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2 years ago

Given f(x)=x-7 and h(x)=2x+3 what is the rule for h(f(x))

Mathematics

1 answer:

Paul [167]2 years ago

6 0

Answer:

h(f(x)) = 2x - 11

Step-by-step explanation:

To evaluate h(f(x)) substitute x = f(x) into h(x)

h(x - 7)

= 2(x - 7) + 3

= 2x - 14 + 3

= 2x - 11

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Let A be a 3 by 6 , B be a 6 by 7 and C be a 7 by 3 matrix. Determine the size of the following matrices (if they do not exist,

kozerog [31]

Answer:

a. AB: 3 by 7

b. BA: N by N

c. A^TB: N by N

d. BC: 6 by 3

Step-by-step explanation:

Given

$A =3\ by\ 6$

$B =6\ by\ 7$

$C =7\ by\ 3$

Required

The dimension of the following matrices

As a general rule:

For A * B to be successful, the columns in a must equal the rows in B

Using this rule, we have:

$A_{m*n} * B_{n * p} = AB_{m*p}$

So:

$(a)\ AB$

$A_{3*6} * B_{6*7} \to AB_{3 * 7}$

$(b)\ BA$

$B_{6*7} * A_{3*6} \to AB_{N * N}$

The column numbers of B does not equal the row numbers of A.

Hence, BA does not exist

$(c)\ A^TB$

$A^T$ implies that:

If $A =3\ by\ 6$ , then

$A^T = 6\ by\ 3$

So:

$A^T_{6*3} * B_{6,7} \to A^TB_{N*N}$

The column numbers of A^T does not equal the row numbers of B.

Hence, $A^TB$ does not exist

$(d)\ BC$

$B_{6*7} * C_{7*3} \to BC_{6,3}$

6 0

3 years ago

Which of the following equations represents a hyperbola with a vertical transverse axis and foci at (0, −10) and (0, 10)?

Taya2010 [7]

Answer: A

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

What is they answer on the sheet of paper for my homework

geniusboy [140]

Um not sure but thanks for asking:)

3 0

2 years ago

To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of

postnew [5]

Answer:

The student's GPA for that term is 3.07

Step-by-step explanation:

So this is a problem where we need to compute a weighted arithmetic mean.

To compute the weighted arithmetic mean of a set, we need to multiply each value of the set by their respective weight, add them, and then divide by the sum of the weights.

I will write the set in a {V,W} way, where V is the value(the grade) and W is the weight of V.

So your set G will be

G = {{3.8, 5}, {1.8,3}, {3.1,5}, {3.1,5}}.

Multiplying each value by it's respective weigth and then adding, we have:

3.8*5 + 1.8*3 + 3.1*5 + 3.1*5 = 19 + 5.4 + 15.5 + 15.5 = 55.4

The sum of the weigths is 5 + 3 + 5 + 5 = 18

So the student's GPA for that term, rounded to two decimal places, is: 55.4/18 = 3.07

4 0

2 years ago

Write the standard form of the line that passes through the point (-2, 4) and is parallel to x - 2y = 6.

Radda [10]

First calculate the function of x-2y=6:
x-2y=6 | - x
-2y=6-x | ÷ (-2)
y=0.5x-3

Now you have the function. Because the slope you search is parallel to this one, the slope is the same (in this case 0.5). A slope of 0.5 means for 2 steps to the right go one up. To define the function you are searching you have to find out the y intercept. For this take your point (-2|4). Now go as many steps to the right until you reach the y intercept or x=0 in this case you need 2 steps. So for 2 steps right you go one up. Now you have the y intercept (5).
The resulting function is: f(x) = 0.5+6.

6 0

3 years ago