In the figure, the horizontal lines are parallel and AB = BC = CD. Find JM.

A.15
B.10
C.5
D. 20

In The Figure, The Horizontal Lines Are Parallel And AB = BC = CD. Find JM.A.15B.10C.5D. 20

Answers

Answer 1

Answer:

By the transversal theorem, if segments on a transversal cut by parallel lines are equal, then similar segments cut by the same parallel lines on another transversal are also equal.

Therefore

JK=KL=LM=5

=>

JM=3*5=15

Step-by-step explanation:


Related Questions

PLS HELP ME, WILL GIVE BRAINLIEST!!!!!!!!!!!!!

Answers

sorry i was going to show work but my water spill on the paper. so answer is 556.05cm^2

What is the value of x? Show all your work.


Please help. 100 points.

Answers

Answer:

12 cm

Step-by-step explanation:

By hypotenuse theorem,

x² + 35² = 37²

x² + 35*35 = 37*37

x² + 1225 = 1369

x² = 1369 - 1225

x² = 144

x² = 12*12

x² = 12²

x = 12 cm

100 Points! Geometry question. Photo attached. Determine whether the pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Please show as much work as possible. Thank you!

Answers

Answer:

∆TSU ~ ∆PJM by SAS since 10/14 = 5/7 and 15/21 = 5/7, and angle S is congruent to angle J.

Select the values that are solutions to the inequality x2 + 3x – 4 > 0.

Answers

Answer: To solve the inequality x^2 + 3x - 4 > 0, we can use the method of factoring.

First, we can factor the quadratic expression:

x^2 + 3x - 4 = (x + 4)(x - 1)

Now we can find the values of x that make the expression greater than zero by looking at the sign of the expression for each factor and applying the sign rules of multiplication:

If both factors are positive, the expression is positive.If both factors are negative, the expression is positive.If one factor is positive and one factor is negative, the expression is negative.

Using this method, we can create a sign chart:

x x + 4 x - 1 x^2 + 3x - 4

-4 0 -5 +6

-1 + - -

1 + + +

0 + - -

2 + + +

From the sign chart, we can see that the expression is greater than zero for x < -4 or x > 1. Therefore, the solutions to the inequality are all real numbers x such that x < -4 or x > 1. We can write this as:

x < -4 or x > 1

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Seventh grade> Y.7 Circles: word problems P56
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millimeters
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The button on Jasmine's pants has a radius of 5 millimeters. What is the button's
diameter?
9

Answers

Answer:

10 millimeters

Step-by-step explanation:

The diameter of the button is twice the radius. Therefore, the diameter of Jasmine's pants button is 10 millimeters.

Cual es la distancia que recorrió luis en su bicicleta rodada 20p (2.54) después que las llantas dieran 50 vueltas completas



porfaaa

Answers

Luis traveled approximately 31,736.8 inches on his bicycle.

We have,

To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.

Given:

Radius of the tires (r) = 20p (2.54) inches

Number of complete turns (n) = 50

The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Substituting the given radius into the formula, we have:

Circumference = 2π * (20p) inches

Now we can calculate the distance traveled (d):

Distance = Circumference x Number of complete turns

Distance = 2π x (20p) x 50 inches

To simplify the calculation, we can approximate π as 3.14:

Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches

Calculating this expression, we find:

Distance ≈ 31736.8 inches

Therefore,

Luis traveled approximately 31,736.8 inches on his bicycle.

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The complete question.

What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns

What is the interquartile range for data set? 27,4,54,78,27,48,79,64,5,6,41,71

Answers

The Interquartile range for the given data set is 51.

The interquartile range for a given data set, the values of the first quartile (Q1) and the third quartile (Q3). The interquartile range is the difference between Q3 and Q1.

First, let's arrange the data set in ascending order:

4, 5, 6, 27, 27, 41, 48, 54, 64, 71, 78, 79

To find Q1, which represents the lower quartile, we need to locate the median of the lower half of the data set. Since the data set has 12 values, the lower half consists of the first 6 values:

4, 5, 6, 27, 27, 41

The median of this lower half is the average of the middle two values, which are 6 and 27:

Q1 = (6 + 27) / 2 = 33 / 2 = 16.5

To find Q3, the upper quartile, we need to locate the median of the upper half of the data set. Again, since the data set has 12 values, the upper half consists of the last 6 values:

48, 54, 64, 71, 78, 79

The median of this upper half is the average of the middle two values, which are 64 and 71:

Q3 = (64 + 71) / 2 = 135 / 2 = 67.5

Finally, we can calculate the interquartile range by subtracting Q1 from Q3:

Interquartile range = Q3 - Q1 = 67.5 - 16.5 = 51

Therefore, the interquartile range for the given data set is 51.

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Help I need the answer to this

Answers

The graph of the logarithmic function is attached below with a vertical asymptote at x = -8 and two integer coordinates at (2, -7) and (1, -10).

What is graph of a logarithmic function?

The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log).

To plot the graph of the given function, we simply need to use a graphing calculator.

The given function is;

f(x) = -3log₃(x + 8) - 4

To find the asymptotes of the graph;

x + 8 > 0

x > -8

The vertical asymptotes is at x = -8

The two points with integer coordinates are (2, -7) and (1, -10)

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Please help me, first time I got it wrong

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The conditional value probability is solved and P ( F | E ) = 6/17

Given data ,

P ( E ) = 0.85

P ( F ) = 0.4

P ( E ∩ F ) = 0.3

Now , the formula for conditional probability to calculate P(F|E):

P(F|E) = P(E ∩ F) / P(E)

We are given that P(E) = 0.85 and P(E ∩ F) = 0.3, so we can substitute those values in:

P(F|E) = 0.3 / 0.85

Simplifying this fraction, we get:

P(F|E) = 6/17

Hence , the probability of F given that E has occurred is 6/17 or approximately 0.35.

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Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles.

3.4 cm, 3.1 cm, 6.6 cm

Answers

We can see here that the given side lengths cannot  be used to form a unique triangle because the shorter sides do not add up to the longer side.

What is a triangle?

The fundamental geometric shape of a triangle has three sides and three angles. It is a triangular polygon with three edges.

We can see here that in order to determine if the given side lengths:

3.4 cm, 3.1 cm, 6.6 cm

can form a unique triangle, many different triangles, or no triangle, we need to check if they satisfy the triangle inequality theorem.

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Let's check the conditions:

3.4 cm + 3.1 cm = 6.5 cm

6.5 cm > 6.6 cm (Not satisfied)

3.4 cm + 6.6 cm = 10 cm

10 cm > 3.1 cm (Satisfied)

3.1 cm + 6.6 cm = 9.7 cm

9.7 cm > 3.4 cm (Satisfied)

he specified side lengths cannot be used to create a triangle because the total of the two shorter sides' lengths (3.4 cm and 3.1 cm) is not larger than the length of the longest side (6.6 cm).

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evaluate 5x - 2y + 4z when x=3 , y=2 and z=4 (a)5 (b) 16 (c) 27 (d) 20​

Answers

When x = 3, y = 2, and z = 4, the value of the expression 5x - 2y + 4z is 27.

The correct answer is (c) 27.

To evaluate the expression 5x - 2y + 4z when x = 3, y = 2, and z = 4, we substitute the given values into the expression and perform the   arithmetic calculations. Here's the step-by-step process:

Step 1: Replace x with 3, y with 2, and z with 4 in the expression:

5(3) - 2(2) + 4(4)Step 2:

Perform the multiplications first:

15 - 4 + 16

Step 3: Perform the additions and subtractions from left to right:

15 - 4 + 16 = 11 + 16 = 27.

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

Answer:

SRTZ is not a parallelogram.

Slope of SZ:

[tex]m = \frac{ - 2 - 1}{1 - ( - 2)} = - 1[/tex]

Slope of RT:

[tex]m = \frac{0 - 3}{2 - 1} = - 3[/tex]

Since the slopes of SZ and RT are not equal, SRTZ is not a parallelogram.

Can someone please answer and provide an explanation for these problems?

Answers

The center and radius for each equation are as follows:

40. Center: (3, 2), Radius: 8

41. Center: (-8, 4), Radius: 6

42. Center: (-4, 12), Radius: 2

43. Center: (4, -15), Radius: 3

What is the center and radius of the equations?

The standard equations of a circle is given as (x - h)² + (y - k)² = r²

Where the center are (h, k) and the radius of the circle is r.

40. (x - 3)² + (y - 2)² = 64

  Center: (3, 2)

  Radius: √64 = 8

41. (x + 8)² + (y - 4)² = 36

  Center: (-8, 4)

  Radius: √36 = 6

42. (x + 4)² + (y - 12)² = 4

  Center: (-4, 12)

  Radius: √4 = 2

43. (x - 4)² + (y + 15)² = 9

  Center: (4, -15)

  Radius: √9 = 3

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Using the image below, answer the following question: you are asked to pick 2
marbles out of the bag, what is the probability of picking a blue marble and then a
green marble, without replacing the blue one?

PLEASE URGENT

Answers

The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.

We have,

We see that there are 10 marbles.

Now,

Number of blue marbles = 2

Number of green marbles = 4

Now,

The probability of picking a blue marble first is 2/10, as there are 2 blue marbles out of 10 in total.

After picking a blue marble, there will be 9 marbles left in the bag.

The probability of picking a green marble second, without replacing the blue one, is 4/9, as there are 4 green marbles remaining out of the 9 marbles in total.

Now,

P(blue marble and green marble) = P(blue marble) x P(green marble)

= (2/10) x (4/9)

= 8/90

= 4/45.

Therefore,

The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.

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Please solve this question

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The solution to the given composite function is calculated as: 12

How to solve Composite functions?

Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, the function  f of g of x is said to be the composition of the two functions.

We are given the functions:

f(x) = 2[tex]x^{\frac{1}{3} }[/tex]

g(x) = -[tex]x^{\frac{4}{3} }[/tex]

Thus:

(f - g)(-8) = 2[tex]x^{\frac{1}{3} }[/tex] + [tex]x^{\frac{4}{3} }[/tex]

= 2∛-8 + (∛-8)⁴

= (2 * -2) + (-2)⁴

= -4 + 16

= 12

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what is 27% in a equivalent form using the two other forms of notian: fraction,decimal,or percent

Answers

You can write 27% as a fraction like this: [tex]\frac{27}{100}[/tex] . (27/100).

Or as a decimal 0.27.

Answer and why!!!!!!

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The expression (yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp) is simplified to obtain

2/y

How to simplify the expression

The given expression is

(yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp)

The expression is simplified individually, using different each equation in the expression

yx + y + px + p

= y(x + 1) + p(x + 1)

= (y + p)(x + 1)

5x² + 10x +5

= 5(x² + 2x + 1)

= 5(x² + 1)

(10x + 10)

= 10(x + 1)

(y² + yp)

= y(y + p)

bringing the equations together and simplifying further

(y + p)(x + 1) / 5(x² + 1) * 10(x + 1) / y(y + p)

= 10(x + 1)(x + 1) / 5y(x² + 1)

= 10(x² + 1) / 5y(x² + 1)

= 2/y

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En el laboratorio de análisis de minerales unas pequeñas gotas de ácido Nítrico (HNO3); cae sobre la piel de un analista y le produce una quemadura. ¿Cuántas moléculas de HNO3 provocaron la quemadura si las gotas presentan una masa de 0,49 g?

Answers

Entonces n is 0,00779 moles,

Los casi 5 sextillones (5 con 21 ceros) de moléculas de HNO3 provocaron la quemadura en la piel del analista.

Para responder a esta pregunta, necesitamos saber la masa molar de HNO3, que es 63,01 g/mol. Usando esta información, podemos calcular el número de moles de HNO3 en los 0,49 g de gotas usando la fórmula: n = m/M, donde n es el número de moles, m es la masa y M es la masa molar.

Como un mol contiene el número de moléculas de Avogadro (6,022 x 10^23), podemos calcular el número de moléculas de HNO3 en las gotas que causaron la quemadura: 0,00779 moles x 6,022 x 10^23 moléculas/mol = 4,69 x 10^21 moléculas .

Es importante recordar que los ácidos concentrados como el HNO3 pueden ser extremadamente peligrosos y pueden causar quemaduras graves, por lo que siempre se deben tomar las precauciones de seguridad adecuadas en un entorno de laboratorio.

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please help. i’m struggling on part C

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a) The area formula for the rectangle is equal to A = r² · sin 2θ.

b) By derivative tests, the maximum possible area of the rectangle is 16 square centimeters.

c) The dimensions of the rectangle are: Width: 5.66 cm, Height: 2.83 cm

How to find the maximum possible area of a rectangle inscribed in a semicircle

In this problem we must determine the maximum possible area of a rectangle inscribed in a semicircle by means of first and second derivative tests. First, derive the area formula of the rectangle:

A = w · h

A = (2 · r · cos θ) · (r · sin θ)

A = 2 · r² · sin θ · cos θ

A = r² · sin 2θ

Where:

w - Width, in centimeters.h - Height, in centimeters.A - Area, in square centimeters.r - Radius, in centiemters. θ - Angle, in degrees.

Second, perform first derivative test: (r - Constant)

A = 2 · r² · cos 2θ

2 · r² · cos 2θ = 0

cos 2θ = 0

θ = 45°

Third, perform second derivative test: (θ = 45°)

A'' = - 4 · r² · sin 2θ

A'' = - 4 · r² (MAXIMUM)

Fourth, determine the maximum possible area of the rectangle:

A = 4² · sin 90°

A = 16 cm²

Fifth, determine the width and the height of the rectangle: (r = 4, θ = 45°)

w = 2 · r · cos θ

w = 2 · 4 · cos 45°

w = 8 · √2 / 2

w = 4√2 cm

w = 5.66 cm

h = r · sin θ

h = 4 · sin 45°

h = 4 · √2 / 2

h = 2√2 cm

h = 2.83 cm

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Gauri Spends 0.75 of her salary every month if she earns rs 12000 per month in how many months will she save rupees 39000

Answers

Answer:

13 months

--------------------

If Gauri spends 0.75 of her salary every month, that means she saves 0.25 of her salary:

0.25 * 12000 = 3000

Divide the total 39000 by her monthly savings:

39000 / 3000 = 13

So it will take Gauri 13 months to save rupees 39000.

Find the value for the side marked below. Round your answer to the nearest tenth 210 37 degrees

Answers

Using the cosine ratio, the value of the marked side in the image given below is approximately: y = 167.7.

How to Find the Value of the Marked Side Using the Cosine Ratio?

The cosine ratio is defined as the ratio of the length of the hypotenuse of the right triangle over the length of the side that is adjacent to the reference angle. It is given as:

cos ∅ = length of hypotenuse/length of adjacent side.

From the image attached below, we have the following:

Reference angle (∅) = 37°

length of hypotenuse = 210

length of adjacent side = y

Plug in the values:

cos 37 = y/210

210 * cos 37 = y

y = 167.7

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NO LINKS!! URGENT HELP PLEASE!!
O is the center of the regular dodecagon below. Find its area. Round to the nearest tenth.

Answers

Answer:

80.4 square units.

Step-by-step explanation:

solution Given:

apothem(a)=5

no of side(n)= 12

Area(A)-?

The area of a regular polygon can be found using the following formula:

[tex]\boxed{\bold{Area =\frac{1}{2}* n * s * a}}[/tex]

where:

n is the number of sidess is the length of one sidea is the apothem

In this case, we have:

n = 12s = ?a = 5

First, we need to find S.

We can find the length of one side using the following formula:

[tex]\boxed{\bold{s = 2 * a * tan(\frac{\pi}{n})}}[/tex]

substituting value:

[tex]\bold{s = 2 * 5 * tan(\frac{\pi}{12})=2.679}[/tex]   here π is 180°

To find the area substituting value in the above area's formula:

[tex]\bold{Area = \frac{1}{2}* 12 * 2.679 * 5=80.37\: sqaure\: units}[/tex]

in nearest tenth 80.4 square units.

Therefore, the area of the regular polygon is 80.4 square units.

Answer:

80.4 square units (nearest tenth)

Step-by-step explanation:

The given diagram shows a regular dodecagon (12-sided polygon) with an apothem of 5 units.

The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.

We can calculate the side length of a regular polygon given its apothem using the following formula:

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Substitute n = 12 and a = 5 into the equation to create an expression for s:

[tex]5=\dfrac{s}{2 \tan \left(\dfrac{180^{\circ}}{12}\right)}[/tex]

[tex]s=10\tan \left(15^{\circ}\right)[/tex]

Now we can use the standard formula for an area of a regular polygon:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

Substitute the found expression for s, n = 12 and a = 5 into the formula and solve for A:

[tex]A=\dfrac{12 \cdot 10\tan \left(15^{\circ}\right) \cdot 5}{2}[/tex]

[tex]A=\dfrac{600\tan \left(15^{\circ}\right)}{2}[/tex]

[tex]A=300\tan \left(15^{\circ}\right)[/tex]

[tex]A=80.3847577...[/tex]

[tex]A=80.4\; \sf square\;units\;(nearest\;tenth)[/tex]

Therefore, the area of a regular dodecagon with an apothem of 5 units is 80.4 square units, rounded to the nearest tenth.

Find the volume of the pyramid above
Find the surface are of the pyramid above pls help

Answers

The volume of the pyramid is 18069333.33 units³ and the surface area is 391600 units ²

What is a pyramid?

A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces.

Surface area of a pyramid is expressed as;

area of 4 lateral face + area of base

area of base = 440²

= 193600 units²

area of a lateral = 1/2 bh

= 1/2 × 440 × 356

= 78320

For four surfaces = 4 × 78320 = 313280

Total surface area = 313280+78320

= 391600 units ²

Volume of a pyramid is expressed as;

V = 1/3base area × height

V = 1/3 × 440² × 280

V = 18069333.33 units³

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The volume of a tree stump can be modeled by considering it as a right cylinder. Xavier measures its height as 2.1 ft and its circumference as 61 in. Find the volume of the stump in cubic inches. Round your answer to the nearest tenth if necessary.

Answers

The volume of the stump is 7451.9 cubic inches.

How to find the volume of the stump in cubic inches?

The volume of a cylinder can be calculated using formula below:

V = πr²h

where r is the radius and h is the height of the cylinder

We have circumference (C) = 61 in.

Let's find the radius (r) using the formula:

C = 2πr

61 = 2 * 22/7 * r

r = 9.70 in

h = 2.1 ft  = 2.1 * 12 = 25.2 in

Substituting into V = πr²h:

V = 22/7 * 9.70² * 25.2

V = 7451.9 cubic inches

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Sobre una embarcación de 160 kg que está en reposo con su proa apuntando a la orilla, comienza a caminar una persona de 70 kg desde la proa hacia la popa, a 0.80 m/s respecto a la embarcación. ¿Cuáles son las velocidades de la embarcación y de la persona respecto a la orilla? Desprecia la resistencia del agua al movimiento.

Answers

The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.

How to calculate the velocity

We can use the conservation of momentum equation:

(mboat + mperson) * vboat = mperson * vperson

(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)

230 kg * vboat = 56 kg * (0.80 m/s + vperson)

vboat = (56/230) * (0.80 m/s + vperson)

vperson = 0.80 m/s + vboat

vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)

(174/115) * vperson = (504/115) * m/s

Dividing both sides by (174/115), we get:

vperson = 2.896 m/s

vboat = (56/230) * (0.80 m/s + vperson)

Substituting the value of vperson, we get:

vboat = 1.337 m/s

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On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.

NO LINKS!! URGENT HELP PLEASE!!!

Solve ΔABC using the Law of Cosines

1. B= 36°, c = 19, a = 11

2. a = 21, b = 26, c = 17

Answers

Answer:

1)  A = 32.6°, C = 111.4°, b = 12.0

2) A = 53.6°, B = 85.7°, C = 40.7°

Step-by-step explanation:

Question 1

Given values of triangle ABC:

B= 36°c = 19a = 11

First, find the measure of side b using the Law of Cosines for finding sides.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

As the given angle is B, change C for B in the formula and swap b and c:

[tex]b^2=a^2+c^2-2ac\cos(B)[/tex]

Substitute the given values and solve for b:

[tex]\implies b^2=11^2+19^2-2(11)(19)\cos(36^{\circ})[/tex]

[tex]\implies b^2=482-418\cos(36^{\circ})[/tex]

[tex]\implies b=\sqrt{482-418\cos(36^{\circ})}[/tex]

[tex]\implies b=11.9929519...[/tex]

Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles A and C.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{19^2+(11.9929519...)^2-11^2}{2(19)(11.9929519...)}[/tex]

[tex]\implies \cos(A)=0.842229094...[/tex]

[tex]\implies A=\cos^{-1}(0.842229094...)[/tex]

[tex]\implies A=32.6237394...^{\circ}[/tex]

To find the measure of angle C, substitute the values of a, b and c into the formula:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{11^2+(11.9929519...)^2-19^2}{2(11)(11.9929519...)}[/tex]

[tex]\implies \cos(C)=-0.364490987...[/tex]

[tex]\implies C=\cos^{-1}(-0.364490987...)[/tex]

[tex]\implies C=111.376260...^{\circ}[/tex]

Therefore, the remaining side and angles for triangle ABC are:

b = 12.0A = 32.6°C = 111.4°

[tex]\hrulefill[/tex]

Question 2

To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

Given sides of triangle ABC:

a = 21b = 26c = 17

Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{21^2+26^2-17^2}{2(21)(26)}[/tex]

[tex]\implies \cos(C)=\dfrac{828}{1092}[/tex]

[tex]\implies C=\cos^{-1}\left(\dfrac{828}{1092}\right)[/tex]

[tex]\implies C=40.690560...^{\circ}[/tex]

To find the measure of angle B, swap b and c in the formula, and change C for B:

[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\implies \cos(B)=\dfrac{21^2+17^2-26^2}{2(21)(17)}[/tex]

[tex]\implies \cos(B)=\dfrac{54}{714}[/tex]

[tex]\implies B=\cos^{-1}\left(\dfrac{54}{714}\right)[/tex]

[tex]\implies B=85.6625640...^{\circ}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{17^2+26^2-21^2}{2(17)(26)}[/tex]

[tex]\implies \cos(A)=\dfrac{524}{884}[/tex]

[tex]\implies A=\cos^{-1}\left(\dfrac{524}{884}\right)[/tex]

[tex]\implies A=53.6468753...^{\circ}[/tex]

Therefore, the measures of the angles of triangle ABC with sides a = 21, b = 26 and c = 17 are:

A = 53.6°B = 85.7°C = 40.7°

Find the area of the stained glass window shown if the diameter of the semi-circle is 61 inches. Use 3.14 for , round your answer to the nearest square inch, and enter the number only.

Answers

Answer:

  1460 square inches

Step-by-step explanation:

You want the area of a semicircle with diameter 61 inches.

Area

The area of a circle is given by ...

  A = (π/4)d²

The area of a semicircle is half that, so is ...

  A = (π/8)d²

  A = (3.14/8)(61 in)² ≈ 1460 in²

The area of the semicircular window is about 1460 square inches.

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The table shows ordered pairs of the function y=8-2x. What is the value of y when x=8?
0-20
X
-3
-1
-
1
4
8
10
Mark this and return
y
14
10
6
0
?
-12
Save and Exit
Next
Submit

Answers

Answer:

The Value of Y is -8

Step-by-step explanation:

I believe it is -8 because giving the function, y = 8 - 2x, given that x = 8, we can replace the value into a function. y = 8 - 2(8) = 8 - 16 = -8.

So therefore, the value of y is -8. Hopes this helps :p

Write 0.75 as a fraction in its simplest form

Answers

Answer:

0.75 can be written as :-

[tex] \frac{75}{100} [/tex]

and in simplest form it is:-

[tex] \frac{3}{4} [/tex]

so the answer is 3/4

Write and solve an equation to find the value of x.

Answers

The equation to solve this is:

20 (20+30) = x^2
1000 = x^2
sqr root of 1000 = x

x = 31.62277660168379
x ≈ 31.62
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