During a sale, CDs that normally cost $6.98 each were priced at 2 for $12.50. Pete bought 4 CDs at the sale price. How much money did he save by buying the 4 CDs on sale?

Answer:

LHS.= Sin 2x /( 1 + cos2x )

We have , sin 2x = 2 sinx•cosx

And. cos2x = 2cos^2 x - 1

i.e . 1+ cosx 2x = 2cos^2x

Putting the above results in the LHSwe get,

Sin2x/ ( 1+ cos2x ) =2 sinx•cosx/2cos^2x

=sinx / cosx

= Tanx

.•. sin2x/(1 + cos2x)= tanx

Step-by-step explanation:

9514 1404 393

Answer:

  d.  3x² +15x

Step-by-step explanation:

The area is the product of length and width.

  A = LW

  A = (3x)(x+5) = 3x(x) +3x(5) . . . . use the distributive property

  A = 3x² +15x

Answer: D) 3x^2 + 15

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

Explanation:

Draw a horizontal line to divide the rectangle into two parts (they don't necessarily have to be equal parts). Refer to the diagram below. The upper rectangle is x by 3x. So its area is length*width = x*3x = 3x^2

The lower rectangle is 5 by 3x, so its area is 5*3x = 15x

Combine those two sub-areas back together to get the overall area of 3x^2 + 15x

You could also use the distribution rule

3x*(x+5) = 3x*(x) + 3x*(5) = 3x^2 + 15x

Answer:

Farah: x

Ibtisam: x-3

Muna: 2(x-3) or 2x-6

Sum of all their ages: 4x-6

Step-by-step explanation:

Farah is x, so we don't need an expression for that.

Ibtisam is 3 years younger than Farah, which means that we need to subtract 3 from Farah, and that would be Ibtisam's age. x-3.

Muna is 2 TIMES Ibtisam's age, so we need to multiply whatever expression taht was used for Ibtisam by 2. Put brackets around the equation with 2 outside: 2(x-3). Solve and you get 4x-6

Now, you have all their ages in expression form, now you need to simplify by adding:

x+x+2x-6

We cannot simplify -6, so we put that aside. Add all the x's and you get 4x, insert the minus 6 at the end:

4x-6

Hope this helps!

--Applepi101

Answer:

a) X -3

b) 4x - 9

Step-by-step explanation:

a) Farah's age is X so Ibtisam will be X - 3 old since he is 3years younger than Farah

b) Farah is X years old

Ibtisam is X - 3 years old

Muna is 2(X -3) since she is 2 times older than Ibtisam.

the sum of Thier ages will be

X + X -3 + 2(x-3)

= 2x - 3 + 2x - 6

= 4x - 9

Answer:

The answer is "12".

Step-by-step explanation:

Lowest number[tex]=20\\\\[/tex]

highest number[tex]=80\\\\[/tex]

Number of classes[tex]=5\\\\[/tex]

Range=highest number-lowest number

          [tex]=80-20\\\\=60\\\\[/tex]

class width [tex]=\frac{Range}{\text{number of classes}}[/tex]

                   [tex]=\frac{60}{5}\\\\=12[/tex]

Answer:

see below

Step-by-step explanation:

CALVIN

v=[tex]\pi[/tex]× r ² × h

v=3.14 × 3² × 12

v=3.14×9 × 12

v=3.14 × 108

v = 339.12

JAMEL

v=[tex]\pi[/tex] × r ²×h

v=3.14× 6 ² × 6

v=3.14 × 36×6

v=3.14×216

v=678.24

Answer:

1/y^3

Step-by-step explanation:

We know that a^-b = 1/a^b

y ^-3 = 1/y^3

Answer:

Step-by-step explanation:

point est. 0.307824427

99% 2.58

Confidence Interval - "P" values  

(0.2914 , 0.3243 )  

Answer:

x= i√30

Step-by-step explanation:

I'm going to go into this under the assumption that you've covered imaginary numbers based on the question. If I'm wrong then sorry about that.

Okay, so first you want to subtract 30 from both sides

x^2=-30

Then you take the square root of each side.

√(x^2)=√-30

x=√-30

Since it's impossible to square a number to get a negative number, you'll end up with an imaginary number. You have to rewrite x=√-30 to get rid of the negative sign under the radical. Rewriting this will also indicate that it's an imaginary number.

Final answer: x = i√30

Answer:

D. Height

General Formulas and Concepts:

Geometry

Area of a Circle: A = πr²

Step-by-step explanation:

In order to find the area of a circle, we must follow the formula. Out of all the options given, height is not incorporated into the formula.

It wouldn't make sense to use height anyways since it would be 3-dimenional and we're talking 2-dimensional.

∴ our answer is D.

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Answer:

  B(8, 4)

Step-by-step explanation:

Reflection across the origin negates both coordinate values.

  (x, y) ⇒ (-x, -y) . . . . . reflection across the origin

  A(-8, -4) ⇒ B(8, 4)

Answer:  [tex]P = \frac{25}{E^2}-Q\\\\[/tex]

Work Shown:

[tex]E = 5\left(\sqrt{\frac{1}{P+Q}}\right)\\\\5\left(\sqrt{\frac{1}{P+Q}}\right) = E\\\\\sqrt{\frac{1}{P+Q}} = \frac{E}{5}\\\\\frac{1}{P+Q} = \left(\frac{E}{5}\right)^2\\\\\frac{1}{P+Q} = \frac{E^2}{25}\\\\P+Q = \frac{25}{E^2}\\\\P = \frac{25}{E^2}-Q\\\\[/tex]

A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have

dy/dx = 6x ² + 2ax + b

and so when x = 3,

0 = 54 + 6a + b

or

6a + b = -54 … … … [eq1]

The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have

2 = 128 + 16a + 4b - 30

or

16a + 4b = -96

4a + b = -24 … … … [eq2]

Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :

(6a + b) - (4a + b) = -54 - (-24)

2a = -30

a = -15   ===>   b = 96

Answer:

c

Step-by-step explanation:

hope it helps!!!!!!!!!!!!!!

Answer:

-5-9i

Step-by-step explanation:

-1-8i-4-i

-1-4-8i-i

-5-9i

Answer:

C

Step-by-step explanation:

15x-10=80

15x=90

x=90/15, x=6

Answer:

x = 6

Step-by-step explanation:

15x - 10 = 80

Add 10 to each side

15x-10+10 = 80+10

15x = 90

Divide each side by 15

15x/15 = 90/15

x = 6

Answer:

x > -3

Step-by-step explanation:

Any negative number greater than -3 will have an absolute value greater than 3.

Answer:

f(x)=5cos(1/3x) this is an equation

Answer:

Option B, cotangent is the reciprocal of tangent

That option is correct

Answer:

Binomial probability refers to the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment).

Answer:

0 is the answer measure 1

Answer:

-3

Step-by-step explanation:

For an expression to be undefined,. the denominator must be equal to 0

Therefore, in order to make that expression undefined, we must equate the denominator to 0

6 + 2v = 0

2v = 0 - 6

2v = -6

v = -6/2

v = -3

So in order to make the expression to be equal to 0, v must be -3

According to my calculations answer is -2

Answer:

The selling price after the markup is $1.82

Step-by-step explanation:

$1.40 * .30 =

Multiply $1.40 times .30 (which is same as 30%)

$1.40 * .30 = $0.42

Add $1.40 and $0.42

= $1.82

Hope this helps.

144 x 1.25 = 180

Answer: 144

Answer:

144

Step-by-step explanation:

144 × 1.25 = 180

We add the 1 to .25 to represent the original value plus the 25% increase.

Or you could have divided 180 by 1.25 to find original price.

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Answer:

Step-by-step explanation:

If we let x represent "a number", then "three times a number" is 3x. The usm of that and 1 is ...

  1 +3x . . . . . . the sum of 1 and 3 times a number

That is said to be -89, so we have the equation ...

  1 +3x = -89

__

To solve this equation, we can subtract 1 from both sides:

  3x = -90

Then we can divide by 3 to find x.

  (3x)/3 = -90/3

  x = -30

Answer:

3

Step-by-step explanation:

The dilation factor is 3

$5531.49

(9×9)×$68.29

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Answer:

  a) RM2256.09 . . . principal paid by 8th payment

  b) RM1791.10 . . . . interest paid by 12th payment

Step-by-step explanation:

First of all, we need to find the payments.

The payment amount is the amount that makes the future value of the series of payments equal to the future value of the loan at the given interest rate.

The future value of a single amount is ...

  FV = P(1 +r)^n . . . . . where r is the annual rate, and n is the number of years in the future

The future value of a series of payments is ...

  FV = P((1 +r)^n -1)/r . . . . . where n is the number of payments of P earning annual rate r

For payments in a series that does not end at the end of the loan, the future value is the product of that of the series and the effect of the accumulation of interest for the remaining time.

__

The first 4 payments will have a future value at the end of the loan period of ...

  s1 = X((1 +0.05)^4 -1)/0.05×(1 +0.05)^11 = X(1.05^15 -1.05^11)/0.05

  s1 = 7.3717764259X

The next 5 payments will have a future value at the end of the loan period of ...

  s2 = 2X((1 +0.05)^5 -1)/0.05×(1 +0.05)^6 = 2X(1.05^11 -1.05^6)/0.05

  s2 = 14.8097486997X

The last 6 payments will have a future value at the end of the loan period of ...

  s3 = 4X((1 +0.05)^6 -1)/0.05 = 27.20765125X

So, the total future value of the series of payments is ...

  payment value = 7.3717764259X +14.8097486997X +27.20765125X

  = 49.3891763756X

__

The future value of the loan amount after 15 years is ...

  loan value = 60,000(1 +0.05)^15 = 124,735.69

In order for these amounts to be the same, we must have ...

  49.3891763756X = 124,735.69

  X = 124,735.69/49.3891763756 = 2,525.57

__

At this point, it is convenient to use a spreadsheet to find the interest and principal portions of each of the loan payments. (We find the interest charge to be greater than the payment amount for the first 4 payments. So, the loan balance is increasing during those years.)

In the attached, we have shown the interest on the beginning balance, and the principal that changes the beginning balance to the ending balance after each payment. (That is, the interest portion of the payment is on the row above the payment number.)

The spreadsheet tells us ...

A) the principal repaid in the 8th payment is RM2,256.09

B) the interest paid in the 12th payment is RM1,791.10

_____

Additional comment

The spreadsheet "goal seek" function could be used to find the payment amount that makes the loan balance zero at the end of the term.

We have used rounding to sen (RM0.01) in the calculation of interest payments. The effect of that is that the "goal seek" solution is a payment value of 2525.56707 instead of the 2525.56734 that we calculated above. The value rounded to RM0.01 is the same in each case: 2525.57.

Answer:

Hello,

What is tan 30°?

[tex]tan(30^o)=\dfrac {\sqrt{3} }{3}[/tex]

Step-by-step explanation:

[tex]sin(30^o)=\dfrac{1}{2} \\\\cos(30^o)=\dfrac{\sqrt{3} }{2} \\\\\\tan(30^o)=\dfrac{sin(30^o)}{cos(30^o)} \\tan(30^o)=\dfrac{\dfrac{1}{2} } { \dfrac{\sqrt{3} }{2} }\\\\ =\dfrac {1*2}{2*\sqrt{3} }\\\\ =\dfrac {\sqrt{3} }{3}[/tex]

The value of tan 30° is 1/√3

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.

Tan 30° = sin 30° / cos 30°

We know that, sin 30° = 1/2

cos 30° = √3/2

Therefore,

Tan 30° = 1/2 ÷ √3/2

Tan 30° = 1/2 x 2/√3

Tan 30° = 1/√3

Hence, the value of tan 30° is 1/√3

Learn more about tangent of an angle, click;

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