I just made a purchase of $130.00 but once I got my car and looked at the receipt, I realized the salesperson who helped me did not apply the 15% discount

Answer:

Option D, [tex]x =[/tex] ± [tex]4/13[/tex]

Step-by-step explanation:

Step 1:  Add 16 to both sides

[tex]169x^2 - 16 = 0[/tex]

[tex]169x^2 - 16 + 16= 0 + 16[/tex]

[tex]169x^2 = 16[/tex]

Step 2:  Divide 169 from both sides

[tex]\frac{169x^2}{169} = \frac{16}{169}[/tex]

[tex]x^2 = 0.09467[/tex]

Step 3:  Square root both sides

[tex]\sqrt{x^2} = \sqrt{0.09467}[/tex]

[tex]x =[/tex] ± [tex]0.30769[/tex]

[tex]x =[/tex] ± [tex]4/13[/tex]

Answer:  Option D, [tex]x =[/tex] ± [tex]4/13[/tex]

Answer:

I'm assuming where you wrote x2, you meant 2x.

Anyway, if csc (x) = 2, since csc(x) = 1/sin(x), we know that 1/sin x = 2, so sin (x) = 1/2. Since sin2x + cos2x = 1, cos2x = 1 - sin2x, so cos x = √1 - sin2x. In this case, cos x = √ 1 - (1/2)2 = √(3/4) = (√3)/2. Finally, since sin x = opp / hyp , cos = adj/ hyp: sin x / cos x = (opp/hyp)/(adj/hyp) = opp/adj = tan x. So this means that tan x = sin x / cos x = 1/2 / √ 3 / 2 = 1/√3 = √3 / 3

At this point, all that is necessary is to use the double angle formulas for sin, cos, and tan.

sin (2x) = 2 sin x cos x = 2 (1/2) (√3/2) = √3 / 2

cos (2x) = cos2x - sin2x = (√3/2)2 - (1/2)2 = 3/4 - 1/4 = 1/2

tan (2x) = 2 tan x / (1 - tan2x) = 2 (√3 / 3) / ( 1 - (√3/3)2) = 2/√3 / (1 - 1/3) = 2/√3 / (2/3) = 3/√3 = √3

To sum up, sin (2x) = √4 / 2, cos (2x) = 1/2, and tan(2x) = ✓3.

Step-by-step explanation:

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[tex]\sin\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{8}}\\\cos\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\\\tan\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{4 - \sqrt{15}}}\\[/tex]

To find sin(x/2), cos(x/2), and tan(x/2), we need to use the half-angle identities for trigonometric functions.

Given: csc(x) = 4 for 90° < x < 180°

Step 1: Find sin(x). Since csc(x) is the reciprocal of sin(x), we have:

csc(x) = 1/sin(x) = 4

Now, find sin(x):

sin(x) = 1/csc(x) = 1/4

Step 2: Find cos(x). To do this, use the Pythagorean identity:

[tex]sin^2(x) + cos^2(x) = 1\\cos^2(x) = 1 - sin^2(x) \\= 1 - (1/4)^2 \\= 1 - 1/16 \\= 15/16[/tex]

Now, find cos(x):

[tex]\cos(x) = \pm \sqrt{\frac{15}{16}}[/tex]

Since x is in the second quadrant (90° < x < 180°), cos(x) is negative. So,

[tex]\cos(x) = - \sqrt{\frac{15}{16}}[/tex]

[tex]= -\sqrt{15} / 4[/tex]

Step 3: Find tan(x). To do this, use the identity:

[tex]\tan(x) = \frac{\sin(x)}{\cos(x)}\\\tan(x) = \frac{\frac{1}{4}}{-\frac{\sqrt{15}}{4}}\\\tan(x) = -\frac{1}{\sqrt{15}}[/tex]

Now, let's find sin(x/2), cos(x/2), and tan(x/2) using the half-angle identities:

Half-angle identities:

[tex]\sin \left ( \frac{x}{2} \right ) = \pm \sqrt{\frac{1 - \cos x}{2}}\\\cos \left ( \frac{x}{2} \right ) = \pm \sqrt{\frac{1 + \cos x}{2}}\\\tan \left ( \frac{x}{2} \right ) = \frac{\sin \left ( \frac{x}{2} \right )}{\cos \left ( \frac{x}{2} \right )}[/tex]

Step 4: Find sin(x/2):

[tex]\sin \left( \frac{x}{2} \right) = \pm \sqrt{\frac{1 - \cos x}{2}}\\\sin \left( \frac{x}{2} \right) = \pm \sqrt{\frac{1 + \frac{\sqrt{15}}{4}}{2}}\\\sin \left( \frac{x}{2} \right) = \pm \sqrt{\frac{4 + \sqrt{15}}{8}}\\\sin \left( \frac{x}{2} \right) = \pm \frac{\sqrt{4 + \sqrt{15}}}{\sqrt{8}}\\\sin \left( \frac{x}{2} \right) = \pm \frac{\sqrt{4 + \sqrt{15}}}{2}[/tex]

Step 5: Find cos(x/2):

[tex]\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 + \cos(x)}{2}}\\\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 + \left(-\frac{\sqrt{15}}{4}\right)}{2}}\\\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1 - \frac{\sqrt{15}}{4}}{2}}\\\cos\left(\frac{x}{2}\right) = \pm\sqrt{\frac{4 - \sqrt{15}}{8}}\\\cos\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\cos\left(\frac{x}{2}\right) = \pm\left(\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\right)[/tex]

Step 6: Find tan(x/2):

[tex]\tan \left ( \frac{x}{2} \right ) = \frac{\sin \left ( \frac{x}{2} \right )}{\cos \left ( \frac{x}{2} \right )} = \pm \frac{\sqrt{4 + \sqrt{15}}}{\sqrt{4 - \sqrt{15}}}[/tex]

So, the values are:

[tex]\sin\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{8}}\\\cos\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 - \sqrt{15}}}{\sqrt{8}}\\\tan\left(\frac{x}{2}\right) = \pm\frac{\sqrt{4 + \sqrt{15}}}{\sqrt{4 - \sqrt{15}}}\\[/tex]

Note: The ± symbol indicates that there are two possible solutions due to the quadrant restrictions.

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Complete Question is:

If csc ( x ) = 4, for 90 ∘ < x < 180, then sin ( x /2 ) = ? cos ( x /2 ) = ? tan ( x /2 ) = ?

Answer:

*select all that apply*

All of these are true

Step-by-step explanation:

Answer choice A:

We-Haul: c = 0.45m + 20

You-Haul: c = 1m

--> TRUE

Answer Choice B:

the y-intercept is the upfront charge bc the charge for "per mile" is attached to "mx" and the "b" (y-intercept) is the upfront charge

--> TRUE

Answer choice C:

We-Haul -

c = 0.45(38) + 20 = $37.10

You-Haul -

c = 1m = $38.00

--> TRUE

answer choice D:

We-Haul -

c = 0.45(35.36) + 20 = $35.91

You-Haul -

c = 1m = $35.36

Since the two costs are very close to being the same, I think this is a true statement also

--> TRUE

Answer choice E:

You-Haul's rate is 1 mph whereas We-Haul's rate is 0.45mph. You-Haul's rate is 0.55 larger than We-Haul's

--> TRUE

Hope this helps :)

Answer:

40

Step-by-step explanation:

16+24=40

40-16=24

Answer:

a = 40

Step-by-step explanation:

Add 16 on both sides

a - 16 + 16 = 24 + 16

a = 24 +16 = 40

a = 40

Verification

LHS = a - 16  a = 40

40 - 16 = 24

RHS = 24

Both LHS and RHS are same so, our answer is correct.

Answer:

answer in order from top to bottom

1. True

2. false

3. true

4. false

Answer:

.

Step-by-step explanation:

1.true

2.true

3.false

4.false

i hope it helps :)

Answer:

Letting f represent the value of the flower and b represent the value of the butterfly, we have f = 20 and b = -53.

Step-by-step explanation:

7f + 2b = 34 ------> 7f + 2b = 34

3f + b = 7-----------> 6f + 2b = 14

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

f = 20, b = -53

Answer:In the following diagram, two parallel lines are cut by a transversal. What is the value of x x? Solution: The two angles 3x −15 3 x − 15 and 2x +7 2 x + 7 are equivalent. That is: 3x −15 = 2x +7 3 x − 15 = 2 x + 7

In the following diagram, two parallel lines are cut by a transversal. What is the value of x x? Solution: The two angles 3x −15 3 x − 15 and 2x +7 2 x + 7 are equivalent. That is: 3x −15 = 2x +7 3 x − 15 = 2 x + 7

Step-by-step explanation: : 3

Answer:

Step-by-step explanation:

Beth's position over time is constant, which makes the problem a lot easier. You are asked for the rate of position versus time, so begin by doing that. Since the rate is constant, clearly from the table, you can take any two data points and take their ratio. Her rate would be 11 feet every 5 seconds, or equivalently 2.2 feet every second. To graph the data, put position on the x-axis and time on the y-axis. The slope will be 2.2 at every point along her bike ride.

Moving on to the third part. If Amy traveled at a rate of 75 feet every 30 seconds, then she would be traveling 2.5 feet every second. Amy's rate is larger than Beth's rate. Since the rate corresponds to the slope of the postion vs. time graph, Amy's graph will have a steeper incline since the slope is 2.5

Answer:

1 mm Hg per year

Explanation:

Here equation : y = x + 95

Comparing with slope intercept formula: y = mx + b

                                    where m is slope and b is y-intercept

Slope determines the increase per year.

Equation given

Comapre to slope intercept form y=mx+b

Rate of change=Slope=1mm HG /year

The function y = 18(0.914)^m is having exponential decay. The decay percent of this function is 8.6%

Consider the function:

[tex]y = a(1\pm r)^m[/tex]

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is plus sign, then there is exponential growth happening by r fraction or 100r %

If there is negative sign, then there is exponential decay happening by r fraction or 100r %

For this case, the exponential growth/decay function given is:

[tex]y = 18(0.914)^m[/tex]

That means, there is multiplication of (0.914) for each growth/decay.

We can rewrite 0.914 as:

0.914 = 1 - 0.086

This shows decay as multiplication with 0 < quantity < 1 makes the number less in magnitude.

A quantity times (1 - 0.086) = that quantity - that quantity times 0.086

and we can write 0.086 = 8.6/100 = 8.6%

Thus, we're decreasing 8.6% each time from a quantity when we multiply that quantity with (1-0.086)

Thus, there is exponential(exponential because of the presence of variable 'm' as exponent in the given function) decay of 8.6%.

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Answer:

-18^6

Step-by-step explanation:

(-18^2)^3   = -18^(2*3)  =  -18^6

Answer:

42.5 ft squared

Step-by-step explanation:

hope this helped brah

Answer:

Hello, so most of your steps are in the correct order. All you need to do is switch is the following steps.

x = -3 ± 5/2 should go before x = -3 + 5/2 and x = -3 - 5/2 as the second seperates the the ± into + and -

[You need to switch steps 4 and 5]

3y - 4

hope it helps...!!!

Answer:

B. Bangladesh

Step-by-step explanation:

he UN has called for Burma to allow access to a Fact Finding Mission to investigate reports of human rights violations and abuses and to work with Bangladesh to facilitate repatriation of Rohingya refugees, and in September 2018 the International Criminal Court (ICC) determined it had jurisdiction to investigate reported human rights abuses against Rohingyas. Burma has rejected charges of ethnic cleansing and genocide, and has chosen not to work with the UN Fact Finding Mission or the ICC.

Answer:

x= 29

Step-by-step explanation:

use Pythagoras because it has a right angle and 2 sides length is given.

when the hypoteneus(side opposite the right angle) is the value you are finding out you use the equation : x²+y²=hypoteneus² (Pythagoras)

then you sub in the values you are given

(21)² + (20)² = hypoteneus²

them take the square root (²) to the opposite side to find the hypoteneus

square root (441+400) = hypoteneus

now you can put into a calculator and you get the value

hypoteneus =29 (for reference to hypoteneus is the same as X-the value you are looking for)

therefore, x=29

for extra reference, say you want to work out a side that is not the hypotenues you use the formula ,

(side u looking for)² = (hypotenues)² - (other side given)²

Answer:

x = 29

Step-by-step explanation:

To find x, we can use the Pythagorean theorem.

a^2 + b^2 = c^2

21^2 + 20^2 = x^2

441 + 400 = x^2

841 = x^2

[tex]\sqrt{841}[/tex] = [tex]\sqrt{x^2}[/tex]

29 = x

Using the given discrete probability distribution, it is found that the probability that a randomly selected student has a grade higher than a C is given by:

P(X > 2).

From the table, it is given by:

Grades A and B are greater than C, hence the probability of getting a grade higher than C is given by:

P(X > C) = P(X = A) + P(X = B) = P(X = 3) + P(X = 4) = P(X > 2).

More can be learned about discrete probability distributions at https://brainly.com/question/24855677

Answer:

6 and -1

Step-by-step explanation:

If you take the equation and set it to be 0, you can find the input values that make it 0.

[tex]x^2-5x-6=0[/tex]

Since this is a quadratic, equation you can use the quadratic formula with the values:

The quadratic formula is:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

If you plug the values for a, b, and c, you get:

x = 6 and x = -1

Answer:Im pretty sure the slope is 2.

Step-by-step explanation:

Answer:

the answer is (3,4)

Step-by-step explanation:

because if you check wich quadrant it is in and you check the number you can see which one it is. x,y that is how it goes so 3,4 should be correct if you line them up.

Answer:

your answer is 280

Step-by-step explanation:

Because you already know what X and Y are all you will have to do is plug them in

10 (10 + 2(9))

2*9= 18

10 (10 + 18)

10+18= 28

10(28)

280

Answer:

arc = 7.5π units

Step-by-step explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

the angle subtended at the centre by the arc is 360° - 90° = 270° , then

arc = 2π × 5 × [tex]\frac{270}{360}[/tex]

     = 10π × [tex]\frac{3}{4}[/tex]

     = [tex]\frac{30\pi }{4}[/tex]

     = 7.5π

Answer:

c+3<22

Step-by-step explanation:

c+3<22

Answer:

20 inmates should leave

Step-by-step explanation:

A camp having 80 inmates, has food sufficient for 70 days.

total=80*70

How many inmates should leave after 10 days so that the

remaining food lasts another 80 days?

the food served for 10 days to 80 inmates

10*80

let x be inmates leave after 10 days food last for 80 days

(80-x)*80

Total=food served for 10 days+x inmates left after 10 days

80*70=10*80+(80-x)*80

70=10+80-x

x=90-70

x=20

Answer:

3/20

Step-by-step explanation:

Answer:

b=-30;c=41

Step-by-step explanation:

I don't really know how to explain it... Vertex form, so factor out 5, divide by two, that has to be three. so .1b=3, b=30... opposite of the square of 3 times 5 add c=-4, so -45+c=-4, c=41. Just learn vertex form, and complete the perfect square. Good luck!

Answer:

5x - 9

Step-by-step explanation:

2x -(-3x + 9)                

2x + 3x - 9)                  DISTRIBUTE -1

5x - 9                           COMBINE LIKE TERMS