Please help! I'm very confused. 20 points.

Answer:

The greatest common factor is [tex]5pq^2[/tex].

Step-by-step explanation:

The given expressions are [tex]25p^2q^3[/tex], [tex]15p^2q^2[/tex] and [tex]35pq^4[/tex].

Greatest common factor of two numbers is the greatest number that divides both numbers completely.

Find factors of each expression.

[tex]25p^2q^3=5\times 5\times p\times p\times q\times q\times q[/tex]

[tex]15p^2q^2=3\times 5\times p\times p\times q\times q[/tex]

[tex]35pq^4=5\times 7\times p\times q\times q\times q\times q[/tex]

The common factors are 5,p,q and q. So, the greatest common factor of given expressions is

[tex]G.C.F.=5\times p\times q\times q[/tex]

[tex]G.C.F.=5pq^2[/tex]

Therefore the greatest common factor is [tex]5pq^2[/tex].

The transformed equations for each of your base functions according to given changes are f(x) = -1.5*(1/2)ˣ⁻⁴, f(x) = ln(4×(x+3))-0.5, and f(x)=e⁻³×(x-1) respectively.

1. The transformed function for your first one, namely f(x)= (1/2)ˣ, after being translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5 would be f(x) = -1.5×(1/2)⁽ˣ⁻⁴⁾.

2. Your second function, f(x) = ln(x), after being translated 3 units left, horizontally compressed by a factor of 1/4, and translated 0.5 units down becomes:
f(x) = ln(4×(x+3))-0.5.

3. Your final function, f(x)=e^x, when it's horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right, would transform into: f(x)=e⁻³×(x-1).

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Final answer:

To factor the expression [tex]y^2+6y+8[/tex] completely, we use the method of factoring binomials. The expression can be factored as (y + 2)(y + 4).

Explanation:

To factor the expression y2 + 6y + 8 completely, we need to find two binomials that multiply together to give us the original expression. Since the coefficient of the y2 term is 1, we know that the binomials will take the form (y + a)(y + b). To find the values of a and b, we need to find two numbers that add up to 6 (the coefficient of the y term) and multiply to give 8 (the constant term).

The numbers that satisfy these conditions are 2 and 4, because 2 + 4 = 6 and 2 × 4 = 8. So, we can factor the expression as (y + 2)(y + 4).

The admission fee at a fair is $2.00 for children and $4.00 for adults.

On Saturday 2,500 people entered the fair and $7,000.00 were collected.

How many children and how many adults attended? Give your answer, using x for children, y for adults.

Form of: x =, and y =

Let K = no. of children

Let A = no. of adults

2500 people mean

Kids + Adults

K + A = 2500

K = 2500 – A

2K + 4A = 7000

K + 2A = 3500

(2500 – A) + 2A = 3500

A = 3500 – 2500

(A = 1000, adults)

K = 2500 – A

K = 2500 -1000

(K = 1500, Kids)

CHECK:

1500*2 = $3000

1000*4 = $4000

(Total = $7000, people.).

Hope this helps:

Answer:IT IS B

Step-by-step explanation:

I GOT A 100 ON MY TEST YOUR WELCOME :D

Answer:

Step-by-step explanation:

________

Good evening ,

_______________

-4x+3y=-12

-2x+3y=-18

This system is the same as

y = (4/3)x - 4

y = (2/3)x - 6

We note that the two coefficients 4/3 and 2/3 are positives

So the right answer is C (graph 2).

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:)

Answer:-14pi/9

Step-by-step explanation:

Answer:

i got 1/4

Step-by-step explanation:

me sorry in wrong

The factorization of the given polynomial 2x3 + x2 - 18x - 9 is (x-3)(x+3)(2x+1) and we achieve this by factoring common terms and applying the formula for difference of squares.

To factor the polynomial 2x3 + x2 - 18x - 9, you would first tie together similar terms (if any), then check for any common factors in all the terms. In this case, we can factor this expression in two steps:

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Answer C

the value of sin(pi/2) =1

the value of sin(pi) = 0

according to the graph sin(3pi/2) = 1 and sin(3pi) =0

so the correct equation for the graph must be f(x) = sin(x/3)

Jesse is incorrect, because the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]

From the question, we understand that the period is 3 times sin x.

The above claim is wrong.

Given that, the period (B) is 3.

i.e B = 3

The function is represented as:

[tex]f(x) = \sin(\frac{2\pi}{B})[/tex]

So, we have:

[tex]f(x) = \sin(\frac{2\pi}{3})[/tex]

Represent [tex]2\pi[/tex] with x

[tex]f(x) = \sin(\frac{x}{3})[/tex]

Hence, the equation of the graph should be [tex]f(x) = \sin(\frac{x}{3})[/tex]

Read more about sine functions at:

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Answer:

use division: 133/19 = 7 picutre frames

Step-by-step explanation:

he difficulty of graphing a quadratic function varies depending on the form you find it in. We'll start things off relatively easily. 

f(x) = a(x – h)2 + k 

No, we're not lying to you; that is a quadratic function. Go ahead, multiply it out. 

f(x) = ax2 + (-2ah)x + (ah2 + k) 

The h and k are constants, so (-2ah) and (ah2 + k) are also constants, which we could call, say, b and c. See, you can trust us, it's totally quadratic. 

When you have a parabola written out like f(x) = a(x – h)2 + k, it's in vertex form. With vertex form, you have several pieces of important information thrown at you right away. When you first meet someone, your first impression tends to stick with you. It's the same with this equation.

The sign of a tells you if the parabola opens up or down. If a is positive, it opens up. If a is being a Negative Nancy, the parabola opens down. You also know that the vertex of the parabola is at the point (h, k). Be careful with the sign of h, though.