Find the value of x in the triangle shown below.​

Answer:

A regional soccer tournament has 64 participating teams.

In the first round of the tournament, 32 games are played.

In each successive round, the number of games played decreases by 1/2.

Part A:

We know;

[tex]a_n=a_1\times r^{n-1}[/tex]

[tex]a_1=32[/tex]

[tex]r=\frac{-1}{2}[/tex]

So, we get;

The rule for the number of games played in the nth round is given by:

[tex]a_n=32(\frac{1}{2})^{n-1}[/tex]

where [tex]1\leq n\leq 6[/tex]

Part B:

As in each successive round the rounds are decreasing by 1/2 we have.

round 1 = 32

round 2 = 16

round 3 = 8

round 4 = 4

round 5 = 2

round 6 = 1

So, the total number of games played in the regional soccer tournament are: [tex]32+16+8+4+2+1=63[/tex]

Answer:

63 games total

Step-by-step explanation:

edge 2021

The first step is to add 7 to both sides, applying the addition property of equality:

[tex]-2(4x-1)-7+7=5+7 \iff -2(4x-1)=12[/tex]

Answer:

The equation can become −2(4x − 1) = 12 by applying the commutative property of addition

Step-by-step explanation:

Answer:

[tex]y=5e^{2x}[/tex]

Step-by-step explanation:

Let (x,y) represents a point P on the curve,

So, the slope of the curve at point P = [tex]\frac{dy}{dx}[/tex]

According to the question,

[tex]\frac{dy}{dx}=2y[/tex]

[tex]\frac{1}{y}dy=2dx[/tex]

Integrating both sides,

[tex]\int \frac{dy}{y}=2dx[/tex]

[tex]ln y=2x+ln C[/tex]

[tex]ln y-ln C = 2x[/tex]

[tex]ln(\frac{y}{C})=2x[/tex]

[tex]\frac{y}{C}=e^{2x}[/tex]

[tex]\implies y=Ce^{2x}[/tex]

Since, the curve is passing through the point (0, 5),

[tex]5=Ce^{0}\implies C=5[/tex]

Hence, the required equation of the curve is,

[tex]y=5e^{2x}[/tex]

Answer:

Step-by-step explanation:

Let f and p represent the costs of a file and a pen, respectively. The two purchases are ...

  f +3p = 32.85

  2f +8p = 83.50

Subtracting twice the first equation from the second gives an equation for the cost of pens:

  (2f +8p) -2(f +3p) = (83.50) -2(32.85)

  2p = 17.80 . . . . simplify

  p = 8.90 . . . . . . divide by 2

The cost of one pen is $8.90.

_____

Comment on "how do you do it?"

You are given two purchases related to the costs of two items. Write equations that describe the purchases. (The total cost is sum of the costs of each of the items, which will be the product of the number of items and the cost of each. You have been shopping, so you know this.)

Once you have a "system of equations", there are many ways they can be solved. You are usually instructed on "elimination" and "substitution" as methods of solution. Above, we used "elimination" to eliminate the "f" variable and give an equation only in "p".

Answer:

  No, the triangles are not similar

Step-by-step explanation:

The (reduced) side length ratios, shortest to longest, are ...

  12 : 18 : 20 = 6 : 9 : 10

and

  5 : 12 : 13

These are not the same, so the triangles are not similar.

Answer:

The last answer is correct.

Also known as E

Step-by-step explanation:

Answer:

The area of triangle DEF is [tex]101\ cm^{2}[/tex]

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its heights is proportional and this ratio is called the scale factor and the ratio of its areas is equal to the scale factor squared

step 1

Find the scale factor

Let

z ----> the scale factor

[tex]z=\frac{13}{5}[/tex] ----> ratio of its heights

step 2

Find the area of triangle DEF

Let

z ----> the scale factor

x ----> the area of triangle DEF

y ----> the area of triangle ABC

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{13}{5}[/tex]

[tex]y=15\ cm^{2}[/tex]

substitute and solve for x

[tex](\frac{13}{5})^{2}=\frac{x}{15}[/tex]

[tex]x=(\frac{169}{25})(15)[/tex]

[tex]x=101\ cm^{2}[/tex]

Answer:

[tex]\text{C.}\quad\left[\begin{array}{cc}22&-8\\7.8&-3\end{array}\right][/tex]

Step-by-step explanation:

It is convenient to let a spreadsheet or calculator do the tedious sum of products. Term C22 will be B21·A12 +B22·A22 = 0.6·0 +3·(-1) = -3, for example. Other terms are similarly computed. In general Crc will be the sum of Brx·Axc, where x = 1 or 2.

[tex]BA=\begin{bmatrix}2 & 8 \\0.6 & 3\end{bmatrix}\cdot \begin{bmatrix}3 & 0 \\2 & -1\end{bmatrix}\\BA=\begin{bmatrix}2\cdot3+8\cdot2 & 2\cdot0+8\cdot(-1) \\0.6\cdot3+3\cdot2 & 0.6\cdot 0+3\cdot(-1)\end{bmatrix}\\BA=\begin{bmatrix}22 & -8 \\7.8 & -3\end{bmatrix}[/tex]

Answer:

x = 16.49

Step-by-step explanation:

By Pythagorean Formula

8.34² + 14.22² = x²

x² = 69.556 + 202.208

x² = 271.764.

x = √271.764

x = 16.4852

x = 16.49 (rounded to 2 dec. pl)

Answer:

[tex]4032x^4[/tex]

Step-by-step explanation:

Use the 10th row of Pascal's Triangle to get you where you need to be.  You need 10 rows because any polynomial raised to the 9th power has 10 terms.  Those 10 terms are, in order:

1, 9, 36, 84, 126, 126, 84, 36, 9, 1

Setting up for the first 6 terms:

[tex]1(x^9)(2^0)+9(x^8)(2^1)+36(x^7)(2^2)+84(x^6)(2^3)+126(x^5)(2^4)+126(x^4)(2^5)+...[/tex]

The 6th term is the last one.  It goes on from there, but I stopped at the 6th term, since that is what you need.

Simplifying gives us:

[tex]126(x^4)(32)[/tex]

and multiplying gives us:

[tex]4032x^4[/tex]

The 6th term in the expansion of (x + 2)^9 is calculated using the binomial theorem, with the result being 4032x^4.

The 6th term in the expansion of the binomial expression (x + 2)9 is found using Binomial Theorem. The general formula for any term in the expansion of (a + b)^n, where n is a positive integer, is C(n, k) * (a^(n-k)) * (b^k), where C(n, k) is the combination of n items taken k at a time, and k is the term number minus 1.

For the 6th term, k equals 5 (since k = term number -1). By substituting these values into formula, you get: C(9, 5) * (x^(9-5)) * (2^5), which equals 126 * x^4 * 32, or 4032x^4.

So, the 6th term in the expansion of (x + 2)9 is 4032x^4.

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The given expression evaluates to 1/(1000x^3).

Option (C) is correct.

The exponent of a number of says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.

As per the given data:

The given expression is (10x)^(–3)?

We can write the expression as:

= [tex]\frac{1}{(10x)^3}[/tex]

= [tex]\frac{1}{10^3x^3}[/tex]

= [tex]\frac{1}{1000x^3}[/tex]

= 1/(1000x^3)

Hence, the given expression evaluates to 1/(1000x^3).

To learn more about Exponents, click:

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(The given question is incomplete, the complete question is given below)

Which expression is equivalent to (10x)^-3?

a. 10/x^3

b. 1000/x^3

c. 1/(1000x^3)

d. 1/10x^3

Answer:

0

Step-by-step explanation:

100 - 10 = 90

90 - 30 = 60

60 - 10 = 40

40 - 10 = 30

Answer:

1 1/3

Step-by-step explanation:

Absolute values are how far away it is from 0, so it is always positive. It is always the positive number of itself, so absolute values of negative numbers are the opposite, and the absolute value of positive numbers and just the same numbers.

Answer:

Step-by-step explanation:

/ -1 1/3​/ = -(-11/3) = 11/3

Answer:

The probability that Andrew will be among the 4 volunteers selected and Karen will not is 2/7.

Step-by-step explanation:

From the given information it is clear that

The total number of volunteers, including Andrew and Karen = 8

The total number of volunteers, excluding Andrew and Karen = 8-2 = 6

We need to find the probability that Andrew will be among the 4 volunteers selected and Karen will not.

Total number of ways of selecting r volunteers from n volunteers is

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Total number of ways of selecting 4 volunteers from 8 volunteers is

[tex]\text{Total outcomes}=^8C_4=70[/tex]

Total number of ways of selecting 4 volunteers from 8 volunteers, so that Andrew will be among the 4 volunteers selected and Karen will not is

[tex]\text{Favorable outcomes}=^1C_1\times ^6C_3=1\times 20=20[/tex]

The probability that Andrew will be among the 4 volunteers selected and Karen will not is

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]P=\frac{20}{70}[/tex]

[tex]P=\frac{2}{7}[/tex]

Therefore the probability that Andrew will be among the 4 volunteers selected and Karen will not is 2/7.

The probability that Andrew is selected and Karen is not from a group of 8 volunteers for a 4-person task is 2/7.

The question is asking about the probability of a specific event happening when a group of volunteers is randomly selected. The key to solving this problem is knowing how to calculate combinations.

There are 8 volunteers in total and we know that 4 people are to be selected. The total number of ways 4 people can be selected from 8 is given by the combination formula C(n, r) = n! / (r!(n-r)!), where n is the total number of elements, r is the number of elements to choose, and ! represents the factorial operator.

So, total combinations = C(8, 4) = 8! / (4!(8-4)!) = 70.

Now, we need to find the combinations in which Andrew is chosen and Karen is not. This situation is equivalent to selecting 3 people from the remaining 6 people (excluding Andrew and Karen). Therefore, these combinations = C(6, 3) = 6! / (3!(6-3)!) = 20.

The probability that Andrew will be among the 4 volunteers selected and Karen will not is therefore 20/70 = 2/7.

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Answer:

Step-by-step explanation:

The length AC is 3, but the corresponding length FD is 1, so the dilation factor is FD/AC = 1/3.

The reflection is a left/right reflection, so it is across a vertical line. We suspect the only vertical line you are interested in is the y-axis. (It could be reflected across x=1/2, and then the only translation would be downward.)

The above transformations will put C' at (1, 0). Since the corresponding point D is at (2, -2), we know it is C' is translated by (1, -2) to get to D.

  C' + translation = D

  (1, 0) +(1, -2) = (2, -2)

Answer:

168.75π cm^3 is your answer.

Volume of a cone is 1/3 πr^2h.

Here, radius is given 7.5cm and height is given 9cm. So by using the formula we get the above answer.

For this case we have that by definition, the volume of a cone is given by:

[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]

Where:

h: It's the height

r: It is the cone radius

According to the data we have:

[tex]h = 9cm\\r = 7.5cm[/tex]

Substituting:

[tex]V = \frac {\pi * (7.5) ^ 2 * 9} {3}\\V = \frac {\pi * 56.25 * 9} {3}\\V = 168.75\pi[/tex]

Thus, the volume of the cone is [tex]168.75 \pi \ cm ^ 3[/tex]

Answer:

Option C

Answer:

⇒ Add 8x to both sides of the inequality

⇒ x>1/5

Step-by-step explanation:

First, you subtract by 5 from both sides of equation.

5-8x-5<2x+3-5

Solve.

-8x<2x-2

Then subtract by 2x from both sides of equation.

-8x-2x<2x-2-2x

Solve.

-10x<-2

Multiply by -1 from both sides of equation.

(-10x)(-1)>(-2)(-1)

Solve.

10x>2

Divide by 10 from both sides of equation.

10x/10>2/10

Solve to find the answer.

2/10=10/2=5 2/2=1=1/5

x>1/5 is final answer.

Hope this helps!

Answer: Add 8x to both sides of the inequality

D) on    e d g e n u i t y

Answer:

Step-by-step explanation:

A. Points A, B, and D are on both planes.

  -- true. These points are on the line of intersection of the planes, so are in both planes.

B. Point H is not on plane R.

  -- true. Point H is not shown as being on either of the identified planes.

C. Plane P contains point F.

  -- false. Point F is shown as being in plane R, not P.

D. Points C, D, and A are noncollinear.

  -- true. Point C is not on the line containing points A and D.

E. The line containing points F and G is on plane R.

  -- true. F and G are both in plane R, so the line containing them will also be in that plane.

F. The line containing points F and H is on plane R.

  -- false. Point H is not in plane R, so will not be on any line in plane R.

The answer to this is a, b, d, e

Answer:

C. t – 3.8 = 45.1

Step-by-step explanation:

Steve's time = 45.1 seconds

Tom finished 3.8 seconds later

So add 3.8 to steve's time to find tom's time (t)

t =s+3.8

t = 45.1 + 3.8

Subtract 3.8 from each side

t -3.8 =45.1 +3.8-3.8

t -3.8 = 45.1

Answer:

Its C.

Step-by-step explanation:

You better give the guy above me brainliest. I got the answer from the king above me

Answer:

15

Step-by-step explanation:

So angle 2 and angle 4 have a relationship that is called same-side interior or consecutive interior angles.  The name there depends what class you are in but they mean the same thing.

If you have the transversal goes through parallel lines, then same-side interior angles will add up to 180 degrees.

So you are trying to solve the following equation for x:

angle2+angle4=180

2x+10+4x+80=180

Combine like terms:

6x+90=180

Subtract 90 on both sides:

6x     =90

Divide both sides by 6:

 x      =90/6

Simplify:

 x      =15

15 is x so that the lines are parallel

Answer:

x = 15°

Step-by-step explanation:

Notice that if A is // to B, then ∠2 and ∠4 are supplementary angles, i.e they add up to 180°. We can write this as:

∠2 + ∠4 = 180

(2x + 10) + (4x + 80) = 180

2x + 10 + 4x + 80 = 180

6x  + 90 = 180

6x  = 180 - 90

6x  = 90

x = 15°

Answer:

-14/9

Step-by-step explanation:

Combine -2, -3, x, 2x, 4, 8.  We get -5 + 3x + 12.  This sum is -7.

Solve this equation for x:  3x + 7 = -7, so 3x = -14/3.

Then x is -14/9.

Answer:

-4.7

Step-by-step explanation:

-2 + (-3) + x + 2x + 4 + 8 =  -7

                    -5 + 3x +12 =  -7

                            3x + 7 =  -7

                                  3x = -14

                                    x = -14/3 = -4.7 °F

The value of x is -4.7.

Check:

-2 + (-3) + (-4.7) + 2(-4.7) + 4 + 8 = -7

                      -5 - 4.7 - 9.3 + 12 = -7

                                               -7 = -7

OK

Answer:

20,845 square meters

Step-by-step explanation:

We can use the formula for area of a triangle to figure this out easily.

Area = [tex]\frac{1}{2}abSinC[/tex]

Where

a and b are the two side lengths of the triangle given, and

C is the ANGLE BETWEEN the two sides

Clearly, we see that one side is 218.5 and other is 224.5 and the angle between them is given by 58.2 degrees. Now we simply substitute these values into the formula and get the area:

[tex]A=\frac{1}{2}abSinC\\A=\frac{1}{2}(218.5)(224.5)Sin(58.2)\\A=20,844.99[/tex]

Rounding, we get the area to be 20,845 square meters

Answer:

20,845 m2

Step-by-step explanation:

I got it correct on founders edtell

Answer: 66.50 inches

Step-by-step explanation:

Given : The distribution of heights of women for a certain country is approximately​ Normal with ,

[tex]\mu=\text{63.6 inches }\\\\\sigma=\text{2.8 inches}[/tex]

To find the height of the shortest 15​% of all women, first we need to find the z-score corresponding to the p-value 0.15 from the standard normal distribution table, we get 1.0364.

Let x be the random variable that represents the height of the randomly selected woman.

Then[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]1.0364=\dfrac{x-63.6}{2.8}\\\\\Rightarrow\ x=2.8\times1.0364+63.6\\\\\Rightarrow\ x=66.50192\approx66.50[/tex]

Hence, the height of the shortest 15​% of all women in this​ country =66.50 inches.

Answer:

x^3+9x^2+14x-24 has roots of -6,-4 and 1

Option D is correct

Step-by-step explanation:

If the polynomial has roots of -6 -4 and 1

then x=-6, x=-4, x=1

Which can be written as:

(x+6)(x+4)(x-1)

Multiplying we get,

(x+6)(x(x-1)+4(x-1))

(x+6)(x^2-x+4x-4)

(x+6)(x^2+3x-4)

x(x^2+3x-4)+6(x^2+3x-4)

x^3+3x^2-4x+6x^2+18x-24

x^3+3x^2+6x^2-4x+18x-24

x^3+9x^2+14x-24

So, x^3+9x^2+14x-24 has roots of -6,-4 and 1

Option D is correct

Answer:

  see below

Step-by-step explanation:

Oddly enough, it is the one that with f(x) reflected over the y-axis. All points on the graph are mirrored across that axis (x is changed to -x, y is left alone).

When a graph gets reflected over y-axis it means that a horizontal reflection reflects a graph horizontally over the y-axis.

The graph of [tex]f(x) = 2^x[/tex] is shown on the grid.

The graph of [tex]g(x) = (\dfrac{1}{2})^x[/tex]  is the graph of f(x) reflected over the y-axis.

For x= 0 , [tex]g(x) = (\dfrac{1}{2})^0=1[/tex]

For x= 1 , [tex]g(x) = (\dfrac{1}{2})^1=\dfrac{1}{2}=0.5[/tex]

For x= 2 , [tex]g(x) = (\dfrac{1}{2})^2=\dfrac{1}{4}=0.25[/tex]

i.e. graph of g(x) passes through (-1,2) , (0,1) , (1,0.5) , (2,0.25)

From all the given graph , the correct graph is shown below .

It is showing the exact mirror-image of the given graph across y-axis and it is passing through the(-1,2) , (0,1) , (1,0.5) , (2,0.25) .

Answer:

0.614

Step-by-step explanation:

Let the time be given by  = t

and P(S )  = probability that a person is sick

      P(s)    = probability that a person is not sick

P(s) = [tex](\frac{17}{23})^{23}* (1-\frac{17}{23})\\[/tex]

Then the probability for that there are at least 3 weeks of no sick students before the 2nd week of at least one sick student is given by:

[tex](\frac{17}{23})(\frac{17}{23})(\frac{17}{23})(\frac{17}{23}) + \frac{6}{23} + 3(\frac{17}{23})^{3}\\ = 0.614[/tex]

Answer:

69.7 ft

Step-by-step explanation:

we know that

The function sine of angle of 35 degrees is equal to divide the opposite side to the angle of 35 degrees (the height of the vulture in a tree) by the hypotenuse ( the distance from the vulture to the roadkill)

Let

z -----> the distance from the vulture to the roadkill

sin(35°)=40/z

z=40/sin(35°)=69.7 ft

Answer:

69.7 feet.

Step-by-step explanation:

Let x represent the distance between vulture and roadkill.

We have been given that a vulture is perched 40 ft up in a tree and looks down at an angle of depression of a 35 and spots roadkill.

We can see from the attachment that vulture, roadkill and angle of depression  forms a right triangle with respect to ground, where, x is hypotenuse and 40 ft is opposite side.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}(35^{\circ})=\frac{40}{x}[/tex]

[tex]x=\frac{40}{\text{sin}(35^{\circ})}[/tex]

[tex]x=\frac{40}{0.573576436351}[/tex]

[tex]x=69.7378718[/tex]  

[tex]x\approx 69.7[/tex]  

Therefore, the roadkill is 69.7 feet away from the vulture.

Answer:

[tex]\frac{8}{17}[/tex] of fish in this aquarium are guppies.

Step-by-step explanation:

Let x be the number of guppies and y be the number of swordtails in the aquarium,

According to the question,

[tex]\frac{3}{4}\text{ of } x=\frac{2}{3}\text{ of }y[/tex]

[tex]\frac{3x}{4}=\frac{2y}{3}[/tex]

By cross multiplication,

[tex]9x=8y[/tex]

[tex]\implies \frac{x}{y}=\frac{8}{9}[/tex]

Thus, the ratio of guppies and swordtail fishes is 8 : 9

Let guppies = 8x, swordtail = 9x

Where, x is any number,

Since, the aquarium contains only two kinds of fish, guppies and swordtails,

So, the total fishes = 8x + 9x = 17x

Hence, the fraction of fish in the aquarium are guppies = [tex]\frac{\text{Guppies}}{\text{Total fishes}}[/tex]

[tex]=\frac{8x}{17x}[/tex]

[tex]=\frac{8}{17}[/tex]

To find what fraction of fish in the aquarium are guppies, you express the given relationship between the number of guppies and swordtails algebraically and solve for the number of guppies relative to the total number of fish, concluding that 8/17 of the fish in the aquarium are guppies.

If 3/4 of the number of guppies is equal to 2/3 of the number of swordtails, we can express this relationship using variables. Let G represent the number of guppies and S represent the number of swordtails in the aquarium. The given relationship can be written as (3/4)G = (2/3)S.

To find the fraction of fish that are guppies, we need to express G in terms of S first. By manipulating the equation, we multiply both sides by (4/3) to get G = (4/3)*(2/3)S = (8/9)S. This equation shows that the number of guppies is (8/9) times the number of swordtails.

Now, to find the total number of fish (T), we add the number of guppies and swordtails: T = G + S. Substituting the value of G from the equation above, we get T = (8/9)S + S = (17/9)S. The fraction of the total that are guppies is then G/T = [(8/9)S]/[(17/9)S] which simplifies to 8/17. Therefore, 8/17 of the fish in the aquarium are guppies.

bearing in mind that, we can always get the common ratio by simply dividing any term by the one before it, and if it's a geometric sequence, all divisions will yield the same "r" value.

Check the picture below.

Answer:

0.2

Step-by-step explanation:

we have given sample space = {1,2,3,4,5,6,7,8,9,10}

favorable outcomes E={2,4}

we know that probability is defined as the ratio of favorable otcomes to the sample space

probability [tex]P=\frac{favorable\ outcomes}{ sample\ space }[/tex]

we have  favorable outcomes E={2,4} that is  favorable outcomes=2

and sample sapce =  {1,2,3,4,5,6,7,8,9,10}

so the probability [tex]p=\frac{2}{10}=0.2[/tex]

The probability of event E={2,4} from the sample space S={1,2,3,4,5,6,7,8,9,10} is 1/5 or 20%, calculated by dividing the number of favorable outcomes (2) by the total number of outcomes (10).

The student asked to compute the probability of event E={2,4} from a sample space S={1,2,3,4,5,6,7,8,9,10}. Since the outcomes are equally likely, we use the formula for theoretical probability, which is the number of favorable outcomes divided by the total number of possible outcomes in the sample space.

To find P(E), first count the number of outcomes in event E, which includes just 2 and 4. There are two favorable outcomes. The total number of outcomes in the sample space S is 10. Therefore, P(E) equals 2/10 or 1/5 when simplified. This means the probability of event E occurring is 0.20 or 20%.