A, B & C form the vertices of a triangle.
CAB = 90°, ABC = 30° and AC = 9.3.
Calculate the length of AB rounded to 3 SF.

Answers

Answer 1

The length of AB = 18.6 .

What is a Triangle ?

A triangle is a polygon with three sides , angles and vertices.

It is given that ABC is a triangle such that

CAB = 90°

ABC = 30° and

AC = 9.3.

AB = ?

As the triangle is a right angled triangle

Trigonometric ratios can be used.

sin x = Perpendicular / base

sin 30 = AC / AB

(1/2) = 9.3 / AB

AB = 9.3 /0.5

AB = 18.6

Therefore the length of AB = 18.6 .

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Related Questions

The question is down below

also I home school and have permission to post this question

Answers

Answer:

960

Step-by-step explanation:

(if i made any typos, sorry it is kind of hard to type on computer over writing on paper.)

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=(a+b+c)/2

Solving forA

A=ah+bh+ch+1/2 sqrt(﹣a^4+2(ab)^2+2(ac)^2﹣b4+2(bc)^2﹣c^4)=10·12+24·12+26·12+1

2·﹣104+2·(10·24)2+2·(10·26)2﹣244+2·(24·26)2﹣264=960

Tony is installing a window that is shaped like a parallelogram. He has 6 square meters of glass and knows that the base of the window needs to be 2 and 1 half meters. What must the height of the window be if he uses all the glass? Write your answer as a mixed number.

Answers

The required height of window of the glass 2.4 meters.

Tony is installing a window that is shaped like a parallelogram. He has 6 square meters of glass and knows that the base of the window needs to be 2 and 1 half meters.

What is parallelogram?

parallelogram is a quadrilateral consist of pairs of parallel side.

Area of parallelogram = base x height
                                    6 = 2.5 x height

               height = 2.4 m

Thus the required height of window is given by 2.4 meters.

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Am I correct with my answers?

Answers

Answer:

w = 70° . . . . alternate interior anglesx = 70° . . . . alternate interior anglesy = 40° . . . . angle sum in a trianglez = ?? . . . . not enough information

Step-by-step explanation:

The alternate interior angles theorem, and the angle sum theorem can be used here.

Alternate interior angles

Alternate interior angles are found on either side of a transversal where it crosses a pair of parallel lines. They are between the parallel lines. Their vertices are at the junction of the transversal and the parallel lines. Alternate interior angles are congruent.

In this diagram, there are two pairs of alternate interior angles where the two transversals AD and BD cross parallel lines AB and CD.

At points A and D, the alternate interior angles are 70° and x, respectively. This tells you ...

  x = 70° . . . . alternate interior angles theorem

At points B and D, the alternate interior angles are w and 70°, respectively. This tells you ...

  w = 70° . . . . alternate interior angles theorem

Angle sum

The angle sum theorem tells you the sum of angles in a triangle is 180°. This fact can be used to find the measure of angle y.

  70° +w +y = 180°

  y = 180° -70° -w = 110° -70°

  y = 40° . . . . angle sum theorem

There is not enough information to determine the measure of angle z.

  z = indeterminate


The slope of the line graphed below is undefined. True or false

Answers

Answer:

False

Step-by-step explanation:

The slope is 0.

What’s the error in these equations with steps will give Brainily

Answers

Answer:

2. (3+4) should be (3*4)

3. x is also x^1, so it should be x^(6+3+1)

4. you have to do 3^4 and 2^3 before timing them together

How many solutions exist for the system of equations in the graph?

Answers

Answer:

Two solutions exist for the system of equations in the graph.

Step-by-step explanation:

Solutions are when the two graphs intersect.

At the end of January 2003, the population of my town was 11,212. The population of my town increases by 322 every month. In what month does the population of my town first exceed 15,000?

Answers

In 11.76 months, the value of the population will be 15000.

We have given that,

At the end of January 2003, the population of my town was 11,212.

the population is increased by 322 every month

So at the end of the second-month population will be 11534.

suppose x represents the year and  y represent the population

The population increased by 322 every month

Therefore the value of m =322

[tex](x_1,y_1)=(0,11212)[/tex]

We have m=332

[tex](x_2,y_2)=(x_2,15000)[/tex]

We have to determine the value of the x_2

What is the slope point form of the line?

[tex](y_2-y_1)=m(x_2-x_1)[/tex]

[tex]322\left(x_2-0\right)=15000-11212[/tex]

[tex]322\left(x_2-0\right)=3788[/tex]

[tex]\frac{322\left(x_2-0\right)}{322}=\frac{3788}{322}[/tex]

[tex]x_2=\frac{1894}{161}[/tex]

[tex]x_2=11.76[/tex]

Therefore in 11.76 months, the value of the population will be 15000.

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Mr. Chan’s lawn grows 2 1/8 inches every 2 week. He mows his lawn every 2 weeks and cuts off the top 1 3/4 inches of lawn. If Mr. Chan’s lawn was 4 inches tall at the beginning of the season, how many inches tall, in decimal form, is Mr. Chan’s lawn after 8 weeks.

Answers

Answer:

5.5 in

Step-by-step explanation:

First we will calculate the total lawn grown after 8 weeks.

Grow Rate = [tex]2\frac{1}{8} in/2 weeks[/tex]

Total lawn grown after 8 weeks = [tex]2\frac{1}{8} *4\\=8.5 in[/tex]

Next we will calculate the total lawn mown after 8 weeks.

Mowing Rate = [tex]1\frac{3}{4} in/2weeks[/tex]

Total lawn mown after 8 weeks = [tex]1\frac{3}{4} *4\\=7 in[/tex]

Lawn Height after 8 weeks = Initial Lawn Height + Total lawn grown - Total lawn mown

= 4 in + 8.5 in - 7 in

= 5.5 in

A company has the following account balances at the end of the year.

Accounts Balances
Equipment $ 22,000
Accounts payable 2,200
Salaries expense 29,000
Common stock 12,000
Land 14,000
Notes payable 16,000
Service revenue 35,000
Cash 5,200
Retained earnings ?

Answers

Based on the account balances at the end of year, the retained earnings are $5,000.

What are the retained earnings?

First, find the net income:

= Service revenue - Salaries

= 35,000 - 29,000

= $6,000

Then find the assets:

= 22,000 + 14,000 + 5,200

= $41,200

Then the liabilities:

= 2,200 + 16,000

= $18,200

Retained earnings:

= Assets - Liabilities - Net income - Common stock

= 41,200 - 18,200 - 6,000 - 12,000

= $5,000

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If P = (-2,7), Find:
Rx-1(P)
([?], [])

Answers

Answer is (4,7)

Step-by-step explanation:

Can a function ever have 2 y-
intercepts?

Answers

Answer:

yes I think I'm new to this but I think that's a yes

The length of a rectangle is 2x-3 feet, and the width is 5 feet. What is the area of the rectangle in square
A. 7x-15
B. 10x-15
C. 10x-8
D. 7x-8

Answers

Answer:

The answer is D. 7x-8

Step-by-step explanation:

We can solve this problem by finding the area of the rectangle, which is equal to the length times the width. In this case, the length is 2x-3 feet and the width is 5 feet. Therefore, the area of the rectangle is (2x-3)(5), or 7x-8.

"Bobby, you should know that the minimum legal speed for this highway is 45 MPH, and the maximum legal speed is 65 MPH."

Answers

Inequalities help us to compare two unequal expressions. The inequality that represents the given statement is 45≤x≤ 65.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the maximum legal speed on the highway is 65 MPH, therefore, the value of x must not exceed 65 MPH.

x ≤ 65

Also, the minimum legal speed on the highway is 45 MPH, therefore, the value of x must not be less than 45 MPH.

45≤x

By combining the two inequalities, we will get,

45≤x≤ 65

Hence, the inequality that represents the given statement is 45≤x≤ 65.

The complete question is:

Write an inequality that accurately represents the following statement: "Bobby, you should know that the minimum legal speed for this highway is 45 MPH, and the maximum legal speed is 65 MPH."

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Write the equation of a sine or cosine function to describe the graph.

Answers

y = A sin(Bx) and y = A cos(Bx). The number, A, in front of sine or cosine changes the height of the graph. The value A (in front of sin or cos) affects the amplitude (height). The amplitude (half the distance between the maximum and minimum values of the function) will be |A|, since distance is always positive.

Which inequality will have a shaded area below the boundary line?
A.
y – x > 5
B.
2x - 3y ≤ 3
C.
2x – 3y
D.
7x + 2y ≤ 2
E.
3x + 4y > 12

Answers

Option c) 2x-3y ≥ 3 is correct inequality which has a shaded area below the boundary line.

Attempting all the equation on the graph to get the solutions

What is inequality?

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.

Since, while attempting all the option on graph. The one equation that satisfies the condition is 2x-3y ≥ 3 of having shaded area below the boundary line.

Thus, the option c) 2x-3y ≥ 3 is correct implification on graph which shows the shaded area below the boundary line.

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What is the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6).....

Answers

The equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)

Equation of a parabola

The standard equation of a parabola is in the form f(x) = (x-a)(x-b)

where a and b are the intercepts of the graph. Given the parabola that has intercepts of x=-2 and x=6, the resulting equation will be:

f(x) = a(x-(-2))(x-6)

f(x) = a(x+2)(x-6)

If the parabola passes through (8, 6), then;

6 = a(8+2)(8-6)

6 = a(20)

a = 6/20

a = 3/10

Substitute

f(x) = 3/10(x+2)(x-6)

Hence the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)

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Find the coefficient of x^7y^3 in the expansion of (x - 2y)^10

Answers

Answer:

-960

Step-by-step explanation:

1) Expand [tex](x - 2y)^{10}[/tex] using the binomial theorem.

Binomial Theorem: [tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]

1.1) Substitute the values into the theorem.

[tex]\sum _{i=0}^{10}\binom{10}{i}x^{\left(10-i\right)}\left(-2y\right)^i[/tex]

1.2) Expand summation.

[tex]=\frac{10!}{0!\left(10-0\right)!}x^{10}\left(-2y\right)^0+\frac{10!}{1!\left(10-1\right)!}x^9\left(-2y\right)^1+\frac{10!}{2!\left(10-2\right)!}x^8\left(-2y\right)^2+\frac{10!}{3!\left(10-3\right)!}[/tex]

[tex]x^7\left(-2y\right)^3+\frac{10!}{4!\left(10-4\right)!}x^6\left(-2y\right)^4+\frac{10!}{5!\left(10-5\right)!}x^5\left(-2y\right)^5+\frac{10!}{6!\left(10-6\right)!}x^4\left(-2y\right)^6+\frac{10!}{7!\left(10-7\right)!}x^3\left(-2y\right)^7+\frac{10!}{8!\left(10-8\right)!}x^2\left(-2y\right)^8+\frac{10!}{9!\left(10-9\right)!}x^1\left(-2y\right)^9+\frac{10!}{10!\left(10-10\right)!}x^0\left(-2y\right)^{10}[/tex]

1.3) Simplify them.

1.4) You will get:

[tex]=x^{10}-20x^9y+180x^8y^2-960x^7y^3+3360x^6y^4-8064x^5y^5+13440x^4y^6-15360x^3y^7+11520x^2y^8-5120xy^9+1024y^{10}[/tex]

2) We are told to find the coefficient of [tex]x^{7} y^{3}[/tex]. Find it from the simplified expansion. The coefficient is -960.

What is the value of g(f(x)) when x = -2 if f(x) = x³

and g(x) =

2x+1
when x < 0

x²-1
when x>0

Answers

Answer:

g(f(-2)) = -15

Step-by-step explanation:

• f(x) = x³

Then

f(-2) = (-2)³ = -8

• When x = -2 → g(f(x)) = g(f(-2)) = g(-8)

Since -8 ≤ 0 then g(-8) = 2×(-8) + 1 = -16 + 1 = -15

Conclusion:

g(f(-2)) = -15

A cuboid measures X cm by 3X cm by 5X cm. Calculate the volume of the cuboid in terms of X.

Answers

Please check this answer


Hope it helps:)

Use the ray tool to graph the function. f(x)=−|x+2|+1

Answers

The graph of the function. f(x)=−|x+2|+1 is illustrated.

How to illustrate the function?

The given function is f(x)=−|x+2|+1.

We will have to draw the graph of the function.

When x = 1, f(1) will be -2. When x = 2, f(2,) will be -3

The points are illustrated based on the information given and the appropriate graph is illustrated and attached.

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(2a+b) (a-b) + (2a-b) (a+b)

Answers

Answer: 4a^2-2b^2 (I think this is right)

Step-by-step explanation:

Using the order of operations I started by multiplying both of the sides separately. The left side of the equation becomes 2a^2-b^2-ab while the right becomes 2a^2-b^2+ab. Then I put the sides together to add them and after combining like terms it becomes 4a^2-2b^2.

Part E
Christopher Columbus set sail from Spain in 1492. In what year did the Civil War end?
I know he died 1865 but you explain the answer

Answers

The year he died was the year 1846

Please answer all parts as I know the answers but need the work to go with them. Thus, I believe that some answers are correct. Thank you!

Answers

The number of the sample that is necessary is 171. The number of employees that would be selected if E is 30 = 476

How to solve for the number of the sample

The standard deviation = 398

error E = 50

Alpha is = 1-0.90 = 0.10

a. We are to find the value of the size of the sample

Z∝/2 = Z0.05

= 1.645

sample size,n >= [Za/2 *(sigma/E)]^2

n >= [1.645 * (398/50)] ^2

n >= 171.46

n = 171

b.

error,E = 30

n >= [1.645 * (398/30)] ^2

n >= 476.27

n = 476

Complete question

A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 90% confident that the sample mean is correct to within ±$50 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately $398. a. How large a sample is necessary?

b. If management wants to be correct to within ±$30, how many employees need to be selected?

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what should be added to 4x²-3x²+1 to make it a perfect square​

Answers

[tex]im \: guessing \: its \: 4x {}^{2} - 3x + 1 \\ (correct \: me \: if \: im \: wrong)[/tex]

[tex](a - b) {}^{2} = a {}^{2} - 2ab + {b}^{2} [/tex]

[tex]4x {}^{2} = a {}^{2} \: \: \: \: \: \: \: \: \: \: \: b {}^{2} = 1 \\ a = 2x \: \: \: \: \: \: \: \: \: \: \: \: \: \: b = 1[/tex]

[tex](2x - 1) {}^{2} = 4x {}^{2} -4x + 1[/tex]

[tex]we \: need \: to \: add \: a \: - x \\ \: to \: the \: original \: equation[/tex]

Note that this problem can be approached in many ways. For instance, we can add to the b² term instead of changing the middle term...
You could solve this by using completing the square and simplifying

12:00,10:00,6:00,4:00. What is the missing time? ​

Answers

I would say 8:00 between 6:00 and 10:00 cause it seems to be progressing in increments of 2 hours

Solve the system using substitution. -x+y=9 and x-y=-9

Answers

Answer:

Infinite Number of Solutions

Step-by-step explanation:

Hello!

We can solve for y in the first equation, and plug that value in for y in the second equation.

Find the Equation for Y-x + y = 9y = 9 + x

Now that we know the equation for y, we can plug that in for y into the second equation to solve for x.

Solve for Xx - y = -9x - (9 + x) = -9x - 9 - x = -9-9 = -9

Since the equations match, there are an infinite number of solutions.

If we take a close look at the equations, we can also see that they are the same equation, but with flipped signs.

Find the perimeter of the triangle whose vertices are (−7,−1), (5,−1), and (5,4). Write the exact answer. Do not round.

Answers

The perimeter of the triangle is 30 units

How to determine the perimeter?

The vertices are (−7,−1), (5,−1), and (5,4).

Start by calculating the distance between the vertices using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]d1 = \sqrt{(-1 + 1)^2 + (5 + 7)^2[/tex]

d1 = 12

[tex]d2 = \sqrt{(-1 - 4)^2 + (5 - 5)^2[/tex]

d2 =5

[tex]d3 = \sqrt{(-1 - 4)^2 + (-7 - 5)^2[/tex]

d3 = 13

The perimeter is then calculated as:

P = d1 + d2 + d3

This gives

P = 12 + 5 + 13

Evaluate

P = 30

Hence, the perimeter of the triangle is 30 units

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estimate 789×215 can any one answer

Answers

Since 789x215 equals to 169,635 the estimate will be 170,000 or round to the nearest hundred thousands will be 200,000.



In the diagram below of AACT, BE | AT.
C
F
If CB = 3, CA = 10, and CE = 6, what is the length
of ET?
1)
5
2)
14
3)
20
4)
26

Answers

Answer:

14

Step-by-step explanation:

CB/AB = CE/ET

3/7 = 6/ET

ET = 14

Question A librarian weighs each book that was returned to the library (to the nearest pound). Below is the data. 245 55 Make a dot plot that represents the library book data. 3 4 3 4 4 2 199 CO 8 5 2 CO 8 3 3 Question A librarian weighs each book that was returned to the library ( to the nearest pound ) . Below is the data . 245 55 Make a dot plot that represents the library book data . 3 4 3 4 4 2 199 CO 8 5 2 CO 8 3 3​

Answers

The dot plot that represents the library book data is shown in the image below.

How to Construct a Dot Plot?

To construct a dot plot, each data point is represented as a dot. The number of dots one data point has represents the frequency at which that data point occurs in the data set.

The data set given in the table will have the following data points and frequencies:

1: 1

2: 3

3: 4

4: 4

5: 4

6: 0

7: 2

8: 2

The dot plot for the data is shown in the image below.

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