Using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall. 6.5 ft 6.5 startroot 2 endroot ft 13 ft 13 startroot 2 endroot ft

Answer:

Step-by-step explanation:

Given quadratic equation is,

y = -2x² + 4x + 5

y = -2(x² - 2x) + 5

y = -2(x² - 2x + 1 - 1) + 5

y = -2(x² - 2x + 1) + 2 + 5

y = -2(x - 1)² + 7

This equation is in the vertex form of the quadratic equation,

y = a(x - h)² + k

where, (h, k) is the vertex of the parabola.

Therefore, vertex of the given quadratic equation is (1, 7)

The equation can be rewritten as y = -2(x - 1)² + 7.

Therefore, the vertex of the graph of the function y = -2x² + 4x + 5 in the xy-coordinate plane is located at the point (1, 7).

Answer:

5 hours

Step-by-step explanation:

The problem is giving you the equation

y =  0.4x; where y is the # of buckets filled and x is the hours.

If they you 2 filled buckets, then how many hours?  

You need to solve for x

y = 0.4x; to get the x by itself, divide by 0.4

x = \(\frac{y}{0.4}\) ; now substitute y with 2 ( for 2 filled buckets)

x = \(\frac{2}{0.4}\) = 5; which means it took 5 hours to fill up 2 buckets.

The similar triangle of the triangle PQR are ΔRQS and ΔPRS.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

In other words, Similar triangles are two or more triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

Therefore, the similar triangles of triangle PQR is as follows:

ΔRQS and ΔPRS are the only similar triangle to ΔPQR

learn more on right triangle here: https://brainly.com/question/29191745

#SPJ1

The air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion.

According to Newton's Second Law of Motion, the rate of change of the airplane's momentum is equal to the sum of all the forces acting on the airplane. As the plane takes off and accelerates, the thrust of the engines acting in the forward direction causes the plane's momentum to increase. This increase in momentum results in an increase in air speed. The air resistance acting against the motion of the plane is another force that affects the plane's speed. As the plane accelerates, the air resistance increases, and the plane's speed decreases.

In summary, the air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion, where the thrust of the engines and air resistance act as forces that influence the plane's air speed.

For more such questions on Newton's Second Law of Motion.

https://brainly.com/question/13447525#

#SPJ11

- For one solution, k must be in the interval [4/3, 4/3].
- For two solutions, k must be in the interval (-∞, 4/3).
- For no solutions, k must be in the interval (4/3, ∞).

To find the values of k that result in one solution, two solutions, or no solutions, we need to consider the discriminant of the quadratic equation.

Recall that for a quadratic equation of the form ax^2 + bx + c = 0, the discriminant is b^2 - 4ac. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. And if it is negative, there are no real solutions.

So let's apply this to the equation kx^2 - 4x + 3 = 0. The coefficients are a = k, b = -4, and c = 3. Therefore, the discriminant is:

(-4)^2 - 4(k)(3) = 16 - 12k

(a) For there to be one solution, the discriminant must be zero. Therefore, we need to solve the equation 16 - 12k = 0. Solving for k, we get k = 4/3. So the interval notation for this case is [4/3, 4/3].

(b) For there to be two solutions, the discriminant must be positive. Therefore, we need to solve the inequality 16 - 12k > 0. Simplifying, we get k < 4/3. So the interval notation for this case is (-∞, 4/3).

(c) For there to be no solutions, the discriminant must be negative. Therefore, we need to solve the inequality 16 - 12k < 0. Simplifying, we get k > 4/3. So the interval notation for this case is (4/3, ∞).

Know more about the quadratic equation

https://brainly.com/question/1214333

#SPJ11

The  slope of the tangent line at a particular point on a graphical plot of time vs. concentration during a reaction gives the option (C)  instantaneous rate of reaction

The slope of the tangent line at a particular point on a graphical plot of time vs. concentration during a reaction gives the instantaneous rate of reaction at that point. Instantaneous rate of reaction is the rate of reaction at a specific moment in time, and it is determined by the change in concentration of a reactant or product with respect to time at that specific moment. The tangent line represents the instantaneous rate of reaction at a specific point on the plot.

Therefore, correct option is (C) instantaneous rate of reaction

Learn more about slope here

brainly.com/question/30510321

#SPJ4

Answer:How do I order fractions from least to greatest if the denominators are different? Make them the same by multiplying both the numerator and the denominator of the smallest fraction, and if necessary, the largest one as well.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

3,6,9,12,15

5,10,15,20,25

15,and 15 are the least common denominators.

The equation 154 = -4(8+6r) + 24r has no solution because the variable becomes 0.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

We have to find the variable r of the equation to solve the equation.

A variable is a number represented with letters in an equation.

Therefore, let's find the variable r in the equation.

154 = -4(8+6r) + 24r

open the brackets on the right side of the equation

154 = - 32 - 24r + 24r

154 = -32 + 0

Therefore, the equation cannot be solved.

learn more on equation here: brainly.com/question/29021902

#SPJ1

Answer:

+4 and -4

Step-by-step explanation:

x² + 16=0

x=-√16

x=-4 or +4

it should be A. 3/4  

Answer:

The slope of the function y = -2x - 3 is -2. This is calculated by taking the coefficient of the x-term and making it the numerator of a fraction, and making the constant term the denominator.

Step-by-step explanation:

mark as brainliest

Answer:

The building is taller than 12ft is b>12

The box contains more than 11 books is b>11

Answer:

b<11 is The board is shorter than 11 cm

b>11 is The box contains more than 11 books

b<12 is There are fewer than 12 beetles in a jar

b>12 is The building is taller than 12 ft.

Step-by-step explanation:

To answer parts (a) through (d), let's analyze the given information step by step.

(a) What is the probability that the sample mean cholesterol level of 45 healthy adults is above 220 mg/dL?

To answer this question, we can use the properties of the sampling distribution of the sample mean, assuming that the population distribution is approximately normal.

The mean cholesterol level in healthy adults from the area is 210 mg/dL, and the standard deviation is 30 mg/dL. Since the sample size is large (n = 45), we can apply the Central Limit Theorem.

The standard error of the mean (SE) is calculated by dividing the standard deviation of the population (σ) by the square root of the sample size (n):

SE = σ / sqrt(n) = 30 / sqrt(45)

To find the probability of the sample mean being above 220 mg/dL, we can calculate the z-score and then use a standard normal distribution table or calculator.

z = (x - μ) / SE = (220 - 210) / (30 / sqrt(45))

Using a z-table or calculator, we can find the probability associated with this z-score. Let's assume we find that the probability is p.

(a) The probability that the sample mean cholesterol level of 45 healthy adults is above 220 mg/dL is p.

(b) What is the probability that the sample mean cholesterol level of 45 healthy adults is between 200 mg/dL and 220 mg/dL?

To find this probability, we need to calculate the z-scores for both values.

For 200 mg/dL:

z1 = (x1 - μ) / SE = (200 - 210) / (30 / sqrt(45))

For 220 mg/dL:

z2 = (x2 - μ) / SE = (220 - 210) / (30 / sqrt(45))

Using a z-table or calculator, we can find the probabilities associated with both z-scores. Let's assume we find that the probabilities are p1 and p2, respectively.

(b) The probability that the sample mean cholesterol level of 45 healthy adults is between 200 mg/dL and 220 mg/dL is p2 - p1.

(c) What sample size would be needed to estimate the population mean cholesterol level to within 5 mg/dL with 95% confidence?

To determine the sample size needed, we can use the formula for the margin of error (E) in a confidence interval for the population mean:

E = z * (σ / sqrt(n))

We want the margin of error to be 5 mg/dL, and we want a 95% confidence level. The z-value associated with a 95% confidence level is approximately 1.96.

Rearranging the formula, we can solve for the required sample size (n):

n = (z^2 * σ^2) / E^2

Plugging in the known values, we have:

n = (1.96^2 * 30^2) / 5^2

Simplifying the equation will give us the required sample size.

(c) The sample size needed to estimate the population mean cholesterol level to within 5 mg/dL with 95% confidence is the value obtained from the equation above.

(d) Suppose the health insurance providers want to estimate the proportion of adults with high cholesterol levels to within 2% with 99% confidence. What sample size is required?

To determine the sample size needed, we can use the formula for the margin of error (E) in a confidence interval for a population proportion:

E = z * sqrt((p * (1 - p)) / n)

We

want the margin of error to be 2%, and we want a 99% confidence level. The z-value associated with a 99% confidence level is approximately 2.58 (assuming a large enough sample size for the normal approximation to be valid).

Since we don't have an estimate of the proportion (p) beforehand, we can conservatively assume p = 0.5, which maximizes the required sample size. Therefore, the equation for the sample size (n) becomes:

n = (z^2 * 0.25) / E^2

Plugging in the known values, we have:

n = (2.58^2 * 0.25) / 0.02^2

Simplifying the equation will give us the required sample size.

(d) The sample size needed to estimate the proportion of adults with high cholesterol levels to within 2% with 99% confidence is the value obtained from the equation above.

To know more about values visit-

brainly.com/question/30289325

#SPJ11

Step-by-step explanation:

12=2x+y

that's what I got hope this helps u broo

Answer:the answer is 5.7 because 4 times 4 is 16 and 16 plus 16 is 32 the square root of 32. ^2 square root of 32 is 5.656 the. You need to round it to the nearest tenth which would be 5.7.

Answer:

5.7

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

It is a rational number because any number that can be rewritten as a simple fraction is a rational number. This means that natural/counting numbers, whole numbers and integers, like 5, are all part of the set of rational numbers as well because they can be written as fractions, as are mixed numbers such as 1 ½.

Answer:

1) 10

2) 22

3) 28

4) 17.5

5) 22

6) 13.5

7) 19.5

8) 11

9) 7.5

Answer: 1306.5 m^3

Step-by-step explanation:

1. The formula for the volume of a cylinder is: V=\(\pi\)r^2h

2. If you substitute the values into the equation, you get

V = pi * 5.7^2 * 12.8 = 1306.5

3. 1306.5 is already to the nearest tenth, so that is the answer.

Answer:

1000=850 5000=4250  5020=4276

Step-by-step explanation:

Multiply 1000, 5000, and 5020 by .15 to get 15 percent of what is taken away each year.

The solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

To solve the given differential equation y''(t) = 1 - t^17 with the initial condition y(1) = 12, we can integrate the equation twice.

Integrating the equation once will give us y'(t):

y'(t) = ∫(1 - t^17) dt

y'(t) = t - (1/18)t^18 + C₁

Now, we need to apply the initial condition y(1) = 12 to determine the value of the constant C₁:

12 = 1 - (1/18) + C₁

C₁ = 12 + (1/18) - 1

C₁ = 217/18

Next, we integrate y'(t) to find y(t):

y(t) = ∫(t - (1/18)t^18 + 217/18) dt

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + C₂

Finally, we apply the initial condition y(1) = 12 to determine the value of the constant C₂:

12 = (1/2) - (1/342) + (217/18) + C₂

C₂ = 12 - (1/2) + (1/342) - (217/18)

C₂ = (20619 - 1 + 6 - 819)/(342)

C₂ = 19805/342

Therefore, the solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

Learn more about equation here:

https://brainly.com/question/10724260

#SPJ11

Answer:

3, 1, 4, 2

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

-10, \(\sqrt{100}\) , 11.5, \(\sqrt{220}\) .

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

k/20

Step-by-step explanation:

Answer:

\(x+7; x+5; 27; 25\)

Step-by-step explanation:

First of all, we need to write \(x^2+12x+35\) as a product. The easiest way is to find a pair of numbers whose product is 35 and sum is 12. Looking at the product, you notice it's 7 and 5, which added together indeed give 12.

The two side length are thus \(x+7\) and \(x+5\).

In the specific case, when \(x=20\) the two sides measures 27 and 25.

Question/Equation:

9/20=__%

Answer/Steps to answer:

1. For the denominator, recognize that 20×5=100.

Multiple = 55

2. Multiply both the numerator and denominator by the multiple 5.

9×5/20×5

3. Simplify.

45/100

4. Simplify.

45% (0.45 Is Decimal Form)

Done by NeighborhoodDealer

Answer:

117

Step-by-step explanation:

Got it from calucaltor and did it to make sure

Answer:

117

Step-by-step explanation:

Preschoolers Building block towers are Jillian and Ashley.  When x=7/3 their towers have the same amount of blocks.

Given that,

Preschoolers Building block towers are Jillian and Ashley. Jillian has already added 10 blocks to her tower and is continuing to do so at a rate of five per minute. Three blocks make up Ashley's tower, and she is continuing to add blocks at a rate of six per minute.

We have to find when will their towers have the same amount of blocks.

We can write as

10+5x=3+6x

3x-6x=3-10

-3x=-7

x=-7/-3

x=7/3

Therefore, When x=7/3 their towers have the same amount of blocks.

To learn more about blocks visit: https://brainly.com/question/3580092

#SPJ10

In this phase II study, researchers evaluated the effects of subcutaneous interleukin-2 (IL-2) in combination with medroxyprogesterone acetate (MPA) and antioxidants in advanced cancer patients who had responded to previous chemotherapy. The study aimed to assess the clinical outcomes, quality of life, and laboratory parameters in these patients.

To conduct the study, the researchers recruited advanced cancer patients who had previously shown a positive response to chemotherapy. These patients were administered subcutaneous IL-2, MPA, and antioxidants as part of the treatment.

The researchers then monitored various parameters to evaluate the effects of the treatment. Clinical outcomes, such as tumor response and overall survival, were assessed to determine the effectiveness of the treatment in controlling cancer progression. Quality of life measurements were used to evaluate the impact of the treatment on patients' well-being and daily functioning. Additionally, laboratory parameters were measured to assess any changes in patients' blood count, liver function, and kidney function.

By analyzing the data obtained from the study, the researchers aimed to determine the efficacy and safety of the combination treatment in advanced cancer patients who had previously responded to chemotherapy. The findings of this phase II study can contribute to our understanding of potential treatment options for this specific patient population.

To know more about chemotherapy visit:

https://brainly.com/question/31143291

#SPJ11

Answer:

150

Step-by-step explanation:

equation is linked below :)

The surface area of the part of the x2 + y2 + z2 = 8z that lies inside the paraboloid z = x2 + y2, using the cylindrical coordinates is given as below:

The integral to find the surface area in the cylindrical coordinates, we can write as,

∫∫ dS = ∫∫ r dθ dr The given surface is x2 + y2 + z2 = 8z and the paraboloid is z = x2 + y2

By substituting the value of z from the paraboloid to the first equation,

we get,x2 + y2 + (x2 + y2)2 = 8(x2 + y2) Simplify it by expanding the square term as,

x2 + y2 + x4 + 2x2y2 + y4 = 8x2 + 8y2Now,

re-write the equation as,

x2 + y2 - 8x2 - 8y2 + x4 + 2x2y2 + y4 = 0On

solving this equation, we get

x2 + y2 - 8x2 - 8y2 + x4 + 2x2y2 + y4 = (x2 - 4x + y2 - 4y + 8)(x2 + 4x + y2 + 4y - 8) = 0

The equation of the paraboloid is given as, z = x2 + y2Hence,

the integral to find the surface area of the given surface in cylindrical coordinates,

∫∫ dS = ∫∫ r dθ dr Bounds of the integral to find the surface area are 0 ≤ θ ≤ 2π and r1 ≤ r ≤ r2,

where r1 and r2 are the radii of the cylinder.

Solve this equation and get the values of r1 and r2,r2 = 2r1

On solving the quadratic equation of (x2 - 4x + y2 - 4y + 8)(x2 + 4x + y2 + 4y - 8) = 0,

we get,

x2 + y2 - 4x - 4y + 4 = 0

The equation of the circle is given as

,x2 + y2 = 4x + 4y - 4 Solve for x and y to get,

x = 2 + cos θ y = 2 + sin θ

The radius of the circle is given as,

√(42 + 42) = √32 Thus,

the limits of integration of r are r1 = 0 and r2 = √32.

Integrating over the limits,

∫0^2π ∫0^√32 r dr dθ= 1/2(32) (2π)= 16πTherefore,

the surface area of the given surface is 16π.

To know more about surface area click here

https://brainly.com/question/31968506

#SPJ11