(x + 4)(3x + 2) = ____________ 2. (3x – 1)(2x – 5) = ____________ 3. (5x + 2)(2x + 5) = ____________ 4. (4x – 1)(2x + 7) = ____________ 5. (2x + 6)(4x + 8) = _n​

Work Shown:

[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(65^{\circ}) = \frac{d}{e}\\\\e\cos(65^{\circ}) = d\\\\e = \frac{d}{\cos(65^{\circ})}\\\\[/tex]

Answer:

See below for answers and explanations (along with a graph attached)

Step-by-step explanation:

Part A

The amplitude of a sinusoidal function is half the distance between the maximum and the minimum. It is given to us that the distance from the highest and lowest point is 6 feet, so our amplitude is 6/2 = 3 feet

Part B

The graph's function would be in the form of [tex]y=acos(bx+c)+d[/tex] where [tex]a[/tex] is the amplitude, [tex]\frac{2\pi}{b}[/tex] is the period, [tex]-\frac{c}{b}[/tex] is the phase/horizontal shift, and [tex]d[/tex] is the average/midline.

We already know our amplitude of [tex]a=3[/tex] from part A.

Since our period is given to us as 26 seconds, then we can use the equation [tex]\frac{2\pi}{b}=26[/tex] to find [tex]b[/tex], which happens to be [tex]b=\frac{\pi}{13}[/tex].

Since the cosine function starts at its maximum and we want it to start at the average where the bottle travels up, we would need to use the cofunction identity [tex]sin(x)=cos(x-\frac{\pi}{2})[/tex] which shifts the cosine graph [tex]\frac{\pi}{2}[/tex] units to the right. This means that [tex]c=-\frac{\pi}{2}[/tex], making our phase shift [tex]-\frac{c}{b}=-\frac{-\frac{\pi}{2}}{\frac{\pi}{13}}=6.5[/tex], or 6.5 feet to the right

Our average/midline would be [tex]d=12[/tex] as given as the average height by the problem.

Therefore, the function is [tex]f(x)=3cos(\frac{\pi}{13}x-\frac{\pi}{2})+12[/tex]

Part C

Using our determined function from Part B, by looking at its graph, we see that the bottle will reach its lowest height of 9 feet after 19.5 seconds (see attached graph).

Part A

The distance from the highest and lowest point is 6 feet. Cut this in half to find the amplitude: 6/2 = 3. The amplitude represents the vertical distance from the midline (aka average height) to either the peak or valley points.

The period is 26 seconds because this is the time difference from one max height to the next max height. This is one of a few ways to measure a full cycle. Another way is from min height to the next min height.

==========================================================

Part B

In this case, the template for cosine is

h = Acos(B(t-C))+D

We found the amplitude A = 3 from the previous section.

The period is T = 26 which means B = 2pi/T = 2pi/26 = pi/13

D = 12 because the average height is 12 feet. The average height is always on the midline.

We are told that t = 0 leads to h = 12, so,

[tex]h = A\cos\left(B\left(t-C\right)\right)+D\\\\h = 3\cos\left(\frac{\pi}{13}\left(t-C\right)\right)+12\\\\12 = 3\cos\left(\frac{\pi}{13}\left(0-C\right)\right)+12\\\\3\cos\left(\frac{\pi}{13}\left(-C\right)\right) = 0\\\\\cos\left(\frac{\pi}{13}C\right) = 0\\\\[/tex]

Let's isolate the C term

[tex]\cos\left(\frac{\pi}{13}C\right) = 0\\\\\frac{\pi}{13}C = \arccos(0)\\\\\frac{\pi}{13}C = \frac{\pi}{2}\\\\C = \frac{\pi}{2}*\frac{13}{\pi}\\\\C = \frac{13}{2}[/tex]

==========================================================

Part C

A full period is 26 seconds.

At t = 0 the bottle is at a height of 12 feet

26 seconds later, the bottle is back again at 12 feet to repeat another cycle indefinitely.

At every quarter cycle, the object is either at a min point, max point, or at the average (midline).

So every 26/4 = 6.5 seconds the object will be in one of those places.

In this case, the object starts at 12 feet, goes up to the max 15 feet when t = 6.5

Then another 6.5 seconds later it's back to the midline again. Another 6.5 seconds later (total time is now 6.5*3 = 19.5 seconds) the bottle dips down to the min height of 9 feet. You should see that (19.5, 9) is one of the infinitely many minimum points on this particular cosine curve.

Answer:

y= 1/4x - 3

Step-by-step explanation:

Answer:4/5

Step-by-step explanation:

=80 out of 80 - 16 out of 80

=64 out of 80

Answer:

4/5

Step-by-step explanation:

substract the number of questions he got correctly from the total number of the questions to yield 80-16=64

then set the fraction as number of incorrect questions as the numerator and the total number of questions as the denominator

64/60=4/5

You can multiply

39 • 24 and it gives you = 936

Answer:

5/18 of a semicircle

5π/18 radians

Step-by-step explanation:

50/180 = 5/18 of a semicircle

5π/18 radians

Answer:

51

Step-by-step explanation:

PEMDAS means parenthesis (there are none), exponents (there are none), multiplication. So you multiply 8x18 to get 144. Then you have division, so 144/4 is 36. Finally, you add this number to 15 to get 51 as your final answer.

By PEMDAS, the solution of the expression 8x18÷4+15 is 51.

The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

Given:

An expression,

8x18÷4+15.

In order to solve the problem by PEMDAS:

First, solve the multiplication operation,

144÷4+15

Now, solving division operations,

36 + 15

Applying addition operation,

51

Therefore, 51 is the solution to the expression.

To learn more about the PEMDAS;

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Answer:

14.0362 degrees (round to 14.0 degrees)

Step-by-step explanation:

1. Assume that the math can be deduced by the sides of a triangle due to the "sightline" nature of the problem. This is a classic trig problem you will see.

2. The base of the triangle would be 12 feet and one of the legs of the triangle will be 3 feet.

3. Arctangent will provide the angle of elevation. The equation can be written as arctan(h/b), in this case h = height and b = base.

4. The calculation will be arctan(3/12) which translates to 14 degrees which is, fortunately, the angle of elevation.

I recommend trying this method out with another example such as the angle of elevation between you and the next plane you see in the sky. For example, the height difference between you and the plane is 7 miles and the plane is x miles away. Again we can create a simple triangle to discover many interesting details.

their income is "x", which oddly enough is the 100% of their income, we also know that 16% of it 240 bucks, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 240&16 \end{array}\implies \cfrac{x}{240}=\cfrac{100}{16}\implies 16x=24000 \\\\\\ x=\cfrac{24000}{16}\implies x=1500[/tex]

Answer:

c hope this help

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

First find the volume of box A (12x2x2)

A=48

Next since box B is half the volume of box A divide 48 by 2

B=24

:)

Answer: A

Step-by-step explanation:

The quotient is x² + 4x +3. Then the correct option is A.

A quotient in mathematics is the amount created by dividing two numbers. In mathematics, the term "quotient" is frequently used to refer to the integer portion of a division, as well as to a fraction or a ratio.

The quotient is calculated as:-

x - 5 ) x³ - x² - 17x -15 ( x² + 4x + 3

         -x³  + 5x²

      _________________

          4x² - 17x - 15

         -4x² + 20x

       _________________

                   3x -15

                 -3x + 15

       _________________

                         0

Hence, the quotient is  x² + 4x +3.

To know more about quotient follow

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Answer: Answer:    2/5. Step-by-step explanation: The prime numbers from 1 to 20 are 2, 3, 5, 7, 11, 13, 17 and 19. A total of 8. ... = 2/5. Still stuck? Get 1-on-1 help

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

What is the probability of rolling a prime number of a standard 20-sided die? (1 is not a prime number.)

a.

7/20

b.

2/5

c.

9/20

d.

1/2

Answer:

Pictured this you have 3/4 of a sandwich and eat half of that 3/4 of the sandwich. you know have eaten 3/8 of a full sandwich and have 3/8 left.

if we were to actually divide 3/4 by 1/2 we would get 1.5 or 1 1/2 which would not make sense, so instead, we multiply and get 3/8

Step-by-step explanation:

first you have to find the lcm of 42 and 33

=462

then you're going to take the lcm and subtract the price of the vase from the lcm

=>462-40

=422

then now you're going to take the answer and divide it by the cost of each rose

=>422 ÷ $2

=211 roses at Weston Florist

then you're going to do the same for Harper's flowers

=>462-30

=432

=>432÷3

=144 roses at Harper's Flowers

Answer:

22

Step-by-step explanation:

The two transversals of a parallelogram equally divides each other, therefore,

x+40 = 2x+18

(collect the "x" to one side, and integers the other side of the equation)

2x-x = 40-18

x = 22

Answer:

8 teams

Step-by-step explanation:

48/6 = 8

Answer:

Billy has 7 toy cars.

Step-by-step explanation:

If Tommy has 12 toy cars, and Billy has 5 less cars than Tommy, then Billy has 7 toy cars.

12 - 5 = 7

Answer:

35cm²

Step-by-step explanation:

(7 x 10) ÷ 2 = 35

Area equation: (b x h) ÷ 2 = a

Answer:

4 pounds and 1/4 ounces

Step-by-step explanation:

8 and 1 half pounds = 8.5 Ibs

One half of 8.5 = 8.5/2 = 4. 25 Ibs or 4 & 1/4  or 4Ibs 4 ounces.

Answer:

2+5+30/2=18.5

or,

37/2=18.5

Answer:

The answer is 1/y^7

[tex] \looparrowright \sf \sqrt{ \dfrac{ {y}^{7} }{ {y}^{21} } } [/tex]

[tex] \\ \\ [/tex]

[tex] \looparrowright \sf \sqrt{ \dfrac{ {y}^{0} }{ {y}^{21 - 7} } } [/tex]

[tex] \\ \\ [/tex]

[tex] \looparrowright \sf \sqrt{ \dfrac{ {y}^{0} }{ {y}^{14} } } [/tex]

[tex] \\ \\ [/tex]

[tex] \looparrowright \sf \sqrt{ \dfrac{ 1}{ {y}^{14} } } [/tex]

[tex] \\ \\ [/tex]

[tex] \looparrowright \sf \dfrac{1}{ {y}^{7} } [/tex]

Answer:

1/36

Step-by-step explanation:

6 can be put over 1.

Our equation:

[tex]\frac{1}{6} \div\frac{6}{1}[/tex]

Find the reciprocal (opposite) of 6/1, then change to sign to multiplication:

[tex]\frac{1}{6} \times\frac{1}{6} =?[/tex]

Solve:

[tex]\frac{1}{6} \times\frac{1}{6} =\frac{1}{36}[/tex]

Your answer is 1/36.

[tex] \sqrt{45} + \sqrt{18} [/tex]

[tex] = \sqrt{3 \times 3 \times 5} + \sqrt{2 \times 3 \times 3} \\ = \sqrt{ {3}^{2} \times 5 } + \sqrt{ {3}^{2} \times 2 } [/tex]

[tex] = 3 \sqrt{5} + 3 \sqrt{2} [/tex]

[tex] = 3( \sqrt{5} + \sqrt{2} )[/tex]

Answer:

[tex]3( \sqrt{5} + \sqrt{2} )[/tex]

Hope you could understand.

If you have any query, feel free to ask.

Answer:

a and b.

Step-by-step explanation:

I’ll explain by giving an example.

Let’s say that: a=3;b=4;c=5; => they all are consecutive -> their sum is 12.

=> if we use a) n=3 => 3*n+3=3*3+3=12 => correct.

b) n+(n+1)+(n+2)= 3+4+5=12=> correct.

c)n+2n+3n=3+6+9=18=>incorrect.

d)3n=3*3=9=>incorrect.

Answer:

x = 4

Step-by-step explanation:

2x - 8 = 0

2x = 8

x = 8/2

x = 4

Answer:

C. 25%

Step-by-step explanation:

.25x13,500=3,375

13,500-3,375=10,125

Hope this helps. :)

gg

Step-by-step explanation:

Answer:

45 students still haven't given their speeches

Step-by-step explanation:

90/6 = 15

90-15 = 75

75/5 = 15

15*2 = 30

75-30 = 45

pls mark me brainliest

Answer:

24

Step-by-step explanation:

area of circle = πr²

πr² = 144π

Cancel out π

r² = 144

r = √144

r = 12

diameter = 2 x radius

diameter = 2 x 12

diameter = 24m

* diameter is the "width of a circle", the distance from the widest points of the circle