Find a negative integer M so that the equation (x-12)(x+m) = m-51

notka56 [123]

$\dfrac{2}{\sqrt3\cos x+\sin x}=\sec\left(\dfrac{\pi}{6}-x\right)\\\\\dfrac{2}{\sqrt3\cos x+\sin x}=\dfrac{1}{\cos\left(\dfrac{\pi}{6}-x\right)}\ \ \ \ \ (*)\\----------------\\\\\cos\left(\dfrac{\pi}{6}-x\right)\ \ \ \ |\text{use}\ \cos(x-y)=\cos x\cos y+\sin x\sin y\\\\=\cos\dfrac{\pi}{6}\cos x+\sin\dfrac{\pi}{6}\sin x=\dfrac{\sqrt3}{2}\cos x+\dfrac{1}{2}\sin x=\dfrac{\sqrt3\cos x+\sin x}{2}\\------------------------------$

$(*)\\R_s=\sec\left(\dfrac{\pi}{6}-x\right)=\dfrac{1}{\cos\left(\dfrac{\pi}{6}-x\right)}=\dfrac{1}{\dfrac{\sqrt3\cos x+\sin x}{2}}\\\\=\dfrac{2}{\sqrt3\cos x+\sin x}=L_s$

6 0

2 years ago

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What is the average size of a highschool diploma?

OlgaM077 [116]

The standard size of diplomas are 11x14''
Law Schools or Medical Schools are bigger for colleges.

4 0

3 years ago

. If her allowance had stayed the same, $9.00 a month, how many carnival tickets could she bu

jarptica [38.1K]

Answer:

a) number of tickets she could buy in a month with her allowance in 2008 = 4 tickets

b) number of tickets she could buy in a month with the same allowance in 2012 = 2 tickets

c) $5, an increase of 55.56%

d) $2, a 100% increase.

e) Hallie was able to buy more tickets in 2008 than in 2012.

f) $16

Step-by-step explanation:

The complete question is presented in the attached image to this answer.

a) Halie's allowance monthly = $9

Price of a ticket in 2008 = $2

number of tickets she could buy in a month with her allowance = (9/2) = 4.5 = 4 tickets (since there are no half tickets)

b) Halie's allowance monthly = $9

Price of a ticket in 2012 = $4

number of tickets she could buy in a month with her allowance = (9/4) = 2.25 = 2 tickets (since there are no quarter tickets)

c) In 2012, Hallie's allowance was $14.00 per month. How much did her monthly allowance increase between 2008 and 2012?

Her monthly allowance in 2008 = $9

Her monthly allowance in 2012 = $14

The increase = new allowance - old allowance = 14 - 9 = $5

In percentage terms,

% increase = 100% × (new - old)/(old)

% increase = 100% × (14 - 9)/9 = 55.56%

d) How much more did a carnival ticket cost in 2012 than it did in 2008?

Price of a ticket on 2008 = $2

Price of a ticket in 2012 = $4

Increase in price = 4 - 2 = $2

% increase = 100% × (4 - 2)/2 = 100%

e) Was Hallie able to buy more carnival tickets in 2008 or in 2012 with one month's allowance?

Hallie was able to buy more tickets in 2008 than in 2012.

f) What would Hallie's allowance need to be in 2012 in order for her to be able to buy as many carnival tickets as she could in 2008?

Hallie could buy 4 tickets in 2008.

Price of a ticket in 2012 = $4.

Price of 4 tickets in 2012 = 4 × $4 = $16

Hope this Helps!!!!

3 0

2 years ago

What is the inverse of the function f(x) = x +3?

Yanka [14]

Answer:

C)h(x) = x-3

Step-by-step explanation:

To find the inverse of a function, switch the "x" and "y" values, then isolate for "x".

f(x) is the y value.

y = x + 3

x = y + 3 Switch x and y

x - 3 = y Subtract 3 from both sides to isolate

y = x - 3 Change back to function of h

h(x) = x - 3

8 0

3 years ago

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Which expression represents the following statement: x is no less than 0. x>0 x≤0 x≥0 x<0

ki77a [65]

Answer: x ≥ 0

Step-by-step explanation:

First, let's define the symbols used:

a < x (this means that a is strictly smaller than x)

a > x (this means that a is strictly larger than x)

a ≤ x (this means that a is smaller than or equal to x)

a ≥ x (this means that a is larger than or equal to x)

Now we have the statement "x is no less than 0"

Then x can be equal to zero, or larger than zero, but never smaller than zero.

Looking at the symbols above, we know that we need to use:

x ≥ 0

(this is equivalent to the statement)

7 0

3 years ago

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Find a negative integer M so that the equation (x-12)(x+m) = m-51​

Find a negative integer M so that the equation (x-12)(x+m) = m-51