what is 9 less than 3 times f

Answer:

[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]

Step-by-step explanation:

We want to find a formula for s in terms of a, b, and cos(x).

Let the point where s intersects AB be D.

Notice that s bisects ∠C. Then by the Angle Bisector Theorem:

[tex]\displaystyle \frac{a}{BD} = \frac{b}{AD}[/tex]

We can find BD using the Law of Cosines:

[tex]\displaystyle BD^2 = a^2 + s^2 - 2as \cos x[/tex]

Likewise:

[tex]\displaystyle AD^2 = b^2+ s^2 - 2bs \cos x[/tex]

From the first equation, cross-multiply:

[tex]bBD = a AD[/tex]

And square both sides:

[tex]b^2 BD^2 =a^2 AD^2[/tex]

Substitute:

[tex]\displaystyle b^2 \left(a^2 + s^2 - 2as \cos x\right) = a^2 \left(b^2 + s^2 - 2bs \cos x\right)[/tex]

Distribute:

[tex]a^2b^2 + b^2s^2 - 2ab^2 s\cos x = a^2b^2 + a^2s^2 - 2a^2 bs\cos x[/tex]

Simplify:

[tex]b^2 s^2 - 2ab^2 s \cos x = a^2 s^2 - 2a^2 b s \cos x[/tex]

Divide both sides by s (s ≠ 0):

[tex]b^2 s -2ab^2 \cos x = a^2 s - 2a^2 b \cos x[/tex]

Isolate s:

[tex]b^2 s - a^2s = -2a^2 b \cos x + 2ab^2 \cos x[/tex]

Factor:

[tex]\displaystyle s (b^2 - a^2) = 2ab^2 \cos x - 2a^2 b \cos x[/tex]

Therefore:

[tex]\displaystyle s = \frac{2ab^2 \cos x - 2a^2 b \cos x}{b^2- a^2}[/tex]

Factor:

[tex]\displaystyle s = \frac{2ab\cos x(b - a)}{(b-a)(b+a)}[/tex]

Simplify. Therefore:

[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]

Answer:

Total student= 600

Step-by-step explanation:

Let x be the number of students

[tex]x \times \frac{80}{100} = 480 \\ = 480 \times \frac{10}{8} \\ x = 600[/tex]

Brainliest please~

Answer:600

Step-by-step explanation:

by taking total number of pupils x

80/100×x=480

48000/80=600

x=600

Step-by-step explanation:

V(-2,1)

U(1,3)

E(0,1)

the dilation is by 1/2 so multiply all numbers by a half, hope you pass!!

Answer:

The length of one side of the hot tub is 4.8ft

Step-by-step explanation:

Given

Shape: Square

[tex]k = 5[/tex] -- scale factor

[tex]B'C' = 24[/tex]

Required

Side length of ABCD (the hot tub)

From the question, we understand that

[tex]ABCD \to D_5 \to A'B'C'D[/tex]  ABCD dilated by 5 to A'B'C'D

This implies that:

[tex]BC * 5 = B'C'[/tex] i.e. the sides of ABCD is multiplied by 5 to get A'B'C'D

So, we have:

[tex]BC * 5 = 24[/tex]

Divide by 5

[tex]BC = 4.8[/tex]

Answer:

Step-by-step explanation:

In the standard form of a quadratic,

[tex]h(x)=-x^2+v_0x+h_0[/tex],

that last term, the h0, is the initial height off the ground that the object is. That means that for the first question, the irrigation system is initially 9.5 feet off the ground.

In order to answer the next question, we need to find the vertex of the parabola, because this is where the max height will occur and at how many feet away from the system. The max height is the k of the vertex and the horizontal distance away is the h of the vertex: (h, k). Thankfully, we have simple formulas to find those:

[tex]h=-\frac{b}{2a}[/tex]  and  [tex]k=c-\frac{b^2}{4a}[/tex]  where a, b, and c come from the coefficients in the equation. For us, a = -1, b = 10, and c = 9.5. Finding h first:

[tex]h=-\frac{10}{2(-1)}=\frac{-10}{-2}=5[/tex]  

and now k:

[tex]k=9.5-(\frac{10^2}{4(-1)})=9.5-(\frac{100}{-4} )=9.5-(-25)=9.5+25=34.5[/tex]

Summing it up, the vertex is at (5, 34.5), The interpretation of that is that "The spray reaches a max height of 34.5 feet at a horizontal distance of 5 feet away from the sprinkler head."

Next we are asked how far away from the sprinkler head the water hits the ground. To do this we factor the expression to find the zeros. The zeros tell us where the water will hit the ground after it reaches its max height and then falls back down to earth.

I used my calculator to factor this for me to get that the water will hit the ground 10.87 feet away from the sprinkler head.

The volume of the solid as shown in the task content is; 2786.2cm³.

It can be obtained from the task content that the solid given is a Cone.

On this note, the volume of the cone can be evaluated by means of the formula;

V = (1/3)π r²h where(r =22/2 = 11 and h=22).

Hence, Volume, V = (1/3) ×3.14× (11)²×22 = 2786.2cm³.

Read more on volume;

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Answer:

11

Step-by-step explanation:

because you have to add 5+6=11

Answer:

270.

Step-by-step explanation:

If the first term = a and 10th term = a + 9d where d = the common difference.

a + 9d - a = 45 - 9

9d = 36

d = 4.

Sum of first 10 terms = (10/2)[2*9 + (10-1)*4]

= 5 * (18 + 36)

= 5 * 54

= 270.

Answer:

15 boxes were shipped late

Step-by-step explanation:

late = 3% = 0.03

500 x 0.03 = 15 boxes

Answer:

I think the answer might be 30%

Step-by-step explanation:

The best estimate of the percent of the company's computers that require an update to the printer driver is 30%.

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

According to the question

A company has 500 computers that are used by its employees. A sample of 40 of these computers finds that 12 of them require an update to the printer driver.

Using unitary method,

[tex]\frac{40}{12} =\frac{500}{x}[/tex]

Where x is the best estimate of the number of the company's computers that require an update.

x  = [tex]\frac{12.(500)}{40}[/tex]

x = 150

To convert it into percentage,

[tex](\frac{150}{500} ).100[/tex]

= 30 %

Hence, the best estimate of the percent of the company's computers that require an update to the printer driver is 30%.

Find out more information about unitary method here

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Answer:

A' (-3,12)

B' (9,6)

C' (-6,-6)

Answered by GAUTHMATH

Answer:

64.

Step-by-step explanation:

The digits used are 1 , 2, 7 and 8

To make a number of three digits, the digits are repeated.

To make the three digit number

The ones place is filled by 4 ways.

The tens place is filled by 4 ways.

The hundred place is filled by 4 ways.

So, the total number of ways to make a three digit number is 4 x 4 x 4 = 64.

Answer:

9²+x²=13²

81+x²=169

x²= 169-81

x²=88

X= 9.38

[tex]x = \sqrt{88} [/tex]

Answer:

] 14/3 ; ♾ [

Step-by-step explanation:

3x-5>9

3x>9+5

3x>14

x>14/3

wich make it ] 14/3 ; ♾ [

when three times a certain number is subtracted from 5 the result is more than 9 find the number.

Let us assume :

The number be x

Data :

A number is 3 times = 3x

Subtracted from 5

The result = 9

Henceforth, the equation we got is :

Transposing 9 to the other side

Hence, the value of x is 14/3 respectively

Answer:

1 Solar day = 86,400 seconds (SI Base Unit)

1 day = 1,440 minutes

Step-by-step explanation:

If need anymore help just ask I'm not really good at explaining but I'll try just comment haha ☺️

Answer:

2.25

Step-by-step explanation:

The lower number will always be on the right side unless its negative numbers , So the lower number is 2.25 , Why it isn't 1.26 is because its much far from 2.26 and so cannot be counted . Thanks

Giá Trị tuyệt đối của  tổng hai số nguyên có hai kết quả là số âm và số dương.Nhưng Giá trị tuyệt đói luôn luôn ra kết quả là số dương nên ta cần kết quả là cả âm và dương khi phá dấu tuyệt đối. khi âm -dương =âm. khi dương- âm=dương

Answer:

P(black|coin fell tails) = ¼

Step-by-step explanation:

Since a coin has a head and a tail, then probability of landing tail is;

P(tail) = ½

Now, if it falls tails, a marble is drawn from Box 2, which contains two white and two black marbles.

Thus, probability of getting a black marble is; 2/4 = ½

Thus;

P(black|coin fell tails) = ½ × ½ = ¼

Answer:

-21

Step-by-step explanation:

comments

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Work Shown:

A = area = 6y^5

b1+b2 = sum of the parallel bases = 4y^2

h = unknown height, i.e. distance between the parallel sides

------

A = 0.5*h*(b1+b2)

6y^5 = 0.5*h*4y^2

6y^5 = 0.5*4y^2*h

6y^5 = 2y^2*h

2y^2*h = 6y^5

h = (6y^5)/(2y^2)

h = (6/2)*y^(5-2)

h = 3y^3

The parallel sides are separated by a distance of 3y^3 units.

Answer:

5/2, 7/3, 9/4, 11/5, 13/6, 15/7,17/8

Step-by-step explanation:

Answer:

2/1

2.5

2whole number6/4

Answer:

The conic section for the equation 5x^2 - y = 12 is parabola

Answer:

The radius vector is (-8, 7) and (-1 , 5).

Step-by-step explanation:

Determine the radius vector of the midpoint of the segment that is formed by joining the points (-8, 7) and (6, 3).

The end points are (- 8, 7) and (6, 3) .

The mid point is given by

[tex]x = \frac{x' + x''}{2}\\\\y = \frac{y' +y''}{2}\\\\x =\frac{- 8 + 6}{2}=-1\\\\y = \frac{7+3}{2} = 5[/tex]

So, the radius vector is (-8, 7) and (-1 , 5).  

Answer:

-11

0

Step-by-step explanation:

Answer:

a = 53

Step-by-step explanation:

Start with d

The ends of d + 53 are diameter ends. That means that d + 53 is a right angle

d + 53 = 90

d = 90 - 53

d = 37

Next, find b. The end points of b are the same end points as for 53 degrees. B is the central angle of 53 which means b = 2 * 53

b = 106

c is the supplement of b

c + b = 180

b = 106

c + 106 = 180

c = 180 - 106

c = 74

The triangle containing a and c is isosceles because 2 of the 3 angles are opposite radii. The lowest angle is also a because it is opposite one of the radii.

a + a + 74 = 180

2a = 180 - 74

2a = 106

a = 106/2

a = 53

Hard to believe, but there it is.

Answer:

240 miles

Step-by-step explanation:

60*4=240

Answer: 240

Step-by-step explanation: If she is traveling 60 miles per hour you can multiply it by 4, which is 240.

Answer:

[tex]\text{C. }21.39\:\mathrm{units^2}[/tex]

Step-by-step explanation:

The area of a triangle with sides [tex]a[/tex] and [tex]b[/tex] and angle [tex]\gamma[/tex] between them is given by [tex]A=\frac{1}{2}ab\sin \gamma[/tex].

Therefore, in the given triangle, we want to find two sides with the angle between them given. In this case, the angle between the two sides 7.39 and 9.75 is marked as [tex]36.43^{\circ}[/tex]. Assign values:

Substituting these values into our area formula, we get:

[tex]A=\frac{1}{2}\cdot 7.39\cdot 9.75\cdot \sin (36.43)^{\circ},\\A=21.3938371858,\\A\approx \boxed{21.39\:\mathrm{units^2}}[/tex]