Amanda bought 2 CDs that were each the same price. Including sales tax, she paid a total of $29.80. Each CD had a tax of $1.10 . What was the price of each CD before tax?
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Given:

The first four terms of a sequence are:

8, 5, 2, -1

To find:

The function that defines the given sequence.

Solution:

We have,

8, 5, 2, -1

The differences between two consecutive terms are:

[tex]5-8=-3[/tex]

[tex]2-5=-3[/tex]

[tex]-1-2=-3[/tex]

The given sequence has a common difference -3. It means the given sequence is an arithmetic sequence with first term 8 and common difference -3.

The nth terms of an arithmetic sequence is:

[tex]f(n)=a+(n-1)d[/tex], for [tex]n\geq 1[/tex]

Where, a is the first term and d is the common difference.

Putting [tex]a=8,d=-3[/tex], we get

[tex]f(n)=8+(n-1)(-3)[/tex]

[tex]f(n)=8-3(n-1)[/tex]

[tex]f(n)=-3(n-1)+8[/tex], for [tex]n\geq 1[/tex]

Therefore, the correct option is A.

Answer:

32º

Step-by-step explanation:

Solve for sin(x). Then use inverse sine to get your angle measurement. From there, convert radians to degrees by multiplying by 180/π.

sin (x) = opp/hyp = 8/15

sin-1(8/15) = x = 0.56253 radians

0.56253 radians * 180/π = 32.23º

Round this to 32º

Answer:

The Pythagorean identity [tex]\sin^2\theta+\cos^2\theta=1[/tex] comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle [tex]\theta[/tex], we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.

The Pythagorean theorem states that in all right triangles, the following must be true:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle.

Therefore, we have the following equation:

[tex](\sin\theta)^2+(\cos\theta)^2=1^2,\\\boxed{\sin^2\theta+\cos^2\theta=1}[/tex]

The Pythagorean identity  comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle , we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.

The Pythagorean theorem states that in all right triangles, the following must be true:

, where  is the hypotenuse of the triangle and  and  are two legs of the triangle.

Therefore, we have the following equation:

Answe545r:

45454

Step-by-step explanation:

Answer:

x = 10.5

Step-by-step explanation:

[tex]cos 65 =\frac {adjacent}{hypotenuse} \\\\0.4226 = \frac{x}{25}\\\\0.4226 \times 25 = x \\\\x = 10.565[/tex]

Answer:

Step-by-step explanation:

take 65 degree as reference angle

using cos rule

cos 65=adjacent/hypotenuse

0.42=x/25

0.42*25=x

10.5=x

Answer:

D

Step-by-step explanation:

u are correct

Answer:

d= 8.3 units

➴➵➶➴➵➶➴➵➶

[tex]Given:[/tex]

[tex]L=7[/tex]

[tex]B=4[/tex]

[tex]H=2[/tex]

[tex]d=\sqrt{L^2+B^2+H^2}[/tex]

[tex]d=\sqrt{7^2+4^2+2^2}[/tex]

[tex]d=\sqrt{49+16+4}[/tex]

[tex]d=\sqrt{69}[/tex]

[tex]d=8.3~units[/tex] ✔︎

•❅────✧❅✦❅✧────❅•

hope it helps...

have a great day!!!

Answer:they are supplementary

Step-by-step explanation:

Answer: [tex]6x^2-2x+4[/tex]

Step-by-step explanation:

Given

The length of a rectangle is given by

[tex]l=2x^2-5x+5[/tex]

and the breadth is given by

[tex]w=x^2+4x-3[/tex]

Perimeter is the sum of the sides of rectangle

[tex]\therefore \text{Perimeter P= }2(2x^2-5x+5+x^2+4x-3)\\\Rightarrow P=2(3x^2-5x+4x+5-3)\\\Rightarrow P=2(3x^2-x+2)\\\Rightarrow P=6x^2-2x+4[/tex]

Thus, the perimeter is given by [tex]6x^2-2x+4[/tex].

Answer:

nfdsBFS>BFBms?FBsbn

Step-by-step explanation:vkhgv

SFsASFWWFmreweebwfjfeWBEfeb

Answer:

she gets paid 6,521 a month

Step-by-step explanation:

just divide 78,252 by 12

Explanation:

Divide the given value by 12 to get the answer. This is the salary before taxes and such. The net salary is after taxes are taken away.

Answer:

6/4

Step-by-step explanation:

Answer:

Exact Form:

3/2

Decimal Form:

1.5

Mixed Number Form:

1 1/2

Step-by-step explanation:

Answer:

you have 48

Step-by-step explanation:

15x2=30

9x2=18

18+30=48

Answer:

D 45

Step-by-step explanation:

90/2 = 45

135/3 = 45

180/4 = 45

Answer:

x=5, y=4. (5, 4).

Step-by-step explanation:

y=2x-6

y=5x-21

--------------

2x-6=5x-21

2x-5x-6=-21

-3x-6=-21

-3x=-21+6

-3x=-15

3x=15

x=15/3

x=5

y=2(5)-6

y=10-6

y=4

Answer:  4.3 cm

Step-by-step explanation:

Leroy's rectangle's width is 7.6 cm in length and the length of the triangle is 11.9 cm.

The length is therefore longer than the width and the difference is:

= Length - Width

= 11.9 - 7.6

= 4.3 cm

Answer:

32 just multiply by four

rectangle = 3 x 2 = 6 cm2

cirrel = pier2 = 3.14 x 7 x 7 = 3.14 x 49 = 153.86 cm2

153.86 - 6 = 147.86cm2

Answer:

96 squared units

Step-by-step explanation:

Please find attached the diagram used in answering this question

The surface area is equal to the area of each shape

Area of a triangle = Area of a triangle = 1/2 x ( base x height)

1/2 x 2 x 3= 3

there are 4 triangles, area of both triangles = 3x4 = 12

Area of rectangle = length x width

Area of middle rectangle = 6 x 7 = 42

Area of two side rectangles = (3 +3) x 7 = 42

surface area = 42 + 42 + 12 = 96

Answer:

(0, 3)

Step-by-step explanation:

y= 3 when x=0

Answer:

[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]

Step-by-step explanation:

we would like to solve the following trigonometric equation on interval of [0,2π)

[tex] \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} [/tex]

remember that,

[tex] \displaystyle \cos(t) = \cos(2\pi - t) [/tex]

so the equation has two solutions

[tex] \begin{cases} \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} \\ \cos \left(2\pi - (2 \theta + \frac{\pi}{3} )\right ) = \frac{ \sqrt{3} }{2} \end{cases}[/tex]

take inverse trig both sides which yields:

[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ 2\pi - 2 \theta - \frac{\pi}{3} = \frac{\pi}{6} \end{cases}[/tex]

simplify the second equation:

[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} \end{cases}[/tex]

add period of 2kπ:

[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} + 2k\pi \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} + 2k\pi\end{cases} [/tex]

By making theta subject of the equation we acquire:

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} - k\pi\end{cases} [/tex]

since [tex]k\in\mathbb{Z}[/tex] we get:

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} + k\pi\end{cases} [/tex]

as we want to Solve the trigonometric equation on the interval of [0,2π) we get

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + \pi \\ \theta = \frac{3\pi}{4} + \pi\end{cases} [/tex]

by simplifying we acquire:

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{23\pi}{12} \\ \theta = \frac{7\pi}{4} \end{cases} [/tex]

and we are done!

hence,

[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]

Answer:

the unknown number of fish is 26

Step-by-step explanation:

I figured this out by subtracting 68 - 47 = x.

x = 26

Answer:

Unknow fishes = 26

Step-by-step explanation:

We are given that 42 and x fishes sum up to 68 fishes, so we can say;

42 + x = 68

x = 68 - 42

x = 26

Therefore the number of unknown fishes = 26

Hope this helps!

Answer:

Number of rack made from total wood = 5 rack

Step-by-step explanation:

Given:

Length of wood Zendaya has = 5/6 yard

Length of each rack = 1/6 yard

Find:

Number of rack made from total wood

Computation:

Number of rack made from total wood = Length of wood Zendaya has / Length of each rack

Number of rack made from total wood = [5/6] / [1/6]

Number of rack made from total wood = [5/6][6/1]

Number of rack made from total wood = 5 rack

Answer:

1.0

2.undefined

Step-by-step explanation:

Answer:1) 0, 2) is undefined

Step-by-step explanation:

Answer:

y=25x+150

Step-by-step explanation:

The slope is 25 and the y-intercept is 150.

Hope this helps.