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aleksandrvk [35]
3 years ago
11

F(x) = 4x + 2; find f(8)

Mathematics
1 answer:
likoan [24]3 years ago
8 0

Answer:

f(8)=34

Step-by-step explanation:

To solve, you just substitute x for 8

4(8) + 2

32 + 2

F(8) = 34

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Maya has 3 times as many dimes as nickels. She has 4 more quarters than nickels. if she has a total of $9.40, how many of each t
puteri [66]

Answer:  nickels = 14, dimes = 42, quarters = 18

<u>Step-by-step explanation:</u>

Let n represent nickels <em>which has a value of $0.05 </em>

Let d represent dimes <em>which has a value of $0.10</em>

Let q represent quarters <em>which has a value of $0.25</em>

It is given that:

                       n = n

                      d = 3n

                      q = n + 4

and their total value is $9.40    ⇒     n + d + q = $9.40

Use substitution to find the quantity of nickels:

.05(n) + .10(3n) + .25(n + 4) = 9.40

 5n    +  10(3n) +   25(n+4)   = 940           <em>multiplied by 100 </em>

 5n    +   30n   +  25n + 100 = 940          <em>distributed</em>

                            60n + 100 = 940          <em>added like terms</em>

                            60n           = 840          <em>subtracted 100</em>

                                 n           = 14            <em>divided by 60</em>

n = 14

                d = 3n

                   = 3(14)

                   = 42

                                       q = n + 4

                                          = (14) + 4

                                           = 18

4 0
3 years ago
The length of a new rectangular playing field is 6 yard longer than the triple the width. If the perimeter of the rectangular pl
Katarina [22]

Answer:width = 53 yards

              Length = 165 yards

Step-by-step explanation:

3 0
3 years ago
Hannah does push-ups in sets of three she did 10 sets of push-ups today then her coach asked her to do 15 more push-ups how many
scoray [572]

Answer:

30+ 15 =45

Step-by-step explanation:

(3×10)+15 =45

4 0
3 years ago
In finding the solution of the equation 5 - 3x = 2x + 9, 3x is added to both sides of the equation first. Which of the following
KIM [24]

Answer:

C should be next

Step-by-step explanation:

Ok after you add 3x to both side you should get this:

5=5x+9

It makes since o subtract 9 from both sides at least for me.

Hope this helps :D

5 0
2 years ago
Read 2 more answers
How to do the inverse of a 3x3 matrix gaussian elimination.
nata0808 [166]

As an example, let's invert the matrix

\begin{bmatrix}-3&2&1\\2&1&1\\1&1&1\end{bmatrix}

We construct the augmented matrix,

\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 2 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 \end{array} \right]

On this augmented matrix, we perform row operations in such a way as to transform the matrix on the left side into the identity matrix, and the matrix on the right will be the inverse that we want to find.

Now we can carry out Gaussian elimination.

• Eliminate the column 1 entry in row 2.

Combine 2 times row 1 with 3 times row 2 :

2 (-3, 2, 1, 1, 0, 0) + 3 (2, 1, 1, 0, 1, 0)

= (-6, 4, 2, 2, 0, 0) + (6, 3, 3, 0, 3, 0)

= (0, 7, 5, 2, 3, 0)

which changes the augmented matrix to

\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 5 & 2 & 3 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 \end{array} \right]

• Eliminate the column 1 entry in row 3.

Using the new aug. matrix, combine row 1 and 3 times row 3 :

(-3, 2, 1, 1, 0, 0) + 3 (1, 1, 1, 0, 0, 1)

= (-3, 2, 1, 1, 0, 0) + (3, 3, 3, 0, 0, 3)

= (0, 5, 4, 1, 0, 3)

\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 5 & 2 & 3 & 0 \\ 0 & 5 & 4 & 1 & 0 & 3 \end{array} \right]

• Eliminate the column 2 entry in row 3.

Combine -5 times row 2 and 7 times row 3 :

-5 (0, 7, 5, 2, 3, 0) + 7 (0, 5, 4, 1, 0, 3)

= (0, -35, -25, -10, -15, 0) + (0, 35, 28, 7, 0, 21)

= (0, 0, 3, -3, -15, 21)

\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 5 & 2 & 3 & 0 \\ 0 & 0 & 3 & -3 & -15 & 21 \end{array} \right]

• Multiply row 3 by 1/3 :

\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 5 & 2 & 3 & 0 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]

• Eliminate the column 3 entry in row 2.

Combine row 2 and -5 times row 3 :

(0, 7, 5, 2, 3, 0) - 5 (0, 0, 1, -1, -5, 7)

= (0, 7, 5, 2, 3, 0) + (0, 0, -5, 5, 25, -35)

= (0, 7, 0, 7, 28, -35)

\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 0 & 7 & 28 & -35 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]

• Multiply row 2 by 1/7 :

\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 4 & -5 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]

• Eliminate the column 2 and 3 entries in row 1.

Combine row 1, -2 times row 2, and -1 times row 3 :

(-3, 2, 1, 1, 0, 0) - 2 (0, 1, 0, 1, 4, -5) - (0, 0, 1, -1, -5, 7)

= (-3, 2, 1, 1, 0, 0) + (0, -2, 0, -2, -8, 10) + (0, 0, -1, 1, 5, -7)

= (-3, 0, 0, 0, -3, 3)

\left[ \begin{array}{ccc|ccc} -3 & 0 & 0 & 0 & -3 & 3 \\ 0 & 1 & 0 & 1 & 4 & -5 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]

• Multiply row 1 by -1/3 :

\left[ \begin{array}{ccc|ccc} 1 & 0 & 0 & 0 & 1 & -1 \\ 0 & 1 & 0 & 1 & 4 & -5 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]

So, the inverse of our matrix is

\begin{bmatrix}-3&2&1\\2&1&1\\1&1&1\end{bmatrix}^{-1} = \begin{bmatrix}0&1&-1\\1&4&-5\\-1&-5&7\end{bmatrix}

6 0
2 years ago
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