(100 POINTS) Question 2: 6 pts
Find the zeros of the quadratic function f(x) = 2x2 + 4x - 6 from the graph.

Answer:

[tex]{x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 [/tex]

Step-by-step explanation:

This too follows the as same process as

recall binomial theorem,

[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

Given binomial:

comparing it to (a+b)ⁿ , we acquire:

Now substitute:

[tex] \displaystyle (x +8 {)}^{5} = \sum _{k = 0} ^{5} \binom{n}{k} {a}^{5- k} {b}^{k} [/tex]

To convert the summation into a sum, substitute the values from k=0 to k=5 into the expression which yields

[tex] \displaystyle (x + 8{)}^{5} = \binom{5}{0} {x}^{5 - 0} \cdot {8}^{0} + \binom{5}{1} {x}^{5 - 1} \cdot {8}^{1} + \binom{5}{2} {x}^{5 - 2} \cdot {8}^{2} + \binom{5}{3} {x}^{5 - 3} \cdot {8}^{3} + \binom{5}{4} {x}^{5- 4} \cdot {8}^{4} + \binom{5}{5} {x}^{5 - 5} \cdot {8}^{5} \\ \implies(x + 8 {)}^{5} = \binom{5}{0} {x}^{5} \cdot 1 + \binom{5}{1} {x}^{4} \cdot {8} + \binom{5}{2} {x}^{3} \cdot 64+ \binom{5}{3} {x}^{2} \cdot 512 + \binom{6}{4} {x}^{1} \cdot 4096+ \binom{5}{5} {x}^{0} \cdot 32768\\ \implies(x + 8{)}^{5} = 1 \cdot {x}^{5 } \cdot 1 + 5\cdot{x}^{4} \cdot {8} + 10 \cdot {x}^{3} \cdot 64+ 10 \cdot {x}^{2} \cdot 512 + 5 \cdot{x}^{1} \cdot 4096+ 1 \cdot {x}^{0} \cdot 32768 \\ \implies \boxed{ (x + 8 {)}^{5} = {x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 }[/tex]

and we're done!

Step-by-step explanation:

4.5 s, 324 ft

Explanation:

The object is projected upward with an initial velocity of

v_0 = 144 ft/sv

0

=144ft/s

The equation that describes its height at time t is

s(t) = -16t^2 + 144 ts(t)=−16t

2

+144t (1)

where t, the time, is measured in seconds.

In order to find the time it takes for the object to reach the maximum height, we must find an expression for its velocity at time t, which can be found by calculating the derivative of the position, s(t):

v(t) = s'(t) = -32t +144v(t)=s

′

(t)=−32t+144 (2)

At the maximum heigth, the vertical velocity is zero:

v(t) = 0

Substituting into the equation above, we find the corresponding time at which the object reaches the maximum height:

\begin{gathered}0=-32t+144\\t=\frac{144}{32}=4.5 s\end{gathered}

0=−32t+144

t=

32

144

=4.5s

And by substituting this value into eq.(1), we also find the maximum height:

s(t) = -16(4.5)^2+144(4.5)=324 fts(t)=−16(4.5)

2

+144(4.5)=324ft

Answer:

[tex]\displaystyle 3286[/tex]

Explanation:

Just multiply 62 and 53 to get 3286.

I am joyous to assist you at any time.

Answer:

43 ffhfhfhfhfhfhchchchchchc

Answer:

It will take 225 days for Evie's chicken to lay 45 eggs

Step-by-step explanation:

Answer:

[tex]588mm^3[/tex]

Step-by-step explanation:

Each side of the blue pyramid is 3 times the size of the red pyramid.

Instead of just dividing by 3 for the volume we must divide by 9 instead because we're working in cubes.

The value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

The difference formula in trignometry for the sine funciton is given as,

[tex]\sin(A-B)=\sin(A)\cos(B) -\cos(A)\sin(B)[/tex]

The trignometric equation given in the problem is,

[tex]\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)[/tex]

Compare this equation with the above eqution, we get,

[tex]A=80^o\\B=20^o[/tex]

Thus, this equation can be written as,

[tex]\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(80-20)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(60)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\dfrac{\sqrt{3}}{2}[/tex]

Hence, the value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

Learn more about the difference formula in trignometry here;

https://brainly.com/question/2142049

Answer:

13

Step-by-step explanation:

7j=91

91/7=j

13

hope that helps:)

The amount of change Lucy receives if she paid with few $20 bills is $12.84

Total cost of pants = $21.79 × 4

= $87.16

If the total cost of the pants exceeds $80, then she paid with 5 $20 bills

5 $20 bills = $100

Her change = $100 - $87.16

= $12.84

Learn more about cost:

https://brainly.com/question/2021001

Total interest:-

Answer:

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The given expression can be solved as shown below.

(2,3) - 3(1,1)

Multiply 3 in the second vector,

= (2,3) - (3,3)

Subtracting vectors

= (2-3, 3-3)

= (-1, 0)

Hence, the value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ5

Answer:

Your answer would be:
3,384 books are left in the library

If each patron has 6 books, and there are 564 patrons:

564 x 6 = 3,384 books left

In conclusion, there are 3,384 books left in the library.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

[tex]\ln(3x+2) = 3x\\\\\implies \log_e (3x+2) = 3x\\\\\implies e^{3x} = 3x+2[/tex]

Answer:

2 is the next number in the sequence

Step-by-step explanation:

in this pattern, you go down by one decimal spot ( zero)

this is a geometric sequence since there is a common ratio between each term.

circles are 360⁰ and lines are 180⁰

Answer:

It should be B

Step-by-step explanation:

2 2 -1 2 - -3 2 (2+-1)

1. Always do what's in parentheses

so we know that 1 is a negative and 2 is bigger than that number so you would just subtract normally.

2 2 -1 2 - -3 2 -1

Then get all exponents done.

4 -1 - 9-1

3-9-1

-6-1

Which should give u -5

Answer:

1.

+4

number: 11

2.

x × 3

number: 48

3.

+5

number 46

4.

÷2

number: 19

5.

-1.5

number: 19.5

6.

-0.2

number: 31.2

First, we know that angle B is congruent to angle E.

2x + 40 = 5x + 10

2x + 30 = 5x

30 = 3x

x = 10

Angle B and Angle E = 60 degrees

Angle C = 14 degrees

Remember that the interior angles of a triangle always add up to 180 degrees. Now that we know 2 of the 3 angles of these triangles, and because they are congruent, all that's left to do is find Angle A/D by setting up a simple equation.

60 + 14 + D = 180

74 + D = 180

D = 106

Angle D = 106 degrees

Hope this helps!

Answer:

Step-by-step explanation:

<E = <A                property of congruency.

<A = 5x + 10        Comes from the fact that <A and <E are equal.

Three angles of the triangle are given. They add to 180 degrees.

2x + 40 + x + 4 + 5x + 10 = 180         Combine like terms

8x + 54 = 180                                     Subtract 54 from both sides.

8x + 54 - 54 = 180 - 54                      Combine  

8x = 126                                              Divide by 8

8x/8 = 126/8

x = 15.75

<B = <D                                               Congruency and parallel lines

<D = 2x + 40                                       Substitute for x

<D = 2*15.75  +  40                             Combine

<D = 31.5 + 40

<D = 71.5

Answer:

and

Step-by-step explanation:

we have

-----> equation A

------> equation B

we know that

The solution of the system of equations is equal to the intersection point of both graphs

Using a graphing tool  

see the attached figure

There are two intersection points

Therefore

The system of equations has two solutions

The solutions of the system of equations are the points  and

Answer:

sin = opp / hyp

cos = Adj / hyp

tan = opp / adj

7. cos 41 = x / 86

8. sin x = 5/13

9. cos x = 9/37

10. tan 61 = x/28

11. sin 41 = x/65

12. tan x = 79/84

Step-by-step explanation:

Answer:

i think the answer will be = 8 × 10^2

Answer:

made a mistake in step 3

Step-by-step explanation:

there, he should have gotten y=5-2x which is then translated to y=-2x+5

this means the y-intercept is correct, but the slope is actually -2

Answer:

1376.1 ft^3

Step-by-step explanation:

The volume of a sphere formula: V=4/3πr^3

r = 6.9 ft

V = 4/3 * π * (6.9^3) = 1,376.055

to the nearest tenth it's 1376.1 ft^3

Answer:

240 Minutes

Step-by-step explanation:

0.6 per minute × 2 = 1.2 gallons .

120 balloons × 2 mins= 240 mins

Answer:

[tex]\frac{21}{40}n[/tex] + [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The important part to understand about this problem is that you need to find a common denominator. You can ONLY add two fractions if they have the same denominator. A way to change the denominator of a fraction is to multiply the numerator and denominator of the fraction by the same number.

So, You want to make the 2/5n and 1/8n to have the same denominator so you can add them. An easy rule of thumb is multiply the one of the fraction by the other fraction's denominator, so in this problem:

[tex]\frac{2 * 8}{5*8} n[/tex] and [tex]\frac{1*5}{8*5}n[/tex]

this comes out as

16/40n and 5/40n

NOW, they have the same denominator and you can add the numerators together to make it one happy fraction

[tex]\frac{16}{40} + \frac{5}{40} = \frac{16+5}{40} = \frac{21}{40}[/tex]

Then, for the 3/6, you can simplify this fraction into:

1/2

This is because if you divide the top and bottom of the fraction by 3 like so:

[tex]\frac{3/3}{6/3}[/tex] (Always make sure you do the same for the top as you do to the bottom)

This comes out as

[tex]\frac{1}{2}[/tex]

Then for the full equation:

[tex]\frac{21}{40} n + \frac{1}{2}[/tex]

The distance between Samir and Ayisha is 2 ft.

Samir and Ayisha are on one side of a river. Since they are on the same side, they may likely be close to each other.

Katia is on the other side of the river. It is likely Katia is far from Samir and Ayisha.

The distance between Samir and Katia is 82 ft. Therefore, the distance between Ayisha and Katia is 80 ft.

The distance between Samir and Ayisha = 82 ft - 80 ft

The distance between Samir and Ayisha = 2 ft

learn more on distance here:https://brainly.com/question/8387377

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between the cosine of an angle and the sides of the triangle.

  Cos = Adjacent/Hypotenuse

__

In the given triangle, the hypotenuse is AC. The side adjacent to angle A is AB, so its cosine is ...

  cos(A) = AB/AC

  cos(A) = 3/5

__

The right angle in the triangle is angle B. The cosine of a right angle is 0.

  cos(B) = 0

__

The side adjacent to angle C is CB, so its cosine is ...

  cos(C) = CB/AC

  cos(C) = 4/5

Answer:

cos <ABC=0

cos <BAC=3/5

cos<ACB=4/5

GIVE 5 STARS IF YOU DO RSM!!!

Answer:

7 units

Step-by-step explanation:

(Background info, skip if not interested or needed for you)

The equation for distance on a cartesian plane coordinate system is based off the pythagorean theorem.

[tex]a^2 + b^2 = c^2[/tex]

a and b being sides of a right triangle, c being the hypotenuse.

When we are solving for distance we are solving for c essentially.

[tex]c[/tex] = [tex]\sqrt{a^2 + b^2}[/tex]

Because a and b are side lengths of the right triangle, we need to find a way to find that in terms of coordinates. So here we might say that a is equal to the horizontal distance between the 2 points or Δx, and we would say that b is the vertical distance between the 2 points Δy.

(solutions)

So essentially distance is:

[tex]d = \sqrt{(x_2 - x_1)^2+ (y_2-y_1)^2 }[/tex]

Now we just use the values given to us, and sub in the x and y values respectively.

(-2,4) [tex]x_1 = -2, y_1 = 4[/tex]

(5,4)[tex]x_2 = 5, y_2 = 4[/tex]

plug these values in:

[tex]d = \sqrt{((5) - (-2))^2+ (4-4)^2 } = \sqrt{(7)^2+ (0)^2 } = \sqrt{7^2 } = 7[/tex]

Therefore the distance is 7 units.