what quantity should be added to both sides of this equation to complete the square x^2+12x=-15

Seems like there is a correction in the first question (RHS is tanx.tany)

(i) For convenience: let tanx = a ; tany = b

Thus, tanx + tany = a + b

Moreover, cotx = 1/tanx = 1/a ; coty = 1/b

Thus,

cotx + coty = 1/a + 1/b = (a + b)/ab

Hence,

=> (tanx + tany)/(cotx + coty)

=> (a + b) / { (a + b)/ab }

=> ab(a + b)/(a + b)

=> ab => tanx.tany , proved.

(ii) For convenience: let sinx = a ; cosx = b

As we know, sin²x + cos²x = 1 => a²+b²=1

=> (a³ + b³)/(a + b)

=> (a + b)(a² + b² - ab) / (a + b)

=> (a² + b² - ab)

=> 1 - ab => 1 - sinx.cosx , proved

(iii): let x/2 = A

=> tan(x/2) + cosx.tan(x/2)

=> tanA + cos2A.tanA

=> tanA [1 + cos2A]

=> tanA (2cos²A) {1+cos2A = 2cos²A}

=> (sinA/cosA) (2cos²A)

=> sinA (2cosA)

=> 2sinAcosA

=> sin2A

=> sin2(x/2)

=> sinx proved

Letting x/2 = A is not mandatory. I did it to decease words*(in a line).

Indentities used:

• sin²A + cos²A = 1

• (a³ + b³) = (a + b)(a² + b² - 1)

• 1 + cosA = 2 cos²(A/2)

• tanA = sinA/cosA.

• 2sinAcosA = sin2A

Answer:

the original volume is lesser than the new volume by 242.47 in³

Step-by-step explanation:

Volume of a cone is;

V = ⅓πr²h

Where;

r is radius

h is height

For the original chamber;

r = 5.7/2 = 2.85 inches

h = 12 inches

Volume of this original chamber is;

V_orig = ⅓ × π × 2.85² × 12

V_orig = 102.02 in³

In the new design, the chamber is scaled by a factor of 1.5.

Thus;

r_new = 2.85 × 1.5 = 4.275 inches

h_new = 12 × 1.5 = 18 inches

V_new = ⅓ × π × 4.275² × 18

V_new = 344.49 inch³

V_new - V_orig = 344.49 - 102.02 =

Thus, the original volume is lesser than the new volume by 242.47 in³

Answer:

432 is the blank

Step-by-step explanation:

I just did this problem

Answer:

ok

Step-by-step explanation:

Answer:

(-21, -38)

Step-by-step explanation:

Given the simultaneous equation

10x-6y = 18 ... 1

9x+6y=39 ...2

Using the Elimination method

Subtract

10x - 9x = 18 - 39

x = -21

substitute x = -21 into 1;

From 1:

10x-6y = 18

10(-21)-6y = 18

-210 - 6y = 18

-6y = 18+210

-6y = 228

y = 228/-6

y =-38

Hence the solution to the system is (-21, -38)

Answer:

5.063 seconds

Step-by-step explanation:

Use a graphing calculator to graph, then use the table functions to solve for 1304

or say

1304= rest of equations and solve for X

Answer:

I.d.k I think 1 :)

Step-by-step explanation:

have a great day

Answer:

Dont say its a test youll get reported and banned by brainly

Step-by-step explanation: also the answer is:  3/5 x 3/5 = 925 = 0.36

Answer: 1/1

Step-by-step explanation:

1/1 because it = 1 so that means 3/5 x 1/1 is 3/5

0.2252

(Please mark me brainliest! thank you in advance!!)

Answer:

30 thousands, or 30,000 units.

Step-by-step explanation:

Since the question refers to 10 x 3 thousands, to determine how many thousands are in the answer, the following calculation must be performed:

10 x 3 = 30

So there are 30 thousand in the answer, which is equal to 30,000.

Answer:jeans = x = 16.85

shirts = y = 8.95

Step-by-step explanation:

That’s the answer bud

Answer: 0.13

Step-by-step explanation:

Answer:

this is a nonlinear function because the point do not have a steady rate of change for example y went up one and x went up 1 but from the next set of pairs y went up one and x went up three so this is a nonlinear function

Answer:

540

Step-by-step explanation:

We need 6 times 90 for the full amount.

Answer:

Total amount = 540

Step-by-step explanation:

let total amount = x

1/6 * x = 90

x = 540

Answer:

y=-3/4x+3

Step-by-step explanation:

The formula is y=mx+b

m is the slope

b is the y-intercept

If you plug it in, you get y=-3/4x+3

Hope this helps!

Answer:

1. C=35m?

2.C=700 or $700

Step-by-step explanation:

1. Total Cost= Rate x Number of Months

2. C=35m

Cost=rate x number of months

C=35(20)

C=700 or Total Cost=$700

Answer:

1. c = 35m

2. c = 35 · 20

20 · 35 = $700

Step-by-step explanation:

Answer:

Cos(π/2 - θ) = A

Step-by-step explanation:

We know that:

Sin(θ) = A

And we want to find the value of Cos(π/2 - θ)

Here we can use the cosine relationship:

Cos(a - b) = Cos(a)*Cos(b) + Sin(A)*Sin(B)

Then:

Cos(π/2 - θ) = Cos(π/2)*Cos(θ ) + Sin(π/2)*Sin(θ)

We know that:

Cos(π/2) = 0

Sin(π/2) = 1

Then:

Cos(π/2 - θ) = Cos(π/2)*Cos(θ ) + Sin(π/2)*Sin(θ) = 0*Cos(θ ) + 1*Sin(θ)

                    = 1*Sin(θ) = A

Cos(π/2 - θ) = A

Answer:

Answer:

1/12

Step-by-step explanation:

Answer:

B. $700

Step-by-step explanation:

The answer is A because.....

Step 1: Find the 7% of 2000.

a.) 7% of 2000 is 140.

b.) Check- So: 140/2000= 0.07 (7%)

Step 2: Multiply 140x5 which equals $700.

Although, I can’t really see the second question‘s options, as the calculations made for the previous question, she paid $140 each year.

I rlly hope this is helpful! If so, please, please, please mark brainliest! Thanks! :)

Answer:

c

Step-by-step explanation:

Answer:

271.25 mg

Step-by-step explanation:

The amount of medicine will be equal to 271.25 mg.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that a veterinarian prescribed Christy, a 31-pound dog, an antibacterial medication in case an infection emerges after her teeth were cleaned. The dosage is 8.75 mg for every pound.

The amount of medicine will be calculated as below:-

Amount = 31 x 8.75

Amount = 271.25 mg

Therefore, the amount of medicine will be equal to 271.25 mg.

To know more about expression follow

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Answer:

$27

Step-by-step explanation:

According to your question. The complete cost was $135 for a fifteen feet long beam. If you are looking for the price per yard, a yard has three feet, therefore in fifteen feet, there are five yards.

15 divided into 3 equals 5

$135 divided into five equals $27

I hope this helps.

Answer:

The dpmo of the process is of 29000

Step-by-step explanation:

Dpmo of a process:

The dpmo of a process is the number of defects per million opportunities.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

First, using the normal distribution, we calculate the proportion of defective bubbles. Then, using this proportion, we calculate the dpmo.

Mean fill volume for rice bubbles is 475 grams and the standard deviation is 10 grams.

This means that [tex]\mu = 475, \sigma = 10[/tex]

The design specifications are [450, 495] grams. Any output outside of design specifications is treated as non-conforming.

Below 450 and Above 495 are non-conforming.

Below 450:

The proportion is the pvalue of Z when X = 450. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{450 - 475}{10}[/tex]

[tex]Z = -2.5[/tex]

[tex]Z = -2.5[/tex] has a pvalue of 0.0062

Above 495:

The proportion is 1 subtracted by the pvalue of Z when X = 495. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{495 - 475}{10}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

The proportion of defectives is 0.0228 + 0.0062 = 0.0290

Dpmo:

Number of defects per million, that is, the proportion multiplied by 1000000.

1000000*0.0290 = 29000

The dpmo of the process is of 29000

Answer:

The answer is A

Step-by-step explanation:

why it is a is...

the first like is the # your arithmetic sentence starts with which is -1

the second line is what you do to get to the next #

each time you are adding 6

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The correct option is A.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

[tex]a_n = a_1 + (n-1)d[/tex]

Also, the recursive formula for any arithmetic series is given by the formula,

[tex]a_n = a_{(n-1)} + d\\\\[/tex]

Or, it can be also written as,

[tex]a_{(n+1)} = a_{n} + d[/tex]

where d is the difference and a₁ is the first term of the sequence.

For the given arithmetic sequence, the common difference can be written as,

Common difference = -1 - (-7)

                                  = -1 + 7

                                  = 6

Now, the recursive formula for this arithmetic sequence can be written as,

[tex]a_n = a_{(n-1)} + 6[/tex]

Also, the first term of the given arithmetic series is -7.

a₁ = -7

Hence, the correct option is A.

Learn more about Arithmetic Sequence:

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Answer: y=300⋅2.03x

Step-by-step explanation:

Answer:

D.) y = 300 ⋅ 2.03x

Step-by-step explanation:

By using the plug-in method, you use "Hours" as the X in this question.

If you plug in 2, 4, 6, 8, 10, and 12 to y = 300 ⋅ 2.03x, you will get the closest answers to "Bateria Count"

1,236.27 = 300 ⋅ 2.03^2
5,094.54= 300 ⋅ 2.03^4
2,0994.11 = 300 ⋅ 2.03^6
86,514.63 = 300 ⋅ 2.03^8
and so on- all are the closest to the chart.

Hope this helped! :)