All categories

3 years ago

Let h(x) = 2x + 5 and g(x) = 8 - 3r. What is the value of h(g(1.5))?

SAT

1 answer:

balandron [24]3 years ago

6 0

<h3>Answer: 12</h3>

===================================

Explanation:

First lets compute the value of g(1.5)

Plug x = 1.5 into the g(x) function

g(x) = 8 - 3x

g(1.5) = 8 - 3*1.5 <<--- note how every x is replaced with 1.5

g(1.5) = 8 - 4.5

g(1.5) = 3.5

We ultimately want the value of h(g(1.5)), but that is the same as h(3.5) because we found g(1.5) = 3.5; effectively, g(1.5) and 3.5 are the same value.

Let's compute h(3.5) by plugging in x = 3.5 into the h(x) function.

h(x) = 2x + 5

h(3.5) = 2(3.5) + 5

h(3.5) = 7+5

h(3.5) = 12

h(g(1.5)) = 12 which is the final answer

----------------

An alternative track is to first figure out what h(g(x)) would be in general, by first doing this

h(x) = 2x + 5

h(g(x)) = 2*( g(x) ) + 5 <<---- every x replaced with g(x)

h(g(x)) = 2*( 8-3x ) + 5 <<---- the g(x) replaced with 8-3x

h(g(x)) = 16 - 6x + 5

h(g(x)) = -6x + 21

From here, we plug in x = 1.5

h(g(x)) = -6x + 21

h(g(1.5)) = -6*1.5 + 21

h(g(1.5)) = -9 + 21

h(g(1.5)) = 12 which is the same answer as before

You might be interested in

(5372 + 100y^2) + 5(10y^2 – 110) Add the two polynomials and write in the form ay^2 + b, where a and b are constants, What is th

dangina [55]

Answer:

The value of a is 150 and b is 4822.

Explanation:

First, you have to expand to remove brackets :

$(5372 + 100 {y}^{2} ) + 5(10 {y}^{2} - 110)$

$= 5372 + 100 {y}^{2} + 50 {y}^{2} - 550$

Next, you have to simplify :

$100 {y}^{2} + 50 {y}^{2} + 5372 - 550$

$= 150 {y}^{2} + 4822$

Next, you have to compare it :

$a {y}^{2} + b = 150 {y}^{2} + 4822$

$a = 150$

$b = 4822$

5 0

3 years ago

Suppose that prolog facts are used to define the predicates mother(m, y) and father(f, x), which represent that m is the mother

erastova [34]

Prolog languages are logics that are used when creating programs that require artificial intelligence.

The prolog rule to define the predicate grandfather(x, y) is grandfather(X,Y) :- mother(M,Y), father(X,M); father(F,Y), father(X,F)

<h3>How to determine the prolog rule</h3>

From the question, we have the following definitions:

mother(m, y): m is the mother of y
father(f, x): f is the father of x

For x to be the grandfather of y, then either of the following definitions must be true

m is the mother of y, and x is the father of m
f is the father of y, and x is the father of f

Using the above highlights, the prolog rule would be

grandfather(X,Y) :-

mother(M,Y), father(X,M);

father(F,Y), father(X,F)

Let h(x) = 2x + 5 and g(x) = 8 - 3r. What is the value of h(g(1.5))?​

Let h(x) = 2x + 5 and g(x) = 8 - 3r. What is the value of h(g(1.5))?