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Answer:

$17000

Step-by-step explanation:

Given

[tex]Total = 18275[/tex]

[tex]Tax = 7.5\%[/tex]

Required

The original price

This is calculated using:

[tex]Price(1 + Tax) = Total[/tex]

Make Price the subject

[tex]Price = \frac{Total}{(1 + Tax)}[/tex]

So, we have:

[tex]Price = \frac{18275}{(1 + 7.5\%)}[/tex]

[tex]Price = \frac{18275}{1.075}[/tex]

[tex]Price = 17000[/tex]

Answer:

Width = 4 cm

Length = 8 cm

Step-by-step explanation:

Hi there!

Let [tex]l[/tex] be equal to the length of the rectangle.

Let [tex]w[/tex] be equal to the width of the rectangle.

1) Determine equations to find the length and width

We're given that the length is two times the length of the width:

[tex]l=2w[/tex]

We're also given that the area of the rectangle is 32 cm². Recall that the area of a rectangle is [tex]A=lw[/tex]:

[tex]A=lw\\32=lw[/tex]

Now, we have our two equations:

[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]

2) Solve for the width using substitution

[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]

Replace [tex]l[/tex] in the second equation with [tex]2w[/tex] from the first equation:

[tex]32=(2w)w\\32=2w^2[/tex]

Divide both sides by 2 to isolate w²:

[tex]16=w^2[/tex]

Take the square root of both sides to isolate w:

[tex]\pm4=w[/tex]

Because width cannot be negative, w=4. Therefore, the width of the rectangle is 4 cm.

3) Solve for the length

[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]

Now, that we have the width (4 cm), we can solve for the length by plugging it back into one of the equations. Either of the equations work, but we can use the first:

[tex]l=2w\\l=2(4)\\l=8[/tex]

Therefore, the length of the rectangle is 8 cm.

3) Draw the rectangle

We can use what you had before as a foundation. You drew a rectangle with width 4 cm and length 7 cm. To draw the correct rectangle, add another row on top to make it 4 cm by 8 cm.

I hope this helps!

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Explanation:

The general cosine template is

y = A*cos(B(t - C)) + D

where in this case

We only really need to worry about the B value. To get the period T, we do the following

T = 2pi/B

T = (2pi)/(pi/4)

T = 2pi * (4/pi)

T = 8

Note how the pi terms canceled. The period is 8 seconds, which is the length of one full cycle. This is the time it takes for the pendulum to do one full swing (eg: start at the right, swing to the left all the way, then swing back to the right again).

The result of 8 we got has nothing to do with the D = 8 value (this D value could be any other number and T = 8 would still be the case as long as B doesn't change of course).

Answer:

the answer is 120

Step-by-step explanation:

a trapezoid should measure 360 when all sides are added together

180-125=55

65+55=120

360-120=240

240÷2=120

Answer:

The answer is one.

Answer:

2/8 or 1/4 simplified

Step-by-step explanation:

If you count how many equal sections there are, you will see there are 8, and 2 or those 8 sections are red so that would easily give you your answer, 2/8.

And to simplify it divide both the top and the bottom by 2 and that gives you 1/4.

Hope the helps! :)

The probability of a red on this spinner would be 1/4.

Used the concept of probability that states,

The term probability refers to the likelihood of an event occurring. Probability means possibility.

Given that,

A spinner is shown in the image.

Since there are a total of 8 parts with different colors.

And, the number of red colors on this spinner is 2.

Hence, the probability of a red on this spinner would be,

P = 2 / 8

P = 1 / 4

Therefore, the probability is 1/4.

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Answer:

false

Step-by-step explanation:

this is because there is no function of an unknown in this set

Answer:

Step-by-step explanation:

This is a "regular" sin graph that's "taller" than the original. The amplitude is 3; other than that, its period is the same and it has not shifted to the right or left, so the equation, judging from the graph, is

[tex]y=3sin(x)[/tex]

Answer:

1/5

Step-by-step explanation:

(f/g)(x) = f(x)/g(x) = sqrt(2x)/sqrt(50x) = 1/5

Answer:

y=-7/4x +10

Step-by-step explanation:

that the graph, you can plug the equation in desmos,

hope it helps! :)

Answer:

42

Step-by-step explanation:

5²+3(2)+5+6

25+6+5+6

31+11

42

Hope it helps

Answer:

The polar coordinates appear in the form (r, θ), where r is the the radius from the center and θ is the angle. To get the radius, do the following.

[tex]r = \sqrt{x^2 + y^2} = \sqrt{1^2 + (-1)^2} = \sqrt{2}\\[/tex]

You can get the angle visually by drawing a point (1, -1) on a graph and seeing that it is 45 degrees from the top right quadrant (you can tell its 45 because both x and y have the same magnitude). Since there are 360 degrees, 360 - 45 = 315.

If you would like to find it mathematically, this is the way to do it

[tex]\theta = atan(y/x) = -45[/tex]

Notice that -45 degrees is just 360 - 45 = 315

Your answer would be

[tex](\sqrt{2}, 315)[/tex]

Answer:

The integer represented by H is -2

Its opposite is 2 and the absolute value is also 2

Answer:The integer represented by H is -2

Step-by-step explanation:

Answer:

2(x+9)^2 + 4

Step-by-step explanation:

.............

Answer:

Step-by-step explanation:

Total amount in cents (unsimplified): 5N +17(10-N)

Simplified: 170-5N

Answer:

x=10, y=-6

Step-by-step explanation:

1) express x from the first equation x+y=4 x=4-y

2) It is the system of equations, so both equations are simultaneous.

you can replace x to 4-y in the second one

2 *(4-y) +3y=2

8-2y+3y= 2

y=-6

x= 4-y=4-(-6)=10

The answer is x=10, y=-6

Answer:

See explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

We are given the following and are trying to find the second derivative at x = 2:

[tex]\displaystyle f(2) = 2[/tex]

[tex]\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}[/tex]

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

[tex]\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}[/tex]

When we differentiate this, we must follow the Chain Rule:                             [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big][/tex]

Use the Basic Power Rule:

[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')[/tex]

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big][/tex]

Simplifying it, we have:

[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big][/tex]

We can rewrite the 2nd derivative using exponential rules:

[tex]\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}[/tex]

To evaluate the 2nd derivative at x = 2, simply substitute in x = 2 and the value f(2) = 2 into it:

[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}[/tex]

When we evaluate this using order of operations, we should obtain our answer:

[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Given:

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

To find:

The surface area and the volume of the sphere.

Solution:

Volume of a sphere:

[tex]V=\dfrac{4}{3}\pi r^3[/tex]              ...(i)

Surface area of a sphere:

[tex]A=4\pi r^2[/tex]                      ...(ii)

Where, r is the radius of the sphere.

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

[tex]V=\dfrac{28}{3}\times A[/tex]

[tex]\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2[/tex]

Multiply both sides by 3.

[tex]4\pi r^3=112\pi r^2[/tex]

[tex]\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}[/tex]

[tex]r=28[/tex]

Using (i), the volume of the sphere is:

[tex]V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3[/tex]

[tex]V\approx 91989[/tex]

Using (ii), the surface area of the sphere is:

[tex]A=4\times \dfrac{22}{7}\times (28)^2[/tex]

[tex]A=9856[/tex]

Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.

Answer:

the answer = um ok

Step-by-step explanation:

Step-by-step explanation:

time = 2 hours

distance travelled(d) = 124 miles

so

speed = d/t

=  124/2

= 62 miles per hour

Therefore, the speed of car is 62 miles per hour.

Answer:

 - 5/3

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -1 -9)/(4 - -2)

   = (-1-9)/(4+2)

  = -10/6

  - 5/3

Answer:

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 1 - 9}{4 - - 2} \\ \frac{ - 10}{6} \\ = - \frac{5}{3} \\ thank \: you[/tex]

Answer:

y = 6x-7

Step-by-step explanation:

product of 6 and x

6x

7 less than the product of 6 and x

6x-7

y = 6x-7

Answer:

13.3650978628

Step-by-step explanation:

Angle A=180-(Angle B+C)=180-117=63

Here,

b=BC, p=AC & AB=12

Using the relation of cos,

cosx=b/h

cos27=BC/15

15cos27=BC

Using a calculator,

BC=13.3650978628

Answer:

k=-1/2

Step-by-step explanation:

u have to change line 4x + ky=11 to this form:

y=11/k-4x/k

then, if 2 lines are parallel, their slopes have to equal

so: 8=-4/k -> k=-1/2

Answer:

don't know

Step-by-step explanation:

Answer:

true

hope it helps

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Answer:

r=7, Center:(4,8)

Step-by-step explanation:

( x - h )^2 + ( y - k )^2 = r^2 is the general formula for circle where radius is square root of r^2 and the center is (h,k).

Answer:

53

Step-by-step explanation:

The value of x in the given figure is 127 degrees.

Given that;

The lines m and n are parallel lines.

Now by definition of vertically opposite angle,

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other.

Hence from the figure we get;

Angle x and 127 degrees are vertically opposite angles.

Hence we get;

x = 127°

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Answer:

answer B:

[tex]x= \dfrac{\pi}{2}\ or\ \dfrac{\pi}{6}\ or\ x=\dfrac{5\pi}{6}[/tex]

Step-by-step explanation:

[tex]2cos^2 x + 3sin x=3\\\\\Longrightarrow\ 2*(1-sin^2 x)+3sin x -3=0\\\\\Longrightarrow\ 2-2sin^2 x+3 sin x -3=0\\\\\Longrightarrow\ -2sin^2 x+3 sin x -1=0\\\\\Longrightarrow\ 2sin^2 x-3 sin x +1=0\\\\\Delta=3^2-4*2*1=1\\\\sin\ x=\dfrac{3-1}{4} \ or\ sin\ x=\dfrac{3+1}{4}\\\\sin\ x=\dfrac{1}{2} \ or\ sin\ x=1\\\\\Longrightarrow\ x= \dfrac{\pi}{6}\ or\ x= \dfrac{5\pi}{6}\ or\ x=\dfrac{\pi}{2} \\[/tex]