4 Divided by 61,630

sin(a+b) = sinacosb + cosasinb

sin(a-b) = sinacosb -  cosasinb

adding we get  sin(a+b) + sin(a-b) = 2sinaccosb

so sinacosb = 1/2sin(a+b) + sin(a-b)

Answer: Sin a

Answer:

sin a

Step-by-step explanation:

A P E X

Answer:

Solution given:

4x²+35x-9=0

comparing above equation with ax²+bx+c.

we get

a=4

b=35

c=-9

we have

x=[tex] \frac{ - b±\sqrt{b²-4ac}}{2a} [/tex]

x=[tex] \frac{ - 35±\sqrt{35²-4*4*-9}}{2*4} [/tex]

x=[tex] \frac{ - 35±\sqrt{1369}}{2*4} [/tex]

x=[tex] \frac{ - 35±37}{8} [/tex]

taking positive;

x=[tex] \frac{ - 35+37}{8} [/tex]

x=[tex] \frac{1}{4} [/tex]

taking negative

x=x=[tex] \frac{ - 35-37}{8} [/tex]

x=-9

Therefore:the roots of 4x²+ 35x − 9 = 0 is [tex] \frac{1}{4} [/tex] or-9.

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

Explanation:

Parallel lines have equal slopes but different y intercepts.

The slope of y = 3x+2 is m = 3 (compare it to y = mx+b)

Any parallel line will also have slope m = 3

The parallel line goes through (x1,y1) = (-7, -6)

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

Turn to point-slope form. Plug in the values mentioned and solve for y

y-y1 = m(x-x1)

y-(-6) = 3(x-(-7))

y+6 = 3(x+7)

y+6 = 3x+21

y = 3x+21-6

y = 3x+15

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

Or you could use slope intercept form

y = mx+b

y = 3x+b

-6 = 3(-7)+b

-6 = -21+b

-6+21 = b

15 = b

b = 15

Since m = 3 and b = 15, we know the equation is y = 3x+15

Answer:  [tex]12x^2+12xh+4h^2-2[/tex]

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

Explanation:

First let's find the expression f(x+h). We replace every copy of x with x+h, expand, and simplify like so.

[tex]f(x) = 4x^3 - 2x\\\\f(x+h) = 4(x+h)^3 - 2(x+h)\\\\f(x+h) = 4(x+h)(x+h)^2 - 2(x+h)\\\\f(x+h) = 4(x+h)(x^2+2xh+h^2) - 2(x+h)\\\\f(x+h) = 4x(x^2+2xh+h^2)+4h(x^2+2xh+h^2) - 2(x+h)\\\\f(x+h) = 4x^3+8x^2h+4xh^2+4hx^2+8xh^2+4h^3 - 2x-2h\\\\f(x+h) = 4x^3+12x^2h+12xh^2+4h^3 - 2x-2h\\\\[/tex]

This may look ugly, but things will simplify a bit when we subtract off f(x)

Note how in f(x+h) we have the following terms

Which are the exact terms found in f(x) as well.

Why is this important? It helps us subtract and cancel. When we subtract off f(x), we cross off the 4x^3 and -2x terms in that f(x+h) equation above.

We'll be left with this

[tex]f(x+h)-f(x) = 12x^2h+12xh^2+4h^3-2h\\\\[/tex]

At this point, every term shown has at least one copy of 'h' as a factor.

This allows us to factor out h

[tex]f(x+h)-f(x) = h(12x^2+12xh+4h^2-2)\\\\[/tex]

Then we can divide both sides by h to get our final answer

[tex]\frac{f(x+h)-f(x)}{h} = \frac{h(12x^2+12xh+4h^2-2)}{h}\\\\\frac{f(x+h)-f(x)}{h} = 12x^2+12xh+4h^2-2\\\\[/tex]

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

Extra info:

h is nonzero to avoid dividing by zero. Though as h gets closer and closer to zero, terms with h in them will drop out since those terms will be very small. We'll be left with 12x^2-2. This is the derivative of f(x).

Answer:

Answer is D on e2020

Step-by-step explanation:

why does vla statistics have little to no answers available for it?

The statement that is correct is If the missing data value were 50, the range of the data would change substantially. The correct option is D.

The range is the difference between the Maximum value of the data set and the Minimum value of the dataset.

Range = Maximum value of the data set - Minimum value of the dataset

The given data observation from the stemplot is given below.

8, 9, 9, 9, 10, 11, 12, 12, 12, 14, 15, 16, 16, 18, 18, 21, 22, 27, 27, 27, 31

Since IQR or the interquartile range is the difference between the quartiles, therefore, it won't be affected much if either of the two values 32 and 50 are added.

Now, the range of the data without 32 or 50 will be,

Range = 31 - 8 = 23

The range of the data when 32 is added,

Range = 32 - 8 = 24

The range of the data when 50 is added,

Range = 50 - 8 = 42

Hence, the statement that is correct is If the missing data value were 50, the range of the data would change substantially.

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Answer:

3/4 ÷ 1/8 = 6

Step-by-step explanation:

first you would have to figure out how to make them even factors.

6/8 ÷ 1/8

Then you would divide, and get 6.

Answer:

Pull out like factors

  2x + 24  =   2 • (x + 12)

2x + 24 = 2x + 24

This equation is a tautology or an Identity meaning it's always true.

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

4x + 37 = 2x + 13

-2x. -2x

2x + 37 = 13

-37. -37

2x = -24

x = -12

Answer:

134494

Step-by-step explanation:

Answer: 134,494

Step-by-step explanation: d=$1,000, the yearly deposit.

r=0.10, or a 10% annual rate.

k=1, since we’re doing yearly deposits and we’ll compound yearly.

N=30, we want the amount after 30 years.

Putting this into the annuity formula:

PN=d⋅((1+rk)N⋅k−1)rkP30=1,000⋅((1+0.101)30⋅1−1)(0.101)P30=1,000⋅((1.1)30−1)(0.10)P30=1,000⋅(17.4494−1)(0.10)P30=1,000⋅(16.4494)(0.10)=$164,494.

The account will grow to $164,494 after 30 years.

Notice that you deposited into the account a total of $30,000 ($1,000 a year for 30 years). The difference between what you end up with and how much you put in is the interest earned. In this case it is $164,494–$30,000=$134,494.

RS = 3?

I will draw a diagram because its easier that way. If QS = 9 since 6 + 3 = 9 and QR = 6 then RS = 3 since 9 - 6 = 3.

Answer:

-12

Step-by-step explanation:

(−3)(−2)( −2)

-3 * -2 = +6

+6 (-2)

Positive times negative is negative

-12

Answer:

no

Step-by-step explanation:

Answer:

A = 112 , C = 85 , B = 90

Step-by-step explanation:

A + B + C = 287

A + C = 197

A + B = 202

C = 197 - A

B = 202 - A

A + 202 - A + 197 - A = 287

A = 112

C = 85

B = 90

Machine A, B and C can produce 112, 90 and 85 bolts per hour.

Per hour defines 1 hour.When ever you see the word per second, per day means in 1 sec, 1 day.

According to the given question In a factory there are three machines, A, B and C.

When all three machines are working they can produce 287 bolts per hour.

∴ A + B + C = 287...(i)

When only  A and C are working, they produce 197 bolts per hour.

∴ A + C = 197...(ii)

When only machines A and B are working, the produce 202 bolts per hour.

∴ A + B = 202...(iii)

Subtracting (ii) from (i) we get

B = 90.

Putting the value of B in (iii) we get

A = 112.

And putting value of A in (ii) we get '

C = 85.

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Answer: 120

Step-by-step explanation:

              Ratio      Quantity

Boys:        5           80 + x                  

Girls:         3              x

                 [tex]\dfrac{5}{3}=\dfrac{80+x}{x}\\\\\\5x=3(80+x)\\\\5x=240+3x\\\\2x=240\\\\x=120[/tex]

Answer:

Improper fraction is 9/4 cups, Mixed number is 2 1/4 cups

9/4 cups of sugar or 2 1/4 cups of sugar

Step-by-step explanation:

36 tsp are in 3/4 of a cup

so you have 1/3 : 36

1/3 is less than a whole teaspoon, so the amount of sugar would be greater than 3/4 cups

1/4 cups of sugar: 1 tsp of butter; or 108 teaspoons of sugar: 1 teaspoon of butter

Hope this helps!

Plz name brainliest if possible!

Answer:

Not being mean but you are in collage you should know this but here is the answer

Step-by-step explanation:

7 balloons to each girls because 7 times 5 = 35

Answer:

7 ballons

Step-by-step explanation:

Five girls =>35 :5 =7 balloons each girl

Answer:

D) x² + 16

A) x − 2

Step-by-step explanation:

(x³ + 3x² + 16x + 48) / (x + 3)

Use grouping:

(x² (x + 3) + 16 (x + 3)) / (x + 3)

Divide:

x² + 16

(x² + x − 6) / (x + 3)

Factor:

(x + 3) (x − 2) / (x + 3)

Divide:

x − 2

Answer: the brother in incorrect

Step-by-step explanation:

No his brother is incorrect because the ratio would go from 8:3 to 4:9

I know this answer is correct because I did this question on edgenuity and it was correct.

Answer:

No his brother is incorrect because the ratio would go from 8:3 to 4:9

Step-by-step explanation:

-7x-1

Step-by-step explanation:

this is extra words

Answer:

irrational

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

Answer:

  $25

Step-by-step explanation:

1/3 of the $60 cost is $20.

1/4 of the $60 cost is $15.

The amount remaining is $60 -20 -15 = $25.

$25 is left.

Answer:

49

Step-by-step explanation:

Answer:

it is 49 for sure

Step-by-step explanation:

it worked for me on khan

Answer:

Step-by-step explanation:

average of 5 numbers=115

total of 5 numbers=115×5=575

total of 4 numbers=116+132+145+106=499

fifth number=575-499=76

Answer:

Step-by-step explanation:

Answer:

[tex]\huge{\fbox{\sf{ x = -3 }}}[/tex]

Step-by-step explanation:

[tex]\sf{ x + 5 = 2}[/tex]

Since , we are asked to find the value of x , move 5 to right hand side and change its sign.

⇒ [tex]\sf{x = 2 - 5}[/tex]

Remember!

⇒[tex]\sf{ x = -3 }[/tex]

Hope I helped!

Best regards!

- TheAnimeGirl

Answer:

1, 2, and 5 :)

Step-by-step explanation:

3: negative times a negative is a positive

4: negative times negative is a positive

hope this helps !! <3

Hi!

Your answer would be: 228ft below the ocean surface.

Reason being: when you subtract 43 from 271, you get 228.

Hope this helps!

If you need anymore help, please let me know!

Yours Truly,

Complete question is;

Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply.

A) Every line connects two vertices.

B) Every line connects the midpoints of 2 sides.

C) Every line bisects a vertex angle.

D) Every line bisects a side.

E) Every line is perpendicular to a side.

Answer:

C: Every line bisects a vertex angle.

D: Every line bisects a side.

E: Every line is perpendicular to a side.

Step-by-step explanation:

A shape will have a line of symmetry when after the perpendicular line is drawn through from one vertex to the centre of one side, it can be folded and the folded part will sit perfectly on top in such a way that all the edges match.

Now, a pentagon has 5 sides and by implication from the explanation of line of symmetry above, it has 5 lines of symmetry.

Attached below is an image showing the 5 lines of symmetry of a pentagon.

From the attached image, we can see that the lines of symmetry bisects a vertex angle, it bisects a side and is perpendicular to a side.

Thus correct answer is Options C, D & E

Answer:

Step-by-step explanation:

The measures of the angle in the triangle are; ∠CDF = 43, ∠GDE = 63°, ∠FDG =  74°

From the way the problem is worded:

∠CDE is a straight angle made up of three angles:  

∠CDF = 43°

∠FDG is unknown

∠GDE = 8x - 1

∠EDH is outside CDE = 6x + 15.  

DE bisects GDH to form GDE and EDH.

Thus, we have;

8x - 1 = 6x + 15

x = 8

Putting 8 for x, both angles are equal to 57°.

Since ∠CDF = 43 and ∠GDE = 63° and ∠CDE ∠ 180° in total.

∠FDG = 180° - 43° - 63° = 74°

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Answer:

Kindly check explanation

Step-by-step explanation:

Assume a normal distribution with:

Mean (m) = 500

Standard deviation (sd) = 10.6

A) The median of the MCAT scores :

For a normal distribution, the Median = mean = 50% = 0.5

Zscore at 0.5 = - 0.0

-0.0 = (x - m) / sd

-0.0 = (x - 500) / 10.6

0 = x - 500

x = 500

B) the first quartile (Q1) score = 25% = 0.25

Using :

Zscore at 25% = 0.25 = -0.675

Zscore = (X - m) / sd

-0.675 = (X - 500) / 10.6

-7.155 = x - 500

x = - 7.155 + 500

X = 492.845

C.) the third quartile (Q3) score = 75% = 0.75

Using :

Zscore at 75% = 0.25 = 0.675

Zscore = (X - m) / sd

0.675 = (X - 500) / 10.6

7.155 = x - 500

x = 7.155 + 500

X = 507.155

D.) The interquartile range :

Q3 - Q1

= 507.155 - 492. 845

= 14.31

2.) Interval which contains 80% of MCAT Scores:

Zscore of the (100-80)% / 2 at the extremes ; = 20%/2 = 0.1 ; 0.1 = - 1.28

Interval:

(-1.28 * sd) + mean and (1.28 * sd) + mean

(- 1.28 * 10.6) + 500 and (1.28 * 10.6) + 500

-13.568 + 500 and 13.568 + 500

486.432 and 513.568