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3 years ago

Find f(x) + g(x) if f(x) = 3x - 4 and g (x) = -5x + 3. Then graph your combined function f(x) + g(x)

Mathematics

1 answer:

nasty-shy [4]3 years ago

3 0

Answer:

f(x) + g(x) = -2x -1

Step-by-step explanation:

Add both equations:

(3x-4) + (-5x+3) | Combine like terms

-2x -1

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У – бх — 11<br> — 2x — Зу = -7

fiasKO [112]

Answer: -2y -8x = 4

Step-by-step explanation:

y - 6x - 11 - 2x - 3y = -7

y -3y -6x -2x = -7 +11

-2y -8x = 4

3 0

3 years ago

Lamar works as a tutor for $7 an hour and as a waiter for $8 an hour . this month he worked a combined total of 92 hours at his

ira [324]

t is the number of hours Lamar worked as a tutor
We know that he worked for 92 hours total, so he worked 92-t hours as a waiter.

So his earnings are: 7t + 8(92-t) = 736 -t dollars

This expression seems logical as if Lamar worked 0 hours as a tutor and 92 as a waiter his earnings would be 8*92 = 736
If he worked as a tutor for 92 hours it would be 7*92= 644
736-92= 644
So our expression seems to be working.

5 0

3 years ago

(7.7) and (9,9)<br> slope =

nekit [7.7K]

Answer:

Step-by-step explanation:

Slope = Change in y/ Change in x

= (9-7)/(9-7)

= 2/2

6 0

3 years ago

Read 2 more answers

The University of Texas at Austin has three times as many students enrolledas the University of Miami. The University of Califor

harina [27]

Answer:

University of Texas has 46,500 students, University of California has 34,000 students and University of Miami has 15,500 students.

Step-by-step explanation:

Represent Texas with T, Miami with M and California with C. With the given information, the following equations were obtained.

T = 3 × M

T – 3M = 0 ………………………….(i)

C = 3,000 + 2 × M

C – 2M = 3,000…………………..(ii)

T + C + M = 96,000…………….(iii)

By rearranging, we have:

1T + 0C – 3M = 0 ………………………….(i)

0T + 1C – 2M = 3,000…………………..(ii)

1T + 1C + 1M = 96,000………….…….(iii)

The Augmented Matrix is:

$\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]$ $\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ = $\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]$

Making $\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ the subject of the formula we have:

$\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ = $\frac{\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]}{\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]}$

Let’s say matrix A = $\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]$ , the inverse of matrix A = $\left[\begin{array}{ccc}\frac{1}{2} &-\frac{1}{2} &\frac{1}{2} \\-\frac{1}{3} &\frac{2}{3} &\frac{1}{3} \\-\frac{1}{6} &-\frac{1}{6} &\frac{1}{6} \end{array}\right]$ is determined by the formula $\frac{Adjoint(A)}{determinant(A)}$ . This can also be computed directly on a scientific calculator.

$\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ = $\left[\begin{array}{ccc}\frac{1}{2} &-\frac{1}{2} &\frac{1}{2} \\-\frac{1}{3} &\frac{2}{3} &\frac{1}{3} \\-\frac{1}{6} &-\frac{1}{6} &\frac{1}{6} \end{array}\right]$ $\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]$

= $\left[\begin{array}{ccc}46,500\\34,000\\15,500\end{array}\right]$

T = 46,500

C = 34,000

M = 15,500

6 0

4 years ago

Read 2 more answers

Book-club members are required to buy a minimum number of books each year. Leslee bought 3 times the minimum. Denise bought 7 mo

kkurt [141]

Answer: 4 books

Step-by-step explanation:

x = minimum number of book

Leslee

= 3x (bought 3 times the minimum)

Denise

= x + 7 (bought 7 more than the minimum)

Together

= (3x) + (x + 7)

(3x) + (x + 7) = 23 (books they bought together)

3x + x + 7 = 23

3x + x = 23 - 7 (isolate the like variables together)

4x = 16 (divide both sides by 4)

x = 4

4 is the minimum number of books

To check:

3(4) + (4+7)

12 + 11 = 23

4 0

3 years ago