, x = # of hours

step 1) identify d (in this case, the money made per hour) which = 10

f(x)=10x

step 2) identify x (# of hours total) which = 480

f(x)=10(480)

step 3) solve the equation

f(x)=4800

independent variable:

the number of hours

dependant variable:

the amount of money made after 12 weeks

5 0

2 years ago

(7q3r2 + 5qr2 + 23q) + (−5qr2 − qr² − 11q − 4q3r2) adding polynomials horizontally

zysi [14]

You can remove the parentheses:-

= 7q^3r^2 + 5qr^2 + 23q + −5qr^2 − qr^2 − 11q − 4q^3r^2 ( because there is + outside)

Bring like terms together

= 7q^3r^2 − 4q^3r^2 + 5qr^2 − 5qr^2 − qr^2 + 23q − 11q

= 3q^3r^2 - qr^2 + 12q answer

5 0

2 years ago