Find the value of x.

Step-by-step explanation:

Proof using Discrimant:

[tex]3 { x}^{2} - 2x + \frac{1}{3} = 0[/tex]

The discrimant is

[tex] \sqrt{ {b}^{2} - 4ac} [/tex]

B is -2, A is 3 and C is 1/3 so we get

[tex] \sqrt{ {2}^{2} - 4( 3)( \frac{1}{3}) } [/tex]

[tex] \sqrt{4 - 4} [/tex]

[tex] \sqrt{0 } = 0[/tex]

Since the discrimant equal zero, there is one real distinct zero.

This zero will also have a multiplicity of 2, so the zero is technically equal to each other.

To get better at solving, let solve for zero.

[tex]3 {x}^{2} - 2x + \frac{1}{3} = 0[/tex]

[tex]3( {x}^{2} - \frac{2}{3} x + \frac{1}{9} )[/tex]

[tex]3( x - \frac{1}{3} )(x - \frac{1}{3} )[/tex]

[tex]3(x - \frac{1}{3} ) {}^{2} = 0[/tex]

[tex]x = \frac{1}{3} [/tex]

That zero is 1/3,1/3

Answer:

Step-by-step explanation:

Answer: D) 45 ft.

Step-by-step explanation:

You have the measurements for the sides BC and CD, if you divide BC by CD you get the dialation. Which is 2.5. Multiply 18 by 2.5, Congrgulations you have the answer!

Answer: 138

Step-by-step explanation:

Answer:

666.66 years

Step-by-step explanation:

In this scenario, we need to find at what year both of the stalagmite crystals are at the exact elevation in the cave. So we need an algebraic formula to calculate this. Since the crystal in the ceiling is at a height of 10 feet (height of the cave) and is growing down we need to subtract its growth from its starting position of 10ft. The second crystal is starting at an elevation of 0 and growing upward so we simply need to chart its growth and equal both equations together to find its meet-up point. In this algebraic equation, x will equal the number of years that we need to find.

[tex]10 - 0.01x = 0.005x[/tex] ... add 0.01x to both sides.

[tex]10 = 0.015x[/tex]  ... divide both sides by 0.015

[tex]666.66 = x[/tex]

Finally, we can see that both crystals will meet-up after 666.66 years. If we plug this value into the equation we see that the crystals will meet-up at a point 3.33 ft above the cave floor.

Answer:

In mathematics education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.Step-by-step explanation:

hope this help

9514 1404 393

Answer:

  follow directions. h represents a horizontal shift, + shifts to the right. k represents a vertical shift, + shifts up.

Step-by-step explanation:

Modern math instruction often tends toward giving you a task that is intended to help you discover for yourself particular mathematical relationships. This is one such task.

Here, you're intended to follow the instructions: using the technology provided (a graphing tool at the link) to discover the effect of changing the values of h and k in the function.

__

The first attachment shows plots from my graphing tool for different values of h. The red curve shows h=-2, the blue curve shows h=0, and the green curve shows h=1. If you look for the marked upward zero crossing, you see that it is unshifted for h=0, shifted left 2 units for h=-2, and shifted right 1 unit for h=1.

You are intended to conclude that the value of h represents the amount by which the function is shifted to the right.

__

The second attachment shows plots from my graphing tool for different values of k. As before, the red curve shows k=-2, the blue curve shows k=0, and the green curve shows k=1. Again, the upward zero crossing has been marked to show the effect. For k=-2, the curve is shifted down 2 units; for k=1, it is shifted up 1 unit. There is no shift when k=0.

You are intended to conclude that the value of k represents the amount by which the function is shifted upward.

__

If you do what the problem tells you to do, you can see these effects in real time, watching changes as they occur. You are expected to describe them. Only you know what the "vocabulary from 9/21-922" is.

_____

Additional comment

Math instruction builds on previously seen concepts. This is not a subject in which you can be successful adopting the strategy of "test and forget." You're better off with a strategy of "learn it thoroughly and remember," working as many problems as necessary to keep it fresh in your mind.

Answer: The salesperson must sell 20 memberships to make the same amount of money under both plans.

Step-by-step explanation:

Let x be the number of memberships.

In first plan,

Weekly salary of $300 plus a commission of $15 for each membership sold.

i.e. Earning (weekly) = 300+15x

In second plan,

The other plan offers no salary but pays $30 commission on each membership sold.

i.e. earning = 30x

According to the question, when [tex]300+15x=30x[/tex]

[tex]\Rightarrow\ 300=30x-15x\\\\\Rightarrow\ 300=15x\\\\\Rightarrow\ x=\dfrac{300}{15}\\\\\Rightarrow\ x=20[/tex]

Hence, the salesperson must sell 20 memberships to make the same amount of money under both plans.

Answer:

4.1

Step-by-step explanation:

Answer:

4.117.....

Step-by-step explanation:

it is corecct answer but it has remainder.

It is an equation because it has an equal sign and it must solve for the variable which is "n".

Step-by-step explanation:

Answer: C) [tex]B= 500(1.101)^{12t}[/tex]

Step-by-step explanation:

Given : The equation for this investment is B = 500(1.13)t, where B represents the balance and t is the number of years.

For monthly interest , Rate = [tex]\dfrac{r}{12}[/tex]

Time = 12 t  [ 1 year = 12 months ]

As r = 0.13 , so rate = [tex]\dfrac{0.13}{12}\approx0.010[/tex]

Now, the equation will be :

[tex]B=500 (1+0.101)^{12t}[/tex]

[tex]\Rightarrow\ B= 500(1.101)^{12t}[/tex]

Correct option : C) [tex]B= 500(1.101)^{12t}[/tex]

Answer:

0.55

Step-by-step explanation:

Answer:

Itz $ 0.55 because 10 × $0.055

Answer:

bearing of Y from X is 074°

Step-by-step explanation:

the bearing of Y from X is the clockwise measure of the angle from the northline N to Y , that is

180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

The value of the bearing of Y from X will be 74°.

What is Supplementary angle?

The sum of two or more angle is 180 degree then the angle is called the  Supplementary angle.

Given that;

The value of measure of ∠X = 106°

Now,

Since, The value of the bearing of Y from X will be calculated as;

∠X + ∠Y = 180°

106° + ∠Y = 180°

∠Y = 180° - 106°

∠Y = 74°

Thus, The value of the bearing of Y from X will be 74°.

Learn more about the supplementary angle visit:

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Answer:

x=37

y=125

Step-by-step explanation:

97+28+x+18=180 (sum of the interior angles of a triangle is 180)

143+x=180

x=180-143

x=37

y+x+18=180 (sum of the angles on a straight line is 180°)

y+37+18=180

y+55=180

y=180-55

y=125

or

y=97+28(exterior angle of a triangle= 2 interior opposite angles)

y= 125

Step-by-step explanation:

Each person's donation ratio is:

Donation 1 is 4/15 of 75

Donation 2 is 4/15 of 75

Donation 3 is 7/15 of 75

4/15(75) = 5 * 4 = 20

7/15(75) = 5 * 7 = 35

Each person's donation amount is:

$20

$20

$35

Check out work:

20 + 20 + 35 = 75!

I might get this wrong but 60 minus 45 equals 1515

Step-by-step explanation:

The family pack would be  £15 cheaper from the normal package.

In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

Given that, A theme park sells entrance tickets. 2 adult tickets and 3 child tickets would cost a total of £72. 3 adult tickets and 1 child ticket would cost a total of £66. A family ticket costs £45 and allows entry for 2 adults and 2 children.

Let A represents adults and C represents children,

Establishing system of equation,

2A+3C = 72

3A+C = 66

On solving the equation, we get,

A = 18 and C = 12

For 2 adults, cost = 18x2 =  £36

For 2 children, cost = 12x2 =  £24

Total cost = 36+24 =  £60

In family pack, £45 allows entry for 2 adults and 2 children.

45 is 15 less 60

Hence, The family pack would be  £15 cheaper from the normal package.

For more references on system of equations, click;

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Answer:

25

Step-by-step explanation:

Step 1: 350:14

Step 2: 175:7

Step 3: 7/7= 1

Step 4: 175/7=25

350:14=25:1

The car will run 25 miles for each gallon of gas

Answer:

1 gallon = 25 miles

Step-by-step explanation:

350 mi 14 gallons =

350   =  x      Underline = fraction bar btw

14          1

use cross mulitplication

350 = 14x

25 = x

So one gallon goes 25 miles

Hope this helps!

Pls Remember to mark brainliest

Answer:

Step-by-step explanation:

Note: If Ava decides to reduce the time she does each activity by 16minute I believe it should be

1. Ava spends 45min per day studying

    reduce this amount be 16min we have=45-16=29min

    in a year she will spend 365*29= 10585min

2. She also practices the piano for an average of 20 minutes per day

   reduce this amount be 16min we have=20-16=4min

    in a year she will spend 365*14= 5110min

3. She practices soccer 1.5 hours three times a week.

   in minutes 1.5hours is 90min three times a week

   in a day 90*3/7= 270/7=38.57

    reduce this amount be 16min we have=38.57-16=22.57min

    in a year she will spend 365*22.57= 8238.05min

in total for the year  she spends studying and practicing

=10585+ 5110+8238.05

=23933.05min to hours =23933.05/60

=398.88hours

Answer:1. Ava spends 45min per day studying

   reduce this amount be 16min we have=45-16=29min

   in a year she will spend 365*29= 10585min

2. She also practices the piano for an average of 20 minutes per day

  reduce this amount be 16min we have=20-16=4min

   in a year she will spend 365*14= 5110min

3. She practices soccer 1.5 hours three times a week.

  in minutes 1.5hours is 90min three times a week

  in a day 90*3/7= 270/7=38.57

   reduce this amount be 16min we have=38.57-16=22.57min

   in a year she will spend 365*22.57= 8238.05min

in total for the year  she spends studying and practicing

=10585+ 5110+8238.05

=23933.05min to hours =23933.05/60

=398.88hours

Step-by-step explanation:

Answer:

El decimal siempre va a la izquierda.

Step-by-step explanation:

Mueve el decimal el número de veces que el exponente es. Por ejemplo: 5.3x10^-2. En el 5.3 vas a mover el decimal 2 veces a la izquierda.

0.053

Answer:

D. the product of x and a factor not depending on x

Step-by-step explanation:

The equation for the given expression is:

[tex]x (2y+7z)^{2}[/tex]

According to the expression, there are two factors:

the first factor is x, and

the second factor is [tex](2y+7z)^{2}[/tex]

Since, the second factor do not contain x, therefore it is independent of x.

Hence, the expression for the given equation will be the product of x and a factor not depending on x.

Answer:

386% is the 1 3/4 and the other is 239% I think?

Step-by-step explanation:    

Answer:

[tex]\huge\boxed{\sf r = 9.42\ m}[/tex]

Step-by-step explanation:

Given Data:

Circumference = C = 18.84 m

Required:

Radius = r = ?

Formula:

r = C / 2

Solution:

r = 18.84 / 2

[tex]\rule[225]{225}{2}[/tex]

Answer:

9.42

Step-by-step explanation:

Half of the circumference is the radius to you do 18.84 divided by 2

to get your answer.

Utilizando el teorema, veremos que la altura de la torre es 7 metros.

El teorema de Tales nos dice que para triangulos similares, la razon entre los catetos debe ser igual.

Esto significa que la razon entre la altura y el largo de la sombra de un objeto debe ser una constante.

Sabemos que Kevin tiene una estatura de 1.75m y proyecta una sombra de 3.5m

El cociente es:

3.5m/1.75m = 2

Es decir, la sombra tiene una longitud de dos veces la altura.

Entonces si la sombra de la torre es de 14m y la altura es h, tendremos:

14m/h = 2

h = 14m/2 = 7m

La altura de la torre es de 7 metros.

Sí quieres aprender más sobre triangulos rectangulos, puedes leer:

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Answer:

4x - 9x + 11 = -24

-5x + 11 = - 24

-5x = -24 - 11

-5x = -35

-5x/-5 = -35/-5

x = 7

Answer:

The answer is 7

Step-by-step explanation:

Firstly, you have to subtract 11 from -24, which is -35. Then, add the values with x. Which is -5. -35 divided by -5 equals 7. You can check the answer by doing (4*7)-(9*7)+11=-24

Step-by-step explanation:

Assuming you want to solve for b,

tan(55)=15/b

b(tan 55)=15

b = (tan 55)/15