How many lines pass
through two points?
A. infinite
B. 1
C. zero
D. 2

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

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[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]

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.

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Answer:

depends on how much each thing costs

Step-by-step explanation:

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

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

Answer:

I believe its D

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

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

Let me know if you want an explanation :)

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! ♡

Answer:

0.002816 or 0.003

Step-by-step explanation:

Be sure to use a calculator to double check the answer

Hope this helps!

Answer:

25%

Step-by-step explanation:

100-80=20

20/80Ⅹ100=25%

Answer:

  frequency = 1/(2π)

Step-by-step explanation:

The frequency of the function is found by comparing the argument of the cosine function to (2πfx), where f is the freuqency.

  2πfx = x . . . . the argument of the cosine is x in f(x)=2cos(x) -4

  2πf = 1 . . . . . . divide by x

  f = 1/(2π) . . . . . the frequency of the function f(x)

Answer:

10

Step-by-step explanation:

The area if a parallelogram is given by the equation, Area = base * height

In this case, area = 200, and the actual height = 20

So, let's say the base is x

Plug these values in to the Area equation

200 = 20 * x

200 = 20x

Divide both sides by 20 to get x alone

200 / 20 = 20x / 20

10 = x

The base is 10

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:

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: 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

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

Combined surface area of the 9 prisms is: 3,420 cm².

Maria DOES NOT have enough cloth for her current design.

The surface area of trapezoidal prism = PH + (b1+b2)h

The custom design is a trapezoidal prism.

Find the surface area of one trapezoidal prism given the following dimensions:

Perimeter of trapezoid = P = 5 + 15 + 10 + 10 = 40 cm

Plug in the values into the formula

Surface area of 1 trapezoidal prism = (40)(6) + (5 + 15)7 = 380 cm²

Combined surface area of the 9 prisms = 9 × 380 = 3,420 cm².

Since Maria's flora cloth is 3,000 cm², therefore, she DOES NOT have enough cloth for her current design.

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For those of you too lazy to read, here is the answer. :-)

The combined surface area of the prisms is 3420 cm², therefore Maria does not have enough cloth for her current design.

Volume:-

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

[tex]p(x)=(x+2)(2x+7)(x-1)(x-3)\\ \\~~~~~~=(2x^2 +7x + 4x +14)(x^2 -3x -x +3)\\\\~~~~~~=(2x^2 + 11x +14)(x^2 - 4x +3)\\\\~~~~~~=2x^4-8x^3 + 6x^2 + 11x^3 - 44x^2+33x + 14x^2 - 56x + 42\\ \\~~~~~~=2x^4+3x^3-24x^2-23x +42[/tex]

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:

38.5

Step-by-step explanation:

70*(0.55) = 38.5

Answer:

Step-by-step explanation:

To find 55% of 70, we need to write an equation.

this equation will be 55x70/100

now, the answer to 55x70 / 100 is

38.5

We get this answer, because 55x70=3850

and 3850 divided by 100 is 38.5

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)

Answer:

y=4(12)x

Step-by-step explanation:

An exponential function is in the general form  

y=a(b)

Answer:

₱ 248,452.51

Step-by-step explanation:

₱ 248,452.51

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