There are three points on a line, A, B, and C, so that AB = 12 cm, BC = 13.5 cm. Find the length of the segment AC . Give all possible answers.

Answer:

[tex]m < C = 60[/tex]

Step-by-step explanation:

From the given right angled triangle, ∆ABC,

[tex] BC = Hypotenuse = 2\sqrt{11} [/tex]

[tex] AC = Adjacent = \sqrt{11} [/tex]

Thus, m<C can be found by applying the following trigonometric ratio formula as shown below:

[tex] cos(C) = \frac{adjacent}{hypotenuse} [/tex]

[tex] cos(C) = \frac{\sqrt{11}}{2\sqrt{11}} [/tex]

Evaluate: √11 cancels √11

[tex] cos(C) = \frac{1}{2} [/tex]

[tex] cos(C) = 0.5 [/tex]

[tex] C = cos^{-1}(0.5) [/tex]

[tex] C = 60 [/tex]

[tex]m < C = 60[/tex]

Answer:

y = x + 0.5

Step-by-step explanation:

This is a very trivial exercise, follow the steps below:

Step 1: Perform the implicit differentiation of the given equation

[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]

[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]

Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:

[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]

Step 3: Find dy/dx at the point (0, 0.5)

[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]

Step 4: The equation of the tangent line to a curve at a given point is given by the equation:

[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]

you can use the value of sin\

sin(theta) = 12/16

Now solve for theta, and do inverse sine

so theta would be 48.59037789 , or around 50 degrees

Answer:

Step-by-step explanation:

Since, it is a right triangle.

Perpendicular (p) = 12

hypotenuse ( h) = 16

now,

[tex]sin \: (x \: degree) = \frac{perpendicular}{hypotenuse} [/tex]

[tex]sin \: x \: = \frac{12}{16} [/tex]

[tex] x = {sin}^{ - 1} ( \frac{12}{16} )[/tex]

[tex]x = 48.59 \: degree[/tex]

hope this helps...

good luck on your assignment..

Hey there! :)

Answer:

m = 4.

Step-by-step explanation:

We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)

Where 'm' is the slope and 'b' is the y-intercept. Therefore:

y = -5 + 4x becomes y = 4x - 5

The 'm' value is equivalent to 4, so the slope of the equation is 4.

Answer:

4

Step-by-step explanation:

because of y= mx + b where m is the slope

m= 4 in the equation

Answer: 120 ice creams total

The answer is option D

Answer:

[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]

Step-by-step explanation:

Radius = r = 9 cm

Angle = θ = 200° = 3.5 radians

Now,

[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]

Area = 1/2 (9)²(3.5)

Area = 1/2 (81)(3.5)

Area = 282.7 / 2

Area of sector = 141.4 cm²

Answer:

45 pi cm^2 or 141.3 cm^2

Step-by-step explanation:

First find the area of the circle

A = pi r^2

A = pi (9)^2

A = 81 pi

A circle has 360 degrees

The shaded part has 200

The fraction that is shaded is

200/360 =5/9

Multiply by the total area

5/9 * 81 pi

45 pi

Using 3.14 for pi

141.3

45 pi cm^2 or 141.3 cm^2

Answer:

Time taken = 6 sec (Approx)

Step-by-step explanation:

Given:

Total distance = 1/12 mi = 0.083333

Speed of train = 50 mph = 50 / 3600 = 0.01388889 mps

Find:

Time taken

Computation:

Time taken = Total distance / Speed

Time taken = Total distance / Speed of train

Time taken = 0.0833333 / 0.01388889

Time taken = 6 sec (Approx)

Answer:The answer is c

Step-by-step explanation:

Answer:

C) y = x + 5

Step-by-step explanation

Add 5 to both sides

Answer:

d ≈ 8.3

Step-by-step explanation:

This is kind of like the pythagorean theorem, but with one extra value.  Thus, [tex]d^2=l^2+w^2+h^2[/tex].

Plug in the values to get:

[tex]d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\[/tex]

Thus d ≈ 8.3

Answer:

y = 1.44

Step-by-step explanation:

What are you aiming to do here?  Please share all instructions with each problem.

If you want to solve 4.5/y = 12.5/4 for y:  Multiply both sides by 4y:

18 = 12.5y.  Then y = 1.44

Answer:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Answer: 10.246950766

Step-by-step explanation:

based on Pythagorean’s theorem:

[tex]\sqrt{19^{2}-16^{2} } =\sqrt{105} = 10.246950766[/tex]

Answer:

5x+8y+2z = 68

Step-by-step explanation:

Given the point P0 = (2, 5, 9), to Find an equation for a plane through that point and normal to the vector n = 5i+8j+2k the following steps must be followed:

The equation for the plane passing through the point is expressed as;

a(x-x0)+b(y-y0)+c(z-z0) = 0 where;

(x0, y0, z0) is the point on the plane and (a,b,c) is the normal vector n.

Given the point (2, 5, 9) and normal vector n =(5, 8, 2)

x0 = 2, y0 = 5, z0 = 9, a = 5, b = 8 and c= 2.

Substituting this values into the equation of the plane above will give;

5(x-2)+8(y-5)+2(z-9) = 0

On expansion:

5x-10+8y-40+2z-18 = 0

5x+8y+2z-10-40-18 = 0

5x+8y+2z-68 = 0

The required equation of the plane is 5x+8y+2z = 68

Answer:

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]

Step-by-step explanation:

Hey there!

Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.

Look at the image below ↓

By looking at the image we can conclude that the equation for the perpendicular line is,

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].

Hope this helps :)

Answer:

[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]

Step-by-step explanation:

Part 1: Finding the new slope of the line

Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.

Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].

Part 2: Using point-slope formula and solving in slope-intercept form

Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].

Then, use the point-slope equation to get b, or the y-intercept of the equation.

[tex](y-y_{1})=m(x-x_{1})[/tex]

[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]

Answer:

144 people competed in the Chess Tournament

Step-by-step explanation:

So as you can see, after the Chess Tournament took place, two boxes were empty, the rest closed. That would mean that there were 2 boxes of medals that were given out to honor the participants in the chess tournament. The spelling bee had twice as many participants, and hence used 2 [tex]*[/tex] 2 = 4 boxes. The remaining box had to have 72 medals in it, as it was the remaining amount of medals.

After the Chess Tournament, 2 boxes were given out, and we can assume they contained 72 medals in them. Therefore, the number of medals given after the chess tournament would be 2 [tex]*[/tex] 71 = 144 medals. Each medal corresponds to a participant, so the number of chess tournament participants would also be 144, 144 participants.

Answer:y=Mx+b

Step-by-step explanation:

Answer:

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

Step-by-step explanation:

You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as   "negation of a" or "  b" in mathematical terms is written like this

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

You can show that they are logically equivalent because they have the same truth table.

Answer:

1) Amplitude; A = 80 ft

Period = 60 ft

2)y = 80 sin ((π/30)x - 5π) + 80

3)y = 40 sin ((π/30)x - 5π) + 80

4)y = 40 sin ((π/30)x - 5π) + 40

5)y = -65sin ((π/30)x - 5π) + 80

Step-by-step explanation:

The general formula for sinusoidal wave equation is given by;

y = A sin (Bx - C) + D

Where;

A is amplitude = D_max or  D_min

Period = 2π/B

So; B = 2π/Period

Phase Shift = C/B  

So; C = B · Phase Shift

D: center

We are Given:

Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft

Thus; A = 80 ft

The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft

Thus; B = 2π/60 = π/30

Field is 300 ft wide and so the center is 300/2 = 150 ft

Thus; Phase Shift = 150.  

C = B × Phase Shift = π/30 · 150 = 5π

1) From the calculations above,

Amplitude; A = 80 ft

Period = 60 ft

2) As they begin to play, from the calculations above and y = A sin (Bx - C) + D, equation of the sine function is now;

y = 80 sin ((π/30)x - 5π) + 80

3) In this, since the sine wave is half as tall, then after the changes, we have;

y = 40 sin ((π/30)x - 5π) + 80

4) since they have moved closer, then equation is now;

y = 40 sin ((π/30)x - 5π) + 40

5) We are Given:

Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft

Since the first person forming the curve now stands at the 5 yard line, the minimum is at 5 yds (15 ft). Thus;

D_min = 80 - 15 = 65. Thus; A = 65 ft

The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft

Thus; B = 2π/60 = π/30

Field is 300 ft wide and so the center is 300/2 = 150 ft

Thus; Phase Shift = 150.  

C = B × Phase Shift = π/30 · 150 = 5π

The band ends down (at 15 feet) and thus A is negative

The equation is;

y = -65sin ((π/30)x - 5π) + 80

Part(1): The required values are,

Amplitude=[tex]80 ft[/tex] and Period: [tex]60 sec[/tex]

Part(2):

The equation of the sine function is

[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80[/tex]

Part(3):

The equation of the sine curve is,

[tex]y=40cos(\frac{\pi x}{30})+80[/tex]

Part(4):

The equation of the  sine curve representing the position of the band members after these changes is [tex]y=40cos(\frac{\pi x}{30})+40[/tex]

Part(5):

The required graph is attached below,

Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position

Part(1):

Amplitude=[tex]\frac{1}{2} width=80ft[/tex]

Period=[tex]2\times 30=60 sec[/tex]

Part(2):

Let the equation be,

[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80\\ y'=-\frac{8\pi}{3} sin((\frac{\pi x}{30}+\pi))[/tex]

Darla is at the point [tex]D(150,80)[/tex] which is on the graph at [tex]x=0[/tex] then,

[tex]80=80 cos(5\pi+\pi)=0\\y=-80 cos (\frac{\pi x}{30} )+80[/tex]

Part(3):

Since the wave is now [tex]\frac{160}{2} =80 ft[/tex] then,

Amplitude=40 ft

[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80\\y=40cos(\frac{\pi x}{30})+80[/tex]

Part(4):

The graph shifts downward 40 ft then,

[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80-40\\y=40cos(\frac{\pi x}{30})+40[/tex]

Part(5):

Start at:[tex]Y(x)=80sin (\frac{2\pi x}{60} )+80\\[/tex]

End at: [tex]Z(x)=80sin[ (\frac{2\pi }{60}(x-15) )]+80\\[/tex]

The graph is attached below:

Learn more about the topic of Simple harmonic motion:

https://brainly.com/question/14446439

Answer:

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Step-by-step explanation:

The rate is -1 4/5 lbs  per hour

The time is 3 1/2 hours

Multiply to find the weight change

-1 4/5 * 3 1/2

Change to improper fractions

- ( 5*1 +4) /5 * ( 2* 3+1)/2

- 9/5 * 7/2

-63/10

Changing back to a mixed number

-6  3/10

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Answer:

-6 3/10 pounds

Step-by-step explanation:

The weight of ice sculpture changes -1 4/5 pounds every 1 hour.

In 3 1/2 hours, multiply the time with the weight.

-1 4/5 × 3 1/2

Multiply.

-9/5 × 7/2

-63/10 = -6 3/10

Answer:

the real deal is that you mistook if

cos(x)=y/z gives y=zcos(x)

Answer:

42 gallons 45% antifreeze

28 gallons 95% antifreeze

Step-by-step explanation:

If x is volume of 45% antifreeze, and y is volume of 95% antifreeze, then the total volume is:

x + y = 70

And the total amount of antifreeze is:

0.45 x + 0.95 y = 0.65 (70)

Solving by substitution:

0.45 x + 0.95 (70 − x) = 0.65 (70)

0.45 x + 66.5 − 0.95 x = 45.5

21 = 0.5 x

x = 42

y = 28

Explanation:

For any quadrilateral that is inscribed in a circle, ie has all four points on the circle like this, the opposite angles are always supplementary. They add to 180 degrees.

x+125 = 180

x+125-125 = 180-125 ... subtract 125 from both sides

x = 55

Answer:

Max area is 16

Step-by-step explanation:

If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.

So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.

The maximal area of a right triangle is 90.496

Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given:

let the perpendicular be 'x'

and base be 'y'

Using Pythagoras theorem

x² + y² = 8²

x² + y² = 64

y²= 64- x²

y = √64-x²

Now, Area of triangle

= 1/2* base* height

=xy/2

=x *√64-x²*1/2

On differentiating both side

A' = 64-2x²/√64-x²*1/2

Setting derivative function equal to zero,

64= 2x²

32=x²

x=5.656

So, Area of triangle = x *√64-x²*1/2

= 90.496

Learn more about differentiation here:

https://brainly.com/question/24898810

#SPJ2

Answer: 1 30/39

Step-by-step explanation:

Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.

Hope it helps <3

Answer:

3 pounds

51 ounces

Step-by-step explanation:

Answer:

1 - Correct

2 - incorrect

3- incorrect

4 - incorrect

5 - Correct

Step-by-step explanation:

Notice that

3x  + 5 + 4x -1  =    3x + 4x + 5 -1 = 7x  + 4

therefore the two expressions are equivalent for ANY number, specially x = 4 and x = 6 therefore

1 - Correct

Since that is true for all numbers  

2 - incorrect

3- incorrect

4 - incorrect

The expressions are equivalent for all numbers therefore

5 - Correct

Answer:

a

   [tex]P(X = 10 ) = 0.0096[/tex]

b

   [tex]P(X = 10 ) = 0.0085[/tex]

c

 Option A is correct

Step-by-step explanation:

From the question we are told that

     The sample size is   n =  15

     The  probability of success is  [tex]p = 0.35[/tex]

     The number of success we are considering is  r = 10  

Now the probability of failure is mathematically evaluated as

        [tex]q = 1- p[/tex]

substituting value

       [tex]q = 1- 0.35[/tex]

       [tex]q = 0.65[/tex]

Now using  the binomial distribution  to find the probability of exactly 10 successes we have that

    [tex]P(X = r ) = [\left n } \atop {r}} \right. ] * p^r * q^{n- r}[/tex]

substituting values

    [tex]P(X = 10 ) = [\left 15 } \atop {10}} \right. ] * p^{10}* q^{15- 10}[/tex]

Where  [tex][\left 15 } \atop {10}} \right. ][/tex] mean 15 combination 10  which is evaluated with a calculator to obtain  

       [tex][\left 15 } \atop {10}} \right. ] = 3003[/tex]

So

      [tex]P(X = 10 ) = 3003 * 0.35 ^{10}* 0.65^{15- 10}[/tex]

       [tex]P(X = 10 ) = 0.0096[/tex]

Now using  the normal distribution to approximate the probability of exactly 10 successes, we have that

  [tex]P(X = r ) = P( r < X < r )[/tex]

Applying continuity correction

          [tex]P(X = r ) = P( r -0.5 < X < r +0.5)[/tex]

substituting values

        [tex]P(X = 10) = P( 10-0.5 < X < 10+0.5)[/tex]

       [tex]P(X = 10 ) = P( 9.5 < X < 10.5)[/tex]

Standardizing  

         [tex]P(X = r ) = P( \frac{9.5 - \mu }{\sigma } < \frac{X - \mu }{\sigma } < \frac{10.5 - \mu}{\sigma } )[/tex]

The  where  [tex]\mu[/tex] is the mean which is mathematically represented as

        [tex]\mu = n * p[/tex]

substituting values

        [tex]\mu = 15 * 0.35[/tex]

         [tex]\mu = 5.25[/tex]

The standard deviation is evaluated as      

     [tex]\sigma = \sqrt{n * p * q }[/tex]

substituting values

    [tex]\sigma = \sqrt{15 * 0.35 * 0.65 }[/tex]

    [tex]\sigma = 1.8473[/tex]

Thus  

     [tex]P(X = 10 ) = P( \frac{9.5 - 5.25 }{1.8473 } < \frac{X - 5.25 }{1.8473 } < \frac{10.5 - 5.25}{1.8473 } )[/tex]

     [tex]P(X = 10 ) = P( 2.30 < Z < 2.842 )[/tex]

     [tex]P(X = 10 ) = P(Z < 2.842 ) - P(Z < 2.30 )[/tex]

From the normal distribution table we obtain the [tex]P(Z < 2.841)[/tex] as

      [tex]P(Z < 2.841) = 0.99775[/tex]

And  the  [tex]P(Z < 2.30)[/tex]

     [tex]P(Z < 2.30) = 0.98928[/tex]

There value can also be obtained from a probability of z calculator at (Calculator dot net website)

So  

    [tex]P(X = 10) = 0.99775 - 0.98928[/tex]

     [tex]P(X = 10 ) = 0.0085[/tex]

Looking at the calculated values for question a and b  we see that the values are fairly different.

Answer: 19!!

Step-by-step explanation:

Answer:

[tex]\boxed{\mathrm{Option \ 4}}[/tex]

Step-by-step explanation:

Given that

[tex]y-4 = x[/tex]

Adding 4 to both sides

[tex]y-4+4 = x+4\\[/tex]

[tex]y = x+4[/tex]