How many lines can you draw using 3 non-collinear points A, B and C on a plane?​

Answer:

40

Step-by-step explanation:

[tex]\frac{RW}{24}=\frac{30}{18} \\ \\ RW=40[/tex]

Answer:

C - On the number line, move 3 units to the left. End at -7. The dolphin was 7 feet below sea level.

Step-by-step explanation:

The dolphin's starting point was -4 (4 feet below sea level). If the dolphin if diving down by 3 feet, you add -3 to its starting point.

-4 + -3 = -7.

Answer:

5,000

[tex]50000 \div 10 = 5000[/tex]

1a. 98 cm ^2

1b. 76. 98 cm^2

2a. 42cm

2b. 7. 19 cm

3. a + b/2 (h)

4. 24 cm ^2

5. πr + 2r

6. 13. 2m

7. 45cm^2

8. 252 cm ^ 2

9. 450 cm^ 2

1a. The shape given is a rectangle

The formula for area of a rectangle is given as;

Area = length × width

Area = 7 × 14

Area = 98 cm ^2

1b The shape given is a semi circle

The formula for area of a semicircle is given as;

Area = 1/2 π r^2

radius = diameter/2 = 14/2 = 7cm

Area = 1/2 × 3.142 × 7 × 7

Area = 76. 98 cm^2

2a. The shape given is a rectangle

The formula for perimeter of a rectangle is given as;

Perimeter = 2 ( length + width)

Perimeter = 2 ( 14 + 7) = 2( 21)

Perimeter = 42cm

2b. The shape is a semicircle

Perimeter = π r + 2r

r= 1.4cm; diameter divided by 2

Perimeter = 3. 142(1.4) + 2(1.4)

Perimeter = 7. 19 cm

3. The formula for area of a trapezium is given as

Area = a + b/2 (h)

4. The area of the trapezium is given as;

Area = 9 + 7/2 (3)

Area = 16/2 (3)

Area = 8 × 3

Area = 24 cm ^2

5. Area of semicircle = 1/2 πr^2

Perimeter of a semicircle = πr + 2r

6. From the information given, we have the following

Area = 480 m^2

a = 20m

b = unknown

h = 13. 2m

Area = a+b/2 (h)

Substitute the values

480 = 20+b/2 (13. 2)

480 = 10+ b (13. 2)

480/13. 2 = 10 + b

10+ b = 480/ 13. 2

10 + b = 36. 36

b = 36.36 - 10

b = 26. 36m

7. The formula for area of a rhombus is given as

Area = p × q/2

Where p and q are the diagonals

Area = 7. 5 × 12/2

Area = 90/2

Area = 45cm^2

8. The formula for area for a quadrilateral is given as;

Area of quadrilateral = (½) × diagonal length × sum of the length of the perpendiculars

sum of the length = 13 + 8 = 21cm

Diagonal A= 24cm

Area = 1/2 × 24 × 21

Area = 252 cm ^ 2

9. Area of a pentagonal park = 1/2 × sum of parallel sides × height

Sum of parallel sides = 15 + 15 = 30 cm

height = 30cm

Area = 1/2 × 30 × 30

Area = 450 cm^ 2

Learn more about area here:

https://brainly.com/question/14137384

#SPJ1

The odds in favor of them winning is 20%

From the information given, we have that the probability of them winning the next game is 80%

P( winning) = 80% = 0. 8

The odds against them winning is given as;

1 - probability of winning

We have;

= 1 - 0. 8

= 0. 2

The odds in favor of them winning is simply the probability of them losing;

= 0. 2 × 100

= 20%

Thus, the odds in favor of them winning is 20%

Learn more about probability here:

https://brainly.com/question/25870256

#SPJ1

Answer:

2500

Step-by-step explanation:

5000 ÷ 2 = 2500

Using the quadratic formula, we solve for [tex]z^2[/tex].

[tex]z^4 - 5(1+2i) z^2 + 24 - 10i = 0 \implies z^2 = \dfrac{5+10i \pm \sqrt{-171+140i}}2[/tex]

Taking square roots on both sides, we end up with

[tex]z = \pm \sqrt{\dfrac{5+10i \pm \sqrt{-171+140i}}2}[/tex]

Compute the square roots of -171 + 140i.

[tex]|-171+140i| = \sqrt{(-171)^2 + 140^2} = 221[/tex]

[tex]\arg(-171+140i) = \pi - \tan^{-1}\left(\dfrac{140}{171}\right)[/tex]

By de Moivre's theorem,

[tex]\sqrt{-171 + 140i} = \sqrt{221} \exp\left(i \left(\dfrac\pi2 - \dfrac12 \tan^{-1}\left(\dfrac{140}{171}\right)\right)\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= \sqrt{221} i \left(\dfrac{14}{\sqrt{221}} + \dfrac5{\sqrt{221}}i\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= 5+14i[/tex]

and the other root is its negative, -5 - 14i. We use the fact that (140, 171, 221) is a Pythagorean triple to quickly find

[tex]t = \tan^{-1}\left(\dfrac{140}{171}\right) \implies \cos(t) = \dfrac{171}{221}[/tex]

as well as the fact that

[tex]0<\tan(t)<1 \implies 0along with the half-angle identities to find

[tex]\cos\left(\dfrac t2\right) = \sqrt{\dfrac{1+\cos(t)}2} = \dfrac{14}{\sqrt{221}}[/tex]

[tex]\sin\left(\dfrac t2\right) = \sqrt{\dfrac{1-\cos(t)}2} = \dfrac5{\sqrt{221}}[/tex]

(whose signs are positive because of the domain of [tex]\frac t2[/tex]).

This leaves us with

[tex]z = \pm \sqrt{\dfrac{5+10i \pm (5 + 14i)}2} \implies z = \pm \sqrt{5 + 12i} \text{ or } z = \pm \sqrt{-2i}[/tex]

Compute the square roots of 5 + 12i.

[tex]|5 + 12i| = \sqrt{5^2 + 12^2} = 13[/tex]

[tex]\arg(5+12i) = \tan^{-1}\left(\dfrac{12}5\right)[/tex]

By de Moivre,

[tex]\sqrt{5 + 12i} = \sqrt{13} \exp\left(i \dfrac12 \tan^{-1}\left(\dfrac{12}5\right)\right) \\\\ ~~~~~~~~~~~~~= \sqrt{13} \left(\dfrac3{\sqrt{13}} + \dfrac2{\sqrt{13}}i\right) \\\\ ~~~~~~~~~~~~~= 3+2i[/tex]

and its negative, -3 - 2i. We use similar reasoning as before:

[tex]t = \tan^{-1}\left(\dfrac{12}5\right) \implies \cos(t) = \dfrac5{13}[/tex]

[tex]1 < \tan(t) < \infty \implies \dfrac\pi4 < t < \dfrac\pi2 \implies \dfrac\pi8 < \dfrac t2 < \dfrac\pi4[/tex]

[tex]\cos\left(\dfrac t2\right) = \dfrac3{\sqrt{13}}[/tex]

[tex]\sin\left(\dfrac t2\right) = \dfrac2{\sqrt{13}}[/tex]

Lastly, compute the roots of -2i.

[tex]|-2i| = 2[/tex]

[tex]\arg(-2i) = -\dfrac\pi2[/tex]

[tex]\implies \sqrt{-2i} = \sqrt2 \, \exp\left(-i\dfrac\pi4\right) = \sqrt2 \left(\dfrac1{\sqrt2} - \dfrac1{\sqrt2}i\right) = 1 - i[/tex]

as well as -1 + i.

So our simplified solutions to the quartic are

[tex]\boxed{z = 3+2i} \text{ or } \boxed{z = -3-2i} \text{ or } \boxed{z = 1-i} \text{ or } \boxed{z = -1+i}[/tex]

Project's cost at time 0 is $46,272.84

What is profitability index?

Profitability index is the present value of future cash flows divided by the project cost at time 0.

The present value of each future cash flow can be determined using the present value formula of a single cash flow as  below;

PV=FV/(1+r)^N

FV=future cash inflows in years 1-4

r=discount rate=8.5%

N=the year of cash flows, 1 for year 1 , 2 for year 2, 3 for year 3 and 4 for year 4.

PV of future cash flows=$12,150/(1+8.5%)^1+$12,600/(1+8.5%)^2+$15,700/(1+8.5%)^3+$10,200/(1+8.5%)^4

PV of future cash flow=$41,553.01

Profitability index=PV of future cash flows/Project cost

Profitability index= .898

Project cost=unknown(assume it is X)

.898=$41,553.01 /X

X=$41,553.01/ .898

X=project's cost=$46,272.84

Find out more on profitability index on:https://brainly.in/question/46258929

#SPJ1

[tex]\boldsymbol{\sf{6-\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}[/tex]

Convert 6 to the fraction 18/3.

                       [tex]\boldsymbol{\sf{\dfrac{18}{3} -\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}[/tex]

Since the fractions 18/3 and 1/3 have the same denominator, we add their numerators to calculate them.

                       [tex]\boldsymbol{\sf{\dfrac{18+1}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 \ \longmapsto \ \ [Add \ 18+1] }}[/tex]

                              [tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 }}[/tex]

Subtract [tex]\bf{\frac{1}{2}x }[/tex] on both sides.

                               [tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x-\dfrac{1}{2}x=5 }}[/tex]

Combine [tex]\bf{-\frac{3}{4}x}[/tex] and [tex]\bf{-\frac{1}{2}x}[/tex] to get [tex]\bf{-\frac{5}{4}x}[/tex].

                                [tex]\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{5}{4}x=5 }}[/tex]

Subtract 19x from both sides.

                                       [tex]\boldsymbol{\sf{-\dfrac{5}{4}x=5-\dfrac{19}{3} }}[/tex]

Convert 5 to the fraction 15/3.

                                      [tex]\boldsymbol{\sf{-\dfrac{4}{5}x=\dfrac{15}{3}-\dfrac{19}{3} }}[/tex]

Since the fractions 15/3 and 19/3 have the same denominator, we add their numerators to calculate them.

                             [tex]\boldsymbol{\sf{-\dfrac{5}{4}x=\dfrac{15-19}{3} \ \longmapsto \ \ [Subtract \ 15-19] }}[/tex]

                                 [tex]\boldsymbol{\sf{-\dfrac{5}{4}x=-\dfrac{4}{3} }}[/tex]

Multiply both sides by -4/3, the reciprocal of -4/3.

                                    [tex]\boldsymbol{\sf{x=-\dfrac{4}{5}\left(-\dfrac{4}{5}\right) }}[/tex]

Multiply -4/3 by -4/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

                   [tex]\boldsymbol{\sf{x=\dfrac{-4(-4)}{3\times5} \ \ \longmapsto \ \ Multiply, \ numerator \ and \ denominator. }}[/tex]

                                 [tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ \ \ x=\frac{16}{15} }}}}}[/tex]

Answer:

A convenient formula to use is

S = ((1 + i)^n - 1) / i where S is the value of 1$ deposited for n periods at an interest rate of i

in this case n = 12 * 28 = 336 periods of deposit at an interest rate of

.0021 / 12 = .00175 = i

S = (1.00175^336 - 1) / .00175 = 456.8338  the value of 1$ after 336 periods

350 * 456.8338 = 159891.81   the value of 350 deposited monthly

Note that 350 * 336 would be 117,600

One must be careful to distinguish the above formula from

(1 - (1 + i)^-n) / i which gives the value of 1$ when the borrower is "paying" an interest rate of i - this would be the case for a mortgage - or what is  the value of 1$ paid for n periods when paying an interest rate of i

The measures of the angles are

Angle JPK

The given parameters are:

∠KPL = 46°

∠NPH = 25°

∠MPN = ∠NPH

By vertical angle theorem, we have:

∠JPK = ∠MPH

Where

∠MPH = ∠MPN + ∠NPH

This gives

∠MPH = ∠NPH + ∠NPH

So, we have:

∠MPH = 25° + 25°

Evaluate

∠MPH = 50°

Recall that:

∠JPK = ∠MPH

So, we have:

∠JPK = 50°

Hence, the measure of angle ∠JPK is 50°

Angle LPM

The angle on a straight line is 180°.

So, we have:

∠LPM +  ∠KPL + ∠MPH = 180°

This gives

∠LPM +  46° + 50° = 180°

Evaluate

∠LPM = 84°

Hence, the measure of angle ∠LPM is 84°

Angle NPM

In (a), we have:

∠NPM = ∠NPH

This gives

∠NPM = 50°

Hence, the measure of angle ∠NPM is 50°

Angle JPI

By vertical angle theorem, we have:

∠JPI = ∠LPM

So, we have:

∠JPI = 84°

Hence, the measure of angle ∠JPI is 84°

Angle HPI

By vertical angle theorem, we have:

∠HPI = ∠KPK

So, we have:

∠HPI = 46°

Hence, the measure of angle ∠HPI is 46°

Read more about vertical angles at:

https://brainly.com/question/24839702

#SPJ1

Answer:

9x3 - 6x2 + 3x

Step-by-step explanation:

(27x 4 - 18x 3 + 9x 2) ÷ 3x

Dividing each term between 3x we have:

9x3 - 6x2 + 3x

We can check the result:

(9x3 - 6x2 + 3x) * (3x)

= (27x4 - 18x3 + 9x2)

Answer:15

Step-by-step explanation: 20 divided by 8=2.5 x 6=15

Answer:9[tex]a^{10}[/tex][tex]b^{-6}[/tex]=[tex]\frac{9a^{10} }{b^6}[/tex]

Step-by-step explanation:

Answer:

9*a^10*(1/(b^6))

Step-by-step explanation:

(-3a^5*b^-3)^2

(-3)^2 * (a^5)^2 * (b^-3)^2

9a^10*b^-6

9*a^10*(1/(b^6))

The equation that represent the total salary that I earn for working x hours in a week is y = 10x

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let y represent the total salary earned by working x hours, hence, if I earn $10 per hour:

y = 10x

The equation that represent the total salary that I earn for working x hours in a week is y = 10x

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

no habla espanol

Step-by-step explanation:

Answer: The slope is -2 and the y-intercept is (0,1)

Step-by-step explanation:

Answer:

The Co-ordinate of C is (4/3, -1/2)

Step-by-step explanation:

We have two equation one is of straight line equation which is:

                                              y=2x-3           (i)

Other equation is of quadratic function which is:

                                         y=-3x^2+5         (ii)

Put the value of y from equation (i) in equation (ii)

So, we have:

                                     2x-3=-3x^2+5

                                      3x^2+2x-8=0

By factorization:

                                    3x^2+6x-4x-8=0

                                   3x(x+2)-4x(x+2)=0

                                        (x+2)(3x-4)=0

              x+2=0                             ;                      3x-4=0

              x=-2                                ;                       x=4/3

Put first x=-2 in equation (i)

                                                y=2(-2)-3

                                                  y=-4-3

                                                    y=-7

Now Put x=4/3 in equation (i)

                                             y=2(4/3)-3

                                                 y=8/3-3

                                                   y=-1/2

So, we have two Order pair One is (-2 , -7) and Second one is (4/3 , -1/2)

Hence the Co-ordinate of C is:

                                               C=(4/3 , -1/2)

Answer:

Point C:  (3, 3)

Point D:  (3, -22)

Step-by-step explanation:

If the distance between points C and D is 25 units, the y-value of point D will be 25 less than the y-value of point C.  The x-values of the two points are the same.

Therefore:

[tex]\textsf{Equation 1}: \quad y=2x-3[/tex]

[tex]\textsf{Equation 2}: \quad y-25=-3x^2+5[/tex]

As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:

[tex]\implies 2x-3-25=-3x^2+5[/tex]

[tex]\implies 3x^2+2x-33=0[/tex]

[tex]\implies 3x^2-9x+11x-33=0[/tex]

[tex]\implies 3x(x-3)+11(x-3)=0[/tex]

[tex]\implies (x-3)(3x+11)=0[/tex]

[tex]\implies x=3, -\dfrac{11}{3}[/tex]

From inspection of the given graph, the x-value of points C and D is positive, therefore x = 3.

To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:

[tex]\begin{aligned} \textsf{Point C}: \quad 2x-3 & =y\\2(3)-3 & =3\\ \implies & (3, 3)\end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Point D}: \quad -3x^2+5 & = y \\ -3(3)^2+5 & =-22\\ \implies & (3, -22)\end{aligned}[/tex]

Therefore, point C is (3, 3) and point D is (3, -22).

The inequalities in the system of inequalities are y > x² – 2x – 3 and y > 3x + 4

The graph that completes the question is added as an attachment

The parabola

It has a vertex of (1,  -4)

So, we have:

y = a(x - 1)^2 - 4

It passes through (3, 0).

So, we have:

0 = a(3 - 1)^2 - 4

This gives

4a - 4 = 0

Solve for a

a = 1

Substitute a = 1 in y = a(x - 1)^2 - 4

y = (x - 1)^2 - 4

Expand

y = x^2 - 2x + 1 - 4

y = x^2 - 2x - 3

The inner part is shaded.

So, we have:

y > x^2 - 2x - 3

The linear equation

It passes through (0, 4).

So, we have:

y = mx + 4

It passes through (1, 7).

So, we have:

7 = m + 4

Solve for m

m = 3

Substitute m = 3 in y = mx + 4

y = 3x + 4

The upper part is shaded.

So, we have:

y > 3x + 4

Hence, the inequalities in the system of inequalities are y > x² – 2x – 3 and y > 3x + 4

Read more about system of inequalities at:

https://brainly.com/question/19526736

#SPJ1

The interpretation based on the confidence interval given is that the population mean will fall within the interval.

Number of observations = 10

Sample mean = 2.60

Standard deviation = 1.07

The degree of freedom will be:

= n - 1

= 10 - 1 = 9

Confidence level = 95% = 0.95

Level of significance = 1 - 0.95 = 0.05

The value of the t critical from the t table will be 2.262.

The margin of error will be:

= 2.262 × 1.07/✓10

= 0.765

We get the 95% confidence interval for the population mean. This will be:

(2.60 - 0.765( <= U =(2.60 + 0.765)

1.83 <= 3.37

Therefore, the interpretation is that the population mean will fall within the interval.

Learn more about confidence interval on:

brainly.com/question/14825274

#SPJ1

Answer: A

Step-by-step explanation:

The total value of the prizes is [tex]1000+500+2(50)=1600[/tex].

The total cost of the tickets is [tex]1000(4.00)=4000[/tex].

So, the total loss is $2400.

Dividing this by 1000 tickets gives $-2.40.

40+1 in dollars per hour

The length of the diagonal that he cut to the nearest whole inch is 36 inches

A red dotted line crosses the rectangle from the upper left corner to the lower right corner to form a triangle.

Length of the diagonal of a rectangle;

Hypotenuse² = adjacent² + opposite²

= 18² + 36²

= 324 + 1296

hyp² = 1620

hyp = √1620

hyp = 35.4964786985976

Approximately,

hypotenuse = 36 inches

Therefore, the length of the diagonal that he cut to the nearest whole inch is 36 inches.

Learn more about triangle:

https://brainly.com/question/2217700

#SPJ1

Answer:

4.12 miles

Step-by-step explanation:

Use distance formula

d^2 = (-8- -4)^2 + ( -9 - -10)^2

d^2 =   16   +   1

d^2 = 17

d = sqrt 17 = 4.12 miles

Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

It states that, for a normally distributed random variable:

Considering the mean of 110 and the standard deviation of 15, we have that:

These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

More can be learned about the Empirical Rule at brainly.com/question/24537145

#SPJ1

Answer:

Step-by-step explanation:

To solve this, you have to divide this fraction from left to right.

Fraction is a division or part of a whole number.

First, do apply the fraction rule.

[tex]\rightarrow: \sf{\dfrac{A}{B}\div \dfrac{C}{D}=\dfrac{A}{B}\times \dfrac{D}{C}}[/tex]

[tex]\sf{-\dfrac{1}{50}\times \dfrac{100}{1}}[/tex]

Cancel the common factor of 50.

[tex]\sf{-\dfrac{2}{1} }[/tex]

Divide.

-2/1=-2

[tex]\rightarrow: \boxed{\sf{-2}}[/tex]

So, the final answer is -2.

I hope this helps, let me know if you have any questions.

To learn more about fraction:

https://brainly.com/question/17205173

#SPJ2

by solving a system of equations, we conclude that there are 7 students with blue eyes in the class.

We know that there are 40 students in the first-grade class, and we also know that:

Let's define the variables.

We know that:

H = 3*B

We also know that there are 3 students that have both blue eyes and blond hair.

And there are 15 students with none of these traits, so:

40 - 15 = 25

There are 25 students that have blue eyes, blond hair, or both.

Because we know that 3 students have both traits, we can write:

B + H - 3  =25

(Where we subtract 3 because we don't want to add these students twice).

Then we created a system of two equations:

H = 3*B

B + H - 3  =25

Replacing the first equation into the second one, we get:

B + (3*B) - 3 = 25

4*B = 25 + 3 = 28

B = 28/4 = 7

Then, by solving that system of equations, we conclude that there are 7 students with blue eyes in the class.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.

she would pay $400 per month to rent a station and keep all of her earnings.

Another option is to work at a franchise, where she would just have to pay the salon $4 for every haircut.

Therefore,

let

x = number of haircut

Hence,

4x = 400

divide both sides by 4

4x / 4  = 400 / 4

x = 100

Therefore, she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.

learn more on equation here: https://brainly.com/question/21528623

#SPJ1