Expand ; 3(1-x/2)^2​

Question 1

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Explanation:

To compute f(g(2)), we'll first need to find g(2).

Locate 2 in the x row. Then read straight down until you get to the g(x) row. You should find that g(2) = 4

This means f(g(2)) becomes f(4). We then repeat the same process as before. Locate 4 in the x row, read straight down til you get to the f(x) row to find that f(4) =  -9

Overall, we can say f(g(2)) = -9

We do the same set of steps to compute g(f(-1)). You should find that f(-1) = -1 and g(f(-1)) = g(-1) = -2

Lastly, we subtract the results we got:  

f(g(2)) - g(f(-1)) = -9 - (-2) = -9+2 = -7

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Question 2

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Explanation:

If you were to graph each equation, you should get what you see below.

The red and blue curves do not intersect in any way. We need an intersection point to have a solution. Because there are no intersections, we don't have any solutions. The system is considered inconsistent.

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Question 3

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Explanation:

x = number of scooters made and sold

Each scooter costs $150 to make. If you made x of them, then it costs 150x dollars. Then tack on the fixed cost of $2000 to get the expression [tex]150x+2000[/tex]

The cost function is [tex]C(x) = 150x+2000[/tex]. We'll subtract this from the revenue function R(x) to get the profit P(x)

[tex]\text{Profit} = \text{Revenue} - \text{Cost}\\\\P(x) = R(x) - C(x)\\\\P(x) = (400x-2x^2) - (150x+2000)\\\\P(x) = 400x-2x^2-150x-2000\\\\P(x) = -2x^2+250x-2000\\\\[/tex]

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Question 4

[tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]

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Explanation:

[tex]g(x) = \frac{1}{x+1}\\\\g(f(x)) = \frac{1}{f(x)+1}\\\\g(f(x)) = \frac{1}{x^2+x-3+1}\\\\g(f(x)) = \frac{1}{x^2+x-2}\\\\g(f(x)) = \frac{1}{(x+2)(x-1)}\\\\(g\circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\[/tex]

I started with the outer function g(x) and replaced each x with f(x) in the second step. Then I plugged in f(x) = x^2+x-3 and simplified. Factoring the denominator is helpful to determine where the denominator becomes zero. Specifically, it happens when x = -2 and x = 1. These x values must be kicked out of the domain to avoid a division by zero error.

So we start off with the real number line, and poke holes at x = -2 and x = 1.

The notation [tex]x \in \mathbb{R}[/tex] means x is a real number. Then we tack on [tex]x \ne -2, x \ne 1[/tex]

Overall, the domain is [tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]

Let's see what happens if we tried plugging x = -1 into this composite function:

[tex](g \circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\(g \circ f)(-1) = \frac{1}{(-1+2)(-1-1)}\\\\(g \circ f)(-1) = \frac{1}{(1)(-2)}\\\\(g \circ f)(-1) = \frac{1}{-2}\\\\(g \circ f)(-1) = -0.5\\\\[/tex]

We don't get a division by zero error, so x = -1 is allowed. The same can be said about any other x value as long as it's not -2 and not 1 either.

Answer:

y= -5x + 25

Step-by-step explanation:

y = mx + b

m(slope) = descending 5ft/sec means the height will decrease so the slope must be negative

b(y-int) = starting height of 25 ft added

Answer:

14

Step-by-step explanation:

4^2=16

16/2=8

8+6=14

Answer:

[tex]14[/tex]

Step-by-step explanation:

This equation would be easier to do if it was: [tex]6+\frac{4^2}{2}[/tex]

So first you have to cancel out: [tex]\frac{4^2}{2}[/tex] so that would become [tex]6+8[/tex]

Finally [tex]6+8=14[/tex]

There you go brainliest pls

Answer:

416

Step-by-step explanation:

you take 520 times .80

Answer:

$100

Step-by-step explanation:

12x5=60

+40= $100

Answer:

$100

Step-by-step explanation:

This is easy

12x5=60

+40=$100

If tall is completely dominant over short, then the mother's genotype is either TT or Tt. The father is short so his genotype is tt.

Crossing TT with tt produces only heterzygous offspring with genotype Tt. Then the genotypic and phenotypic ratios are 0 TT : 1 Tt : 0 tt and 1 tall : 0 short, respectively. As percentages, these would

• geno:   0% TT : 100% Tt : 0% tt

• pheno:   100% tall : 0% short

Crossing Tt with tt on the other hand produces offspring with genotype either Tt or tt with equal probability, so that the geno and pheno ratios are 0 TT : 1 Tt : 1 tt and 1 tall : 1 short. As percentages,

• geno:    0% TT : 50% Tt : 50% tt

• pheno:   50% tall : 50% short

Mi hermano ha ganado un dinero devengado de 8835 pesos en 15 días.

En esta pregunta debemos determinar el dinero devengado por un período de 15 días a partir de una tasa diaria constante. Esa cantidad es igual al producto de la tasa diaria constante, en pesos por día, y el número de días trabajados, en días:

[tex]x = 589\,\frac{\$}{dia}\times 15\,dias[/tex]

[tex]x = 8835\,\$[/tex]

Mi hermano ha ganado un dinero devengado de 8835 pesos en 15 días.

Para aprender más sobre álgebra y aritmética, invitamos cordialmente a ver esta pregunta: https://brainly.com/question/953809

Answer: Jon Pardi - Tequila Little Time

Step-by-step explanation:

I don't even know what this song is, but I searched it up.

Answer: 5

Step-by-step explanation:

Answer:

k < 3  should do it

Step-by-step explanation:

Answer:

where are you from me

Step-by-step explanation:

:philipines

btw ty sayo

Bill was for $28.35.  A 20% tip would come to $5.67.  If we add this tip to the $28.35 bill, we get a total of $28.35 + $5.67 + 0.0625($28.35)

                                                 = $35.79 (total)

please give brainlist

Answer:

1/24

Step-by-step explanation:

multiply 1/9 and 3/8. The product of the two factors is 3/ 72. Seeing the two factors on the other hand, we can cancel out 3. Hence the final answer to this problem in lowest terms becomes 1/24.

The value of x in the given triangle is 25

The triangle shown is a right triangle.

Each side of the triangle can be found by using the Pythagora's theorem

The Pythagora's theorem states that the "square of the hypotenuse equals the sum of the squares of the other two sides"

Applying the Pythagora's theorem:

[tex]x^2=24^2+7^2\\\\x^2=576+49\\\\x^2=625\\\\x=\sqrt{625}\\\\ x=25[/tex]

Learn more on missing sides of right triangle here: https://brainly.com/question/23987176

Answer:

jeri drew a plgon with exatly three sides

Answer:

could you add the choices please

Step-by-step explanation:

it doesnt help without the choices

Answer:

3.90

Step-by-step explanation:

4.25

+1.85=6.10

10-6.10=3.9

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Work Shown:

4.25+1.85 = 6.10

It costs $6.10 to get the sandwich and drink.

If the customer pays with a $10 bill, then they get 10.00 - 6.10 = 3.90 dollars in change.

One way to represent $3.90 is to have:

The coins add up in value to 75+10+5 = 90 cents.

Or another option is to have 9 dimes and no other coins. Or perhaps you could have nothing but nickels and you'd need 18 nickels. There are a few ways to determine what coins to use.

Answer:

C

Step-by-step explanation:

Since the weight is proportional to the cost, let's find the slope of the chart.

(x,y) corresponds to (weight, cost)

Pick 2 coordinate points with both the weight and cost.

(4, 23.96) (6, 35.94)

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{35.94-23.96}{6-4}= 5.99[/tex]

One pound is 5.99 dollars.

So to fill in the chart, multiply 5.99 by the number of pounds.

y=5.99x

2 lbs | $11.98

3 lbs | $17.97

4 lbs | $23.96

5 lbs | $29.95

6 lbs | $35.94

With this information, C would be the correct answer.

Answer:

17/12

Step-by-step explanation:

In order to add fractions, you have to have a common denominator. The denominators in these fractions are 3, 2, and 4 (the bottom numbers). To get a common denominator, figure out what number all three of them can go into. Their common factor would be 12 because all three numbers go into 12.

Multiply each numerator in the fraction (the top number) by how much it takes to get from our current denominators (3,2,4) to our final denominator (12).

For example, in 2/3 we know that 3 times 4 equals 12. Multiply the top number by 4 to get 8/12.

In 1/2 we know that 2 times 6 equals 12. Multiply by 6 to get 6/12.

In 1/4 we know that 4 times 3 equals 12. Multiply by 3 to get 3/12.

Add the fractions to get 17/12.

Answer:

102 degrees below horizontal

Step-by-step explanation:

if the first angle is 78 degrees, the angle on the other side of the line is 102 degrees because a straight line is 180 degrees, and a box would have a total of 360 degrees in it

because the same line passes through both horizontal lines, the angle 3 is equal to the opposite angle to the 78

180-78 = 102

another way to look at it is that the 78 degrees is the same angle directly above angle 3 because the horizontal lines are parallel, and if it is 78 degrees, that makes the angle below it (angle 3) 102 degrees since a straight line must add to 180 degrees

Answer:

102

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1/2, 11/6

Step-by-step explanation:

y=-4+9y

9y-y=4

8y=4

y=1/2

3x-5=1/2

3x=5+1/2=11/2

x=11/6

Step-by-step explanation:

[tex]f( x) {}^{ - 1} \\ f(x) = 5x \\ y = 5x \\ x = 5y \\ y = \frac{x}{5} \\ f(x) {}^{ - 1} = \frac{x}{5} [/tex]

Answer:

150*2/3=100

take school size then multiply it by the ratio to get the amount of student who prefer such toothpaste.

Step-by-step explanation:

Answer:

y=-2x+3

Step-by-step explanation:

Comment if you need steps.

Answer:

Agree

Step-by-step explanation:

Just copy and paste (without quotations): "I agree because r < -5 is just a flipped inequality of -5 > r. In other words, 'r is less than -5' is the same as '-5 is greater than r'."

Answer: I dont understand the question

Step-by-step explanation:

Answer:

Factors of 20 and 10: P ∪ Q

Factors of 20 but not 10: U ∩ (P ∪ Q)c

Neither factors of 20 or 10: (P ∪ Q)c