Solve for x in the diagram below.

Answer:

Since I don't know the accuracy of the diagram i would advise you to measure using a divider or a ruler.

Answer:

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line

Step-by-step explanation:

u single?

The displacement during the interval [1, 4] is 17.5 centimeters, and the distance traveled during the interval [1, 4] is also 17.5 centimeters.

To find the displacement during the interval [1, 4], we need to calculate the integral of the velocity function \(v(t) = t - 8/t^2\) with respect to t over the interval [1, 4].

(a) Displacement during the interval [1, 4]:

∫\(^1 _4 (t - 8/t^2) dt\)

To find the antiderivative of \(t - 8/t^2\), we can rewrite it as \(t^3/t^2 - 8/t^2\):

∫\(^1 _4 (t^3/t^2 - 8/t^2) dt\)

Using the properties of integrals, we can separate the terms:

∫\(^1 _4 (t^3/t^2) dt\) - ∫\(^1 _4 (8/t^2) dt\)

Simplifying:

∫\(^1 _4 (t)\) dt - 8∫\(^1 _4 (1/t^2)\) dt

Substituting the limits:

\([1/2 * 4^2] - [1/2 * 1^2] - 8 * [-1/4] + 8 * [-1]\)

Simplifying:

8 - 1/2 + 2 + 8

Displacement = 17.5 centimeters

(b) To find the distance traveled during the interval [1, 4], we need to calculate the integral of the absolute value of the velocity function |v(t)| over the interval [1, 4].

Distance traveled during the interval [1, 4]:

∫\(^1 _4 (t - 8/t^2) dt\)

We need to consider two cases:

Case 1: \(t - 8/t^2\) is positive or zero

∫\(^1 _4 (t - 8/t^2) dt\)

Using the same calculation as in part (a), we found the displacement to be 17.5 centimeters.

Case 2: \(t - 8/t^2\) is negative

∫\(^1 _4 (t - 8/t^2) dt\)

Using the same calculation as in part (a), we found the displacement to be -17.5 centimeters.

Since distance is always positive, we take the absolute value:

Distance = |17.5| centimeters

= 17.5 centimeters

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To maximize profits, the firm should produce a quantity of goods x = 5 and y = 10, based on the cost function and price constraints.

To maximize profits, the firm needs to find the quantities of goods x and y that will yield the highest profit. The profit function can be defined as the revenue minus the cost. Revenue is calculated by multiplying the quantity of each good produced with their respective prices, while the cost function is given as C(x, y) = 10x + xy + 10y.

The firm is committed to delivering a total of 15 units, which can be expressed as x + y = 15. To determine the optimal production quantities, we need to maximize the profit function subject to this constraint.

By substituting the price expressions Ps = 50 - x + y and Py = 50 - x + y into the profit function, we obtain the profit equation. To find the maximum profit, we can take the partial derivatives of the profit equation with respect to x and y, set them equal to zero, and solve the resulting system of equations.

Solving the equations, we find that the optimal production quantities are x = 5 and y = 10, which maximize the firm's profits.

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Answer: 63

Step-by-step explanation:

14.5x1.5=21.75

15x2.75=41.25

21.75+41.25=63

Answer:

y-intercept: (0, -2)

x-intercept: (4, 0)

Step-by-step explanation:

The x intercept occurs when y = 0, so you can substitute 0 in for y and solve for x as shown:

-4x+8y=-16

-4x+8(0)=-16

-4x+0=-16

-4x=-16

x=4 ---------- format correctly in (x, y) : (4, 0)

The y intercept occurs when x = 0, so you can substitute 0 in for x and solve for y as shown:

-4x+8y=-16

-4(0)+8y=-16

0+8y=-16

8y=-16

y=-2 ---------- format correctly in (x, y) : (0, -2)

Step-by-step explanation:

hope helps you

have a good day

Step-by-step explanation:

(6-2)/(6+4)= 4/10= 2/5 is the slope

answer is D

Given the equation:

to solve for x, first we have to move the constant 10 to the right side of the equation. When we do this, we have to change its sign to a negative sign:

Now we can divide both sides of the equation by 2 to get the following:

therefore, x = 9

Answer:

The answer is 7b+14.

Step-by-step explanation:

z-z +2b+5b + 18-4

Thee factory is able to provide 94.38 boxes per hour to the warehouse.

Rate = (2000 - 1245) / 8 = 94.38 boxes per hour

Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.

Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2

Therefore, the inventory at the end of a 40-hour work week would be:

1245 + 3775.2 = 5020.2 boxes

rate = (50000 - 1245) / time

Simplifying this equation, we get:

time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).

Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,

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Population dynamics must consider the number of individuals that are lost per unit of time, also called the mortality rate.

Mortality, or mortality, is a measure of the number of deaths (generally or due to a particular cause) in a particular population, scaled to the size of that population per unit of time.

The relative incidence of deaths in a particular population over a particular time period. Often expressed as the rate of human deaths or wildlife deaths from environmental hazards during a public health crisis. The highest mortality rate for patients over the age of 80 was during the last flu season.

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The equations that have the same solution as 2X -5 equals 15 is option B and option D.

Given equation:

2x -5 = 15

solve for value of x

2x = 15 + 5

2x = 20

divide by 2 on both sides

x = 20/2

x = 10

A. 2x =10

x = 10/2

x = 5

B. 2x = 20

x = 20/2

x = 10

C. 2(x -5) = 15

2x -10  = 15

2x =25

x = 25/2

x = 12.5

D. 2x - 20 = 0

2x = 20

x = 20/2

x = 10

E. 15 = 5 - 2x

2x = 5 - 15

2x = -10

x = -5

From the option A,B,C,D,E we observe that only options B , D x value matches with the given equation x value so option B and option D is correct.

Therefore he equations that have the same solution as 2X -5 equals 15 is option B and option D.

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Answer:

x = 3; y = 6

Step-by-step explanation:

Using elimination method:

2x + y = 12

+. (the y will cancel out)

3x - y = 3

5x = 15

therefore, x = 15

5

x = 3

substitute x in one of the equations

2(3) + y = 12

6 + y = 12

y = 12 - 6

y = 6

therefore y = 6

Therefore, the indicated z-score is 2.45.

To find the indicated z-score, we need to use a standard normal distribution table. From the graph, we can see that the area to the right of the z-score is 0.9850.
Looking at the standard normal distribution table, we find the closest value to 0.9850 in the body of the table is 2.45. This means that the z-score that corresponds to an area of 0.9850 is 2.45.
It's important to note that the standard deviation of the standard normal distribution is always 1. This is because the standard normal distribution is a normalized version of any normal distribution, where we divide the difference between the observed value and the mean by the standard deviation.

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The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer: Sum = 540° ; x = 127°

Step-by-step explanation:

So a Pentagon's interior angles is always equal to 540°.

90° + 143° + 77° + 103° + x = 540°

413° + x = 540°

x = 127°

90° + 143° + 77° + 103° + 127°  = 540°

Hope this helps!!! :)

Answer:

132.7 feet.

Step-by-step explanation:

tan 37 = height of cliff / distance of the ship

=  100/d

d = 100/tan37

= 132.7 feet.

Step-by-step explanation:

5. To find the area of any rectangle, multiply length and width

6. To find the area of any triangle, multiply base times height

i don't know about question 4 sorry :(

find dy/dx

x= t sin(t); (Given in the question)

y= t²+8t; (Given in the question)

then, x= t sin(t)

dx/dt = sin t + t cos t ;

y= t²+8t

dy/dt = 2t + 8;

then, dy/dx = dy/dt x dx/dt

dy/dx = (2t+8)/(sin t + t cos t)

dy/dx = 2(t+4)/(sin t + t cos t)

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Answer:

1,4,5

Step-by-step explanation: it ees what it ees

The shortest distance between planet Q and planet R is  1.64 × 10⁷ .

RP = 1.6 * 10⁷

most compact distance

The Pythagoras theorem x₂ = R * P² + Q * P² is then used to determine the shortest distance (x).

This results in x = (3.6 * 10⁶) + (1.6 * 10⁷) = 2.

x² = 12.96 * 10¹²  + 2.56 * 10¹⁴ should be evaluated.

Write the equation as: x²= 12.96 * 10¹² + 256 * 10¹²

Sums x² = 268.96*10¹² should be evaluated.

multiply both sides' square roots.

x = 16.4 * 10⁶

Replace with: x = 1.64 * 10⁷

In light of this, the distance between planet Q and planet R is 1.64 * 10⁷ km.

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The complete  question is

The distances between some planets are given below.

Planet Q is 3.6 x 10⁷ to the power of 6 km from planet P.

Planet R is 1.6 x 10⁷ to the power of 7 km from planet P.

Work out the shortest distance between planet Q and planet R. Give your answer in standard form.

Step-by-step explanation:

so, there are 14 people with 1 ticket each, and I have 2 tickets.

that means there are 16 tickets (14+2) in the raffle.

each ticket has therefore a winning probability of 1/16.

I have 2 tickets, so my winning probabilty is therefore

1/16 + 1/16 = 2/16 = 1/8

Your twin is likely to visit the dentist more frequently than you due to the difference in insurance plans.

Based on the given information, your insurance plan has a fixed copay of $40 for each doctor's visit, while your twin's copay is 20% of the total cost. Considering the local dentist charges $150 for a cleaning, you would pay a fixed copay of $40 regardless of the total cost. On the other hand, your twin's copay would be 20% of $150, which amounts to $30. Therefore, your twin would have a lower out-of-pocket expense for each dentist visit compared to you.

Due to the lower copay, your twin is more likely to visit the dentist more frequently. The difference in copayments means that your twin would save $10 on each visit, making it more cost-effective for them to seek dental care. This financial advantage would incentivize your twin to take better advantage of their insurance plan and visit the dentist more often.

Based on this reasoning, it is unlikely that you and your twin would visit the dentist the same number of times. Furthermore, there is no indication in the given information that your twin would switch insurance plans, as their plan offers a more favorable copayment structure for dental visits.

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Answer:

c. Yes because ∠2 and ∠6 are congruent.

Step-by-step explanation:

From the picture attached,

m(∠2) = m(∠3) = m(∠6) = 40°

m(∠1) = 140°

Since (∠2 ≅ ∠6) (corresponding angles)

Therefore, by the converse theorem of corresponding angles lines c and d are parallel.

Option c is the answer.

Check the picture below.

well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}\)

Answer:

angle CED 90°. CE = 21. EB = 8.

Step-by-step explanation:

angle CED = 90° (right angle).

the radius (centre to edge) is the same right around the circle.

so that means that distance CD = 29.

draw a line from C to D. notice how that has just become an hypotenuse?

we know that DE = 20.

we have a right-angled triangle.

CE² = hypot² - DE²

       = 29² - 20²

       = 841 - 400

       = 441

CE = √441 = 21.

EB must be radius subtract CE. that is, 29 - 21 = 8.

Identifying Eigenvalues and Eigenvectors, A should be a n x n matrix. By resolving the det(λI−A)=0 problem, first determine the eigenvalues of A. Find the fundamental solutions to (λI−A)X=0 to determine the fundamental eigenvectors X≠0 for each.

In linear algebra, a nonzero vector is said to have an eigenvector, or characteristic vector, when a linear transformation is applied to it; this characteristic vector only changes by a scalar amount. The scaling factor for the eigenvector is known as the associated eigenvalue, frequently represented by the symbol. Linear transformations are made intelligible by the usage of eigenvectors. Eigenvectors can be thought of as a non-directional stretching or compressing of an X-Y line chart. In mathematics, eigenvalues are regarded as the factor by which a transformation is stretched, whereas eigenvectors are the real non-zero eigenvalues that point in the direction stretched by the transformation. The direction of the transformation is negative if the eigenvalue is negative.

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Answer: y = -1

Step-by-step explanation:

Coordinate: (-3, -1)

Slope: Parallel to y axis, 0 slope.

Plug in the numbers to slope-intercept form: -1 = 0(-3) + b (b is the y-intercept)

Solve for b:

-1 = 0(-3) + b

-1 = b

Final Equation: y = -1

The faster cyclist's speed is 46 km/hr and the slower cyclist's speed is 36 km/hr.

Let the speed of the faster cyclist be x km/hr. Then the speed of the slower cyclist is x-10 km/hr.
As they are travelling towards each other, their relative speed will be the sum of their speeds. So,
Relative speed = x + (x-10) = 2x - 10 km/hr
Time taken to meet = 5 hours
Distance travelled = relative speed x time taken
210 = (2x-10) x 5
Solving for x, we get x = 46 km/hr (approx.)
Therefore, the faster cyclist's speed is 46 km/hr and the slower cyclist's speed is 36 km/hr.

To solve this problem, we need to use the formula Distance = Speed x Time. Since the two cyclists are travelling towards each other, we need to find their relative speed by adding their speeds. Then we can use the distance and time given to calculate their speeds individually using the formula Speed = Distance / Time.

The faster cyclist is travelling at a speed of 46 km/hr, while the slower cyclist is travelling at a speed of 36 km/hr.

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