Factor –7x3 21x2 3x – 9 by grouping. what is the resulting expression? (3 – 7x)(x2 – 3) (7x – 3)(3 x2) (3 – 7x2)(x – 3) (7x2 – 3)(3 x)

Answer:

Part (a)

It depends how your calculator calculates quadratic regressions.

For my calculator:

a = 1.177142857 = 1.18 (nearest hundredth)

b = 42.22257143 = 42.22 (nearest hundredth)

c = -12.87142857 = -12.87 (nearest hundredth)

⇒ y = 1.18 + 42.22x - 12.87x²

Therefore, the quadratic regression equation in standard form is:

[tex]y = -12.87x^2+ 42.22x + 1.18[/tex]

Part (b)

To estimate the height of the rocket after 5 seconds, input x = 5 into the regression equation:

[tex]\implies -12.87(5)^2+ 42.22(5) + 1.18=-109.47[/tex]

As this gives us a negative value, this means that the rocket would have come back to the ground before 5 s.  Therefore, the height of the rocket at 5 s will be 0 ft.

(see attached graph → the rocket will hit the ground at approx 3.3 s)

An equation is formed of two equal expressions. The quadratic equation that can be used to find x, the smaller number is x²+x-272.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the first number be x.

Now since the two numbers are consecutive numbers the other number will be (x+1). Also, it is mentioned in the problem that the product of the two numbers is 272. Therefore, the equation that can represent the product will be,

[tex]x \times (x+1) = 272\\\\x^2 + x =272\\\\x^2 + x -272 = 0[/tex]

Thus, the quadratic equation that can be used to find x, the smaller number is x²+x-272.

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Answer:

c. x2 + x − 272 = 0

Step-by-step explanation:

The total amount that Williana's mother would spend to buy the glass table top is $120.04.

The first step is to determine the area of the glass table top.

Area of a hexagon = [(3√3)/2] x a²

a = side length

2.598 x 27.75² = 2000.68 in²

Cost of the table top = 2000.68 in² x 0.06 = $120.04

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Answer:

80.2

Step-by-step explanation:

Answer:80.2

Step-by-step explanation:

i did the test so yeh edg 2023

Answer: The function is growing exponentially at a rate of 2.5% every day.

Step-by-step explanation:

Answer:

the sum is the total amount resulting from the addition of two or more numbers, amounts, or items.

Answer:

last option

Step-by-step explanation:

7pi/6,11pi/6

Answer:

D

Step-by-step explanation:

the answer is D

this is essentially sin theta = -1/2 which I already solved for you a few mins ago :)

Step-by-step explanation:

please mark me as brainlest

Answer:

A    Y= 5x-9

Step-by-step explanation:

Answer:

C: 8/15

A: 4/25

Step-by-step explanation:

put it into a fraction, four times out of 25 = 4/25, for the first question you would have to simplify it to 8/15.

Answer:

1 degree

Step-by-step explanation:

360 degrees / 360  = 1

Answer :

[tex] \: [/tex]

Explanation :

[tex] \: [/tex]

Solution :

[tex] \: [/tex]

Where,

[tex] \: [/tex]

We know that,

[tex]{\longrightarrow \pmb{\mathbb {\qquad (UV) {}^{2} + (UW) {}^{2} =( VW) {}^{2} }}} \\ \\ [/tex]

Now, we will substitute the given values in the formula :

[tex]{\longrightarrow \pmb{\sf {\qquad (6) {}^{2} + (UW) {}^{2} =( 9) {}^{2} }}} \\ \\ [/tex]

We know that, (6)² = 36 and (9)² = 81. So,

[tex]{\longrightarrow \pmb{\sf {\qquad 36 + (UW) {}^{2} =81}}} \\ \\ [/tex]

Now, transposing 36 to the other side we get :

[tex]{\longrightarrow \pmb{\sf {\qquad (UW) {}^{2} =81 - 36 }}} \\ [/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad (UW) {}^{2} = 45}}} \\ \\ [/tex]

Now, we'll take the square root of both sides to remove the square from UW :

[tex]{\longrightarrow \pmb{\sf {\qquad \sqrt{(UW) {}^{2}} = \sqrt{ 45}}}} \\ \\ [/tex]

When we take the square root of (UW)² , it becomes UW,

[tex]{\longrightarrow \pmb{\sf {\qquad UW = \sqrt{45}}}} \\ \\ [/tex]

We know that, square root of 45 is 6.708.

[tex]{\longrightarrow \pmb{\sf {\qquad UW \approx6.708}}} \\ \\ [/tex]

So,

p = -4 and q = -6

hope it helps...!!!

Answer:

Question B is (12,-7)

Step-by-step explanation:

The 2nd question is asking for the preimage. You did what the image would be if (4,-3) was the preimage.

A group of students formed a circle during a game. The circumference of the circle was about 50.24 feet, and the diameter of the circle was 16 feet. The required expression for value of π is: 3.14

A circle is a form made up of all points on a plane that are at a specific distance from the centre point. In other words, it is the path a moving point in a plane takes to travel around a curve while maintaining a constant distance from another point.

Given that,

The circumference of the circle was about 50.24 feet,

And the diameter of the circle was 16 feet

We have to determine,

Which expression best represents the value of π.

According to the question,

Circumference of the circle = 50.24 feet

Diameter f the circle = 16 feet

Then,

Circumference of the circle = π × d

Circumference of the circle = 50.24 feet

Therefore,

50.24 = π × d

or. π × 16 = 50.24

or,  π = 3.14

Hence, The required expression for value of π is: 3.14

For the more information about the circle refer to:

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Answer:

3/50.

Step-by-step explanation:

There are 10 marbles in the bag.

Probability( a green marble) =  2/10 = 1/5.

Now we replace the green marble in the bag so it contains 10 marbles again.

Probabilty(a yellow marble) = 3/10.

So Probability(Choosing a green then a red with repeacemen)

= 1/5 * 3/10

= 3/50.

Answer:

64%

Step-by-step explanation:

Answer:

hi how do you do I actually don't know sorry very much

Answer:

y intercept: 4, x-intercept: None

Step-by-step explanation:

Took the test and got it right

The sequence an = 2(an-1 - 3) is a recursive sequence

The 4th term of the sequence is -42

The given parameters are:

a1 = 0

a2 = -6

an = 2(an-1 - 3)

Start by calculating a3 using:

a3 = 2(a2 - 3)

This gives

a3 = 2 * (-6 - 3)

a3 = -18

Calculate a4 using:

a4 = 2(a3 - 3)

This gives

a4 = 2 * (-18 - 3)

a4 = -42

Hence, the 4th term of the sequence is -42

Read more about sequence at:

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Answer:

I think a possible equation can be; f(n) = 4(2)ⁿ

f(n) = a * bˣ

Where;

f(n) = the function of f for every n value

a = Initial value (in this case it would be 4)

b = Rate of change (in this case it would be 2, since the bacteria doubles)

x = exponent (in this case it would be n)

So our final equation would be:

f(n) = 4(2)ⁿ

Hope this helps!

(7x + 4)(7x + 4) and (x – 9)(x – 9) are Perfect square trinomial. (5x + 3)(5x – 3) and (–3x – 6)(–3x + 6) shows the Difference of squares.

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

The following are the answers

(5x + 3)(5x – 3) Difference of squares

(7x + 4)(7x + 4) is a Perfect square trinomial

(2x + 1)(x + 2) has Neither a difference of squares nor a perfect square trinomial.

(4x – 6)(x + 8) has Neither a difference of squares nor a perfect square trinomial.

(x – 9)(x – 9) is Perfect square trinomial

(–3x – 6)(–3x + 6) = [tex](-3x)^2- ( -6)^2[/tex]  Difference of squares.

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Answer:

A. B, E, F

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Just by using process of elimination, we can delete all but 1 answer. 95% is greater than 50% and half of the first second and fourth answers are all greater than 57

Answer:

Step-by-step explanation:

67 becaue you divide all the numbers together then add then multiply then subtract divide that number and you get 67

Answer:

x^32

Step-by-step explanation: because its (x^4)^8 you mutiply 4 by 8 so you get 32 and 32 is the new power so it is now x^32.

Answer:

6 cm²

Step-by-step explanation:

Since 3 side lengths are given, I assume that this figure is a triangle. The area of a triangle can be determined by using hero's formula.

[tex]\text{Area of triangle} = \sqrt{\text{s(s - a)(s - b)(s - c)}[/tex]

⇒ s = Perimeter/2

⇒ a, b, and c = side lenths of triangle

Replacing a, b, and c as the given side lengths:

[tex]\implies \text{Area of triangle} = \sqrt{\text{s(s - 5)(s - 3)(s - 4)}[/tex]

Determining the perimeter of the triangle:

[tex]\text{Perimeter of triangle = Sum of it's side lengths}[/tex]

[tex]\implies \text{Perimeter of triangle =}\ 5 + 4 + 3[/tex]

[tex]\implies \text{Perimeter of triangle =}\ 12 \ \text{cm}[/tex]

Determining the half of perimeter:

[tex]\text{Half of perimeter} = s = \dfrac{\text{Perimeter}}{2}[/tex]

[tex]\implies s = \dfrac{12}{2}[/tex]

[tex]\implies s = 6[/tex]

Replacing the value of "s" in the formula:

[tex]\implies \text{Area of triangle} = \sqrt{\text{6(6 - 5)(6 - 3)(6 - 4)}[/tex]

Evaluating the area:

[tex]\implies \text{Area of triangle} = \sqrt{\text{6(6 - 5)(6 - 3)(6 - 4)}[/tex]

[tex]\implies \text{Area of triangle} = \sqrt{\text{6(1)(3)(2)}[/tex]

[tex]\implies \text{Area of triangle} = \sqrt{\text{6(6)}[/tex]

[tex]\implies \text{Area of triangle} = 6 \ \text{cm}^{2}[/tex]