Write the equation of the line that passes through the points (3, 4) and (5, 8)

Answer:

i don't know either

Step-by-step explanation:

Answer:

\(\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}\)

Step-by-step explanation:

We can use the following trigonometrical identity:

\(\sin (\alpha - \beta) = \sin \alpha \cdot \cos \beta - \cos \alpha \cdot \sin \beta\) (1)

Where \(\alpha\), \(\beta\) are angles, measured in sexagesimal degrees.

If we know that \(\alpha = 135^{\circ}\) and \(\beta = 30^{\circ}\), then the value of the given function is:

\(\sin 105^{\circ} = \sin 135^{\circ}\cdot \cos 30^{\circ} - \cos 135^{\circ}\cdot \sin 30^{\circ}\)

\(\sin 105^{\circ} = \left(\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{\sqrt{3}}{2}\right)-\left(-\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{1}{2}\right)\)

\(\sin 105^{\circ} = \frac{\sqrt{6}}{4}+\frac{\sqrt{2}}{4}\)

\(\sin 105^{\circ} = \sqrt{\frac{6}{16} }+\sqrt{\frac{2}{16} }\)

\(\sin 105^{\circ} = \sqrt{\frac{3}{8} }+\sqrt{\frac{1}{8} }\)

\(\sin 105^{\circ} = \frac{\sqrt{3}+1}{2\cdot \sqrt{2}}\)

\(\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}\)

Answer: D) sqrt(2 + sqrt3)/2

Step-by-step explanation: Nah

Answer:

5.6ft squared

Step-by-step explanation:

4x7 = 28 divided by 5 which is 5.6

They send 32 coupons to existing members. Option C is correct.

What is a linear equation in two variables?

A Linear equation in two variables x and y is of the form

Ax + By = C.

Given,

They provide 5 times as many to potential members than existing members.

Let, there are y potential members and x existing members.

Therefore, x + 5y = 192

Also, x and y are whole numbers.

Hence, x=32 satisfy the equation.

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Answer:

732×pi cm³

Step-by-step explanation:

we have all the data and the formula.

so, we only need to do the raw calculations.

Vc = pi×r²×h/3

r = the radius of the basic circle

h = the height.

since the volume of the frustum is the volume of the large cone minus the volume of the small cone, we need to calculate both volumes and then subtract the smaller from the larger number.

oh, and we need to calculate also the radius of the base circle of the small cone. since they are similar bodies, all lines use the same ratio or scaling factor to convert from one cone to the other.

that includes height and radius.

we know the height of the large cone is 16+4=20 cm.

and set know that the height of the small cone is 16 cm.

so, the scaling factor is 16/20 = 4/5 to go from the large to the small cone.

that means that the radius of the small cone is

15 × 4/5 / 3×4 = 12 cm

so, now to the 2 cone volumes :

the large cone

Vcl = pi×15²×20/3 = pi×225×20/3 = pi×75×20 =

= pi×1500 cm³

the small cone

Vcs = pi×12²×16/3 = pi×144×16/3 = pi×48×16 =

= pi×768 cm³

the volume of the frustum is therefore

Vf = Vcl - Vcs = 1500×pi - 768×pi = 732×pi cm³

Hope it Helps

Mark me as brainliest please

Answer:

18 = 3y - 39

3y = -39+18 = -21

3y - 21

y = 21 - 3

y = 19

Answer:

∑[ (250)2 (400)2 (250)2 (350)^2 (100)2 (50)2] = 420,000.

Step-by-step explanation:

You first calculate the mean which is  is 2150.

You then subtract 2150 from the 6 values in turn

The first one = 2400 - 2150 = 250.

Then you square each of the 6 results and add them up - this comes to 420,000.

The final answer is (b), a z-score of 1.645 separates the top 5% from the remainder of the distribution in a normal distribution.

The z-score that separates the top 5% from the remainder of the distribution is found by looking up the area in the standard normal distribution table.

The normal distribution is a continuous probability distribution that is commonly used in statistical analysis. It is a symmetric bell-shaped curve that describes a large number of natural phenomena, such as human heights, test scores, and measurements of physical phenomena. The distribution is characterized by its mean and standard deviation.

The area in the tail of the distribution is 0.05, which corresponds to a z-score of approximately 1.645.

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The solution to the initial value problem is given by:

ln|u| = -t + ln(2)

|u| = e^(-t + ln(2))

|u| = e^(ln(2)/e^t)

u = ± e^(ln(2)/e^t)

To determine the solution to the given initial value problem using the previous exercise, we need to find the characteristics of the equation and solve them.

The characteristic equations corresponding to the given partial differential equation are:

dx/dt = 1, dt/dt = u^2, du/dt = -u

From the second equation, we have dt/u^2 = dx. Integrating both sides gives us t = -1/(3u) + C1, where C1 is a constant of integration.

From the first equation, dx/dt = 1, we have dx = dt. Integrating both sides gives us x = t + C2, where C2 is another constant of integration.

From the third equation, du/dt = -u, we have du/u = -dt. Integrating both sides gives us ln|u| = -t + C3, where C3 is another constant of integration.

Now let's use the initial condition u(x,0) = 2 to find the values of the constants C1, C2, and C3.

When t = 0, x = 0 (since x > 0 for all x in R), and u = 2. Substituting these values into the characteristic equations, we get:

C1 = -1/6

C2 = 0

ln|2| = C3

C3 = ln(2)

Therefore, the solution to the initial value problem is given by:

ln|u| = -t + ln(2)

|u| = e^(-t + ln(2))

|u| = e^(ln(2)/e^t)

u = ± e^(ln(2)/e^t)

Since we know that u(0) = 2, we can take the positive sign to obtain:

u = e^(ln(2)/e^t)

So the solution to the initial value problem is u(x, t) = e^(ln(2)/e^t).

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Answer:

they both are multiplucation Which means they both increse so ether the answers are wrong or the question its self is wrong.

Answer:480cm^3

Step-by-step explanation:

the length of the repel line needed is approximately 44 feet (rounded to the nearest whole number).

what is length ?

Length is a physical dimension that describes the extent of an object or distance between two points. In geometry, length refers to the distance between two points, and it is usually measured in units of length such as meters, centimeters, feet, inches,

In the given question,

(a) The correct trigonometric ratio to use in this problem is the sine ratio, which relates the opposite side to the hypotenuse in a right triangle. In this case, we are given the angle A and we want to find the length of the opposite side, which is the distance from the top of the ravine to Lucy. Therefore, we can use the sine ratio as follows:

sin(A) = opposite/hypotenuse

(b) We can set up the equation using the given information as follows:

sin(17°) = opposite/150

where opposite is the length of the repel line that we want to find.

(c) To solve for the length of the repel line, we can rearrange the equation as follows:

opposite = sin(17°) x 150

opposite = 0.2924 x 150

opposite ≈ 44

Therefore, the length of the repel line needed is approximately 44 feet (rounded to the nearest whole number).

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Answer:

Step-by-step explanation:

well the x is 1/1 and the 2 is over 1 so divided and it is B is what i got

The area of a circle with diameter 22 is 380.1

Answer:

18 milky ways = 60%

3 twix = 10%

9 snickers = 30%

Step-by-step explanation:

18/30 = 0.6

0.6 x 100 = 60%

3/30 = 0.1

0.1 x 100 = 10%

9/30 = 0.3

0.3 x 100 = 30%

Given treatment and placebo group dataThe null and alternative hypotheses for the test of claim that two samples are from populations with the same mean are as follows:A. H0: μ1 = μ2B. H0: μ1 = μ2 , H1: μ1 ≠ μ2  C. H0: μ1 < μ2D. H0: μ1 ≠ μ2H1: μ1 > μ2H1: μ1 < μ2Calculation of degrees of freedom is given bydf = n1 + n2 - 2 = 30 + 25 - 2 = 53

The two samples have a normal distribution and standard deviations are not equal, therefore the two-sample t-test is used for testing the hypothesis.Hypothesis testing is done as follows: t = (x1 - x2) - (μ1 - μ2) / sqrt [ s1^2 / n1 + s2^2 / n2] where x1 - x2 = -1.2 (from the table), μ1 - μ2 = 0 (given), s1^2 = 7.2 and s2^2 = 10.6, n1 = 30 and n2 = 25.

Substituting the values in the formula, we get,t = (-1.2 - 0) / sqrt [ 7.2^2 / 30 + 10.6^2 / 25]t = -1.47Test statistic = -1.47 and degrees of freedom = 53.

Using a t-distribution table, we get that the p-value is 0.073.

As the p-value is greater than the level of significance, we fail to reject the null hypothesis. Therefore, the claim that the two samples are from populations with the same mean is not rejected. Answer more than 100 words

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The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

Answer:

slope = 25

Step-by-step explanation:

Using The slope intercept formula y = mx + b whereas m is the slope and b is the y-intercept

so y = 25x + 15

=> m = 25

Answer:

17b + bx + a over 34 =x

Answer:

Shoot I don't know but this is as far as I got until I got confused.

Step-by-step explanation:

17b + bx = 24x - a

-17b        =   - 17b

-24x       =   -24x

------------------------------

-24x + bx = -17b - a

-24x + bx/b = -17b/b - a/b

-24x + x = -17b - a/b

-23x = -17b - a/b

-23x/-23 = -17b/-23 - a/b/-23

x =

Answer:

114 mi

Step-by-step explanation:

\(6h*\frac{19 mi}{h}\)=\(\frac{6h*19mi}{h} \frac{6*19mi}{1} =114mi\)

Dr. Fahrrad breaks down 0.23 moles of ATP to get to work.

The first step is to calculate the work done by Dr. Fahrrad on his bike ride. We can use the following equation:

W = F * d

where:

W is the work done in joules

F is the force in newtons

d is the distance in meters

The force is equal to the mass of Dr. Fahrrad times his acceleration. We can convert the acceleration from kilometers per second squared to meters per second squared by multiplying by 1000/3600. This gives us a force of 102.8 newtons.

The distance of Dr. Fahrrad's bike ride is 4.6 kilometers, which is equal to 4600 meters.

Plugging these values into the equation for work, we get:

W = 102.8 N * 4600 m = 472320 J

The breakdown of a mole of ATP releases 29 kilojoules of energy. So, the number of moles of ATP that Dr. Fahrrad breaks down is:

472320 J / 29 kJ/mol = 162.6 mol

To one decimal place, this is 0.23 moles of ATP.

Here are the assumptions that we made in this calculation:

No friction

No mass of the bike

A flat ride with no change in altitude

These assumptions are not always realistic, but they are a good starting point for this calculation. In reality, Dr. Fahrrad would probably break down slightly more than 0.23 moles of ATP to get to work.

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Answer:

Sorry about the person above. The answer would be:

C. \(3x + 2y = 22\) and \(5x + 2y = 39\)

Explanation:

I just did the test.

Answer:

C

Step-by-step explanation:

1) The value of the missing variables x and y are; y = 21°, x = 45°

2) The value of the variable x and the angle are; x = 6 and ∠ABC = 108°

3) Supplement of 51° is 129°

Complement of  51° is 39°

1) We know that sum of angles on a straight line is 180°.

We see that ∠QNP and ∠QNM form a straight line and so;

∠QNP + ∠QNM = 180°

3y + 34 + 4y - 1 = 180

7y = 180 - 33

7y = 147

y = 21°

Similarly;

3x - 52 + 2x + 7 = 180

5x - 45 = 180

5x = 225

x = 225/5

x = 45°

2) We are told that the line BD bisects ∠ABC where;

m∠ABD = 9x°

m∠DBC = (4x + 30)°

Thus;

9x = (4x + 30)°

9x - 4x = 30

5x = 30

x = 30/5

x = 6

Thus;

∠ABC = 9(6) + (4(6) + 30)°

∠ABC = 108°

3) We are given the angle as 51°.

Now, supplementary angles sum up to 180° while complementary angles sum up to 90°. Thus;

Supplement = 180 - 51 = 129°

Complement = 90 - 51 - 39°

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Answer:

the answer is 7 it always is.

Answer:

the 4th one

Step-by-step explanation:

it says "maximum" and maximum is equal to or more than.

Without even reading the rest of the question, you should be able to tell that the answer is 3x + 3.50y ≤ 50.

This symbol ≤ means "less than or equal to." In the question, it mentions that he has a maximum of $50 to spend which tells us that the cost has to be less than $50 but can be exactly $50.

You can then use the other information to verify your answer. Lilies are represented by the variable \(x\) and costs $3.00 each, so it makes sense that the formula says \(3x\). Roses on the other hand is represented by the variable \(y\\\) and costs $3.50 each, so it makes sense that the formula says \(3.50y\).

Answer:

67 degrees

Step-by-step explanation:

Angle 2 and angle 7 are vertical angles since l is the transversal.

so that means <2=<7

4x+39=12x-17

Simplify: isolate the variable:

56=8x

divide by 8:

7=x

now plug it in to m<2

4(7)+39=m<2

28+39

67=m<2

i hope this helps!

Answer:

\( {x}^{2} - 12x + 23 = 0\)

\( {x}^{2} - 12x = - 23\)

\( {x}^{2} - 12x + 36 = 13\)

\( {(x - 6)}^{2} = 13\)

x - 6 = +√13

x = 6 + √13

Converting the force from newtons to pounds can help us determine the chances of a driver being able to stop a child. The conversion factor is 1 pound (lb) = 4.45 newtons (N).

To convert the force from newtons to pounds, we use the conversion factor of 1 lb = 4.45 N. If we have a force in newtons, we can divide it by 4.45 to obtain the equivalent force in pounds. For example, if the force is 20 N, we divide it by 4.45 to get approximately 4.49 lb.

Now, in order to assess the chances of the driver stopping the child, we need to consider various factors such as the mass and speed of the child, the friction between the driver's shoes and the ground, and the force applied by the driver. If the force applied by the driver, converted to pounds, is greater than or equal to the force exerted by the child, there is a higher chance of stopping the child.

However, it's important to note that other factors, such as the driver's reaction time and the coefficient of friction between the shoes and the ground, also play significant roles in determining the outcome. Thus, the chances of the driver stopping the child depend on a combination of these factors, making it essential to consider them comprehensively when evaluating the situation.

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Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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