If x - 4y = -10 and 2x + 9y= -3 are true equations, what would be the value of 3x+5y?​

The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.

To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.

Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.

Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.

Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.

Therefore, the correct answer is option c. π/4.

To know more about circle refer here:

https://brainly.com/question/11987349

#SPJ11

Answer:

The answer 5 Nickels and 4 Quarters

Step-by-step explanation:

The reason for this answer is simple I will do the math real quick.

So you have 5 nickels right so 5(5) would be your equation which equals 25.

Alright so for the quarters the equation is 4(25) which equals 100.

Now if you take 100 and add 25 to it you will get 125 which means problem solved hope this helped.

False. The correlation coefficient can vary between -1 and 1, and it can be negative.

The correlation coefficient is a statistical measure that quantifies the strength and direction of the relationship between two variables. It ranges from -1 to 1, inclusive. A value of 1 indicates a perfect positive correlation, meaning that as one variable increases, the other variable increases proportionally. A value of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other variable decreases proportionally. A correlation coefficient of 0 indicates no linear relationship between the variables.

Therefore, the statement that the correlation coefficient varies between 0 and 1 and can never be negative is false. The correlation coefficient can indeed be negative, indicating a negative relationship between the variables. It is important to note that the correlation coefficient only measures the strength and direction of the linear relationship between the variables and does not capture other types of relationships, such as non-linear or causal relationships.

Learn more about correlation coefficient here:

brainly.com/question/29978658

#SPJ11

Answer:

x² + 9x + 15

Step-by-step explanation:

Given

(2x + 3)² - 3(x - 1)(x + 2) ← expand factors using FOIL

= 4x² + 12x + 9 - 3(x² + x - 2) ← distribute

= 4x² + 12x + 9 - 3x² - 3x + 6 ← collect like terms

= x² + 9x + 15

The economic significance suggested by the slope coefficient helps you determine whether the coefficient implies a "big" effect of X on Y.

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. 

Given

The slope coefficient suggests economic significance.

The economic significance suggested by the slope coefficient helps you determine whether the coefficient implies a "big" effect of X on Y.

To know more about slope visit :-

https://brainly.com/question/3605446

#SPJ4

Answer:

15minutes / 2miles = 7.5 minutes to run a single mile.

7.5minutes * 5miles = 37.5minutes

37.5minutes to run 5 miles

Step-by-step explanation:

Answer:

A. 12

Step-by-step explanation:

I hope this helps!

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

for such more question on lengths

https://brainly.com/question/24176380

#SPJ8

The diameter of the gold cylinder ≈ 0.00654 meters.

To determine the diameter of a gold cylinder with the provided length and mass, we can use the formula for the volume of a cylinder and the known mass and length.

Here are the steps to calculate the diameter:

1. Convert the mass from grams to kilograms:

  mass = 17.6 g = 0.0176 kg

2. Convert the length from centimeters to meters:

  length = 5.25 cm = 0.0525 m

3. Determine the density of gold.

The density of gold is typically known to be approximately 19,300 kg/m³.

4. Use the formula for the volume of a cylinder:

  Volume = π * (radius)² * length

Since we want to obtain the diameter, we need to calculate the radius first.

5. Rearrange the volume formula to solve for the radius:

  radius = sqrt(mass / (density * length * π))

6. Substitute the known values into the formula and calculate the radius:

  radius = sqrt(0.0176 kg / (19,300 kg/m³ * 0.0525 m * π))

7. Calculate the diameter by multiplying the radius by 2:

  diameter = 2 * radius

Let's perform the calculations:

radius = sqrt(0.0176 kg / (19,300 kg/m³ * 0.0525 m * π))

radius ≈ 0.00327 m

Now:

diameter = 2 * radius

diameter ≈ 2 * 0.00327 m

diameter ≈ 0.00654 m

To know more about diameter refer here:

https://brainly.com/question/32968193#

#SPJ11

The relative risk of insomnia for those who receive the new drug is approximately 1.72.

To calculate the relative risk of insomnia for those who receive the new drug, we first need to calculate the risk of insomnia in each group.

The risk of insomnia in the new drug group is the number of patients who experienced insomnia in that group divided by the total number of patients in that group:

Risk of insomnia in new drug group = 52/278 = 0.187

The risk of insomnia in the traditional drug group is the number of patients who experienced insomnia in that group divided by the total number of patients in that group:

Risk of insomnia in traditional drug group = 36/331 = 0.109

The relative risk is the ratio of the two risks:

Relative risk = Risk of insomnia in the new drug group / Risk of insomnia in the traditional drug group

Relative risk = 0.187 / 0.109 ≈ 1.72

Therefore, the relative risk of insomnia for those who receive the new drug is approximately 1.72.

For more such questions on Relative risk: brainly.com/question/28499564

#SPJ4

The correct question should be:

Doctors are testing a new antidepressant. A group of patients, all with similar characteristics, take part in the study. Some of the patients receive the new drug, while others receive the traditional drug. During the study, a number of patients complain about insomnia. The data are shown in the contingency table below. What is the relative risk of insomnia for those who receive the new drug? Round to two decimal places.

                                Insomnia     No insomnia      Total

New drug                52                  226              278

Traditional drug        36                  295              331

Total                        88                  521                      609

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

Read more about Linear equation graph at: https://brainly.com/question/28732353

#SPJ1

Answer:

- 2, 7 , - 8

Step-by-step explanation:

substitute the given values of x into the expression

(a)

x = 0 : 3(0) - 2 = 0 - 2 = - 2

(b)

x = 3 : 3(3) - 2 = 9 - 2 = 7

(c)

x = - 2 : 3(- 2) - 2 = - 6 - 2 = - 8

Answer:

Independent variable (thing you change): Hours worked

Dependent variable (thing you measure): Amount paid

Answer: $45  

($30 + $15)

The ratio that best explains why the slope of AB is the same as the slope of AC in similar right triangles ABD and ACE is the ratio of the corresponding side lengths. In similar triangles, corresponding sides are proportional to each other.

This ratio indicates that the slopes of AB and AC are equal because the corresponding side lengths of the similar triangles are proportional.

Let's consider the sides of the triangles that are parallel to the x-axis. In triangle ABD, side AB corresponds to side AC in triangle ACE. Since the triangles are similar, the ratio of the lengths of these sides will be the same as the ratio of their slopes.

Therefore, the ratio of the slopes can be expressed as:

Slope of AB / Slope of AC = Length of AB / Length of AC

This ratio indicates that the slopes of AB and AC are equal because the corresponding side lengths of the similar triangles are proportional.

Learn more about proportional here:

https://brainly.com/question/1496357

#SPJ11

Answer:

6.75

Step-by-step explanation:

The term 6.75 is within absolute value bars. These bars force any term inside of them to be positive. Since 6.75 is already positive, the bars have no effect.

The term 6.75 is already simplified.

Answer:

p = .46E

Step-by-step explanation:

The system that is represented by the graph is inequality 3

What is system of inequalities?

A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem requires a variety of solutions and those solutions must satisfy multiple constraints, systems of inequalities are used.

We are given the graph of inequalities and given 4 choices out which 1 is the correction representation of the inequalities given in the graph

Now As you  can see one the parabolas open downwards that means the term x^2 is negative in that case where as the other parabola opens upwards hence the term x^2 is positive.

So second and third options are the options which satisfies this criteria

if we put x = 0 in the second equation of both the inequalities we get y= 4

This criteria is satisfied by only inequality 3 hence the correct system of inequality is inequality 3

To learn more about system of inequality please refer the following link

https://brainly.com/question/28230245

#SPJ1

Answer:y ≥ x2 – 2x + 4

y < –x2 + 4

Step-by-step explanation:

Answer:

y = 5x - 21

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (5, 4 ) and (x₂, y₂ ) = (8, 19 )

m = \(\frac{19-4}{8-5}\) = \(\frac{15}{3}\) = 5 , then

y = 5x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, 4 ) , then

4 = 5(5) + c = 25 + c ( subtract 25 from both sides )

- 21 = c

y = 5x - 21 ← equation of line

The expression that fails to compute the area of a triangle correctly is option b: (1 / 2) * b * h.

The correct formula to compute the area of a triangle is one-half times the base multiplied by the height, which can be written as (1/2) * b * h. Option a, c, and d correctly represent this formula. However, option b is incorrect because it uses integer division instead of decimal division.

In option b, (1 / 2) is computed using integer division, which results in truncating the decimal part. Therefore, (1 / 2) evaluates to 0 instead of 0.5. As a result, the expression (1 / 2) * b * h would yield incorrect and significantly smaller results than the actual area of the triangle.

To accurately calculate the area of a triangle using this formula, it is essential to use decimal division or explicitly represent the fraction as a decimal. Options a, c, and d correctly account for this by using either 1.0/2.0 or 0.5, ensuring the proper calculation of the area.

Learn more about area of a triangle here:

https://brainly.com/question/27683633

#SPJ11

A second linearly independent solution of y₂ is \(-\frac{1}{6x^3}\)

The general Equation is y" + P(x)y' + q(x)y = 0 ...............(i)

where P(x), Q(x) are continues in the internal I ≤ R.

If y₁(x) is a solution of equation 1 in I then y₁(x) ≠ 0.

Then y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\) is another solution.

The differential equation is x²y" + xy' – 9y = 0 where x > 0.

As y₁(x) = x³ is one solution of differential equation.

Divide throughout by (x²) to given differential equation.

1/x² (x²y" + xy' – 9y = 0)

y" + (y'/x) – (9/x²)y = 0 ................(ii)

By comparing equation (i) & (ii) we get:

p(x)=1/x , q(x)= –are continuous for x>0

So, another solution,

y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\)

Now putting the values of P(x) And Q(x)

y₂(x) = \(x^3\int\limits {\frac{e^{\int(1/x)dx} }{(x^3)^2}} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{\frac{1}{x} }{x^6} }} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{1}{x^7} }} \, dx\)

y₂(x) = \(x^3\int\limits {x^-7} } \, dx\)

y₂(x) = \(x^3\left[\frac{x^{-7+1}}{-7+1}\right]\)

y₂(x) = \(-\frac{1}{6}(x^3\times x^{-6})\)

y₂(x) = \(-\frac{1}{6x^3}\)

So, the answer of this question is \(-\frac{1}{6x^3}\).

To learn more about Differential equation link is here:

brainly.com/question/14620493

#SPJ4

Answer:

9 dam

Step-by-step explanation:

1 km = 100 dam

0.09 km = 0.09 × 100

              = 9 dam

∴ 0.09 km = 9 dam

The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

Learn more about polygons at: https://brainly.com/question/1592456

#SPJ1

Answer:

Step-by-step explanation:

The difference of sales between the first and the second days is the cost of 85 tickets:

Cost of a ticket:

Find the slope of these two points that's the cost

Slope

Answer:  \(-1 \le y \le 1\)

The range is the set of all possible y outputs of a function. The graph shows the smallest possible y value is y = -1, while the largest is y = 1. The value of y can be anything in between.

If you need the range in interval notation, then you would write [-1, 1]. The square brackets indicate we include each endpoint.

Note: This is likely the graph of y = sin(x)

A truck can carry either 576 1-foot boxes, 72 2-foot boxes, or 21 3-foot boxes.

The combination of boxes that will result in the highest payment for one truckload is 89 1-foot boxes, 3 2-foot boxes, and 3 3-foot boxes, for a total payment of $3,422.

To find how many boxes of one type will fill a truck, calculate the volume of the truck and divide it by the volume of one box.

Volume of the truck = 12 ft × 6 ft × 8 ft = 576 cubic feet

Volume of a 1-foot box = 1 ft × 1 ft × 1 ft = 1 cubic foot

Number of 1-foot boxes that will fill the truck = 576 cubic feet / 1 cubic foot = 576 boxes

Volume of a 2-foot box = 2 ft × 2 ft × 2 ft = 8 cubic feet

Number of 2-foot boxes that will fill the truck = 576 cubic feet / 8 cubic feet = 72 boxes

Volume of a 3-foot box = 3 ft × 3 ft × 3 ft = 27 cubic feet

Number of 3-foot boxes that will fill the truck = 576 cubic feet / 27 cubic feet = 21.33 boxes (rounded down to 21 boxes)

Therefore, a truck can carry either 576 1-foot boxes, 72 2-foot boxes, or 21 3-foot boxes.

To determine the combination of box types that will result in the highest payment for one truckload, calculate the total payment for each combination of box types.

Let x be the number of 1-foot boxes, y be the number of 2-foot boxes, and z be the number of 3-foot boxes in one truckload.

The volume of the boxes in one truckload is:

V = x(1 ft)³ + y(2 ft)³ + z(3 ft)³

V = x + 8y + 27z

The payment for one truckload is:

P = 5x + 25y + 100z

To maximize P subject to the constraint that the volume of the boxes does not exceed the volume of the truck:

x + 8y + 27z ≤ 576

Use the method of Lagrange multipliers to solve this optimization problem:

L(x, y, z, λ) = P - λ(V - 576)

L(x, y, z, λ) = 5x + 25y + 100z - λ(x + 8y + 27z - 576)

Taking partial derivatives and setting them equal to zero:

∂L/∂x = 5 - λ = 0

∂L/∂y = 25 - 8λ = 0

∂L/∂z = 100 - 27λ = 0

∂L/∂λ = x + 8y + 27z - 576 = 0

From the first equation, we get λ = 5.

Substituting into the second and third equations, y = 25/8 and z = 100/27. Since x + 8y + 27z = 576, x = 268/3.

Round these values to the nearest integer because no fraction for a box. Rounding down, x = 89, y = 3, and z = 3.

Therefore, the combination of boxes that will result in the highest payment for one truckload is 89 1-foot boxes, 3 2-foot boxes, and 3 3-foot boxes, for a total payment of $3,422.

Find out more on volume here: https://brainly.com/question/27710307

#SPJ1

Answer: 30%

15/50=.3

30%

I hope this is good enough:

Answer:

A i think

Step-by-step explanation:

cause its gonna be more than 6- so yeah if it is right then b

Answer:The amounts of the three parts of the investment are:

x = $14,072.73

y = $3,127.27

z = $24,800

Step-by-step explanation:

Let's assume that the first part of the investment is x.

Then the second part of the investment is y and the third part of the investment is z.

We know that the total investment is $42,000. Therefore:

x + y + z = 42,000

We also know that the total interest earned is $3,480. Therefore:

0.08x + 0.06y + 0.09z = 3,480

Finally, we know that the interest earned from the first investment is 6 times the interest earned from the second investment. Therefore:

0.08x = 6(0.06y)

0.08x = 0.36y

x = 4.5y

Now we can substitute x = 4.5y into the first equation:

4.5y + y + z = 42,000

5.5y + z = 42,000

We can also substitute x = 4.5y into the second equation:

0.08(4.5y) + 0.06y + 0.09z = 3,480

0.36y + 0.06y + 0.09z = 3,480

0.42y + 0.09z = 3,480

Now we have two equations with two variables. We can solve for y in the first equation:

5.5y + z = 42,000

5.5y = 42,000 - z

y = (42,000 - z)/5.5

We can substitute this expression for y into the second equation:

0.42y + 0.09z = 3,480

0.42((42,000 - z)/5.5) + 0.09z = 3,480

Simplifying this equation, we get:

3,818.18 - 0.07636z + 0.09z = 3,480

0.01364z = 338.18

z = 24,800

Now we can use this value of z to find y:

5.5y + z = 42,000

5.5y + 24,800 = 42,000

5.5y = 17,200

y = 3,127.27

Finally, we can use the values of y and z to find x:

x = 4.5y

x = 4.5(3,127.27)

x = 14,072.73

The bends on a track for car racing are semicircular, and the track is banked at an angle of 28.0° to the horizontal. Suppose the radius of the curvature of the bends is 120 m.

a) The formula to calculate the minimum velocity is given as follows:Vmin = √(rgtanθ)Where;Vmin is the minimum velocity needed to stay on the track;g is the acceleration due to gravity;r is the radius of the turn;θ is the angle of banking.r = 120 m, θ = 28.0°, and g = 9.8 m/s²Substitute the values into the formula, we get;Vmin = √(rgtanθ)=√(9.8 m/s² * 120 m * tan(28.0°))=40.6 m/sTherefore the minimum velocity the car should maintain is 40.6 m/sb) If the car speed is twice that in (a).

(i) The free-body diagram of the car is as shown below;

(ii) The value of the frictional force f is as follows;There are two forces acting on the car, namely; the normal force and the gravitational force. When the car moves at a constant speed around the bend, the centrifugal force Fc is also acting towards the center of the circular path. The centrifugal force Fc is given by the formula;Fc = mv²/rWhere;F c is the centrifugal force;m is the mass of the carv is the velocity of the car in m/sr is the radius of the curve.

Therefore;f = F s, max= μsNWhere;Fs, max is the maximum static frictional force that can be applied;N is the normal force acting on the car;μs is the coefficient of static friction.Because the car is not sliding, the maximum frictional force that can act is equal to the centripetal force, Fc.Thus;Fs, max = F c= 21,333.3 NThe frictional force f can now be determined as;f = Fs, max= μsN= 21,333.3 N= μsmgCosθwhere m is the mass of the car, and g is the acceleration due to gravity.

Substitute the values into the formula;μ s = f/mgCosθ= 21,333.3 N / 800 kg * 9.8 m/s² * Cos(28.0°) = 0.58Therefore the coefficient of static friction is 0.58.

To know more about bends visit:

https://brainly.com/question/32686061

#SPJ11

Answer: X = -9

Step-by-step explanation:

You can set up a ratio to solve this.

208/13 = -144/x

208x=-1872

x = -9

\(\mathbb{ANSWER:}\)

Step 1: Write the equation of variation

Step 2: Solve for k or the constant of proportionality

Step 3: Solve for x