{y=6x+14
{2x-y=2



thanks bud lol

Answer:

E

Step-by-step explanation:

Since rectangle have 90 degree angles, Angle D is a 90 degree angle.

Side CD is 3

AD is 4

We found both of those using the definition of rectangle.

\( \tan(x) = \frac{opp}{adj} \)

\( \tan(x) = \frac{4}{3} \)

E is correct

Answer:

see explanation

Step-by-step explanation:

Calculate AC and AB using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = A(1,8) and (x₂, y₂ ) = C(4,2)

AC = \(\sqrt{(4-1)^2+(2-8)^2}\)

      = \(\sqrt{3^2+(-6)^2}\)

       = \(\sqrt{9+36}\)

       = \(\sqrt{45}\) = \(\sqrt{9(5)}\) = 3\(\sqrt{5}\)

Repeat with

(x₁, y₁ ) = A(1, 8) and (x₂, y₂ ) = B(2, 6)

AB = \(\sqrt{(2-1)^2+(6-8)^2}\)

      = \(\sqrt{1^2+(-2)^2}\)

       = \(\sqrt{1+4}\)

       = \(\sqrt{5}\)

So AB = \(\sqrt{5}\) and AC = 3\(\sqrt{5}\)

Thus

AC = 3AB

Answer:

Proven below

Step-by-step explanation:

Distance Between Points in the Plane

Given two points A(x,y) and B(w,z), the distance between them is:

\(d=\sqrt{(w-x)^2+(z-y)^2}\)

Let's calculate the distance AC, where A(1,8) and C(4,2):

\(d_{AC}=\sqrt{(4-1)^2+(2-8)^2}\)

\(d_{AC}=\sqrt{3^2+(-6)^2}\)

\(d_{AC}=\sqrt{9+36}=\sqrt{45}\)

Since 45=9*5:

\(d_{AC}=\sqrt{9*5}=3\sqrt{5}\)

Calculate the distance AB, where A(1,8) and B(2,6)

\(d_{AB}=\sqrt{(2-1)^2+(6-8)^2}\)

\(d_{AB}=\sqrt{1^2+(-2)^2}\)

\(d_{AB}=\sqrt{1+4}=\sqrt{5}\)

It follows that:

\(d_{AC}=3d_{AB}\)

(i × j) × k = 0, is the vector, not with determinants, but by using properties of cross products.

The procedure for multiplying two vectors is called the cross product of the two vectors. The sign(×) of multiplication between two vectors indicates a cross product. It is a three-dimensional system-defined binary vector operation.

A cross product in three dimensions is a binary operation on two vectors. It generates a vector that is parallel to both vectors. A and B together form a vector product, which is represented by the symbol a b. The vector that results from it is parallel to both a and b. Cross products and vector products are similar terms.

As we know,

i × j = | i | × | j | × sin 90° × k

or, i × j = 1 × 1 × 1 × k

or, i × j = k

thus,  (i × j) × k = k × k

or,  (i × j) × k = 0

To know more about cross products refer to:

https://brainly.com/question/29178479

#SPJ4

Answer:

c=263

Step-by-step explanation:

Answer:

Step-by-step explanation:

50^2 is 2500, 3 times that is 7500, minus 1 and the answer would be 7499

The number of rotations made by the pulley in hour is 16 rotations

Front the question given above, the following data were obtained:

We'll begin by calculating the time to rotate 360 degrees since a complete rotation has an angle of 360 degrees. This can be obtained as illustrated below:

97 degree rotation = 1 mimute

Therefore,

360 degrees = 360 / 97

360 degrees = 3.71 minutes

The number of rotation made in 1 hour (i.e 60 minutes), can be obtained as follow:

3.71 mins = 1 rotaion

Therefore,

60 mins = 60 / 3.71

60 mins = 16 rotations

Thus, the pulley will made an approximate of 16 rotations in 1 hour

Learn more about rotation of pulley:

https://brainly.com/question/18651351

#SPJ4

Thus, , the physical therapist should form a sample size of 601 to determine the difference in the proportion of men and women.

To determine the sample size needed for a physical therapist to estimate the difference in the proportion of men and women participating in regular sustained physical activity within four percentage points and with 95% confidence, we can use the formula for sample size estimation in proportion-based studies.

The formula is: n = (Z^2 * p * (1-p)) / E^2

Where:
- n is the sample size
- Z is the Z-score for the desired confidence level (1.96 for 95% confidence)
- p is the estimated proportion (use 0.5 if no prior information is available)
- E is the margin of error (0.04 for four percentage points)

Plugging in the values, we get:

n = (1.96^2 * 0.5 * 0.5) / 0.04^2
n ≈ 600.25

Since the sample size must be a whole number, we round up to the nearest whole number, which is 601.

Therefore, the physical therapist should obtain a sample size of 601 to estimate the difference in the proportion of men and women participating in regular sustained physical activity within four percentage points and with 95% confidence.

Know more about the sample size

https://brainly.com/question/28583871

#SPJ11

Answer:

C 40 inches

Step-by-step explanation:

You can use the pythagorean theorem to solve for the second leg. When you plug in 42 for a and 58 for c, you get 42^2 + b^2 = 58^2, then you can isolate b, which should be 40 inches.

Answer:

10,305.99 cm^3

Step-by-step explanation:

V=4/3πr^3=4/3·π·13.5^3≈10305.9947

Answer:

523.5988in³

Step-by-step explanation:

input Data :

Length = 5 in

Objective :

Find what is volume of the sphere for given input data?

Formula :

Volume =

4πr3

3

Solution :

Volume =

4 x 3.1416 x 53

3

=

4 x 3.1416 x 125

3

=

1570.7963

3

Volume = 523.5988 in³

A) The annual growth rate between 1993 and 2004, is approximately 5.68%.  B) Converting the growth rate from part A to percentage form, is approximately 5.68%.  C) Assuming the house value continues to grow at the same annual growth rate, the estimated value in the year 2009 would be approximately $215,000

A) The annual growth rate between 1993 and 2004, assuming exponential growth, can be calculated using the formula: growth rate = (final value / initial value) ^ (1 / number of years) - 1. In this case, the initial value is $95,000, and the final value is $165,000. The number of years is 2004 - 1993 = 11. Plugging these values into the formula, we get: growth rate = (165,000 / 95,000) ^ (1 / 11) - 1 ≈ 0.0568.

B) Converting the growth rate from part A to percentage form, we multiply it by 100. Therefore, the correct answer in percentage form is approximately 5.68%.

Now let's move on to part C. Assuming the house value continues to grow at the same percentage, we can calculate the value in the year 2009. We know that the value in 2004 was $165,000. To find the value in 2009, we need to calculate the growth over a period of 5 years. Using the growth rate of 5.68% (or 0.0568 as a decimal), we can calculate the value in 2009 as follows: value in 2009 = value in 2004 (1 + growth rate) ^ number of years = 165,000 (1 + 0.0568) ^ 5 ≈ $215,291.

learn more about growth rate here:

https://brainly.com/question/18485107

#SPJ11

The parallels and transversal is discussed above.

Parallel lines - Two lines are said to be parallel if they never intersect each other.

Transversal line - In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points.

Given are parallel lines and a transversal line.

When a transversal line that passes through the pair of parallel lines, it forms 8 angles. We can write them as -

Therefore, the parallels and transversal is discussed above.

To solve more questions on transversal line, visit the link below -

https://brainly.com/question/29478231

#SPJ1

Answer:

No!!

Step-by-step explanation:

For every 1 pound it costs $2⁵⁰

For every 2 pounds it costs $5⁰⁰

For every 3 pounds it costs $7⁵⁰

and so on going by 2.50 each pound.

Answer:

C. b = 0 and b = 4

Trust me, I know its right :)

Answer:

b = 0,4

Step-by-step explanation:

_______________________________________________
(5)/(3b^(3)-2b^(2)-5)=(2)/(b^(3)-2)

you can solve by cross multiplying

5(b^3-2)=2(3b^3-2b^2-5)

use distributive property which you get 5b^3-10=6b^3-4b^2-10

and you can solve it from that point.
________________________________________________

Answer:

I think 334 is the answer

The values of θ in [0,2π] that satisfy the equation sin(3x) = (√3)/2 are:

θ = π/9, π/3, 5π/9, 2π/3, 7π/9, 4π/3, 11π/9, 5π/3.

We can begin by taking the inverse sine of both sides to isolate the variable:

sin(3x) = √3/2

arcsin(sin(3x)) = arcsin(√3/2)

3x = π/3 + 2πn or 3x = 5π/3 + 2πn   where n is an integer

Dividing through by 3 gives us:

x = π/9 + (2π/3)n or x = 5π/9 + (2π/3)n

To find all values of θ in [0,2π], we can simply substitute the values of n that satisfy this condition into our solutions for x:

x = π/9 + (2π/3)n, n = 0,1,2

x = 5π/9 + (2π/3)n, n = 0,1,2

Thus, the values of θ in [0,2π] that satisfy the equation sin(3x) = (√3)/2 are:

θ = π/9, π/3, 5π/9, 2π/3, 7π/9, 4π/3, 11π/9, 5π/3

Learn more about   equation here:

https://brainly.com/question/10724260

#SPJ11

The theoretical probability of event E, denoted by P(E), is the number of favorable outcomes divided by the total number of possible outcomes.

The theoretical probability of an event E, denoted by P(E), is the ratio of the number of favorable outcomes to the total number of possible outcomes in a given sample space.

In other words, it represents the likelihood of occurrence of event E based on the underlying theoretical assumptions.

Theoretical probability is derived from a theoretical or mathematical model and is based on the assumption that all outcomes in the sample space are equally likely.

It provides a theoretical expectation of the probability of an event occurring under ideal conditions.

To calculate the theoretical probability, we divide the number of favorable outcomes (the outcomes that meet the criteria for event E) by the total number of possible outcomes in the sample space.

This ratio represents the probability of event E occurring.

For example, if we have a fair six-sided die and we want to calculate the theoretical probability of rolling a 3, there is only one favorable outcome (rolling a 3) out of six possible outcomes (numbers 1 to 6).

Therefore, the theoretical probability of rolling a 3 is 1/6 or approximately 0.1667.

It's important to note that theoretical probability assumes ideal conditions and equal likelihood of all outcomes, which may not always reflect the real-world situation.

In practice, empirical probability based on observed frequencies is often used when actual data is available.

In summary, the theoretical probability of event E is the ratio of the number of favorable outcomes to the total number of possible outcomes in the sample space, providing a mathematical estimate of the likelihood of event E occurring.

To know more about theoretical probability refer here:
https://brainly.com/question/30604977#

#SPJ11

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

To know more about trigonometric visit :

https://brainly.com/question/29156330

#SPJ11

The group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

The correct inequality is B. 1.4x + 0.75y ≥ 150. This inequality states that the group must sell at least $150 worth of items in order to make a profit. The cost of a granola bar is $1.40, and the cost of a bottle of water is $0.75. Therefore, the total cost of the items must be greater than or equal to $150. The formula for this inequality is 1.4x + 0.75y ≥ 150, where x represents the number of granola bars sold and y represents the number of bottles of water sold.

To solve this inequality, we can first multiply both sides of the inequality by 100. This will give us 140x + 75y ≥ 15000. Next, we can subtract 75y from both sides to get 140x ≥ 14250. Finally, we can divide both sides of the equation by 140 to get x ≥ 102.86. This means that the group needs to sell at least 103 granola bars in order to make a profit of at least $150. This can be further simplified by rounding up the granola bars sold to 104. Therefore, the group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

Learn more about inequality here :

https://brainly.com/question/20383699

#SPJ4

Answer:

The absolute value is 8

Step-by-step explanation:

the absolute value of a number is always going to be positive. if you have a negative number and need the absolute number, you just put the opposit of the number.

Answer:

The absolute value is 8

Answer:

The second and the third options are the correct answers.

Step-by-step explanation:

For the second option, 8 times 3 would equal 24, and z^7 and z^4 would have its exponents to be added together to form a final answer of 24z^11.

For the third option, 9 and -3 would multiply to equal -27. a^5 and a^2 would multiply, causing their exponents to be added. The final answer for the third option would then be -27a^7

Answer: 10, 5, and 2

Step-by-step explanation: they're all divisible numbers and could lead up to some sort of possibility of how much candy is in each barrel

To express a product as a sum or difference containing only sines or cosines, we can use trigonometric identities such as the sum and difference identities. These identities allow us to rewrite products involving sines and cosines as sums or differences of sines or cosines.

Let's consider an example:

Suppose we have the product cos(x)sin(x). We can rewrite this product using the double angle identity for sine:

cos(x)sin(x) = (1/2)sin(2x)

In this case, we have expressed the product as a sum of sines.

Similarly, if we have the product sin(x)cos(x), we can use the double angle identity for cosine:

sin(x)cos(x) = (1/2)sin(2x)

In this case, we have also expressed the product as a sum of sines.

In summary, to express a product as a sum or difference containing only sines or cosines, we can use trigonometric identities like the double angle identity for sine or cosine. By applying these identities, we can rewrite the product in terms of sums or differences of sines or cosines.

Know more about  trigonometric identities here,

https://brainly.com/question/24377281

#SPJ11

The given statement is True because If the sample mean is close to the population parameter, it suggests representative sampling regarding the variable of interest, although other factors should be considered too.

When the sample mean closely approximates the population parameter, it indicates that the sample is capturing the central tendency of the population. The mean is a measure of central tendency that reflects the average value of the variable of interest in the population.

If the sample mean is similar to the population mean, it suggests that the sample is a good representation of the population in terms of that particular variable.

However, it is important to note that representativeness is a relative concept. A sample may be considered representative in one sense but not necessarily in all aspects. Other factors, such as the sampling method, sample size, and sampling bias, also influence the representativeness of a sample.

In summary, when the obtained mean of the observations in a research study is close to the population parameter, it provides evidence that the sample is representative of the target population to some degree, indicating that the sample captures the central tendency of the population for the variable under investigation.

However, representativeness should be assessed in consideration of other factors as well.

For more question on population visit:

https://brainly.com/question/30396931

#SPJ8

Answer:

1 : 4

Step-by-step explanation:

Triangles : Total Shapes

3 : 12

1  : 4

*reduce as if it was the fraction \(\frac{3}{12}\), because fractions are ratios, and ratios are fractions. They're the same thing written in different ways*

Answer: 168 people

Step-by-step explanation:

If 120 people attended on Friday, 120% of that will be:

= 120 * 140/100

= 168 people

The true mean sleep time of the population is believed to fall between 6.03 and 6.97 hours at the 96 percent confidence level based on Aaron's sample.

Based on his sample, Aaron computed t* to be 2.22. The t-value may be used to construct the confidence interval as follows:

Mean ± t* (standard error) Where the standard error is the standard deviation divided by the square root of the sample size.

Mean = 6.5

Standard deviation = 2.14

Sample size = 101

t* = 2.22

Standard error = standard deviation / sqrt (sample size)

= 2.14 / sqrt (101) = 0.21

The confidence interval may now be computed as follows:

6.5 ± 2.22 (0.21)

6.5 ± 0.47

= (6.03, 6.97)

To know more about standard deviation visit:

https://brainly.com/question/13498201

#SPJ11

Answer:

angle CDE

Step-by-step explanation:

there are two triangles in that whole diagram the first is: CAB then if you look care there is angle CDE so try next time to closely see the similiar triangle.

The mass of the bicycle rider is approximately 68.75 kg.

Kinetic energy  is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. The formula for kinetic energy is:

Kinetic Energy = 1/2 * mass * velocity²

where mass is the mass of the object and velocity is the speed at which it is moving. Kinetic energy is a scalar quantity and is measured in joules (J) in the SI system.

We can use the formula for kinetic energy to solve for the mass of the bicycle rider:

Kinetic Energy = 1/2 * mass * velocity²

Substituting the given values, we have:

550 J = 1/2 * mass * (4 m/s)²

Simplifying and solving for mass, we get:

mass = 550 J / (1/2 * (4 m/s)²

mass = 550 J / (8 kg m²/s²

mass = 68.75 kg

Therefore, the mass of the bicycle rider is approximately 68.75 kg.

To learn more about kinetic energy, visit the link:

https://brainly.com/question/25959744

#SPJ1

Hello and greetings lilliepruiett.

The mass of the cyclist who is going at 4 m/s, and who has a kinetic energy of 550 Joules, is 68.75 kilograms.

It is an exercise of kinetic energy, which is the energy that an object possesses due to its movement. It is defined as the energy required to accelerate an object of a given mass from rest to its current speed. Kinetic energy can be calculated using the following formula:

Ek = (m × v²)/2

where:

This formula indicates that the kinetic energy increases as the mass of the object increases and/or its speed increases. Kinetic energy is a direct measure of an object's ability to do work due to its motion.

We have that the cyclist is going at a speed of 4 m/s, when his kinetic energy is 550 Joules, we calculate the mass.

As we are asked to calculate the mass, we solve the formula:

What we do now is; substitute the data into the cleared formula and solve for the mass of the cyclist.

m = (2 * Ek)/v²

m = (2 × 550 J)(4 m/s)²

m = (1100 J)/(16 m²/s²)

m = 68.75 kg

The mass of the cyclist who is going at 4 m/s, and who has a kinetic energy of 550 Joules, is 68.75 kilograms.

＼(^_^ )If you want to learn more, I share this link to complement your learning:

https://brainly.com/question/21831383

Answer:

two hundred eighty two dollars