If f(x) = 2^x + 4 and g(x) = x^2 – 4 what is the value of f(5) +g(-3)

Find the values of a and b such that

Varvara68 [4.7K]

Answer:

a = 1.5

b = 1.75

Step-by-step explanation:

First, we need to solve $(x+a)^2$ and replace the result in the initial equation as:

$x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b$

Then, this equality apply only if the coefficient of $x$ is equal in both sides and the constant is equal in both sides.

It means that we have two equations:

$3x=2ax\\4=a^2+b$

So, using the first equation and solving for a, we get:

$3x=2ax\\3=2a\\a=\frac{3}{2}=1.5$

Finally, replacing the value of a in the second equation and solving for b, we get:

$4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75$

3 0

3 years ago

Find a value for y for which the expression (1-y)(3-y)(6-y) has each given value

erik [133]

$\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=-70$

$\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=-70$

$\\ \tt\Rrightarrow y(2)(4)(7)=70$

$\\ \tt\Rrightarrow y(56)=70$

$\\ \tt\Rrightarrow y=\dfrac{70}{56}$

$\\ \tt\Rrightarrow y=\dfrac{5}{4}$

#2

$\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=120$

$\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=120$

$\\ \tt\Rrightarrow -y(2)(4)(7)=120$

$\\ \tt\Rrightarrow 56y=-120$

$\\ \tt\Rrightarrow y=\dfrac{-120}{56}$

$\\ \tt\Rrightarrow y=\dfrac{-15}{7}$

7 0

2 years ago

Read 2 more answers

What is the result of isolating y2 in the equation below?

lyudmila [28]

STEP-BY-STEP SOLUTION:

( x + 4 )^2 + y^2 = 22

x^2 + 2 × x × 4 + 4^2 + y^2 = 22

x^2 + 8x + 16 + y^2 = 22

y^2 = 22 - x^2 - 8x - 16

y^2 = - x^2 - 8x + 6

FINAL ANSWER:

Therefore, the answer is:

D. y^2 = - x^2 - 8x + 6

Please mark as brainliest if you found this helpful! :)
Thank you <3

6 0

3 years ago

Question 1 (Multiple Choice Worth 4 points)

zalisa [80]

Answer:

The answer is "Analysis the information by chart and number processes".

Step-by-step explanation:

They already have articulated a query and also gathered information unless you are searching only at the distribution of your results. Those who are ready to analyze your results for all are there.

6 0

3 years ago

If a club charges dues of $200 a year, it will have 50 members. For each $5 it raises its dues, it loses a member. USE AN EQUATI

Vikentia [17]

Answer:

The value is $y = \$ 225$

Step-by-step explanation:

From the question we are told that

The amount charge per year is $k = \$ 200$

The number of members it will have at this amount is $n = 50$

The amount amount increase that will lead to the loss of a single member is $z = \$ 5$

Generally the total amount the club would obtain from its members is mathematically represented as

$I = Amount \ due\ paid * Number \ of members$

Now let x denote the number of member lost

Hence

$I = (k + zx) (n-x )$

=> $I = (200 + 5x) (50-x )$

=> $I = 10000+50x-5x^2$

Thus the number of members that be removed to give the maximum income from dues is obtained by differentiating the above equation and equating it to zero

$\frac{dI}{dx} = 50-10x$