P(x)equals=​R(x)minus−​C(x). Given ​R(x)equals=59 x minus 0.3 x squared59x−0.3x2 and Upper C left parenthesis x right parenthesis equals 3 x plus 14C(x)=3x+14​

Since the product of 4x is written as the sum log 4 and log x hence the  expression log2(4x) = log2(4)+log2(x) illustrates the product rule for logarithmic equations

According to the law of logarithm

log (ab) = loga + logb

The product of log becomes sum

From the given log functions,

log2(4x) = log2(4)+log2(x)

Since the product of 4x is written as the sum log 4 and log x hence the  expression log2(4x) = log2(4)+log2(x) illustrates the product rule for logarithmic equations

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Answer:

the correct answer is 4. because the cube root of 64 is 4

Answer:

Step-by-step explanation:

Recall that 4^3 = 64.

Thus, the opposite operation is the cube root of 64:  ∛64 = 4

Answer:

The answer to your question is x = 12

Step-by-step explanation:

Data

BC = 7

DE = x

AB = 7

BD = 5

Process

To solve this problem use proportions and cross multiplication. Compare the ΔADE and ΔABC.

             DE / (AB + BD) = BC / AB

-Solve for DE

             DE = BC (AB + BD) / AB

-Substitution

             DE = 7(7 + 5) / 7

-Simplification

             DE = 7(12) / 7

             DE = 84/7

-Result

             DE = 12

Answer:

The dimensions that will produce a maximum area of the rectangular region is 50 meters or 5000/Pi

Step-by-step explanation:

From the question given, let us recall the following formula

The perimeter = 200 which is,

P=2L + C

where L is = length of the rectangular region

The circumference of a circle denoted as C

The Circumference of the semi-circle is denoted as,

C=Pi x D, which is  D=C/Pi.

Thus the equation becomes,

200 = 2L+C

A=L x (C/Pi)

We now have Two equations and three variables, from these two equations, we can get a single equation,

200=2L+C means that C = 200-2L

For C in the Area equation. Substitute 200-2L:

A=Lx (C/Pi) which is  A = Lx (200-2L)/Pi.

We Simplify: A = (1/Pi)(-2L² + 200L)

Now take a  derivative of A with respect to L: dA/dL = (1/Pi)(-2L + 200)

(1/Pi)(-2L+200)=0

Let Solve for L: L = 50.

when L is 50 we have the MAXIMUM area. this is a negative quadratic so it MUST therefore not be a minimum but maximum

Then,

Plug in L=50 into the formula for A: A = 50(200-2(50))/Pi = 5000/Pi.

Final answer:

To find the dimensions that maximize the area of the rectangular region for a 200-meter running track with semicircle ends, we can use the perimeter constraint and optimization techniques to solve for the variable x that will give the maximum area when substituted back into the area formula. Therefore, the dimensions of the rectangular region that yield the largest area are [tex]\( x = 50 \) and \( y = \frac{100}{\pi} \).[/tex]

Explanation:

The student is asking about optimizing the area of a rectangular region with semicircles on each end, with a constraint on the perimeter. This is a typical optimization problem that can be solved using calculus, where we need to maximize the area function A(x) = x*y subject to the perimeter constraint P = 2x + πy = 200, considering y as the diameter of the semicircles.

To maximize the area, we'd typically take the derivative of the area function with respect to one of the variables, substitute the relationship given by the perimeter constraint, and solve for the variable that will give us the maximum area. However, since this is a high school level question, it might be expected that the student uses algebraic methods instead of calculus.

To find the value of \( x \) that maximizes the area [tex]\( A(x) = \frac{x(200 - 2x)}{\pi} \)[/tex], we'll follow the steps you provided.

1. Express \( y \) in terms of \( x \) using the perimeter constraint:

  Given that the perimeter of the rectangle is \( 200 \), we have:

 [tex]\[ P = 2x + 2y = 200 \][/tex]

  Rearranging for \( y \):

 [tex]\[ 2y = 200 - 2x \] \[ y = \frac{200 - 2x}{2} \] \[ y = \frac{200 - 2x}{\pi} \][/tex]

2. Substitute \( y \) in the area formula:

  Now, we substitute the expression for \( y \) in terms of \( x \) into the formula for the area:

[tex]\[ A(x) = x \times \left( \frac{200 - 2x}{\pi} \right) \][/tex]

3. Maximize the area:

  To maximize \( A(x) \), we'll find the critical points by taking the derivative of \( A(x) \) with respect to \( x \), setting it equal to zero, and solving for \( x \).

 [tex]\[ A'(x) = \frac{dA}{dx} = \frac{d}{dx} \left( x \times \frac{200 - 2x}{\pi} \right) \] Using the product rule, we get: \[ A'(x) = \frac{d}{dx} \left( x \right) \times \frac{200 - 2x}{\pi} + x \times \frac{d}{dx} \left( \frac{200 - 2x}{\pi} \right) \] \[ A'(x) = \frac{1}{\pi} (200 - 2x) - \frac{2x}{\pi} \][/tex]

  Setting \( A'(x) \) equal to zero and solving for \( x \):

 [tex]\[ \frac{1}{\pi} (200 - 2x) - \frac{2x}{\pi} = 0 \] \[ 200 - 2x - 2x = 0 \] \[ 200 - 4x = 0 \] \[ 4x = 200 \] \[ x = \frac{200}{4} \] \[ x = 50 \][/tex]

So, \( x = 50 \) maximizes the area. To find the corresponding value of \( y \), we substitute \( x = 50 \) into the expression we found for \( y \):

[tex]\[ y = \frac{200 - 2 \times 50}{\pi} = \frac{200 - 100}{\pi} = \frac{100}{\pi} \][/tex]

Therefore, the dimensions of the rectangular region that yield the largest area are [tex]\( x = 50 \) and \( y = \frac{100}{\pi} \).[/tex]

Answer: 0; one real number

Step-by-step explanation:

Answer: [tex]x=10[/tex]

Subtract 4 from both sides

[tex]2x+4-4=24-4\\2x=20[/tex]

Divide both sides by 2

[tex]2x/2=20/2[/tex]

[tex]x=10[/tex]

Answer:

9 in

Step-by-step explanation:

The missing length of the right angle triangle is approximately 12 in.

The missing length of the right-angle triangle can be found using the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In this case, the length of one side of the triangle is 5.6 in and the length of the other side is 10.6 in. Let's substitute these values into the formula:

a² + b² = c²

(5.6 in)² + (10.6 in)² = c²

31.36 in² + 112.36 in² = c²

143.72 in² = c²

Now, we can take the square root of both sides to find the length of the hypotenuse:

c = √143.72 in² ≈ 12 in

Therefore, the missing length of the right angle triangle is approximately 12 in.

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Answer:

55/48

Step-by-step explanation:

We can find the  tangent of ∠G using the trigonometrical ratios which may be expressed in the form SOA CAH TOA Where,

SOA stands for

Sin Ф = opposite side/hypotenuses side

Cosine Ф = adjacent side/hypotenuses side

Tangent Ф = opposite side/adjacent side

Considering triangle ΔFGH, where ∠H=90°

The opposite side is FH, the hypotenuse side is GF and the adjacent side is HG hence,

Tan ∠G = FH/HG

= 55/48

Answer:

55:48

Step-by-step explanation:

Given a right angles triangle ∆FGH

where  ∠H=90°, HG = 48, FH = 55, and GF = 73,

Based on the diagram attached

To find the tangent of angle G, we will use the concept of SOH CAH TOA in trigonometry identity.

According to TOA:

Tan ∠G = Opposite/Adjacent

Note that the opposite side will be the side facing the angle we are considering i.e ∠G

Opposite = 55

Adjacent will be the base of the triangle = 48

Tan∠G = 55/48

The ratio that represents the tangent of ∠G is 55:48

Answer:

The iguana can is larger

Step-by-step explanation:

Plug in the measurements into the equation for a cylinder (V=πr^2h) to find out which volume is bigger. Remember to divide the diameter by 2 to radius.

(Hampster) V≈196.35 < V≈226.19 (Iguana)

Answer:

the slope of the line is 2.75

Slope intercept form (y = mx + b) y = 2.75x + 5

Answer: 485 matinee tickets, 7045 regular tickets and 970 student tickets were sold.

Step-by-step explanation:

Let x represent the number of matinee tickets that were sold.

Let y represent the number of regular tickets that were sold.

Let z represent the number of student tickets that were sold.

Last Tuesday regal cinemas sold a total of 8500 movie tickets. It means that

x + y + z = 8500

Tickets can be bought in 3ways :matinee cost $5, students cost $6 all day and regular cost $8. Proceeds totaled $64605. It means that

5x + 8y + 6z = 64605- - - - - - - - -2

if twice as many students tickets were sold as matinee tickets, it means that

z = 2x

Substituting z = 2x into equation 1 and equation 2, it becomes

x + y + 2x = 8500

3x + y = 8500

y = 8500 - 3x - - - - - - - - - 3

5x + 8y + 6 × 2x = 64605

5x + 8y + 12x = 64605

17x + 8y = 64605- - - - - - - - - 4

Substituting equation 3 into equation 4, it becomes

17x + 8(8500 - 3x) = 64605

17x + 68000 - 24x = 64605

17x - 24x = 64605 - 68000

- 7x = - 3395

x = - 3395/-7

x = 485

z = 2x = 2 × 485

z = 970

Substituting x = 485 and z = 970 into equation 1, it becomes

485 + y + 970 = 8500

1455 + y = 8500

y = 8500 - 1455

y = 7045

Final answer:

To determine the needed x-value when the required value of y is -108.5, substitute the value of y into the fit line equation and solve for x. The rounded x-value is 100.

Explanation:

To determine the needed x-value when the required value of y is -108.5 using the fit line equation y = -2.61x + 152.51, we can substitute the value of y into the equation and solve for x.

-108.5 = -2.61x + 152.51

Subtract 152.51 from both sides: -108.5 - 152.51 = -2.61x

Simplify: -261.01 = -2.61x

Divide both sides by -2.61: x = -261.01 / -2.61

Rounding to the nearest whole number, x = 100.

Option B is correct, it will take 2hrs to reach it.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

A car leaves town, A at the speed of 90 km/h.

Distance covered by A: 90t

Three hours later leaves the same city another car in pursuit of the first with a speed of 120 km / h

Distance covered by B: 120(t - 3)

90t = 120(t - 3)

Apply distributive property

90t = 120t - 360

30t = 360

Divide both sides by 360

t = 12

Hence, option B is correct, it will take 2hrs to reach it.

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Answer:

David gets 20 sweets.

Step-by-step explanation:

If you want the ratio, 2:2:1, Krustika gets 20 more than mark, you will need to have double what mark got.

So, the only number I can think of that is half, but also 20 more than the "1" ratio, is 20; as 20 is half of 40, however, 40 is also 20 more than the "1" ratio.

David gets 40 sweets when the sweets are divided in a 2:2:1 ratio among Krutika, David, and Mark, and where Krutika receives 20 more sweets than Mark.

The problem presents a ratio which is the relation between three persons sharing sweets: Krutika, David, and Mark. The ratio is given as 2:2:1 respectively. This means that for every 2 sweets Krutika gets, David gets 2 sweets, and Mark gets 1 sweet.

Krutika gets 20 more sweets than Mark in this arrangement, so we can say that Mark's share (1 part of the ratio) is equivalent to Krutika's share - 20, which is 20 sweets. Therefore, 1 part of the ratio represents 20 sweets.

Since David's share is 2 parts of the ratio, and each part of the ratio is equivalent to 20 sweets, David gets 2 * 20 = 40 sweets.

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Answer:

  B.   Figure A was rotated 180° about the midpoint of FF'

Step-by-step explanation:

Points ABC are oriented clockwise, as are points A'B'C', so two reflections or rotation are involved. Segment AB is directed in the opposite direction of segment A'B', so the rotation must be 180°. These effects cannot be accomplished by translation or single reflections, nor can they be accomplished by rotation of 90°.

The midpoints of segments joining a point and its image all intersect at the center of rotation of 180°. The appropriate choice is B:

  Figure A was rotated 180° about the point in the middle of the line segment connecting F and F' to create Figure B.

Answer:

4

Step-by-step explanation:

Hope this helps

Answer:

Search web.

Web results= absolute value of 6 is 6.

Step-by-step explanation:

Answer: 10 units

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

Answer:rate of the plane in calm air = 380 mph

rate of the wind = 100 mph?

Step-by-step explanation:all you have to do is divide 1520 mi by 4 hrs because distance/time. You will get the speed of the plane in calm air this way. The rate of the wind is most likley wrong though, please correct me.

The plane's speed in calm air is 330 mi/h, and the wind's speed is 50 mi/h. These values were calculated by setting up and solving a pair of linear equations.

To solve this problem, we will use the formula for rate, which is distance = rate × time. We can set up two equations to represent the plane's flight with and against the jet stream. When the plane is flying with the jet stream, its speed is increased by the speed of the wind, while when it's flying against it, its speed is reduced by the wind speed.

We can then divide these equations by 4 to get the rates:

By solving this system of linear equations, we find that the plane's speed in calm air (plane speed) is 330 mi/h and the speed of the jet stream (wind speed) is 50 mi/h.

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Answer:

12 m3

Step-by-step explanation:

Answer:

12m3

Step-by-step explanation:

Answer:

p=4 d=2

Step-by-step explanation:

To do this, we can set up a system of equations.

Special Deal 1:

2p+4d=16

Special Deal 2:

4p+7d=30

Now we can set this up for elimination, and try to eliminate the p variable.

Let's do this by multiplying the entire equation for Special Deal 1 by 2.

2(2p+4d=16)

4p+8d=32

Now we can eliminate p by subtracting the equation for special deal 2, by the equation for special deal 1.

4p+8d=32 minus

4p+7d=30 equals

d=2

Now we can plug that into the original equation to find the cost of p.

2p+4(2)=16

2p+8=16

Subtract 8 from both sides.

2p=8

p=4

Therefore, a pizza costs $4 and a drink costs $2.

Answer: p=4 d=2

Step-by-step explanation:

just did the assignment, it's right

Answer:

Step-by-step explanation:

A right angle triangle is formed.

The length of the guy wire represents the hypotenuse of the right angle triangle.

The height of the antenna represents the opposite side of the right angle triangle.

The distance, h from base of the antenna to the point on the ground to which the antenna is attached represents the adjacent side of the triangle.

To determine h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

41² = 32.8² + h²

1681 = 1075.84 + h²

h² = 1681 - 1075.84 = 605.16

h = √605.16

h = 24.6 m

To determine the angle θ that the wire makes with the ground, we would apply the the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos θ = 24.6/41 = 0.6

θ = Cos^-1(0.6)

θ = 53.1°

Answer:

Vanessa made 6.25 batches of appetizers last weekend and made 18.75 batches of appetizers this weekend.

Step-by-step explanation:

Let b represent the number of appetizers Vanessa made last weekend.

Since Vanessa made 4 times what made last weekend, let the number of appetizers she made this weekend by represented by 4 × b.

Total batches of appetizers made for the two weekends = 25

Thus, to determine the batches of appetizers made last weekend we perform this operation:

[tex]4 \times b = 25[/tex]

[tex]4b = 25[/tex]

Divide both sides by 4

[tex] \frac{4b}{4} = \frac{25}{4} [/tex]

[tex]b = 6.25[/tex]

Hence, Vanessa made 6.25 batches of appetizers last weekend.

Since total batches of appetizers made by Vanessa for the two weekends is 25, to determine what she made this weekend we say:

[tex]25b - 6.25b = 18.75b[/tex]

Thus, Vanessa made 18.75 batches of appetizers this weekend. By implication, she made 6.25 batches + 18.75 batches of appetizers = 25 batches of appetizers for the two weekends.

Answer:$5075

Step-by-step explanation:

$5075

Hope this helps

Pls gimme brainlest.

Step-by-step explanation:

length x width x height is how to get the answer

Take the numbera and plug them into the equation.

Once youve finished you should get the answer.

Exact form: 105/8

Decimal form: 13.125

Mixed number form: 13 1/8

Answer: 13.125 cubic inches.

Or 13 1/8 cubic inches.

Step-by-step explanation: Volume is length×width×height

Multiply the given dimensions:

(3/2)(5/2)(7/2) = 105/8

Simplify that to get 13.125

or 13 1/8 cubic inches. we

Answer: 5F < 5( X + x )

Step-by-step explanation:

Let each finger = F and

The index finger = X

The shortest index finger = x

the combined length of all 5 of her fingers on one hand should be less than 5 times the length of index finger

From the statement above, we get

5F < 5X

Tessa add the second shortest index finger.

That is

5F < 5( X +x)

Answer:x= -1

Step-by-step explanation:

Answer:

7.12m

Step-by-step explanation:

THIS IS THE CORRECT QUESTION:

Howard is designing a chair swing ride. The swing ropes are 5 meters long, and in full swing they tilt in an angle of 29 degrees. Howard wants the chairs to be 2.75 meters above the ground in full swing. How tall should the pole be? Round your answer, if necessary, to 2 decimal places.

From the question:

Length of the rope is = 5 m long.

The tilted angle is 29°

The distance from the ground is 2.75 m

To Find the height of the pole,

SEE THE ATTACHMENT BELOW;

Answer:

the probability that exactly three of four randomly selected students do not prefer water is;

P = 125/1296 = 0.096

Completed question:

Students at Freeman Middle School have a choice of water, milk, or juice for breakfast. From a survey, it was determined that 50 students prefer water, 100 prefer juice, and 150 prefer milk. You want to know the probability that exactly three of four randomly selected students do not prefer water.

Step-by-step explanation:

Preference from survey results;

Water = 50

Juice = 100

Milk = 150

Total = 50+100+150 = 300

the probability that a selected students do not prefer water;

P1 = (100+150)/300 =250/300 = 5/6

the probability that a selected students prefer water;

P2 = 50/300 = 1/6

the probability that exactly three of four randomly selected students do not prefer water is;

P = P1 × P1 × P1 × P2

P = (5/6)^3 × 1/6

P = 125/1296 = 0.096

Answer:

0.096

Step-by-step explanation:

Answer: 360 degrees

Step-by-step explanation:

Multiply by 1/3. 360(1/3)=120.

Final Answer:

The measure of an angle that turns through 1/3 of a circle is 120 degrees.

Explanation:

To find the measure of an angle that turns through 1/3 of a circle, you would follow these simple steps:
1. Understand what a full circle represents in terms of angle measure: A full circle rotation is equal to 360 degrees. This is because a degree is defined such that there are 360 of them in a full rotation.

2. Calculate a third of this full circle: Since we're interested in finding what 1/3 of a full rotation is, you simply divide the full circle angle measure by 3.

So you take the 360 degrees and divide by 3:
360 degrees / 3 = 120 degrees

Therefore, the measure of an angle that turns through 1/3 of a circle is 120 degrees.

Answer:

x = -7

Step-by-step explanation:

Steps of solution:

The roots are:

Correct answer option is:

Answer:

B,     x =  -7

Step-by-step explanation: