What is the length of the hypotenuse of the triangle below?

A 7-foot-high rectangular door needs 2 lengths of trim that make an X on the door.




If the door width is 3 feet, what is the length of the diagonal in feet?


10
�
�
10
​
ft

21
�
�
21
​
ft

40
�
�
40
​
ft

58
�
�
58
​
ft

Answer:

\(t=k+\frac{e}{2}\)

Step-by-step explanation:

\(k=t-\frac{e}{2}\\t=k+\frac{e}{2}\)

Answer:

2.56 kgs

Step-by-step explanation:

76.8kg ÷ 30 days = 2.56 kgs

Amount of sugar used - 76.8 kg

No. Of Days in Month of April - 30 days

∴ Sugar used each day is = 76.8 ÷ 30

\(76.8 \div 30 \\ \\ = \frac{76.8}{30} \\ \\ = \frac{768}{30 \times 10} \\ \\ = \frac{ \cancel{768}}{ \cancel{30} \times 10} \fbox{cancelling by 3} \\ \\ = \frac{256}{10 \times 10} \\ \\ = \frac{256}{100} \\ \\ = 2.56 \: kg\)

Answer:

x^3+6x^2+9x

if you are trying to find the original function

if not, and you are trying to find the zeros is

x=-3

x=0

Step-by-step explanation:

multiply x(x+3)

x^2+3x

then multiply that by x+3 and that should give you the answer

Answer:

x = 0 or x = -3 or x = -3

Step-by-step explanation:

set up factors as:

x = 0

x + 3 = 0

x + 3 = 0

the first will remain as x = 0 while the others become x = -3 once subtracted

i hope this helped!

The given initial value problem's exact solution: y(t) = 1, and thus y(1) = 1. The Euler approximation of y(1) using a step-size h = 0.5 i: y(1) ≈ 1. Given the initial value problem:

y' = ty ' (0)

 = 0

We are to determine the exact solution y(t) and compute y(1), and also find the Euler approximation of y on the interval [0, 1] using a step-size h = 0.5 (half step size).

(a) The given initial value problem is a first-order linear differential equation, whose standard form is:

y' + P(t)y = Q(t), where P(t) = 0 and Q(t) = 0. Thus, the integrating factor is:

I(t) = e^∫ P(t)dt

      = e^∫ 0 dt

      = 1.

The exact solution y(t) is obtained by multiplying both sides of the differential equation by the integrating factor,

I(t) = 1, and integrating:

y' + P(t)y = Q(t) becomes

y' + 0y = 0, which implies

y' = 0.

Hence, y(t) = Ce^0 = C, where C is a constant determined using the initial condition y(0) = 1. Therefore, we have:

C = y(0) = 1.

Hence, the initial value problem's exact solution is y(t) = 1, and thus y(1) = 1.

(b) Euler Approximation of y using step-size h = 0.5We have h = Δt = 0.5, t0 = 0, tn = 1. The number of steps, n, is given by:

n = (tn - t0)/h

n = (1 - 0)/0.5

n = 2.

Therefore, we have two grid points:

t0 = 0, and

t1 = 0 + 0.5

  = 0.5

For the Euler approximation of y on [0, 1], we use the formula:

yi+1 = yi + h * f(ti, yi), for i = 0, 1, 2, ..., n - 1, where

f(ti, yi) = tiyi

= (0)(yi)

= 0, for i = 0, 1, 2, ..., n - 1.

Hence, we have:

y0 = y(0) = 1, and

y1 = y0 + h * f(t0, y0)

= y0 + h * 0

= 1 + 0

= 1

Therefore, the Euler approximation of y(1) using a step-size h = 0.5 is: y(1) ≈ y1 = 1. Therefore, y(1) ≈ 1. The exact solution of the given initial value problem is: y(t) = 1, and thus y(1) = 1. The Euler approximation of y(1) using a step-size h = 0.5 is: y(1) ≈ 1.

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First we need to select the subject to create the great paper outline template. Then follow the steps to create a paper.

Step 1: Choose the topic for the paper.

Step 2: Make a list of all the concepts you wish to discuss or incorporate.

Step 3: Separate similar concepts into smaller groupings.

Step 4: Put your concepts in order of importance: What ought the reader to discover first? What matters the most? Which conclusion will best suit your paper?

Step 5: Make good headers and subheadings for your documents.

Step 6: Format the outline in decimal, full-sentence, or alphanumeric form.

Step 7: State and review the paper by oneself first.

Follow all the steps to create the great paper outline template.

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Answer:

10.1%

Step-by-step explanation:

Interest = PRT/100

Interest = 77136.06 - 70060 = 7076.06

Interest = PRT/100

7076.06 = [(70060) × R × 1] / 100

7076.06 = 70060R/100

Cross multiply

(7076.06 × 100) = 70060R

707606 = 70060R

R = 707606/70060

R = 10.1%

Answer:

18.87 square cm.

Step-by-step explanation:

The area of the rectangle will be (4 + 4) * 4, since the length of the rectangle would be the diameter of the circle, and the width of the rectangle would be the radius. (4 + 4) * 4 = 8 * 4 = 32 square cm.

Then, we can calculate the area of the semicircle. The area of a circle is pi * r^2, so the area of a semicircle will be half of that. pi * (4^2) / 2 = pi * 16 / 2 = 8pi. 8 * 3.14159265 = 25.1327412 square cm.

The shaded area of the middle of the shape will then be 32 - 25.1327412 = 6.8672588 square cm.

The two triangles will have the same area. Their bases will be 14 minus the diameter of the circle, then divide that by 2 to get each separate base. 14 - 8 = 6 / 2 = 3. The heights of the triangles will be the radius of the circle, or 4 cm.

1/2 * 3 * 4 = 1/2 * 12 = 12/2 = 6. That is the area of one triangle, so the area of both triangles would be 6 * 2 = 12 square cm.

6.8672588 + 12 = 18.8672588, or 18.87 square cm.

Hope this helps!

Answer:

(44 - 8(pi)) cm^2    Exact area

18,9 cm^2    Approximate area

Step-by-step explanation:

The shaded area is the area of the trapezoid minus the area of the semicircle.

area of trapezoid = (b1 + b2)h/2

area of semicircle = (pi)(r^2)/2

The triangles at both sides are right triangles. Each of the horizontal legs has length (14 cm - 8 cm)/2 = 3 cm. Each of the vertical legs is congruent to the radius of the semicircle.

b1 = lower base = 14 cm

b2 = upper base = 14 cm - 3 cm - 3 cm = 8 cm

shaded area = (b1 + b2)h/2 - (pi)(r^2)/2

= (14 cm + 8 cm)(4 cm)/2 - (pi)(4 cm)^2 / 2

= 44 cm^2 - 8(pi) cm^2

= (44 - 8(pi)) cm^2    Exact area

= 18.9 cm^2    Approximate area

Answer:

The value of x is 54 degrees.

Explanation:

The two angles are in a right triangle.

The angles in a right triangle add up to 90. So:

Next, solve for x.

The value of x is 54 degrees.

The correct value of mn - 2√5 is -4.

To solve this problem, we'll break it down into smaller steps.

Step 1: Find the integer part and decimal part of √5.

The square root of 5 (√5) is approximately 2.23607.

The integer part (m) of √5 is 2.

The decimal part (n) of √5 is 0.23607.

Step 2: Calculate mn.

mn = 2 * 0.23607 = 0.47214.

Step 3: Calculate 2√5.

2√5 = 2 * √5 = 2 * 2.23607 = 4.47214.

Step 4: Calculate mn - 2√5.

mn - 2√5 = 0.47214 - 4.47214 = -4.

Therefore, mn - 2√5 is equal to -4.

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The product of (3 x 107) and (2 x 107) is 6.8694 x 10^4

To find the product of (3 x 107)and (2 x 107), we can use the distributive property of multiplication which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In this case, we can multiply the numbers outside the parentheses first, and then multiply the result by the common factor of 107 to simplify the expression:

(3 x 107) x (2 x 107) = 6 x (107 x 107)

Next, we can calculate the product of 107 and 107, which is 11,449:

6 x 11,449 = 68,694

In scientific notation, this can be written as:

= 6.8694 x 10^4

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Answer:

-10, -1, 5

Step-by-step explanation:

The zeroes of the function are -

x = -10, 5, -1

We have the following function -

f(x) = (x + 10)(x − 5)(x + 1)

We have to determine its zeroes.

In order to find the zeroes of the function, equate f(x) = 0.

(x + a)(x + b) = 0

(x + a) = 0     or     (x + b) = 0

x = - a     or      x = -b

Zeroes = -a , -b

According to question, we have -

f(x) = (x + 10)(x − 5)(x + 1)

Equate f(x) = 0

(x + 10)(x - 5)(x + 1) = 0

(x + 10) = 0       or      (x - 5) = 0      or       (x + 1) = 0

x = -10        x = 5      x = -1

Hence, the zeroes of the function are -

x = -10, 5, -1

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Answer:

D.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

42/6=7

Answer:

x = 10

Step-by-step explanation:

\(3 + \frac{x}{5} = 5 \\ = > \frac{15}{5} + \frac{x}{5} = 5 \\ = > \frac{15 + x}{5} = 5 \\ = > 15 + x = 5 \times 5 \\ = > 15 + x = 25 \\ = > x = 25 - 15 \\ = > x = 10\)

Answer: \(\dfrac{3}{8}\)

Step-by-step explanation:

Given

Julio traveled \(\frac{3}{8}\) of distance to his aunt's house on Saturday

they have traveled \(\frac{3}{5}\) of the remaining distance on Sunday

suppose the total distance is \(x\)

Distance traveled on Saturday

\(\dfrac{3x}{8}\)

Remaining distance is

\(x-\dfrac{3x}{8}=\dfrac{5x}{8}\)

Distance traveled on Sunday

\(\Rightarrow \dfrac{3}{5}\times \dfrac{5x}{8}=\dfrac{3x}{8}\)

The fraction of distance traveled on Sunday is

\(\Rightarrow \dfrac{\frac{3x}{8}}{x}=\dfrac{3}{8}\)

According to the output analysis, the model presented above is of Discrete-event simulation (DES) type.

What is Discrete-event simulation (DES)?

Discrete-event simulation (DES) is indeed a type of computer-based simulation where events occur at specific points in time. In DES, a system's behavior is modeled by specifying the sequence of events that occur during the system's lifespan.

In a discrete-event simulation, the state of the system changes only when events occur, rather than continuously evolving over time. Events represent significant occurrences or activities within the system, such as customer arrivals, service completions, or resource allocations. Each event is associated with a specific time or occurrence point, and the simulation progresses by processing events in chronological order.

DES is particularly useful for modeling complex systems where the timing of events and their interactions play a crucial role. It allows for capturing the dynamic nature of the system, simulating the flow of entities (such as customers, vehicles, or messages) through the system, and observing the effects of event sequencing and resource allocation on system performance.

By simulating the system and observing the events and their consequences, DES enables analysts to evaluate different scenarios, study the impact of various parameters, and optimize system design or operation. It provides insights into system performance measures, such as throughput, waiting times, resource utilization, or customer satisfaction.

Overall, discrete-event simulation is a powerful technique for modeling and analyzing complex systems with discrete changes, events, and interactions over time.

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The model above is known as a discrete-event simulation model according to the output analysis.

A discrete event simulation is a type of computer-based modeling where a series of discrete events in a system are simulated.

In such models, the system under consideration evolves through a series of discrete events that are instantaneous.

For example, in the retail establishment model, each customer arriving at the store would be considered a separate, discrete event.

The simulation would model the sequence of events that occur between the time the store opens at 9 am and when the last customer leaves before closing time at 5 pm.

The objective of the simulation would be to estimate some measure of the quality of customer service during this time period.

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Answer:

81

Step-by-step explanation:

9x9=81

Answer:

81

Step-by-step explanation:

9x9

Answer:

n = -8, 7

Step-by-step explanation:

Your equation is:

\(\displaystyle{n^2+n=56}\)

Arrange the terms in the quadratic expression, ax² + bx + c:

\(\displaystyle{n^2+n-56=0}\)

Factor the expression, thus:

\(\displaystyle{\left(n+8\right)\left(n-7\right)=0}\)

This is because 8n-7n = n (middle term) and 8(-7) = -56 (last term). Then solve like a linear which results in:

\(\displaystyle{n=-8,7}\)

Hello!

\(\sf n^2 + n = 56\\\\n^2 + n - 56 = 0\\\\\\n = \dfrac{-b\±\sqrt{b^2-4ac} }{2a} \\\\\\n = \dfrac{-1\±\sqrt{1^2-4*1*(-56)} }{2*1}\\\\\\n = \dfrac{1\±15}{2} \\\\\\\boxed{\sf n = 7 ~or ~-8 }\)

Answer:

7.67

Step-by-step explanation:

7.67x7.5%=.58

7.67+.58=8.25

"Basketball players are generally taller.

Basketball player heights vary slightly more.

Step-by-step explanation:

I hope this helps!

Basketball players are taller because the average (mean) of basketball players is greater than soccer players.

Basketball player heights vary more because the MAD is greater or more than the soccer players."

If the dead space tidal volume ratio is 0.65 and the tidal volume is 700, the dead space volume would be 455 mL. Dead space volume is calculated by multiplying the tidal volume by the dead space tidal volume ratio.

The dead space tidal volume ratio represents the proportion of the tidal volume that does not participate in gas exchange. To calculate the dead space volume, we multiply the tidal volume by the dead space tidal volume ratio.

Given that the dead space tidal volume ratio is 0.65 and the tidal volume is 700 mL, we can calculate the dead space volume as follows:

Dead space volume = Tidal volume * Dead space tidal volume ratio

Dead space volume = 700 mL * 0.65

Dead space volume = 455 mL

Therefore, the dead space volume would be 455 mL. This means that out of the total tidal volume of 700 mL, 455 mL does not participate in gas exchange and represents the dead space volume.

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Answer:

C. 9

Step-by-step explanation:

15/100*60

3/20*60

180/20

9

Answer:

The answer is 9

Step-by-step explanation:

15% * 60

"OF" mean multiplication so we multiple

¹⁵/100 * 60

we cancel "Zero cancel Zero"

we left with

¹⁵/10 * 6

but we can make the fraction to be uniform

so we say ¹⁵/10 * ⁶/1

we multiply

15 * 6=90

10 * 1=10

⁹⁰/10

we divide

10 into 90 is 9

10 into is 1

so we say ⁹/1 is the same as 9.

Hence our answer is 9

Answer:

20, for 8.50

Step-by-step explanation:

6 + 6 = 12, which is 4.50 + 4.50, which would be about 10, so 20 for 8.50 would be better.

1. Let's call the first number "x" and the second number "y". We know that:

x = 4 + 2y (equation 1)

x - y = 27 (equation 2)

We can use equation 1 to substitute x in equation 2:

(4 + 2y) - y = 27

Simplifying the equation:

3y = 23

So the second number is:

y = 23/3

Using equation 1, we can find the first number:

x = 4 + 2(23/3) = 50/3

Therefore, the numbers are 50/3 and 23/3.

2. Let's call the length of the equal sides of the triangle "x" and the length of the third side "y". We know that:

y = x + 10 (equation 1)

2x + y = 100 (equation 2)

We can use equation 1 to substitute y in equation 2:

2x + (x + 10) = 100

Simplifying the equation:

3x = 90

So the length of the equal sides is:

x = 30

Using equation 1, we can find the length of the third side:

y = 30 + 10 = 40

Therefore, the lengths of the sides are 30, 30, and 40.

The difference quotient of the function f(x) = 4x² - 5x is 8x + 4h - 5.

The formula for difference quotient is expressed as:

\(\frac{f(x+h)-f(x)}{h}\)

Given the function in the question:

f(x) = 4x² - 5x

To solve for the difference quotient, we evaluate the function at x = x+h:

First;

f(x + h) = 4(x + h)² - 5(x + h)

Simplifying, we gt:

f(x + h) = 4x² + 8hx + 4h² - 5x - 5h

f(x + h) = 4h² + 8hx + 4x² - 5h - 5x

Next, plug in the components into the difference quotient formula:

\(\frac{f(x+h)-f(x)}{h}\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - (4x^2 - 5x)}{h}\\\\Simplify\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - 4x^2 + 5x)}{h}\\\\\frac{(4h^2 + 8hx - 5h)}{h}\\\\\frac{h(4h + 8x - 5)}{h}\\\\8x + 4h -5\)

Therefore, the difference quotient is 8x + 4h - 5.

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The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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Answer:x= -9/2 which is -4.5

Step-by-step explanation:

8(x+5)=4

first divide by 8

(x+5)=4/8

simplify

(x+5)=1/2

subtract 5

x=1/2-5

change 5 to have a denominator of 2

5 x 2/2

=10/2

x= 1/2-10/2

=-9/2

Answer:-6

Step-by-step explanation:

X=-6

3 and -3 cancel out.

Answer:

-6

Step-by-step explanation:

The positives and negatives added cancel eachother out.

-6+3=-3

-3+-3=-6