2 triangles. One triangle has side lengths x, 3 units, 4 units. The other triangle has side lengths 11 units, y, 8 units. The two figures are the image and pre–image of a dilation. Find the lengths of the missing sides. x = units, y = units

Answer:

[tex]2 \cos(4x) [/tex]

Step-by-step explanation:

The highest and lowest value is 2 and -2 respectively so the amplitude is 2.

That also means the vertical translation is 0.

The graph is reaches it max every pi/2 units so the period is

pi/2.

Since the graph intersects a non zero value at 0, it will be the cosine function.

Step 2: A cosine function is

[tex]a \cos(b(x - c)) + d[/tex]

where a is the amplitude

[tex] \frac{2\pi}{ |b| } [/tex]

is the period

C is the horinzontal shift

d is the vertical shift

We know a is 2

D is 0.

To find b,

[tex] \frac{2\pi}{b} = \frac{\pi}{2} [/tex]

[tex]b = 4[/tex]

So as of right now we have

[tex]2 \cos(4x) [/tex]

Answer(s):

[tex]\displaystyle y = 2sin\:(4x + \frac{\pi}{2}) \\ y = 2cos\:4x[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{8}} \hookrightarrow \frac{-\frac{\pi}{2}}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 2[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2sin\:4x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{8}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{8}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{8}} = \frac{-\frac{\pi}{2}}{4}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2sin\:(4x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [\frac{5}{8}\pi, 0],[/tex]from there to [tex]\displaystyle [\frac{\pi}{8}, 0],[/tex]they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

400

Step-by-step explanation:

48 is 12% of x

12/100 = 48/x

3/25 = 48/x

1/25 = 16/x

x = 25 × 16

x = 400

Answer: 400

Answer:

400

Step-by-step explanation:

(48 x 100) / 12 = 400

Answer:

a) 37º

b) 143º

c) 2x - 5 = 143

Step-by-step explanation:

a) Angles 5 and 7 are vertical angles and therefore have the same measurements.

b) Angles 5 and 6 form a straight line and are therefore supplementary (add up to 180º). 180 - 37 = 143.

c) We found the measure of angle 6 is 143º in part b. We can set that equal to 2x - 5. Therefore the equation is 2x - 5 = 143.

The expression that can be used to show the relationship between the number of days and the total dollars (t) he spends is t = 30d

The equation:

Total = cost per day × number of days

t = 30 × d

t = 30d

Learn more about equation:

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Answer:

  A.  coterminal angle = 4π/3

  B.  sin(θ) = -√3/2; csc(θ) = -2√3/3; cos(θ) = -1/2;

       sec(θ) = -2; tan(θ) = √3; cot(θ) = √3/3

Step-by-step explanation:

Any angle that is a multiple of 2π added to the given angle will be coterminal. You want one in the range [0, 2π], so we need to add 4π to the given angle

  coterminal angle = -8π/3 +4π = -8π/3 +12π/3

  coterminal angle = 4π/3

__

The reference angle is 4π/3 -π = π/3. θ is a quadrant III angle, so both the sine and cosine are negative.

  sin(θ) = -√3/2 . . . csc(θ) = -2√3/3

  cos(θ) = -1/2 . . . sec(θ) = -2

  tan(θ) = √3 . . . cot(θ) = √3/3

Answer: 20x + 32   or   $20 spent on the nail polish & $32 spent on the kits

Formula:

bags($polishx + $kit)

Work:

8(2.5x + 4)

8 x 2.5x = 20x

8 x 4 = 32

Answer: area of the circle is [tex]3.14ft^{2}[/tex]

Step-by-step explanation:

1. the equation to find the area of a circle is [tex]\pi r^{2}[/tex]

2. the diameter is equal to 2r, meaning to get the radius, divide the diameter by 2.     [tex]\frac{2}{2} =1[/tex]

3. plug in the the radius into the equation. [tex]3.14*1^{2} =3.14ft^{2}[/tex]

hope this helped! ♡

Apply Thales theorem

[tex]\\ \rm\rightarrowtail \dfrac{MR}{RN}=\dfrac{MQ}{QP}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{10}{RN}=\dfrac{8}{5}[/tex]

[tex]\\ \rm\rightarrowtail 8RN=50[/tex]

[tex]\\ \rm\rightarrowtail RN=50/8[/tex]

[tex]\\ \rm\rightarrowtail RN=6.25[/tex]

Answer:

RN = 6.25

Step-by-step explanation:

Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

Therefore,

MQ : MP = MR : MN

⇒ 8 : (8 + 5) = 10 : (10 + RN)

⇒ 8 : 13 = 10 : (10 + RN)

⇒ [tex]\sf\dfrac{8}{13}=\dfrac{10}{10+RN}[/tex]

Cross multiply and solve:

⇒ 8(10 + RN) = 10 × 13

⇒ 80 + 8RN = 130

⇒ 8RN = 130 - 80

⇒ 8RN = 50

⇒ RN = 50 ÷ 8

⇒ RN = 6.25

Volume of the bead = Volume of the sphere - volume of the cylindrical hole = 242.95 mm³.

Volume of the bead = Volume of the sphere - volume of the cylindrical hole

= 4/3π(4³) - π(1²)(8)

= 268.08 - 25.13

Volume of the bead = 242.95 mm³

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[tex]\text{Area of parallelogram QRST} = QR \times TU = 20 ~in \times 18~in =360 in^2[/tex]

Step-by-step explanation:

width is 6 units

P=2(l+w)

p=2(l+6)

l+6=p/2

l= (p/2)-6

The length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.

A perimeter is a closed route that surrounds, outlines, or embraces a rectangle. The perimeter of a rectangle is given by the formula,

[tex]\rm Perimeter= 2(Length +width)[/tex]

As it is given that the width of the rectangle is 6 units, while the perimeter of the rectangle is P. Now if we write about the perimeter of the rectangle, it can be written as,

[tex]\rm Perimeter= 2(Length +width)[/tex]

[tex]P = 2(l+6)\\\\\dfrac{P}{2} = (l+6)\\\\l = \dfrac{P}{2}-6[/tex]

Hence, the length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.

Learn more about Perimeter:

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Answer:

40.2 years

Step-by-step explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), in which n represents the number of compounding periods per year.  In this case n = 4.  Solve the following equation for t (years):

$10,000 = $2,000(1 + 0.04/4)^(4t):

This is equivalent to

          5   =  1.01^(4t).  Taking the natural logarithm of both sides, we get:

ln 5 = 4t·㏑ 1.01, or

    ln 5                 1.609

-------------- = t = -------------- = 40.2 years

4·ln 1.01             4(0.010)

Changing the coefficient of x to 6 changes the meaning of the expression as 5 is added to 6 times x

Solution:

Given that number 2 in the expression 5 + 2x is called the coefficient of x

We are asked to find what happens when changing the coefficient to 6 changes the meaning of the expression

In the expression,

5 + 2x

This means 5 is added to 2 times x or 5 is added to twice of x

Number 2 is called the coefficient of x

When we change this coefficient to 6, the expression becomes,

5 + 6x

So now the meaning of expression becomes,

5 is added to 6 times x

So changing the coefficient of x changes the meaning of the expression

We will see that for Stuart the maximum height is 30ft, and for Francisco it is 46.0625 ft

In the case of Stuart it is simple, as we have a graph, we just need to see the largest y-value on the graph. We can see that it is y = 30, then for Stuart, the largest distance from the ground is 30ft.

In the case of Francisco, we need to find the maximum of:

g(x)= -16x^2 + 50x +7

Notice that this is a quadratic of negative leading coefficient, so the maximum is at the vertex.

x = -50/(2*-16) = 25/16

Evaluating the function in 25/16 we get:

g(25/16) = -16*(25/16)^2 + 50*(25/16) +7 = 46.0625 ft

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Let the original price be x.

x * (1 - 0.25) = $41.25

0.75x = $41.25

x = $41.25 / 0.75 = $55

Answer:

$55

Step-by-step explanation:

____ decrease by 25%= $41.25, which the unknown number is $55.

Answer:

See below ↓

Step-by-step explanation:

a. 4 ÷ (2/3) = 12/3 ÷ 2/3 = 12 ÷ 2 = 6

b. 4 ÷ 1 = 4

Attachment below.

Answer:

1: 6
2:4

Step-by-step explanation:

Answer:

$1225

$33,775

Step-by-step explanation:

Given:

To find a percentage of an amount, convert the percentage into a decimal and multiply it by the amount:

3.5% = 3.5/100 = 0.035

⇒ Decrease in price = 0.035 × 35000 = $1225

Price of next model = price of current model - decrease in price

                                 = 35000 - 1225

                                 = $33,775

Decrease amount:-

So

New price:-

Answer:

58

Step-by-step explanation:

its basically saying that pam spent 24 dollars less than you. soo 82 - 24 = 58

Answer:

38.5

Step-by-step explanation:

The equation says

S - 1.8x = 6.1, where x is the amount of years after 1998.

2016 is 18 years after 1998.

S - 1.8*18 = 6.1

S= 32.4 + 6.1

S= 38.5

The exponential equation that correctly models the ball's peak height, h, in meters, after b bounces is given by:

[tex]H(b) = 4(0.79)^b[/tex]

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem:

Thus, the equation is given by:

[tex]H(b) = 4(0.79)^b[/tex]

More can be learned about exponential equations at https://brainly.com/question/25537936

Answer:

I believe its D

Step-by-step explanation: X and Y are both -3

Answer:

0.002816 or 0.003

Step-by-step explanation:

Be sure to use a calculator to double check the answer

Hope this helps!

The probability of getting at least 1 blue is 6/11

Let me know if you want an explanation :)

Answer:

C. 61 degrees

Step-by-step explanation:

a line is 180 degrees

so e and 119 degrees makes a line

so you subtract 180-119= 61 degrees

Answer:

₱ 248,452.51

Step-by-step explanation:

₱ 248,452.51

Answer:

By Pythagoras theorem

H^2=P^2+B^2

25^2=x^2+24^2

625=x^2 + 576

625-576=x^2

49=x^2

x^2=49

x=√49

x=7cm

Hope this helps uhh

Answer:

depends on how much each thing costs

Step-by-step explanation:

[tex]4x^2+12x=32\\\\\implies x^2+3x=8\\\\\implies x^2 +2 \cdot \dfrac 32 \cdot x+\left(\dfrac 32 \right)^2 - \left(\dfrac 32\right)^2 =8\\ \\\implies \left(x+\dfrac 32 \right)^2 = 8 + \dfrac 94 = \dfrac{41}4\\\\\implies x+\dfrac 32 = \pm\dfrac{\sqrt{41}}2\\\\\implies x = \pm \dfrac{\sqrt {41}}2 - \dfrac 32\\\\\text{The roots are}~ x = -\dfrac 32-\dfrac{\sqrt{41}}2~ \text{and}~~ x = -\dfrac 32+\dfrac{\sqrt{41}}2[/tex]