MATHEMATICS COLLEGE

Maggie rewrote the expression 36 + 27 as two factors using the greatest common factor and the distributive property. Write the expression Maggie created.

Answers

Answer 1

Answer:

Answer:

9(4+3)

Step-by-step explanation:

The GCF of 36 and 27 is 9. Dividing 36 and 27 by 9, I used the distributive property and got the equation 9(4+3)

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The difference between seven and triple the input

Answers

Answer: 3x - 7

x = some input number

3x = triple the input

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Graph the following function and then find the specified limits. When necessary, state that the limit does not exist.f(x)equals=left brace Start 3 By 2 Matrix 1st Row 1st Column x minus 3 2nd Column if x less than 5 2nd Row 1st Column 2 2nd Column if 5 less than or equals x less than or equals 6 3rd Row 1st Column x plus 4 2nd Column if x greater than 6 EndMatrixx−3 if x<52 if 5≤x≤6x+4 if x>6;findModifyingBelow lim With x right arrow 5limx→5 f(x)andModifyingBelow lim With x right arrow 6limx→6 f(x)

Answers

If I'm reading the question right, you have

$f(x)=\begin{cases}x-3&\text{for }x<5\n2&\text{for }5\le x\le6\nx+4&\text{for }x>6\end{cases}$

and you have to find

$\displaystyle\lim_(x\to5)f(x)\text{ and }\lim_(x\to6)f(x)$

The limits exist if the limits from either side exist. We have

$\displaystyle\lim_(x\to5^-)f(x)=\lim_(x\to5)(x-3)=2$

$\displaystyle\lim_(x\to5^+)f(x)=\lim_(x\to5)2=2$

$\implies\displaystyle\lim_(x\to5)f(x)=2$

and

$\displaystyle\lim_(x\to6^-)f(x)=\lim_(x\to6)2=2$

$\displaystyle\lim_(x\to6^+)f(x)=\lim_(x\to6)(x+4)=10$

$\implies\displaystyle\lim_(x\to6)f(x)\text{ does not exist}$

Final answer:

The function f(x) is a piecewise function. The limit as x approaches 5 equals 2 and the limit as x approaches 6 does not exist as the values from both sides are not the same.

Explanation:

The function f(x) given is a piecewise function which is defined differently on different intervals of x.

First let's graph these three conditions:

For x < 5, f(x) = x - 3. It is a straight line that crosses the Y-axis at -3.
For 5 ≤ x ≤ 6, f(x) = 2. It is a horizontal line along the height of 2 from x=5 to x=6.
For x > 6, f(x) = x + 4. It is a straight line that crosses the Y-axis at 4.

Next, we'll find the specified limits:

limx→5 f(x): As x approaches 5, we will look at values from both sides. From the left (x < 5), it would be 5 - 3 = 2. From the right (5 ≤ x ≤ 6), f(x) = 2. The value is the same from both sides, so the limit as x approaches 5 equals 2.
limx→6 f(x): As x approaches 6, from the left (5 ≤ x ≤ 6), f(x) = 2. From the right (x > 6), it would be 6 + 4 = 10. The values are not the same from both sides, so the limit as x approaches 6 does not exist.

Learn more about Mathematical Limits here:

brainly.com/question/36891684

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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.

Answers

Answer:

D. F(x) = 2(x-3)^2 + 3

Step-by-step explanation:

We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)

We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.

The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.

Our two equations left are:

B. F(x) = 2(x+3)^2 + 3

D. F(x) = 2(x-3)^2 + 3

Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.

y = 2(3+3)^2 + 3 =

2(6)^2 + 3 =

2·36 + 3 =

72 + 3 =

That one didn't give us a y value of 3.

y = 2(3-3)^2 + 3 =

2(0)^2 + 3 =

2·0 + 3 =

0 + 3 =

This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:

D. F(x) = 2(x-3)^2 + 3

Hopefully this helps you to understand parabolas better.

Caitlin earns money as a lifeguard and as a pet sitter. In one week, she earned $25 pet sitting. The total amount of money she earned that week was less than $75. The inequality g + 25 less-than 75 represents g, the possible amount of money she made as a lifeguard.

Answers

Answer:

I actually needed help with the answer but now I think about it the answer is answer C. $50

Step-by-step explanation:

Answer:

I think that it is B. 49.99

Step-by-step explanation:

Factorise : 64a cube minus 27b cube minus 144a square b plus 108ab square . Plz Answer this question

Answers

Answer:

The answer is $4a(16a^2+27b^2)-3b(9b^2+48b)$

Step-by-step explanation:

step one:

let us re-write the expression in mathematical terms for clarity

we have the expression stated below

$64a^3-27b^3-144b^2+108ab^2$

step two:

We are going to collect like terms before factorization we have

$64a^3+108ab^2-27b^3-144b^2$

We can now factorize the expression we have

$4a(16a^2+27b^2)-3b(9b^2+48b)$

how much 45% acid solution should be mixed with a 30% acid solution to make 450 ml of a 40% acid solution?

Answers

We do as follows:

let x = amount of 45% solution
y = amount of 30% solution

overall balance => x + y = 450
acid balance => .45x + .30y = .40(450)

Solving simultaneously, we will have:

x = 300 mL
y = 150 mL

This is assuming that partial molar properties does not affect the volume greatly. Hope this answers the question. Have a nice day.

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