The legs of a 45-45-90 triangle has lengths of 21. What is the length of the hypotenuse?

Using proportions, it is found that option A gives a figure that is a scale drawing of the same courtyard using the scale 1 centimeter = 3 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching this problem on the internet, the figure with a scale of 1 cm = 4 feet has the dimensions of:

51 cm, 75 cm, 30 cm and 72cm.

For a scale of 1 centimeter = 3 feet, these measures will be multiplied by 4/3, hence the figure is given in option A, as:

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Answer:

40

Step-by-step explanation:

P=2(l+w)

2·(10+10)

          =40

The values of X and Y are 30 and 11 respectively

The figure that represents the complete question is added as an attachment

The given parameters are:

DH = X +3

HF  = 3Y

GH = 2X -5

HE = 5Y

From the attached parallelogram, we have:

DH = HF

GH = HE

Substitute the known values in the above equation

X + 3 = 3Y

2X - 5 = 5Y

Make X the subject in X + 3 = 3Y

X = 3Y - 3

Substitute X = 3Y - 3 in 2X - 5 = 5Y

2(3Y - 3) - 5 = 5Y

Expand

6Y - 6 - 5 = 5Y

Evaluate the like terms

Y = 11

Substitute Y = 11 in X = 3Y - 3

X = 3*11 - 3

Evaluate

X = 30

Hence, the values of X and Y are 30 and 11 respectively

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Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

Slope/Gradient = [tex]\frac{y1-y2}{x1-x2}[/tex]

P = (-8 , 3) (x1, y1)

Q = (-6 , 2) (x2, y2)

Slope = [tex]\frac{3-2}{-8-(-6)}[/tex] =[tex]\frac{1}{-8+6}[/tex] = [tex]\frac{1}{-2}[/tex] = [tex]-\frac{1}{2}[/tex]

Answer:

-1/2

Step-by-step explanation:

The formula for the slope is (change in y)/(change in x) or Rise/Run.

The change in y for the two points is: 3 --> 2 which is -1

The change in x for the two points is: -8 --> -6 which is +2

If we input these numbers in the slope equation, we end up with -1/2.

Since we cannot simplify -1/2 further, that is our final answer.

The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².

The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;

P(x) = (x-3) (x-3) (x) (x) (x+1)

The expanded form is therefore;

P(x) = x^5 - 5x⁴- 6x³+ 18x².

Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².

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Answer:

A., B.

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary, so their sum must equal 180°.

A. 72° + 108° = 180° Answer: yes

B. 66° + 114° = 180° Answer: yes

C. 80° + 90° = 170° Answer: no

D. 64° + 106° = 170° Answer: no

Answer: A., B.

The angle measures ABD = 45, DBC = 45 and ABC = 90 imply that ray l bisect ∠ABC?

From the figure, we have the following highlights:

This means that the points ABC can be joined to form a right triangle

Yes, it does.

This is so because it divides the angle ABC into equal segments.

i.e.

ABC = 90

DBC = 45

So, we have

ABD = 90 - 45

ABD = 45

The angle measures ABD = 45, DBC = 45 and ABC = 90 imply that ray l bisect ∠ABC?

You would need the measures of ABC and ABD

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Answer:

9:8:2

Step-by-step explanation:

3/4 : 2/3 : 1/6 Multiply by 12.
9 : 8 : 2

Answer:

  a) 30 yr: $1597.75; 25 yr: $1773.75

  b) $43065.00

Step-by-step explanation:

The monthly payment for each loan can be found using the amortization formula, or a spreadsheet or calculator. The shorter 25-year loan has fewer and larger payments, but the net result is less interest paid.

The attached calculator shows the monthly payments to be ...

  30 year loan: $1597.75 monthly

  25 year loan: $1773.75 monthly

The number of payments is the product of 12 payments per year and the number of years. The total repaid is the monthly payment times the number of payments.

The difference in amounts repaid is the difference in interest charged.

  360×1597.75 -300×1773.75 = $43065 . . . . savings using 25-year loan

__

Additional comment

The monthly payment on a loan of principal P at annual rate r for t years is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

Some calculators and all spreadsheets have built-in functions for calculating this amount.

Answer:

converges

Step-by-step explanation:

the individual fraction terms go against 0 with larger and larger n.

and therefore the sum converges.

the numerator of the fractions stays constant (4) but the denominator (bottom) of the fraction increases more and more with investing n (it does not matter that it uses roots, compared to the constant 4 they too grow immensely large with large n).

the limit of a/infinity is defined as 0.

Answer:

{(4,1), (-6, 6), (5,-2), (-4,1)} set of ordered pairs represents a function.

Step-by-step explanation:

Because every element or component of domain has unique image in co-domain.

Hope its helpful :-)

If so, please mark me as brainlist :-)

Answer:

x = 2

Step-by-step explanation:

3x - 2 = - 2x + 8

→ Add 2x on both sides

5x - 2 = 8

→ Add 2 on both sides

5x = 10

→ Divide both sides by

x = 2

Answer:

x = 2, y = 4 (2,4)

Step-by-step explanation:

Put both the equation in ax + by = c

-3x + y = -2

2x + y = 8

Find x:  

Multiply 8 times 1, -2 by 1, 2 times 1, and -3 by 1

8 - (-) 2/2 - (-) 3 = x

10/5

x = 2

Plug x back into equation:

-3(2)+y = -2

y = 4

Answer:

22.34021442

Step-by-step explanation:

22.34021442

Only one triangle possible with angle 38.2° at C.

According to the given statement

we have to seek out that the measurement of m with the help of the a and c.

Then for this purpose, we all know that the

The ambiguous case occurs when one uses the law of sines to see missing measures of a triangle when given two sides and an angle opposite one in every of those angles (SSA).

According to the this law

The equation become

35/sin(60) = 25/sinC

sinC = 0.6185895741

C = 38.2, 141.8

Since 141.8+60 = 201.8 > 180

It will not form a triangle.

So, only 1 triangle possible with angle 38.2° at C

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Law of Sines and the Ambiguous Case.

In ∆ ABC, a =35, c = 25, and m < A = 60*

How many distinct triangles can be drawn given these measurements?

Answer:

Option A

Here you go.

Hope this help!!

Good luck!!

Horizontal asymptote

The range is

Or

Option A

a. The arc length is given by the integral

[tex]L(r) = \displaystyle \int_3^\infty \sqrt{x'(t)^2 + y'(t)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\left(\frac{t\cos(t) - r\sin(t)}{t^{r+1}}\right)^2 + \left(-\frac{t\sin(t) + r\cos(t)}{t^{r+1}}\right)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\frac{(t^2+r^2)\cos^2(t) + (t^2+r^2)\sin^2(t)}{\left(t^{r+1}\right)^2}} \, dt \\\\ ~~~~~~~~ = \boxed{\int_3^\infty \frac{\sqrt{t^2+r^2}}{t^{r+1}} \, dt}[/tex]

b. The integrand roughly behaves like

[tex]\dfrac t{t^{r+1}} = \dfrac1{t^r}[/tex]

so the arc length integral will converge for [tex]\boxed{r>1}[/tex].

c. When [tex]r=3[/tex], the integral becomes

[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2+9}}{t^4} \, dt[/tex]

Pull out a factor of [tex]t^2[/tex] from under the square root, bearing in mind that [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex].

[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2} \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{|t| \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{t \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{\sqrt{1+\frac9{t^2}}}{t^3} \, dt[/tex]

since for [tex]3\le t<\infty[/tex], we have [tex]|t|=t[/tex].

Now substitute

[tex]s=1+\dfrac9{t^2} \text{ and } ds = -\dfrac{18}{t^3} \, dt[/tex]

Then the integral evaluates to

[tex]L(3) = \displaystyle -\frac1{18} \int_2^1 \sqrt{s} \, ds \\\\ ~~~~~~~~ = \frac1{18} \int_1^2 s^{1/2} \, ds \\\\ ~~~~~~~~ = \frac1{27} s^{3/2} \bigg|_1^2 \\\\ ~~~~~~~~ = \frac{2^{3/2} - 1^{3/2}}{27} = \boxed{\frac{2\sqrt2-1}{27}}[/tex]

a) The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].

b) r > 1 for a spiral with finite length.

c) The length of the spiral when r = 3 is (1 - 2√2) / 9 units.

a) The arc length formula for 2-dimension parametric functions is defined below:

L = ∫ √[(dx / dt)² + (dy / dt)²] dt, for [α, β]         (1)

If we know that [tex]\dot x (t) = \frac{t \cdot \cos t - r \cdot \sin t}{t^{r+1}}[/tex], [tex]\dot y(t) = \frac{t\cdot \sin t + r\cdot \cos t}{t^{r + 1}}[/tex], α = 0 and β → + ∞ then their arc length formula is:

[tex]L = \int\limits^{\infty}_{3} {\sqrt{\left(\frac{t\cdot \cos t - r\cdot \sin t}{t^{r + 1}}\right)^{2}+\left(\frac{t\cdot \sin t + r\cdot \cos t}{t^{r+1}}\right)^{2}} } \, dt[/tex]

By algebraic handling and trigonometric formulae (cos ² t + sin² t = 1):

[tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex]      (2)

The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].

b) By ratio comparison criterion, we notice that √(t² + r²) is similar to √t² = t and [tex]\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}}[/tex] is similar to [tex]\frac{t}{t^{r +1}} = \frac{1}{t^{r}}[/tex].

The integral found in part a) has a finite length if and only the governing grade of the denominator is greater that the governing grade of the numerator. and according to the ratio comparson criterion, the absolute value of the ratio is greater than 0 and less than 1. Therefore, r > 1 for a spiral with finite length.

c) Now we proceed to integrate the function:

L = ∫ [√(t² + 9) / t⁴] dt, for [3, + ∞].

L = ∫ [t · √(1 + 9 / t²) / t⁴] dt, for [3, + ∞].

By using the algebraic substitutions: u = 1 + 9 / t², du = - (18 / t³) dt → - (1 / 18) du.

L = ∫ √u du, for [3, + ∞].

L = - (1 / 9) · √(u³), for [3, + ∞].

L = - (1 / 9) · [√(1 + 9 / t²)³], for [3, + ∞].

L = - (1 / 9) · [√(2³) - √(1³)]

L = - (1 / 9) · (2√2 - 1)

L = (1 - 2√2) / 9

The length of the spiral when r = 3 is (1 - 2√2) / 9 units.

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Answer:

[tex]\boxed {AB = 52 m}[/tex]

Step-by-step explanation:

This forms a right triangle.

Therefore, by using the Pythagorean Theorem, we can find AB.

AB = √AC² + BC²

I hope it helped you solve the problem.

Good luck on your studies!

Answer: Distance AB = 52 m

Step-by-step explanation:

Given information

Point A = 20 m north of point C

Point B = 48 m east of point C

Please refer to the attachment below for a graphical understanding

Concept

According to the graph drawn, Point A, Point B, and Point C form a right angle, and the distance between Point A and B would form a right triangle.

Therefore, we can use the Pythagorean theorem to find the distance between points A and B.

Given formula

a² + b² = c²

Substitute values into the formula

a² + b² = c²

(20)² + (48)² = c²

Simplify exponents

400 + 2304 = c²

Simplify by addition

2704 = c²

c = √2704

c = 52  or  c = -52 (reject, since no distance can be negative)

Therefore, the distance AB is [tex]\Large\boxed{52~m}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Mean 7.4

Median 7

Mode 7, 11

Step-by-step explanation:

Let me know if this is correct!

Answer: 7.4, 7, 7 and 11

Step-by-step explanation:

The mean is the sum of all the numbers divided by the number of numbers. In this case, there are 10 numbers.

[tex]Mean=\frac{6+7+11+5+8+7+4+13+11+2}{10}=\frac{74}{10}=7.4[/tex]

The median is the number (or the average of the two numbers) in the middle of the set when it is ordered in ascending order. Let's first order it from least to greatest.

[tex]2,4,5,6,7,7,8,11,11,13[/tex]

The two middle numbers are 7 and 7. The median is the mean of these two numbers.

[tex]Median=\frac{7+7}{2}=\frac{14}{2}=7[/tex]

The mode is the number that is most repeated number in the set. The numbers 7 and 11 are repeated twice. Hence, the modes are 7 and 11.

Answer:

Side b is the longest because the longer side always lie opposite the bigger angle. Angle B is the biggest angle, and since side b is opposite angle B, side b is the longest.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The side opposite to the largest angle is the longest side of a triangle.

[tex] \qquad \large \sf {Conclusion} : [/tex]

hence, we can conclude that the longest side is b

( since it's opposite angle is the largest, i.e 91° )

The answers to the question are:

This is the number of calls for the help desk

160000/3200 = 50per call

network center

735000/9800

= 75 per device that was monitored

Electronic mail

100000/10000 =

10 for the mail account

For smart phone support

124600/8900

= 14 per phone extension

for helpdesk

5200 * 0.25 * 0.96 *1.5 calls * $50

= 93600

For network center

(5200 * 0.25 * 0.96) + 600] x 75

= 138600

For Electronic mail

5200 * 0.25 * 0.96 * 10 per email account

= 12480

Smart support charge

5200 * 0.25 * 14 = 18200

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The Elements can be defined as a mathematical treatise which comprises 13 books that are attributed to the ancient Greek mathematician who lived in Alexandria, Ptolemaic Egypt c. 300 BC and called Euclid.

Basically, the Elements is a collection of the following geometric knowledge and observations:

Based on my experiences so far, an approach to geometry which I prefer is Euclidean geometry because it's much easier than analytical geometry.  Also, an approach that is easier to extend beyond two-dimensions is Euclidean geometry because it can be extended to three-dimension.

A situation in which one approach to geometry would prove to be more beneficial than the other is when dealing with flat surfaces. In Euclidean geometry, a correspondence can be established between geometric curves and algebraic equations.

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Answer:

Step-by-step explanation:

Linear Programming Problems (LPP): Linear programming or linear optimization is a process which takes into consideration certain linear relationships to obtain the best possible solution to a mathematical model. It is also denoted as LPP. It includes problems dealing with maximizing profits, minimizing costs, minimal usage of resources, etc. These problems can be solved through the simplex method or graphical method.

Linear Programming For Class 12

Linear Programming

Linear Programming Worksheet

The Linear programming applications are present in broad disciplines such as commerce, industry, etc. In this section, we will discuss, how to do the mathematical formulation of the LPP.

Mathematical Formulation of Problem

Let x and y be the number of cabinets of types 1 and 2 respectively that he must manufacture. They are non-negative and known as non-negative constraints.

The company can invest a total of 540 hours of the labour force and is required to create up to 50 cabinets. Hence,

15x + 9y <= 540

x + y <= 50

The above two equations are known as linear constraints.

Let Z be the profit he earns from manufacturing x and y pieces of the cabinets of types 1 and 2. Thus,

Z = 5000x + 3000y

Our objective here is to maximize Z. Hence Z is known as the objective function. To find the answer to this question, we use graphs, which is known as the graphical method of solving LPP. We will cover this in the subsequent sections.

Graphical Method

The solution for problems based on linear programming is determined with the help of the feasible region, in case of graphical method. The feasible region is basically the common region determined by all constraints including non-negative constraints, say, x,y≥0, of an LPP. Each point in this feasible region represents the feasible solution of the constraints and therefore, is called the solution/feasible region for the problem. The region apart from (outside) the feasible region is called as the infeasible region.

The optimal value (maximum and minimum) obtained of an objective function in the feasible region at any point is called an optimal solution. To learn the graphical method to solve linear programming completely reach us.

Linear Programming Applications

Let us take a real-life problem to understand linear programming. A home décor company received an order to manufacture cabinets. The first consignment requires up to 50 cabinets. There are two types of cabinets. The first type requires 15 hours of the labour force (per piece) to be constructed and gives a profit of Rs 5000 per piece to the company. Whereas, the second type requires 9 hours of the labour force and makes a profit of Rs 3000 per piece. However, the company has only 540 hours of workforce available for the manufacture of the cabinets. With this information given, you are required to find a deal which gives the maximum profit to the décor company.

Linear Programming problem LPP

Given the situation, let us take up different scenarios to analyse how the profit can be maximized.

He decides to construct all the cabinets of the first type. In this case, he can create 540/15 = 36 cabinets. This would give him a profit of Rs 5000 × 36 = Rs 180,000.

He decides to construct all the cabinets of the second type. In this case, he can create 540/9 = 60 cabinets. But the first consignment requires only up to 50 cabinets. Hence, he can make profit of Rs 3000 × 50 = Rs 150,000.

He decides to make 15 cabinets of type 1 and 35 of type 2. In this case, his profit is (5000 × 15 + 3000 × 35) Rs 180,000.

Similarly, there can be many strategies which he can devise to maximize his profit by allocating the different amount of labour force to the two types of cabinets. We do a mathematical formulation of the discussed LPP to find out the strategy which would lead to maximum profit.

Answer:

Step-by-step explanation:

According to the construction we have:

It gives us:

Then, corresponding angles of congruent triangles are congruent:

So,

Then,

Answer: -6

Step-by-step explanation:

[tex]-3x+\frac{1}{2}y=-3\\\\\frac{1}{2}y=3x-3\\\\y=6x-6[/tex]

For there to be infinite solutions, b = -6.

Answer:

303.66 in²

Option 4 is the correct answer

For a standard normal distribution, the value of the z-score represented as c in P(-0.78≤Z≤c)=0.7657 is 0.0166

We want to find the p-value between 2 z-scores expressed as;

P(-0.78 < z < c) = 0.7657

To solve this, we will solve it as;

0/7657= 1 - [P(z < -0.78)  + P(z > c)]

From normal distribution table, we have that;

P(z < -0.78) =  0.217695

Thus;

0.7657 = 1 - (0.217695 + c)

c = 1 - 0.7657 - 0.217695

c = 0.0166

Thus, For a standard normal distribution, the value of the z-score represented as c in P(-0.78≤Z≤c)=0.7657 is 0.0166

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Answer:

(6 / 4) * (7 + 9)

Step-by-step explanation:

sry that took me so long lol

The graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The graph of equations is shown in the graph.

As we know, if two equations of a function intersect on the coordinate plane that means they have a solution.

If there will be no intersection then the equations have no solution.

Thus, the graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.

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Answer:

it depend on your total credit load u register, if it's d only credit load it affect your gpa alot

The time it would take for the print to reach 100 percent completion is 12,101 minutes 9 seconds.

The mathematical operations that would be used to determine the required value are division and multiplication. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is  ÷. Multiplication is the process of determining the product of two or more numbers. The sign used to denote multiplication is ÷.

Other mathematical operations that are used to solve problems include addition and subtraction.

Time it would take to reach 100% completion = (minutes it takes to print 87% of the words x 100%) / 87%

Time it would take to reach 100% completion = (10,528 x 1) / 0.87 =

10.528 / 0.87

= 12,101. 15

= 12,101+ (0.15 x 60)

= 12,101 minutes 9 seconds

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