The midpoint of
¯¯¯¯¯¯
C
D
is
E
(
−
1
,
0
)
. One endpoint is
C
(
5
,
2
)
. What are the coordinates of the other endpoint?

Answers:

1.             The graph is in the shape of a parabola, there is a vertex point at (20, 400), and the zeros (x-intercepts) of the graph are at the origin of the coordinate plane (0, 0) and (40, 0).

2.            The greatest area possible for a rectangle with a perimeter of 80 meters is 400 \(m^2\), and the dimensions of this rectangle will be 20 meters in length and 20 meters in width.

3.             The area of the rectangle whose length is 10 meters and the area of the rectangle whose length is 30 meters are the same, both being 300 \(m^2\). This is because the perimeter is set as 80 meters total, and as they are both rectangles, the opposite sides must be the same length.

               For the rectangle with a length of 10 meters, 2 of the 4 sides will use 20 meters of material, so there will be 60 meters of material left for the remaining 2 sides, or 30 meters per side. So the dimensions of that rectangle would be 10 meters in length and 30 meters in width.

               For the rectangle with a length of 30 meters, it's the same thing, except the length is 30 meters, and the width is 10 meters. And for both rectangles, their areas are 30 meters multiplied by 10 meters, which equals 300 \(m^{2}\), so the way these two rectangles are related is that they have the same area.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

1.  See below.

2.  400 m²

    20 m x 20 m

3.  300 m²

Step-by-step explanation:

The graph is a parabola that opens downwards.

Its vertex is (20, 400) and its axis of symmetry is x = 20.

From inspection of the given graph, the greatest possible area (y-value) is 400 m².  This is when the length of the rectangle is 20 m.

The largest possible area of a rectangle is when the length equals the width. Therefore, the dimensions of the rectangle with the greatest area possible are:

From inspection of the graph, when the length of the rectangle is 10 m, its area is 300 m².

Similarly, when the length of the rectangle is 30 m, its area is also 300 m².

A rectangle has two pairs of parallel sides of equal length.

Therefore, as both rectangles have the same area, this means that the one pair of parallel sides is 10 m in length and the other pair of parallel sides is 30 m in length.  The dimensions of both rectangles are the same: 10 m x 30 m, where the width and length are interchangeable.

Answer:

15:24, 20:32 and 40:64.

Step-by-step explanation:

hope this helps

Answer:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Step-by-step explanation:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Answer:

the x value is 41

x=77

y=62

z=41

Step-by-step explanation:

part 1:

2y-5+y+21+y=180

4y+17=180

4y=164

y=41

part 2:

w-2(41)-5=77

x-41+21=62

y-41

To solve this question we must use the concept of the sum of the internal angles of the triangles and therefore the measures of each angle are x = 62º, y = 41º, w = 76º.

The sum of the internal angles of a triangle is of 180º. In this problem, the angles are w, x and y, hence:

x + y + w = 180.

The measure of angle w is five less than twice the measure of angle y, hence:

w = 2y - 5.

The measure of angle x is 21 more than the measure of angle y, hence:

x = y + 21.

Replacing in the first equation, we can find angle y as follows:

y + 21 + y + 2y - 5 = 180.

4y = 164.

y = 164/4

y = 41.

Then:

w = 2y - 5 = 2(41) - 5 = 76.

x = y + 21 = 41 + 21 = 62.

Therefore the measures of the angles are given as follows:

x = 62º, y = 41º, w = 76º.

To learn more about sum of the internal angles of a triangle, here:

brainly.com/question/25215131

#SPJ5

First, you should simplify the function expression.

3(x2 + 10x + 5) - 5(x-k) = 3x2 + 30x + 15 - 5x + 5k = 3x2 +15x +15 +5k

In order for the polynomial to be divisible by x, all terms need to divide by x with no remainder.  The first two terms clearly divide by x.  However, the last two do not.  In order for this to work out where k is constant, 5k would have to cancel out the  +15 term, leaving nothing to divide by x.

So: 15 + 5k = 0

5k = -15

k = -3

Given that, two lines having the same y-intercept are perpendicular. And the given equation is,

Here, slope is -4/5, and y intercept is 6.

The slope of the perpendicular line is the negative reciprocal.

Therefore the equation for the perpendicular line is,

Step-by-step explanation:

Let's rewrite y' as differential and put everything else on the right hand side:

\(\dfrac{dy}{dx} = x^4 - 3x^2 - 6\)

Multiplying both sides by dx, we get

\(dy = x^4dx - 3x^2dx - 6dx\)

Integrating this, we get

\(\displaystyle y = \int{x^4dx} - 3\int{x^2dx} - 6\int{dx}\)

or

\(y = \frac{1}{5}x^5 - x^3 -6x + C\)

\(\displaystyle\int~4t(5t^2-1)^6 dt \\\\[-0.35em] ~\dotfill\\\\ u=5t^2-1\implies \cfrac{du}{dt}=10t~\hspace{10em} \cfrac{du}{10t}=dt \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~4t~u^6\cdot \cfrac{du}{10t}\implies \int~\cfrac{4t~u^6}{10t}\cdot du\implies \int~\cfrac{2~u^6}{5}du\implies \cfrac{2}{5}\int~u^6\cdot du \\\\\\ \cfrac{2}{5}\cdot \cfrac{u^7}{7}\implies \cfrac{2(5t^2-1)^7}{35}\)

Decrease in the price is $1887, the price of the next model car is $35,113.

Percentage is a measurement to find value of the given number out of hundred.

Given that,

Price of current model = $37,000

The price of next model car is 5.1% less than the current model.

The price of the next model car = 94.9% of price of current model car

                                                     = 94.9 x 37,000/100

                                                      = 35,113

The decrease in the price = 37,000 - 35,113 = 1887

The price of the next model car is $35,113 and decrease in the price is $1887.

To learn more on Percentage:

https://brainly.com/question/24120406

#SPJ1

For the correlation between the fund returns is .0459, the reward-to-volatility ratio of the best feasible CAL is equals to 0.1621 or 16.21%.

A probability distribution is helps to determine the future what frequency distribution is to the past. Standard deviation is used in the concept of risk of portfolio of investment. Risk refer to the dispersion of a probability distribution.

Stock fund (S) Bond fund (B)

Expected Return 14% 7%

Standard Deviation 43% 37%

Risk-free returns , Rf = 5.3%

Correlation coefficient = 0.459

Covariance : 0.459 = COV(s,b)/0.43×0.37

Covariance = 0.073

Stock Fund =( (σB)²− σS× σB× correationco, SandB)/((σS)²(σB)² - 2 × σS× σB× correationco, SandB)

= ((0.37)²− 0.43× 0.37× 0.0459) /((0.43)²(0.37)² −2× 0.43× 0.37× 0.0459)

Weight of S = 42.18%

Weight of B = 1 - 42.18 = 57.82%

Expected Return of the portfolio (Rp) = WS× E(RS) + WB × E(RB) = 42.18 × 14% + 57.82 × 7%

= 5.90 + 4.05 = 9.95

Standard Deviation of the portfolio (SDp)

= (WS²SD² + WB²× lSD²+ 2WS WBCov(S,B))1/2

= 28.68

Reward to volatility = (Expected return - Rf) / SD of Portfolio

= (9.95- 5.3) / 28.68

=0.1621

Hence, the required volatility is 0.1621 or 16.21%.

To learn more about probability distribution, refer:

https://brainly.com/question/28021875

#SPJ4

Answer:

\(\bold{495\pi} \approx \bold{1555.088 cm^3}\)

Step-by-step explanation:

There was no figure but the question is clear

Volume of a cylinder is given by the formula \(\bold{\pi r^2h}\\\)

where r is radius of base of cylinder, h is the height

Volume of a cone is given by \(\bold{\frac{1}{3} \pi r^2 h}\)

where r is the radius of base of cone, h is the height

The radius of the cylinder = \(\frac{1}{2}\)(diameter) = \(\frac{1}{2}\)(12) = 6cm

Height of cylinder = 15cm

Volume of cylinder \(V_{cyl} = \pi (6)^2 15 = \pi (36)15 = \bold{540\pi}\)

Radius of cone = \(\frac{1}{2}\) (radius of cylinder) = \(\frac{1}{2}\)(6) = 3 cm

Height of cone same as height of cylinder = 15cm

Volume of cone, \(V_{cone} = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (3)^2 15 = \frac{1}{3}(9)15\pi = \bold{45\pi}\\\)

Difference is the volume of the remaining solid

\(V_{cyl} - V_{cone} = 540\pi - 45\pi = \bold{495\pi} \approx \bold{1555.088 cm^3}\)

Answer: (3c+4)

Step-by-step explanation:

The probability that both are red marbles = \(\bold{\frac{17}{147} }\)

"It is finding out the possibilities of the occurrence of an event."

"P(A) = n(A) / n(S)

where, n(A) is the number of favorable outcomes of an event A

n(S) is the total number of outcomes for an experiment"

For given example,

A jar contains 17 red marbles and 32 blue marbles.

If we pull out 2 marbles at random, we need to find the probability that both are red.

The number of possible outcomes,

\(\Rightarrow n(S)=^{49}C_2\\\\ \Rightarrow n(S)=\frac{49!}{2!(49-2)!}\\\\ \Rightarrow n(S)=1176\)

The number of possible outcomes of selecting both the red marbles.

\(\Rightarrow n(A)=^{17}C_2\\\\ \Rightarrow n(A)=\frac{17!}{2!(17-2)!}\\\\ \Rightarrow n(A)=136\)

The probability that both the marbles are red,

\(\Rightarrow P(A)=\frac{n(A)}{n(S)}\\\\ \Rightarrow P(A)=\frac{136}{1176}\\\\ \Rightarrow P(A)=\frac{17}{147}\)

Therefore, the probability that both are red marbles = \(\bold{\frac{17}{147} }\)

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

The values are y₁=-0.5, y₂=-3.25, y₃=-7.825 and y₄=-15.3125 when the initial - value problem y' = y-2x. y(2)=1.

Given that,

Use Euler's method with step size 0.5 to compute the approximate y-values y₁, y₂, y₃ and y₄ of the solution of the initial - value problem y' = y-2x. y(2)=1.

We have to find the values y₁

We know that,

At Euler's approach, the curve of the solution can be roughly approximated at steps of h by the tangent in each interval (i.e., by a series of brief line segments). In general, using a short step size improves approximation accuracy.

By Euler approximation,

y₁ = y₀+hf(x₀,y₀)

=1+0.5(1-2(2))

=1-1.5

y₁=-0.5

Similarly,

y₂=-3.25, y₃=-7.825 and y₄=-15.3125

Therefore, The values are y₁=-0.5, y₂=-3.25, y₃=-7.825 and y₄=-15.3125 when the initial - value problem y' = y-2x. y(2)=1.

To learn more about values visit: https://brainly.com/question/24503916

#SPJ4

The weight of the candy in each bowl is 5(1/2) pounds.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Weight of each bag = 2(3/4) pounds

Number of bags bought = 6 bags

Total weight of all the bags.

= 6 x 2(3/4) pounds

= 6 x 11/4 pounds

= 33/2 pounds

Number of bowls = 3

The weight of candy in each bowl.

= 33/2 ÷ 3

= 33/(2x3)

= 33/6

= 11/2 pounds

= 5(1/2) pounds

Thus,

The weight of the candy in each bowl is 5(1/2) pounds.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

For more such answers on supplementary angle

https://brainly.com/question/12919120

#SPJ8

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

Read more about distance from angle of elevation at: https://brainly.com/question/25748640

#SPJ1

To graph the inequality k > 5 on a number line, mark an open circle at 5 and shade the region to the right.

To graph the solutions to the inequality k > 5 on a number line, follow these steps:

Draw a horizontal line and mark a point for the number 5 on the line.

-------------------|---|---|---|---|---|---|---|---|---|---|

0 1 2 3 4 5 6 7 8 9 10

Since the inequality is k > 5, the solution includes all values greater than 5. Therefore, draw an open circle (○) at the number 5 to represent that 5 itself is not included in the solution.

-------------------|---|---|---|---○---|---|---|---|---|---|

0 1 2 3 4 5 6 7 8 9 10

Shade the region to the right of the open circle. This shading represents all values that are greater than 5 and satisfy the inequality k > 5.

-------------------|---|---|---|---○===================>

0 1 2 3 4 5 6 7 8 9 10

The resulting number line graph illustrates that any value to the right of the open circle (excluding 5 itself) satisfies the inequality k > 5.

for such more question on inequality

https://brainly.com/question/17448505

#SPJ8

Answer:

4*9

Step-by-step explanation:

It's obvious.

160 students ordered a yearbook.

Step-by-step explanation:

Batman, cross multiply 400×40 then divide by 100 and you get your answer.

Answer:

192in^3

Explanation

Volume of a triangular prism = Base area * Height of prism

Since the base is triangular shaped, then;

Base Area = 1/2 * base * height

BAse Area = 1/2 * 8 * 4

Base Area = 8 * 2

Base Area = 16m^2

Height of prism = 12m

Volume of the prism = 16 * 12

Volume of the prism = 192m^2

Hence the volume of the right triangular prism is 192in^3

Answer:

60.48

Step-by-step explanation:

Answer:51.52

Step-by-step explanation:

Answer: 5.13 square cm

Step-by-step explanation:

Answer:

a) 13 m

b) 0.4 mm

Step-by-step explanation:

side length = x, area = x²

a) x² = 169, x = √169 = 13 m

b) x² = 0.16, x = √0.16 = 0.4 mm

The probability that there will be a seat available for every passenger that shows up is given as follows:

0.6276 = 62.76%.

The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.

The mass probability formula is given by the equation presented as follows:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters, along with their meaning, are listed as follows:

The parameters for this problem are given as follows:

n = 42, p = 0.95.

(p is the probability of a person showing up).

The probability of more than 40 people showing up is obtained as follows:

P(X > 40) = P(X = 41) + P(X = 42).

In which:

Hence:

P(X > 40) = 0.2564 + 0.1160 = 0.3724.

Hence the probability of a vacant seat is of:

1 - 0.3724 = 0.6276 = 62.76%.

More can be learned about the binomial distribution at https://brainly.com/question/24756209

#SPJ1

The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

For more questions on integral

https://brainly.com/question/30094386

#SPJ8

As per the slope-intercept form of a straight line, the equation of the required line is 5y = 6x + 8.

What is the slope-intercept form of a straight line?

The slope-intercept form of a straight line is: y = mx + c

Here, m = slope of the line , c = y-intercept

If the slope of a line is 'a', then the slope of the line that is perpendicular to the given line is (- 1/a).

The given coordinates of the points A, B, C are (2, 9); (8, 4); and C(- 3, - 2) respectively.

Therefore, the slope of the line AB is (m)

= (y₂ - y₁)/(x₂ - x₁)

= (4 - 9)/(8 - 2)

= (- 5)/6

Slope of the required line is perpendicular to AB.

Therefore, the slope of the required line is

= - 1/(- 5/6)

= 6/5

This line passes through point C(- 3, - 2).

- 2 = - 3(6/5) + c

⇒ c = -2 + 18/5

⇒ c = 8/5

The equation of the required line is

y = (6/5) x + (8/5)

⇒ 5y = 6x + 8

To Learn more about the slope-intercept form of a straight line here: brainly.com/question/19465597

#SPJ1

There are 152 red pens and 190 blue pens in Max's drawer, given that there are a total of 342 pens altogether.

Let's solve the problem step by step:

Identify the given information:

The ratio of red pens to blue pens is 4 to 5.

There are a total of 342 pens in the drawer.

Set up the ratio equation:

Let's assume the number of red pens is 4x, and the number of blue pens is 5x.

Here, 'x' is a scaling factor that allows us to find the actual number of pens.

We can write the equation as: 4x + 5x = 342.

Simplify and solve the equation:

Combining like terms, we have 9x = 342.

Divide both sides of the equation by 9 to solve for 'x':

x = 342 / 9 = 38.

Calculate the number of red pens and blue pens:

Now that we have the value of 'x', we can find the number of red and blue pens:

Number of red pens: 4x = 4 × 38 = 152.

Number of blue pens: 5x = 5 × 38 = 190.

For similar questions on pens

https://brainly.com/question/16820350

#SPJ8

The solution of the function on the interval is x = 0.524 radians.

The solution of the function on the interval is calculated as follows;

cot(x)= √3

1/tan(x) = √3

Simplify the expression as follows;

1 = √3tan(x)

tan(x) = 1/√3

The solutions of this equation in the interval [-2,2], is calculated as;

x = tan⁻¹(1/√3)

x = 0.524 radians

Another solution of x;

x = tan⁻¹(1/√3) + π = 3.67 radians

This value is not in the given interval, so there is only one solution to the equation cot(x) = √3 in the interval [-2,2], which is approximately x = 0.524 radians.

Learn more about Solution of cot function here: https://brainly.com/question/30570696

#SPJ1

Answer:

The price of the shirt is $24.63.

Step-by-step explanation:

Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:

x + (x - 15) = 34.26

Simplifying, we get:

2x - 15 = 34.26

Adding 15 on both sides:

2x = 49.26

Dividing by 2:

x = 24.63

Therefore, the price of the shirt is $24.63.