The center of the circle is at the point, and its radius is units. The equation of this circle in standard form is
.

Answer:

Step-by-step explanation:

(f-g)(x) = f(x) - g(x) = |5x + 1| - 3  - 4 = |5x + 1| - 7

need the coordinates to be able to answer

The possible values of k are -0.56, -3.56, -2 and -1.

We have the equation of the parabola, y = 0.5 (x- 3 ) ( x+ k)

Substituting x=0, we get that i.e. y =0.5 * (-3) * k -1.5k

So, the y-intercept is (0,-1.5k).

Thus, the height of the triangle becomes |-1.5k| = 1.5k

Again, substituting y=0, 0 = 0.5 (x-3) (x+k) i.e. i.e. x0=(x-3) (x+k)=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.

As, area of a triangle = 1/2 * (base )* (height )

Substituting the values, we get,

1.5=1/2 *(3+k)*(1.5k)

i.e.3= 4.5 k + 1.5k ²

i.e. k = -0.56 and k = -3.56

or

1.5=1/2* (-3-k )*(1.5k)

i.e.

3 = -4.5 k - 1.5²

i.e. k = -2 and k = -1.

Thus, the possible values of k are -0.56, -3.56, -2 and -1.

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9514 1404 393

Answer:

  1. vertex: J, sides: JH and JK

  5. angle 3, angle M, angle LMN, angle NML

  10. angles 1, 3, 6, HVJ, HVK, HVL, JVK, JVL, KVL, JVH, KVH, LVH, KVJ, LVJ, LVK

Step-by-step explanation:

Your question has too many parts for the kind of answers Brainly is intended to provide. So, we hope to alleviate your confusion by providing examples of the way these questions are answered.

__

An angle can be named by any of ...

Note that angle ABC consisting of rays BA and BC sharing end point B can also be named angle CBA.

__

1. The rays share end point J. That is the vertex of the angle. The rays are named using the end point first, so the rays in this diagram are JH and JK.

The vertex is J; the sides are JH and JK.

__

5. We note there is an angle designator inside near the vertex, point M. That designator can be used to name the angle: angle 3.

There are only two rays that meet at vertex M, so the angle can also be named by naming the vertex: angle M.

The angle can also be named by naming an point on each ray, with the vertex in the middle: angle LMN or angle NML.

The four ways to name this angle are: angle 3, angle M, angle LMN, angle NML.

__

10. All of the angles with numeric designators have V as a vertex. Those angles are angle 3, angle 1, angle 6.

In this case, we cannot use V to name an angle, because many angles have vertex V. That name would be ambiguous, not referring to a specific angle.

The other angles that have V as a vertex can be named by naming their rays. There are 4 rays that meet at vertex V. Any two will identify an angle. There are 4·3 = 12 permutations of 4 rays taken 2 at a time. For example, if we choose to use rays VJ and VK as the two rays of our angle, we can name it two ways: JVK or KVJ. (This particular angle is also angle 1.)

So, the angles that have V as a vertex are ...

  angles HVJ, HVK, HVL, JVK, JVL, KVL, JVH, KVH, LVH, KVJ, LVJ, LVK

The number of hours each 12 inches candle will last, found using the linear equation  obtained from Mason's measurement  is 24 hours

A linear function is a relationship between  two variables, that when plotted produces a straight line graph.

The initial length of the candle = 12 inches

Number of hours the candle has been lit, 1 1/2 hour = 1.5 hour

4 1/2 hour = 4.5 hour

11 1/4 inches = 11.25 inches

9 3/4 inches = 9.75 inches

The ordered pair of the height of the candle and height are;

(1.5, 11.25), (4.5, 9.75)

The slope of the line that represent the height as a function of time is therefore;

(9.75 -  11.25)/(4.5 - 1.5) = -0.5

The equation of the line in point-slope form is therefore;

y - 11.25 = (-0.5) × (x - 1.5) = -0.5·x + 0.75

y - 11.25 = -0.5·x + 0.75

y   = -0.5·x + 0.75  + 11.25

y = -0.5·x + 12

The above equation  produces the height y after a time x

When the candle finishes, the  height is zero, therefore;

y = 0 = -0.5·x + 12

0.5·x = 12

x = 12 ÷ 0.5 = 24

The number of hours the candle will last, x = 24 hours

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Answer:

x is equal to 3/2

Step-by-step explanation:

Let's solve it!

5(4x - 10) + 10x = 4(2x - 3) + 2(x - 4)

expand:

20x - 50 + 10x = 8x - 12 + 2x - 8

group like terms:

30x - 50 = 10x - 20

factor out common multiples:

3x - 5 = x - 2

group terms again:

3x - x = -2 + 5

2x = 3

and divide both sides by two:

x = 3/2

You solve the first two the same way

Answer:

$2800

Step-by-step explanation:

let x represent the amount earned on the sale of a car

let y represent the amount earned on the sale of a truck

6x+3y=4800-eqn 1

8x+y=4600-eqn 2

Make y the subject of eqn 2

y=4600-8x

Plug y=4600-8x into eqn 1

6x+3(4600-8x)=4800

6x+13800-24x=4800

13800-4800=18x

18x=9000

x=9000/18=500

Now plug the value of x into eqn 2

8(500)+y=4600

4000+y=4600

y=600

So the amount earned on the sale of a car is $500 and $600 on the sale of a truck

Therefore,if 2cars and 3trucks are sold then

2($500)+3($600)

$1000+$1800

=$2800

Answer:

work is shown and pictured

Answer:

500 gallons

Step-by-step explanation:

25/5=5 5*100=500

Answer:

You need 500 gallons for 25 fish

Step-by-step explanation:

If 5 fish = 100 gallons, you need to find out 25 = ? gallons.

25 ÷ 5 = 5. 100 x 5 = 500 gallons.

a. The efficiency of Expedition Everest is approximately 87.8%.

b. The utilization of Expedition Everest is approximately 94.7%.

c.  The demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.

To calculate the efficiency and utilization of Expedition Everest, we need to compare the actual number of riders with the design capacity and effective capacity.

Given:

Demand = 3,000 riders/hour

Average riders = 1,800 riders/hour

Design capacity = 2,050 riders/hour

Effective capacity = 1,900 riders/hour

a. Efficiency:

Efficiency is calculated as the average riders divided by the design capacity, multiplied by 100%.

Efficiency = (Average riders / Design capacity) * 100%

= (1,800 / 2,050) * 100%

≈ 87.8%

Therefore, the efficiency of Expedition Everest is approximately 87.8%.

b. Utilization:

Utilization is calculated as the average riders divided by the effective capacity, multiplied by 100%.

Utilization = (Average riders / Effective capacity) * 100%

= (1,800 / 1,900) * 100%

≈ 94.7%

Therefore, the utilization of Expedition Everest is approximately 94.7%.

c. Capacity Analysis:

To determine if the operation is overcapacity or undercapacity, we compare the demand with the effective capacity.

Demand > Effective capacity

3,000 > 1,900

Since the demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.

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Answer:

soln;

given equation is 6x + 5 = 2y

or, 6x -2y + 5 = 0

comparing with ax + by + c = 0

a = 6, b = -2, c = 5

The coordinate vector of x relative to the given basis B is [x] = [-22; 39; -21; -10; 16].

We are required to find the coordinate vector [x] of x relative to the given basis B = {b₁, b₂} and x = -10i + 5j - 4k + 3l - 8m.

In order to find the required coordinate vector, we use the following formula:

x = [x]B[b₁ b₂]

where [b₁ b₂] is the matrix of column vectors of the basis B.

Since, B = {b₁, b₂} = {4, -3, 2, 1, -2}, we have,[b₁ b₂] = [4 2 -2; -3 1 -1; 2 -1 1; 1 0 0; -2 0 1]

So, x = [x]B[b₁ b₂]

implies x = [x₁, x₂, x₃, x₄, x₅] [4 2 -2; -3 1 -1; 2 -1 1; 1 0 0; -2 0 1] [-10; 5; -4; 3; -8]

x = [ (4)(-10) + (2)(5) + (-2)(-4) ; (-3)(-10) + (1)(5) + (-1)(-4) ; (2)(-10) + (-1)(5) + (1)(-4) ; (1)(-10) + (0)(5) + (0)(-4) ; (-2)(-10) + (0)(5) + (1)(-4) ]

x = [ (-40) + 10 + 8 ; 30 + 5 + 4 ; (-20) - 5 + 4 ; -10 + 0 + 0 ; 20 + 0 - 4 ]

x = [ -22; 39; -21; -10; 16]

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The inequality to determine the number of runs per inning, p Kim's team could have scored is; 4r + 6 > 17

Let r represent the number of runs per inning. Thus for 4 innings, we have 4r.

The team already has 6 runs. Now add the additional runs to this to get;

4r + 6

The team wants to score more than the other team, this means they need more than 17 and so the inequality required is;

4r + 6 > 17

Subtract 6 from each side to get;

4r + 6 - 6 > 17 - 6

4r > 11

Divide both sides by 4 to get:

r > 2.75

Approximating to a whole number gives;

r > 3

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Answer:

6+4p> 17
3

Step-by-step explanation:

Given data:

The depth of water increases per hour is d= 13.5 in/hour.

The given time is t= 6 hours.

The amount of water added is,

Thus, 6.75 feet of water added in 6 hours.

To find the number of triangles with vertices of three different colors, we need to consider the combinations of colors we can choose from the given set of points.

We have 8 red points, 4 green points, and 6 blue points. To form a triangle with vertices of three different colors, we need to choose one point from each color group.

First, let's choose one red point. We have 8 options for this.

Next, let's choose one green point. We have 4 options for this.

Finally, let's choose one blue point. We have 6 options for this.

To determine the total number of triangles, we need to multiply the number of options for each color:

Total number of triangles = Number of options for red points × Number of options for green points × Number of options for blue points

                      = 8 × 4 × 6

                      = 192

Therefore, there are 192 triangles with vertices of three different colors.

It's worth noting that the order in which we choose the points does not matter because we are counting the number of distinct triangles. So, we are not considering permutations but rather combinations of colors.

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Answer:

-39

Step-by-step explanation:

 12 - {1+2[-1(3-8)]²}

=12 - {1+2[-1(5)]²}     solve the parenthesis first

=12 - {1+2[5]²}         multiple the 5 by -1

=12 - {1+2[25]}        then square the 5

=12 - {1+50}            multiple 25 by 2

=12 - 51                  solve the curly bracket

= -39                      finally solve it

By converting -1 2/3 to an improper fraction, we get -5/3. To add these fractions, we need to find a common denominator, which is 6. Adding the fractions gives us 5/6. Therefore, -1 2/3 - (-5/6) is equal to 5/6.

To perform the addition and subtraction of rational numbers, we start by converting -1 2/3 to an improper fraction. We multiply the whole number (-1) by the denominator of the fraction (3), which gives us -3. Adding the result to the numerator (2) gives us -3 + 2 = -1. So, -1 2/3 can be represented as -5/3.

Next, we rewrite the expression as -5/3 - (-5/6). When we subtract a negative number, it is equivalent to adding the positive value. So, -(-5/6) becomes +5/6.

To add fractions, we need a common denominator. In this case, the common denominator is 6. We multiply the numerator and denominator of -5/3 by 2 to get -10/6. Therefore, the expression becomes -10/6 + 5/6.Now that the fractions have the same denominator, we can add the numerators. -10/6 + 5/6 equals -5/6.

Hence, the final result of -1 2/3 - (-5/6) is 5/6.

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1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters

2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters

Since we know that the wavelength = speed of light / frequency

The speed of light is 3.00 × \(10^8\) meters per second.

For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;

wavelength of A = (3.00 ×  \(10^8\)  m/s) / (4.30 × 10^15 Hz)

wavelength of A = 6.98 ×  \(10^{-8}\) meters

For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;

wavelength of B = (3.00 ×  \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)

wavelength of B = 3.45 ×  \(10^{-11}\)  meters

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Answer:

c. 1/5x

Step-by-step explanation:

what times 5 would equal 1. 1/5 times 5 is 1. So the solution is 1/5x

Answer:

Step-by-step explanation:

Given function

To find the inverse of f(x), replace x with y and f(x) with x, then solve for y:

Replace y with f⁻¹(x):

Correct option is C

Answer:

\(5x = 15 - 10 \\ 5x = 5 \div 5 \\ 5x = 1\)

Winning lottery 5 times most likely, guessing 64-bit key, 128-bit key, hit by lightening.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.

1) Being hit by lightning this year (probability is 1/105) - The probability is the lowest because the odds of being hit by lightning in a given year are relatively low.

2) Guessing a 128-bit key on the first try - The probability of guessing a 128-bit key on the first try is very low because of the large number of possible key combinations.

3) Guessing a 64-bit key on the first try - The probability of guessing a 64-bit key on the first try is lower than guessing a 128-bit key, but still relatively low because of the large number of possible key combinations.

4) Winning a lottery with 1 million (106) contestants five times in a row (the probability is (1/106)5) - The probability of winning a lottery with such large number of contestants is relatively low, but it is still much higher than the first three events.

So the order is:

1) Being hit by lightning this year

2) Guessing a 128-bit key on the first try

3) Guessing a 64-bit key on the first try

4) Winning a lottery with 1 million contestants five times in a row,

Winning lottery 5 times most likely, guessing 64-bit key, 128-bit key, hit by lightening.

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Answer:

Step-by-step explanation:

The statement "the ratio of female birds to male birds was 85" means that for every 85 female birds at the pet store, there was 1 male bird. The ratio is typically written as "85:1" or "85/1" to show the comparison between the number of female birds and male birds.

Answer:

d/2 = r if you are talking about circles, if that's the case then the r would be 5

Answer:

We could think of the Earth as a sphere, where the diameter of this sphere will the mean diameter between the measure from the North pole to the Soth pole and the measure from opposite points of the equator.

Remember that the mean between two numbers A and B is:

Mean = (A + B)/2

In this case, the mean diameter will be:

D = (7,899.83mi + 7,926.41mi)/2 = 7,913.115 mi

And we know that the surface of a sphere of diameter D is:

S = 4*pi*(D/2)^2

Where pi = 3.14

Then the surface of the Earth will be something like:

S = 4*3.14*(7,913.115mi/2)^2 = 196,618,601.47 mi^2

b) We know that 75% of the Earth's surface is water, now we will use the diameter 7,926.41 mi to compute the surface.

First, the total surface of the Earth will be:

S = 4*3.14*(7,926.41mi/2)^2 = 197,279,843.03 mi^2

And 75% of this is water, then the total water surface is 0.75 times that area, this is:

water surface = 0.75*197,279,843.03 mi^2 = 147,959,882.27 mi^2

Answer:

x=11°

Step-by-step explanation:

We can see that the square is split into 4 triangles. We also have the midpoint T. Because Each angle of a square is 90 degrees and ∠PQR is divided in half, m∠PQT=45 degrees. By substitution, (4x+1)=45°

Solve:

(4x+1)=45°

4x=44°

x=11°

Answer:

29

Step-by-step explanation:

Given

- 5x + 4 ← substitute x = - 5 into the expression

= - 5(- 5) + 4 = 25 + 4 = 29

Answer:

becuase it is evil

Step-by-step explanation:

the will be evil and will become bad :)

Answer:

6dquare 2

Step-by-step explanation:

The square root of 108 in radical form is 6√(3). In general, to find √(a) in radical form, when a is not a perfect square, we use the.