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Which expression is equivalent to (-11x² +1.4x - 3) + (4x² -2.7x+8)?
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Answers

Answer 1

Answer:

Final answer:

To simplify the given expression, we need to combine the like terms by adding their coefficients.

Explanation:

To find the expression that is equivalent to (-11x² +1.4x - 3) + (4x² -2.7x+8), we need to combine the like terms. Like terms are terms that have the same variables and their exponents. In this case, we have terms with x², x, and constants.

By adding the coefficients of the like terms, we get: (-11x² + 4x²) + (1.4x - 2.7x) + (-3 + 8).

This simplifies to: -7x² - 1.3x + 5.

Learn more about Combining Like Terms here:

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Oct 16, 10:30:54 AMA rocket is shot into the air. The function f (x) = -16x2 + 64x + 8 gives the
height of the rocket (in feet) as a function of the rockets horizontal distance from
where it was initially shot.
a. What was the initial height of the rocket when it was shot?
b. What is the maximum height the rocket reaches in the air?
a. The initial height of the rocket was
feet.
b. The maximum height the rocket reaches is
feet.

Answers

Answer:

A) 8 feet.

B) 72 feet

Step-by-step explanation:

We have the function $f(x)=-16x^2+64x+8$ which gives the height of the rocket (in feet) as a function of the rocket's horizontal distance.

Part A)

We want to find the initial height of the rocket when it was shot.

At the initial height, the rocket has not moved anywhere. So, the horizontal distance will be 0.

Therefore, to find the initial height, we will substitute 0 into our function. This yields:

$f(0)=-16(0)^2+64(0)+8$

Evaluate:

$f(0)=8$

Therefore, the initial height was 8 feet.

Part B)

Notice that our function is a quadratic.

Therefore, the maximum height will be given by the vertex of our quadratic.

To find the vertex, we use:

$(-(b)/(2a),f(-(b)/(2a)))$

Let's label our coefficients. We have $-16x^2+64x+8$

Therefore, a=-16, b=64, and c=8.

Substitute them into the vertex formula to find the x-coordinate:

$x=-(64)/(2(-16))\n\Rightarrow x=64/32=2$

Now, to find the maximum height, substitute 2 back into our function f(x):

$f(2)=-16(2)^2+64(2)+8$

Evaluate:

$f(2)=-16(4)+64(2)+8\n\Rightarrow f(2)=-64+128+8\n\Rightarrow f(2)=72\text{ feet}$

Therefore, the rocket reaches a maximum height of 72 feet.

4y-x=2x-4=x+y
solve for x

Answers

X=12

Explanation: in the photo

Answer:

a system of equations , as below

Step-by-step explanation:

4y-x

2x-4

x+y

use any two of the above to find a formula for one of the variables since they are all equal to each other.. btw.. it makes it much easier .. that they are all equal. :)

2x-4=x+y ⇒ x-4=y use this to plug into the y in the top formula

4(x-4)-x=2x-4 ⇒ 4x-16-x=2x-4 ⇒ 3x-16=2x-4 ⇒ x=12 yay! ;) now plug in 12 for x

2(12)-4=(12)+y ⇒ 24-4 = 12 +y ⇒ 8=y yay ! now we have both x and y

x=12

y= 8

this checks by plugging in the two number found for x & y (btw I had to try this about 4 times ) :P I kept messing up the algebra which is soooo easy to mess up.

Solve for brainliest

Answers

Answer:

but not sure because I'm not that good

Over the interval [-3, 0[, the local minimum is

Answers

Answer:

-16

Step-by-step explanation:

What does the expression (8x)2 represent

Answers

Option D is correct.

We have an expression that is used to calculate the area of a square - $s^(2)$ , where s is the side of the square.

We have to estimate the value of the expression $(8x)^(2)$

What is the area and perimeter of a square of side 'a' ?

The area of a square is - Area = $a^(2)$ and the perimeter is - P = 4a.

In the question, we have to estimate the value of the expression $(8x)^(2)$ .

Let f(x) = $(8x)^(2)$

The expression given to us is $s^(2)$ .

Let f(s) = $s^(2)$

Compare f(s) and f(x), you will get -

s = 8x

Hence, the expression $(8x)^(2)$ represents the area of square with side length of 8x.

Hence, Option D is correct.

To solve more questions on squares, visit the link below -

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Answer:

option d

Step-by-step explanation:

please mark brainlist

A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? We would assign a probability of to the design 1 outcome, to design 2, to design 3, to design 4, and to design 5. In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Design Number of Times Preferred 1 10 2 5 3 30 4 40 5 15 Do the data confirm the belief that one design is just as likely to be selected as another? Explain. Yes, the sum of the assigned probabilities is 1. No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely. Yes, the average of the assigned probabilities is 0.20. No, a probability of about 0.50 would be assigned using the relative frequency method if selection is equally likely.

Answers

Answer:

Correct option: "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."

Step-by-step explanation:

The assumption made is that all the 5 different packages are equally likely, i.e. the probability of selecting a package is $(1)/(5)=0.20$ .

The probability distribution is shown below.

According to the probability distribution:

The probability of a person preferring design 1 is,

$P(X=1)=0.10$

The probability of a person preferring design 2 is,

$P(X=2)=0.05$

The probability of a person preferring design 3 is,

$P(X=3)=0.30$

The probability of a person preferring design 4 is,

$P(X=4)=0.40$

The probability of a person preferring design 1 is,

$P(X=5)=0.15$

So it can be seen that the probability of preferring any of the 5 designs are not same.

Thus, the designs are not equally likely.

The correct option is "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."

The selection Probability determined using the relative frequency method do not match the assigned probabilities, suggesting that the data do not confirm the belief that one design is as likely to be selected as another.

The given data can be used to calculate the relative frequencies of each package design selected by the consumers.

To determine the selection probabilities using the relative frequency method, divide the number of times a design was preferred by the total number of consumers.

For example, for design 1, the selection probability would be 10/100 = 0.1.

Similarly, for design 2, the selection probability would be 5/100 = 0.05.

The selection probabilities for designs 3, 4, and 5 would be 0.3, 0.4, and 0.15 respectively.

Comparing these probabilities to the assigned probabilities, it can be observed that the assigned probabilities do not match the observed relative frequencies, indicating that the data do not confirm the belief that one design is just as likely to be selected as another.

Learn more about Probability here:

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