Select the correct option.
In a game, bonus points are awarded based on the number of the level that is cleared. The bonus points are calculated by a function
that is 15 times the cube root of the level cleared and rounded to the closest integer value.
Which of the following options represents the bonus points scored as the levels advance?

Answer:

The answer is 4 + √15 .

Step-by-step explanation:

You have to get rid of surds in the denorminator by multiplying it with the opposite sign :

[tex] \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } [/tex]

[tex] = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } [/tex]

[tex] = \frac{ {( \sqrt{5} + \sqrt{3} ) }^{2} }{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3}) } [/tex]

[tex] = \frac{ {( \sqrt{5} )}^{2} + 2( \sqrt{5} )( \sqrt{3}) + {( \sqrt{3}) }^{2} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3} )}^{2} } [/tex]

[tex] = \frac{5 + 2 \sqrt{15} + 3 }{5 - 3} [/tex]

[tex] = \frac{8 + 2 \sqrt{15} }{2} [/tex]

[tex] = 4 + \sqrt{15} [/tex]

Answer:

Correlation Coefficient

Step-by-step explanation:

Explanation:

The tickmarks show which pieces are congruent to one another, which in turn show the segments have been bisected (cut in half). The square angle markers show we have perpendicular segments. So we have three perpendicular bisectors. The perpendicular bisectors intersect at the circumcenter. The circumcenter is the center of the circumcircle. This circle goes through all three vertex points of the triangle.

A useful application is let's say you had 2 friends and you three wanted to pick a location to meet for lunch. Each person traveling from their house to the circumcenter's location will have each person travel the same distance. We say the circumcenter is equidistant from each vertex point of the triangle. In terms of the diagram, LH = LJ = LK.

Answer: B.) Circumcenter

Step-by-step explanation:

Answer:

[tex] x = 2 [/tex]

Step-by-step explanation:

Given a right-angled triangle as shown above,

Included angle = 60°

Opposite side length = 3

Adjacent side length = x

To find x, we would use the following trigonometric ratio as shown below:

[tex] tan(60) = \frac{3}{x} [/tex]

multiply both sides by x

[tex] x*tan(60) = \frac{3}{x}*x [/tex]

[tex] x*tan(60) = 3 [/tex]

Divide both sides by tan(60)

[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]

[tex] x = \frac{3}{tan(60} [/tex]

[tex] x = 1.73 [/tex]

[tex] x = 2 [/tex] (approximated to whole number)

Answer: hundredths place

Step-by-step explanation:

Answer:

x = -3 and x = 9.

Step-by-step explanation:

2|x - 3| - 5 = 7

2|x - 3| = 12

|x - 3| = 6

x - 3 = 6

x = 9

-(x - 3) = 6

-x + 3 = 6

-x = 3

x = -3

Hope this helps!

Answer:

x=9            x=-3

Step-by-step explanation:

2|x-3|-5=7

Add 5 to each side

2|x-3|-5+5=7+5

2|x-3|=12

Divide by 2

2/2|x-3|=12/2

|x-3|=6

There are two solutions to an absolute value equation, one positive and one negative

x-3 =6           x-3 = -6

Add 3 to each side

x-3+3 = 6+3      x-3+3 = -6+3

x=9                     x = -3

Answer:

D

Step-by-step explanation:

D because they are congruent try measuring it.

Answer:

[tex]\boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

The triangles are congruent.

The angles that are corresponding on both triangles must be congruent.

Angle Q in triangle PQR must be congruent to angle T in triangle STU.

Answer:

Step-by-step explanation:

If  x and y be real numbers satisfying 2/x=y/3=x/y, then any two of the equation are equated as shown;

2/x = y/3 ... 1 and;

y/3 = x/y... 2

From equation 1, 2y = 3x ... 3

and from equation 2; y² = 3x ... 4

Equating the left hand side of equation 3 and 4 since their right hand sides are equal, we will have;

2y = y²

2 = y

y = 2

Substituting y = 2 into equation 3 to get the value of x;

2y = 3x

2(2) = 3x

4 = 3x

x = 4/3

The value of x³ will be expressed as (4/3)³ = 4*4*4/3*3*3 = 64/27

Answer:

b. (10,10,0)

Step-by-step explanation:

r+v can be evaluated if the vectors/matrices have the same dimensions.

These do. They are both 1 by 3 vectors.

Just add first to first in each.

Just add second to second in each.

Just add third to third in each.

Example:

(5,-5,6)+(1,2,3)

=(5+1,-5+2,6+3)

=(6,-3,9)

Done!

In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).

r+v

=(7,3,9)+(3,7,-9)

=(7+3,3+7,9+-9)

=(10,10,0)

Done!

Answer:

The probability of the event BC

= the probability of B * C = 48.6667% * 70%

= 34.0667%

Step-by-step explanation:

Probability of A, students with children = 44/150 = 29.3333%

Probability of B, students enrolled in at least 12 credits = 73/150 = 48.6667%

Probability of C, students working at least 10 hours per week = 105/150 = 70%

Therefore, the Probability of BC, students enrolled in 12 credits and working 10 hours per week

= 48.6667% * 70%

= 34.0667%

Answer:

The center is (1,4)

Step-by-step explanation:

The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.

Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:

[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]

So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:

[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]

Answer:

3

Step-by-step explanation:

Use this equation

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute

-6-3/0-3 subtract

-9/-3 simplify

-3/-1 two negitives cansle out

3/1=3

Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.

Have a good day! :)

Answer:

3

Step-by-step explanation:

To find the slope, we use the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -6 -3)/(0 -3)

    = -9/-3

    = 3

In any coordinate pair, the first number is the x-value and the second number is the y-value.

To find the slope, simply take the difference of the y values and divide by the difference in the x values: (14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is -5/3.

It is find the slope of the line.

The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

The slope is always calculated from the rise divided by the run. Typically, the equation is presented as:

m = Rise/Run

If you have two points, the points should be [tex]P_{1} (x_{1} ,y_{1} )[/tex] and [tex]P_{2} (x_{2} ,y_{2} )[/tex]  So, the equation would be:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

In any coordinate pair, the first number is the x-value and the second number is the y-value.

The difference of the y values and divide by the difference in the x values:

m=(14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is  -5/3.

Learn more about slope here:

https://brainly.com/question/17114095

#SPJ5

Answer:

Step-by-step explanation:

Hello,

We can write three equations thanks to Pythagoras

   [tex]AB^2+AC^2=(7+3)^2\\x^2+7^2=AB^2\\x^2+3^2=BC^2\\[/tex]

So it comes

[tex]x^2+7^2+x^2+3^2=(7+3)^2\\\\2x^2=100-49-9=42\\\\x^2 = 42/2=21\\\\x = \sqrt{\boxed{21}}\\[/tex]

Hope this helps

Answer:

x = [tex]\sqrt{21}[/tex]

Step-by-step explanation:

Δ BCD and Δ ABD are similar thus the ratios of corresponding sides are equal, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{CD}{BD}[/tex] , substitute values

[tex]\frac{x}{7}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )

x² = 21 ( take the square root of both sides )

x = [tex]\sqrt{21}[/tex]

Answer:

option: D

51200

Step-by-step explanation:

64000 x 80/100 = 51200

Answer:

Hi there!!!

your required answer is option D.

explanation see in picture.

I hope it will help you...

Answer:

[2.5 ,4]

Step-by-step explanation:

The graph in this interval has a vertex while opening up wich means it's a minimum

Answer:

14 Quarters and 28 dimes

Step-by-step explanation: 14 quarters $3.50

28 dimes is $2.80 total is $6.30

Answer:

Loss = $80000

Step-by-step explanation:

To determine if it's a profit or loss is simple.

He predicted the sugar cane stock to fall so he sold , but few days later the stock grew and went bullish.

He sold at$ 40 for 2000 shares

=$ 80000

But the stock went up to $80 per share that is gaining extra $40

So it was actually a loss.

The loss is =$40 * 2000

The loss = $80000

Answer:

[tex]\sqrt{x-4} +5[/tex]

Step-by-step explanation:

the conjugate of [tex]\sqrt{x-4} -5[/tex]  is the term that completes a²-b² when multiplied by each other

a²-b² = (a+b)(a-b)

Answer:

0.40

Step-by-step explanation:

The computation of the probability for the second student be sophomore and the first is a freshman is shown below:

Let us assume

Sophomore = S

Freshman = F

Based on this assumption, the probability is as follows

So,

[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]

= 0.40

Hence, the probability for the second student be sophomore and the first student be freshman is 0.40

Answer:

Hey there!

The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.

The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.

The circumference of the circle is 50.24 yards.

Hope this helps :)

Answer:

Option (3)

Step-by-step explanation:

[tex](x-i\sqrt{3})[/tex] is a factor of a polynomial given in the options, that means a polynomial having factor as [tex](x-i\sqrt{3})[/tex] will be 0 for the value of x = [tex]i\sqrt{3}[/tex].

Option (1),

3x⁴ + 26x² - 9

= [tex]3(i\sqrt{3})^{4}+26(i\sqrt{3})^2-9[/tex] [For x = [tex]i\sqrt{3}[/tex]]

= 3(9i⁴) + 26(3i²) - 9

= 27 - 78 - 9 [Since i² = -1]

= -60

Option (2),

4x⁴- 11x² + 3

= [tex]4(i\sqrt{3})^4-11(i\sqrt{3})^2+3[/tex]

= 4(9i⁴) - 33i² + 3

= 36 + 33 + 3

= 72

Option (3),

4x⁴ + 11x² - 3

= [tex]4(i\sqrt{3})^4+11(i\sqrt{3})^2-3[/tex]

=  4(9i⁴) + 33i² - 3

= 36 - 33 - 3

= 0

Option (4),

[tex]3x^{4}-26x^{2}-9[/tex]

= [tex]3(i\sqrt{3})^4-26(i\sqrt{3})^{2}-9[/tex]

= 3(9i⁴) - 26(3i²) - 9

= 27 + 78 - 9

= 96

Therefore, [tex](x-i\sqrt{3})[/tex] is a factor of option (3).

Answer:

Hey there!

A=1/2bh

14=1/2(28)h

14=14h

h=1

Hope this helps :)

Answer:

Step-by-step explanation:

Area of a triangle is

[tex] \frac{1}{2} \times b \times h[/tex]

where b is the base

h is the height

From the question

Area = 14in²

b = 14 inches

So we have

[tex]14 = \frac{1}{2} \times 28 \times h[/tex]

which is

[tex]14 = 14h[/tex]

Divide both sides by 14

That's

[tex] \frac{14}{14} = \frac{14h}{14} [/tex]

We have the final answer as

h = 1

Therefore the height is 1 inch

Hope this helps you

Answer:

x=3.9 or 39/10 and   y=3.13333 or 47/15

Step-by-step explanation:

Since both expressions (6x-3y) and (3-2x+6y) are equal to 14, separate the equations:

       6x-3y=14 and 3-2x+6y=14

Simplify the equations

       6x-3y=14 and -2x+6y=11

Now, line the equations up and pick a variable (either x or y) to eliminate

        6x-3y=14

        -2x+6y=11

In this case, let's eliminate y first. To do so make the y values in both equations the same but with opposite signs. Make both be 6y but one is +6y and the other -6y

Multiply (6x-3y=14) by 2 to get:

      12x-6y=28

Line the equations up and add or subtract the terms accordingly

      12x-6y=28

      -2x+6y=11

This becomes:

     10x+0y=39

Isolate for x

   x= 39/10 or x= 3.9

Now substitute the x value into either of the original equations

    6x-3y=14

    6(3.9)- 3y=14

Isolate for y

   23.4-14=3y

   3y= 9.4

  y= 3.1333 (repeating)  or y= 47/15

Answer: x = 39/10, y = 94/30

Step-by-step explanation:

6x - 3y = 3 - 2x + 6y,

Now solving this becomes

6x + 2x -3y - 6y = 3

8x - 9y = 3 ------------------- 1

3 - 2x + 6y. = 14

-2x + 6y = 14 - 3

-2x. + 6y = 11

Now multiply both side by -1

2x. - 6y = -11 ----------------- 2

Solve equations 1 & 2 together

8x - 9y. = 3

2x - 6y = -11

Using elimination method

Multiply equation 1 through by 2 ,and equation 2 be multiplied by 8

16x - 18y = 6

-16x - 48y = -88 ------------------------- n, now subtract

30y = 94

Therefore. y = 94/30.

Now substitute for y in equation 2

2x - 6y = -11

2x - 6(94/30) = -11

2x - 94/5 = -11

Now multiply through by 5

10x - 94 = -55

10x = -55 + 94

10x = 39

x = 39/10

Answer:

6[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

y + 1[tex]\frac{1}{6}[/tex] = 7[tex]\frac{5}{6}[/tex]

y + [tex]\frac{7}{6}[/tex] = [tex]\frac{47}{6}[/tex]

y = 40/6 = 20/3 = 6[tex]\frac{2}{3}[/tex]

Answer:

105.6

Step-by-step explanation:

If the mean is 8.8, than that means that in total the sum must be (8.8 * 12) which equals 105.6.

This is because the sum of all the numbers in a list divided by the amount of numbers in a list equals the mean.

Answer:

The first statement is incorrect. They have to be complementary.

Step-by-step explanation:

You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.

You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.

The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.

Answer:

[tex]\boxed{\sf A}[/tex]

Step-by-step explanation:

The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:

[tex]T = 180^{\circ}[/tex] (Period)

[tex]z_{min} = -4[/tex] (Minimum)

[tex]z_{max} = 5[/tex] (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:

1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]

[tex]\Delta z = \frac{5+4}{2}[/tex]

[tex]\Delta z = \frac{9}{2}[/tex]

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]

[tex]z_{m} = \frac{1}{2}[/tex]

The new function is:

[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]

Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:

[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

Answer:

Q(1,1), N(3,2) A(2,5)

Step-by-step explanation:

Answer:

h = 7.1 cm

Step-by-step explanation:

To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:

[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:

[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]

So the area of the triangle is:

[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]

[tex]S = 60\ cm^2[/tex]

Now, to find the height, we can use the following equation for the area of the triangle:

[tex]S = base * height/2[/tex]

The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:

[tex]60 = 17 * h/2[/tex]

[tex]h = 120/17[/tex]

[tex]h = 7.06\ cm[/tex]

Rounding to the nearest tenth, we have h = 7.1 cm

Answer:

7.1 cm

Step-by-step explanation:

:D