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3 years ago

DVDS are on sale for $24 each Felipe writes expression 4*24 to find the cost in dollars of

Mathematics

2 answers:

kirill115 [55]3 years ago

8 0

4(18+6) = 4*18 + 4*6 = 72 + 24 = 96

klemol [59]3 years ago

5 0

we know that

The distributive property tells us how to solve expressions in the form of

$a(b + c)=ab+ac$

then

we need to remember to multiply first, before doing the addition

in this problem

Let

$a=4$

$(b+c)=24$

$(b+c)=20+4$

substitute

$4*24=4*(20+4)\\=4*20+4*4\\=80+16\\=\$96$

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F:[1/2,infinity)—>[3/4,infinity) f(x)=x^2-x+1 find the inverse of f(x);please explain

dexar [7]

Answer:

$f^{-1}(x)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}$

Step-by-step explanation:

y=x^2-x+1

We want to solve for x.

I'm going to use completing the square.

Subtract 1 on both sides:

y-1=x^2-x

Add (-1/2)^2 on both sides:

y-1+(-1/2)^2=x^2-x+(-1/2)^2

This allows me to write the right hand side as a square.

y-1+1/4=(x-1/2)^2

y-3/4=(x-1/2)^2

Now remember we are solving for x so now we square root both sides:

$\pm \sqrt{y-3/4}=x-1/2$

The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.

This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.

That is we want:

$\sqrt{y-3/4}=x-1/2$

Add 1/2 on both sides:

$1/2+\sqrt{y-3/4}=x$

The last step is to switch x and y:

$1/2+\sqrt{x-3/4}=y$

$y=1/2+\sqrt{x-3/4}$

$f^{-1}(x)=1/2+\sqrt{x-3/4}$

8 0

3 years ago

What is the domain of the function mc022-1.j pg? mc022-2.jp g mc022-3.jp g mc022-4.jp g mc022-5.jp g

snow_tiger [21]

Answer:

$0\leq x < infinite$

Step-by-step explanation:

we have

$y=\sqrt{x} +4$

Find out the domain

we know that

The radicand must be greater than or equal to zero

$x\geq 0$

The domain is the interval -----> [0,∞)

All real numbers greater than or equal to zero

$0\leq x < infinite$

3 0

3 years ago

What is the first term of the geometric sequence whose fifth term is 1/24 and tenth term is 1/768

Neporo4naja [7]

An=a1r^(n-1)

given
a5=1/24
a10=1/768

we know that
a5=1/24=a1r^(5-1) and
a10=1/768=a1r^(10-1)

so
1/24=a1r^4
1/768=a1r^9

(a1r^9)/(a1r^4)=r^5=(1/768)/(1/24)=1/32

r^5=1/32
take 5th root of both sides
r=1/2

we have
a5=a1r^4=1/24
evaluate r^4 or (1/2)^4
1/16
a1(1/16)=1/24
times both sides by 16/1
a1=16/24
a1=2/3

the first term is 2/3

7 0

3 years ago

A sine function has an amplitude of 3, a period of pi, and a phase shift of pi/2. What is the y-intercept of the function?

jarptica [38.1K]

Based on the calculations, we can logically deduce that the y-intercept of this sine function is equal to: A. 3.

Given the following data:

Amplitude = 3

Period = π

Phase shift = π/2

<h3>How to determine the y-intercept of this function?</h3>

Mathematically, a sine function is modeled by this equation:

y = Asin(ωt + ø)

Where:

A represents the amplitude.

ω represents angular velocity.

t represents the period.

ø represents the phase shift.

Also, the period of a sine wave is given by:

t = 2π/ω

2 = 2π/ω

ω = 2

Substituting the given parameters into the equation, we have;

y = 3sin(2t + π/2)

At t = 0, we have:

y = 3sin(2(0) + π/2)

y = 3sin(π/2)

y = 3sin(90)

y = 3 × 1

y = 3.

In conclusion, we can logically deduce that the y-intercept of this sine function is equal to 3.

Read more on phase shift here: brainly.com/question/27692212

#SPJ1

5 0

2 years ago

What is the product? (y3+3y+7) x (8y2+y+1)

Nataly [62]

Answer:

I believe that this is what you mean. (y^3+3y+7)*(8y^2+y+1)

Step-by-step explanation:

So your answer would be: 8y^5+y^4+25y^3+59y^2+10y+7

Have a nice day!

I really hope this helps!

5 0

2 years ago