Find the total cost, to the nearest cent, for a sweater that costs $22.95 with an additional 5.5% sales tax. Show your work.

Answer:  see proof below

Step-by-step explanation:

You will need the following identities to prove this:

[tex]\tan\ (\alpha-\beta)=\dfrac{\tan \alpha-\tan \beta}{1+\tan \alpha\cdot \tan \beta}[/tex]

[tex]\cos\ 2\alpha=\cos^2 \alpha-\sin^2\alpha[/tex]

LHS → RHS

[tex]\dfrac{2\tan\ (45^o-A)}{1+\tan^2\ (45^o-A)}\\\\\\=\dfrac{2\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)}{1+\bigg(\dfrac{\tan\ 45^o-\tan\ A}{1+\tan\ 45^o\cdot \tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)}{1+\bigg(\dfrac{1-\tan\ A}{1+\tan\ A}\bigg)^2}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{1+\bigg(\dfrac{1-2\tan\A+\tan^2 A}{1+2\tan A+\tan^2A}\bigg)}\\[/tex]

[tex]=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{(1+2\tan A+\tan^2A)+(1-2\tan A+\tan^2 A)}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\dfrac{2+2\tan^2A}{1+2\tan A+\tan^2A}}\\\\\\=\dfrac{2\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{2\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}\\\\\\=\dfrac{\bigg(\dfrac{1-\tan A}{1+\tan A}\bigg)}{\bigg(\dfrac{1+\tan^2A}{(1+\tan A)^2}\bigg)}[/tex]

[tex]=\dfrac{1-\tan A}{1+\tan A}}\times \dfrac{(1+\tan A)^2}{1+\tan^2A}\\\\\\=\dfrac{1-\tan^2 A}{1+\tan^2 A}\\\\\\=\dfrac{1-\dfrac{\sin^2 A}{\cos^2 A}}{1+\dfrac{\sin^2 A}{\cos^2 A}}\\\\\\=\dfrac{\bigg(\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A}\bigg)}{\bigg(\dfrac{\cos^2 A+\sin^2 A}{\cos^2 A}\bigg)}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{\cos^2 A+\sin^2 A}\\\\\\=\dfrac{\cos^2 A-\sin^2 A}{1}\\\\\\=\cos^2 A-\sin^2 A\\\\\\=\cos 2A[/tex]

cos 2A = cos 2A   [tex]\checkmark[/tex]

Answer:

-1=-2

4=-7

Step-by-step explanation:

for x=-1

y=(-1^2)+(2*-1)+1

y=-1-2+1

y=-2

for x=1

y= (-1^2)+(2*1)+1

y= -1+2+1

y=2

for x=4

y=(-4^2)+(2*4)+1

y=-16+8+1

y=-7

Answer:

sqrt of (m-7) = n+3

m = (n+3)^2 + 7 or m= n^2 + 6n + 16

sqrt of (m)-7 = n+3

m = (n+10)^2 or m =n^2 + 20n + 100

Step-by-step explanation:

(2) move the constants to the other side, and square

or  (1) square and move constants

then you can solve for m

Answer:

[tex]n^2+6n+16[/tex]

Step-by-step explanation:

I'm going to assume you meant [tex]\sqrt{m-7} = n+3[/tex], not  [tex]\sqrt{m} - 7 = n+3[/tex].

[tex](\sqrt{m-7}) ^2 = (n+3)^2\\\\(\sqrt{m-7}^2) = (n+3)^2\\\\(m-7)^{\frac{2}{2} } = (n+3)^2\\\\m - 7 = (n+3)^2\\\\m - 7 = n^2 + 2n\cdot3 + 3^2\\\\m - 7 = n^2 + 6n + 9\\\\m - 7 + 7 = n^2 + 6n + 9 + 7\\\\m = n^2 + 6n + 16[/tex]

Hope this helped!

Answer:

16,848+17,160+17,576+18,200+18,720+19,240+21,840=

129,584

Step-by-step explanation:

[tex]$8.10, $8.25, $8.45, $8.75, $9.00, $9.25, and $10.50\\[/tex]

Annually= Yearly, A year has 365 days.

They work 40 hours a week, 8*5=40.

There are aprox, 10 holidays in a year. (You can change this in your work)

They have 2 weeks unpaid vacation, 14 days.

There are aprox, 52 weeks in a year. (You can change this in your work)

52 weeks - 2 weeks of unpaid vacation= 50 weeks.

Now Let's calculate the weekly income, for

$8.10*40=$324 per week.

$8.25*40=$330 per week.

$8.45*40=$338  per week.

$8.75*40=$350 per week.

$9.00*40=$360  per week.

$9.25*40=$370 per week.

$10.50*40=$420  per week.

Now Let's calculate the annually income, for each clerk.

324*50=16,200 + 648=16,848

330*50=16,500 + 660=17,160

338*50=16,900 + 676=17,576

350*50=17,500  + 700=18,200

360*50=18,000 + 720=18,720

370*50=18,500 + 740=19,240

420*50=21,000 + 840=21,840

Now the total annual payroll=

16,848+17,160+17,576+18,200+18,720+19,240+21,840=

129,584

Answer:

1. EF = 65m

2. DF = 73m

Step-by-step explanation:

1. EF = height of the building = h = 33 / tan 27 = 65m

2. DF = sqrt (65² + 33²) = 73m

The building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.

From the triangle DEF, we find the value of EF by using tan function.

tan function is a ratio of opposite side and adjacent side.

tan(27)= 33/FE

0.5095 = 33/FE

Apply cross multiplication:

FE=33/0.5095

FE=64.76

Now DF is the hypotenuse, we find it by using pythagoras theorem.

DF²=DE²+EF²

DF²=33²+64.76²

DF²=1089+4193.85

DF²=5282.85

Take square root on both sides:

DF=72.68

In a triangle the the sum of three angles is 180 degrees.

∠D + 27 +90 =180

∠D + 117 =180

Subtract 117 from both sides:

∠D =63 degrees.

Hence, the building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.

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Answer:

x = 162 degrees.

Step-by-step explanation:

m < RSP = 180 - 72

= 106 degrees (adjacent angles)

m < Q = m < RSP ( Opposite angles in a parallelogram are equal).

So m < Q = 180 degrees.

m < x = 360 - 90 - 108

= 360 - 198

= 162 degrees.

Using the appropriate angle theorems, the value of the angle, x in the parallelogram would be 162°

At angle S :

S + 72 = 180 (sum of straight line angles)

S = 180° - 72°

S = 108°

S = Q (opposite angles of a parallelogram)

Q = 108°

Hence,

108° + x + 90 = 360

x = 360 - (108 + 90)

x = 162°

Hence, the value of x is 162°

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The decimal 0.1894528 is not a repeating decimal.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system. The numbers are first in fractions and then divided by the number to give a decimal number.

The given decimal number is “0.1894528. In the decimal number if the numbers are repeating then it is called the repeating decimal number if the numbers are not repeating then it is called a nonrepeating decimal number. Here the given decimal is nonrepeating decimal.

Therefore, the decimal 0.1894528 is not a repeating decimal.

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Answer:

The first one

Step-by-step explanation:

This line is the best fit for the scatter plot because it touches a lot more points than the second

Answer:

The first line

Step-by-step explanation:

Hey there!

Well the first lie is a positive slope just like the dots whereas,

the second line is a negative slope.

Therefore, the first line is the line of best fit.

Hope this helps :)

Answer:

7

Step-by-step explanation:

Negative Correlation - These variables point towards the left making them negative.

Positive Correlation - These variables point towards the right making them positive.

No Correlation - These variables have the same x coordinates or same y coordinates.

Hope that helped!!! k

Answer:

B

Step-by-step explanation:

Answer:

Bottom right option

Step-by-step explanation:

To find this, we can calculate:

1/2 * 4.32 * 10⁻⁴

= (1/2 * 4.32) * 10⁻⁴

= 2.16 * 10⁻⁴

The diameter of a new cell is 2.16×10−⁴millimeters

First step is to calculate 4.32×10−⁴ to the original numbers

4.32×10−⁴ =0.000432

Second step is to determine the diameter of a new cell

New cell diameter=0.000432×1/2

New cell diameter=0.000216

New cell diameter=2.16×10−⁴millimeters

Inconclusion The diameter of a new cell is 2.16×10−⁴millimeters

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Answer:

x = 75

Step-by-step explanation:

FGE is a straight line so it equals 180 degrees

FGA + AGC + CGE = FGE

x + 90 + 15 = 180

Combine like terms

x+ 105 = 180

Subtract 105 from each side

x = 180-105

x = 75

Answer:

x = 75º

Step-by-step explanation:

The Vertical Angle Theorem shows that:

∠CGE ≅ ∠DGF

So:

∠DGF = 15º

∠AGD = 90º

90º - 15º = 75º

x = 75º

Answer:

convert them to decimasls

Step-by-step explanation:

convert thhem to decimals to make it easier

Answer:

1/2 2/4 4/8 6/12 9/18

Step-by-step explanation:

Step-by-step explanation:

The three main types of exercise are cardiovascular exercise, strength training and stretching. All three types of exercise are important for physical fitness. Cardiovascular aerobic exercise is repetitive, rhythmic exercise that increases your heart rate and requires you to use more oxygen.

Answer:

6.67

Step-by-step explanation:

Answer:

1 1/2 miles / hour

Step-by-step explanation:

We want distance / time

3/4 miles

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

1/2 hour

3/4 ÷ 1/2

Copy dot flip

3/4 * 2/1

3/2

1 1/2 miles / hour

Answer:

D

Step-by-step explanation:

Multiple (3/4)  by 2 to find the information for one hour)

6/4 in one hour

3/2 or 1 + 1/2 mi/h

D is the answer

Answer:

A. 24+24+120+160+200

Step-by-step explanation:

Surface area of the triangular prism= addition of the area of each shape that forms the prism

There are two triangles

Area of a triangle=1/2*base*height

=1/2*8*6

=1/2*48

=24

Area of two triangles=24+24

There are 3 rectangles with different dimensions

Back rectangle=length×width

=20×6

=120

Bottom rectangle=length ×width

=20x8

=160

Top rectangle=length × width

=20×10

=200

Surface area =Area of two triangles + Back rectangle + Bottom rectangle + Top rectangle

=24+24+120+160+200

Using it's concept, it is found that the exterior angles of the triangle are given as follows:

B. <5

C. <4

The exterior angles of a triangle are the angles that are outside the triangle.

In this problem, the angles are 4 and 5, which means that options B and C are correct.

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Triangle inequality theorem:

In any triangle, the length of any side must be:

For the problem you have:

x must be greater than 8.0 - 2.5 and less than 8.0 + 2.5

5.5 < x < 10.5

Answer:

5.5<x<10.5

Step-by-step explanation:

Answer:

-7 is a Negative Number, which is also an integer.

Step-by-step explanation:

Negative numbers are any number less than 0. The greater a negative number is, is the smaller its value.

Answer:

-2+12=10

-10+20=10

1+9=10

9+1=10

8-(-2)=10

2-(-8)=10

-30+40=10

Step-by-step explanation:

Answer:

24.43

Step-by-step explanation:

first find the price of One sachets

next Find the no. of sachets consumed for four weeks..

and at last the product of the price of one sachet and no. of sachets consumed will give the answer...

Mathematical operation are above...

Answer:

the answer is d

Step-by-step explanation:

cause its d

Answer:

20%

Step-by-step explanation:

Answer:

f(4) = 3

Step-by-step explanation:

f(x) = -[tex]x^{2}[/tex] + 8x - 13

To find f(4), substitute 4 for all instances of x:

f(4) = -(4[tex])^{2}[/tex] + 8(4) - 13

Simplify the exponent:

f(4) = -16 + 8(4) - 13

Multiply:

f(4) = -16 + 32 - 13

Combine terms:

f(4) = 3

Answer:

3

Step-by-step explanation:

You plug in 4.

f(4)= -(4)^2+8(4)-13

f(4)= -16+32-13

f(4)= 16-13

f(4)=3

Answer:

x = 180 - [(180 - 3x) + (180 - 2x)]

Step-by-step explanation:

Start off by finding the angles of the triangle

Angle F = 180 - 3x

The angle across from I (which I will call I) = 180 - 2x

Angle G = 180 - (F + I)

Now that we know what G is, we know what x is because the Alternate Exterior Angles Theorem states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent. So pretty much X = G

Therefore x =  180 - (F + I) or otherwise said as:

x = 180 - [(180 - 3x) + (180 - 2x)]

I hope this is helpful :)

Answer:

d = √8

d ≈ 2.82843

Step-by-step explanation:

Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Simply plug in our coordinates into the distance formula:

[tex]d = \sqrt{(-3 + 5)^2+(-8 + 6)^2}[/tex]

[tex]d = \sqrt{(2)^2+(-2)^2}[/tex]

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

[tex]d = \sqrt{8}[/tex]

To find the decimal, simply evaluate the square root:

√8 = 2.82843

Answer:

Step-by-step explanation:

Let the points be A and B

A ( - 5 , - 6 ) ⇒ ( x₁ , y₁ )

B ( -3 , - 8 )⇒( x₂ , y₂ )

Now, let's find the distance between these two points:

AB = [tex] \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]

Plug the values

⇒[tex] \mathsf{ \sqrt{( - 3 - ( - 5) )^{2} + {( - 8 - ( - 6))}^{2} } }[/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

⇒[tex] \mathsf{ \sqrt{ {( - 3 + 5)}^{2} + {( - 8 + 6)}^{2} } }[/tex]

Calculate

⇒[tex] \mathsf{ \sqrt{ {(2)}^{2} + {( - 2)}^{2} } }[/tex]

Evaluate the power

⇒[tex] \mathsf{ \sqrt{4 + 4} }[/tex]

Add the numbers

⇒[tex] \mathsf{\sqrt{8} }[/tex]

Simplify the radical expression

⇒[tex] \mathsf{ \sqrt{2 \times 2 \times 2}} [/tex]

⇒[tex] \mathsf{2 \sqrt{2} }[/tex] units

Hope I helped!

Best regards!

Answer:

[tex]$\[x^2 + 22x + 121\]$[/tex]

Step-by-step explanation:

Given

[tex]$\[x^2 + 22x + \underline{~~~~}.\]$[/tex]

Required

Fill in the gap

Represent the blank with k

[tex]$\[x^2 + 22x + k\]$[/tex]

Solving for k...

To do this, we start by getting the coefficient of x

Coefficient of x = 22

Divide the coefficient by 2

[tex]Result = 22/2[/tex]

[tex]Result = 11[/tex]

Take the square of this result, to give k

[tex]k= 11^2[/tex]

[tex]k= 121[/tex]

Substitute 121 for k

[tex]$\[x^2 + 22x + 121\]$[/tex]

The expression can be factorized as follows;

[tex]x^2 + 11x + 11x + 121[/tex]

[tex]x(x + 11)+11(x+11)[/tex]

[tex](x+11)(x+11)[/tex]

[tex](x+11)^2[/tex]

Hence, the quadratic expression is [tex]$\[x^2 + 22x + 121\]$[/tex]

Answer:

Hey there!

We have an=a1(r^n-1), which is the formula for a geometric sequence.

The common ratio is 3, and 2 is the 1st term.

Thus, we have a1=2(3)^(n-1)

Hope this helps :)

Answer:

Hey there!

We have an=a1(r^n-1), which is the formula

for a geometric sequence.

The common ratio is 3, and 2 is the 1st

term.

Thus, we have a1=2(3)^(n-1)

Answer:

24.2

Step-by-step explanation: