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In order to unload clay easily, the body of a dump truck must be elevated to at least 50°. The body of a dump truck that is 15 feet long has been raised to 9 feet. Will the clay pour out easily? Show your work and draw a diagram to support your answer.

Please include the following:

• A diagram



• The trig equation you are solving and the steps you take to solve it.



• An answer in the context of the problem.
_________ (Yes or No), The clay ___________ (will or will not) pour out easily when the body of the dump truck is raised to 9 feet. I know this because ______________________________________.

Answer:

B

Step-by-step explanation:

If you put (x,y) values in here

(0,2)

2x + 5y = 10

2.0 + 5.2 = 10

0 + 10 = 10

4x + 10y = 20

4.0 + 10.2 = 20

0 + 20 = 20

And the other is

(5,0)

2x + 5y = 10

2.5 + 5.0 = 10

10+0= 10

4x + 10y = 20

4.5 + 10.0 = 20

20 + 0 = 20

All of them is OK.

Answer:

2x + 5y = 10

4x + 10y = 20

Step-by-step explanation:

just took the test

Explanation:

There is nothing to "solve." This equation is a trig identity.

Often, it works well to express all trig functions in terms of sine and cosine. When you're trying to prove an identity, you usually pick one side to rearrange, and leave the other side alone. Here, we will rearrange the right side.

[tex]\csc\theta=\dfrac{\cot\theta+1}{\cos\theta+\sin\theta}\\\\\csc\theta=\dfrac{\dfrac{\cos\theta}{\sin\theta}+1}{\cos\theta+\sin\theta}=\dfrac{\left(\dfrac{\cos\theta+\sin\theta}{\sin\theta}\right)}{\cos\theta+\sin\theta}=\dfrac{1}{\sin\theta}\\\\\csc\theta=\csc\theta[/tex]

XV is 1/2 a circle , which is equal to 180 degrees ( a full circle is 360).

ZW = WY, so ZV = VY = 43.

XY = XV-43 = 180 - 43 = 137

The answer is B. 137

Answer:

  x = 2

Step-by-step explanation:

The vertex form tells you the vertex is (x, y) = (2, 3). The vertical line through the vertex, x=2, is the axis of symmetry.

Answer:

x = 2

Step-by-step explanation:

took the test on edge

Answer:

The coordinates of triangle A'B'C' are A' (-1 , 1) , B' (2 , 0) , C' (1 , 2)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

* Lets solve the problem

- ABC is a triangle, where A = (1 , -1) , B = (0 , 2) , C = (2 , 1)

- The Δ ABC reflected over the line y = x to form ΔA'B'C'

∵ The image of the point (x , y) after reflected across the line y = x

   is (y , x)

∴ We will switch the coordinates of each point in Δ ABC to find the

  coordinates of Δ A'B'C'

# Vertex A

∵ A = (1 , -1) ⇒ x = 1 , y = -1

∴ The x-coordinate of the image is -1

∴ The y-coordinate of the image is 1

∴ A' = (-1 , 1)

# Vertex B

∵ B = (0 , 2) ⇒ x = 0 , y = 2

∴ The x-coordinate of the image is 2

∴ The y-coordinate of the image is 0

∴ B' = (2 , 0)

# vertex C

∵ C = (2 , 1) ⇒ x = 2 , y = 1

∴ The x-coordinate of the image is 1

∴ The y-coordinate of the image is 2

∴ C' = (1 , 2)

* The coordinates of triangle A'B'C' are A' (-1 , 1) , B' (2 , 0) , C' (1 , 2)

Answer:

$9 per hour

Step-by-step explanation:

given that falicity babysat for 2 hours each night for 10 nights

Total hours spent babysitting = 10 nights x 2 hours = 20 hours

hourly rate = total amount earned / total time spent babysitting

= $180 / 20 hrs = $9 per hour

Answer:

219.9  feet to the nearest tenth.

Step-by-step explanation:

Use trigonometry:

tan 35 = opposite / adjacent side

= 154/x

x =  154 / tan35

= 219.93

Answer:

219.9 ft

Step-by-step explanation:

After looking at pic, cross multiply to get x tan(35)=154

then divide both sides by tan(35) giving x=154/tan(35)

x is approximately 219.9 ft

Answer:

  20 dimes

Step-by-step explanation:

We can group the coins into groups that are ...

  4 quarters + 2 dimes + 1 nickel

Then each group satisfies the ratio requirements, and the total value of a group is $1.25.

Since the total value in the register is $12.50, there must be 10 such groups, hence 20 dimes.

Answer:

The correct answer option is c. the net deposit amount.

Step-by-step explanation:

We know that Michael is making a deposit with a check and wants some cash back.

According to The Federal Reserve System and The Federal Deposit Insurance Corporation, the deposit slip must have the name his name, his account number, date, amount of the check, amount of cash that he want, his signature and the net deposit amount.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let c represent the number of liters of champagne Lauren uses. Then (15-c) will be the number of liters of orange juice. The total cost of the mix will be ...

  12c +1.50(15-c) = 5.00(15)

  10.5c = 52.50 . . . . . subtract 22.50, simplify

  52.50/10.5 = c = 5 . . . . divide by the coefficient of c

Then the amount of orange juice is ...

  15 -c = 15 -5 = 10 . . . . liters

Lauren should use 5 liters of champagne and 10 liters of orange juice.

Answer:

  see below

Step-by-step explanation:

A regular tessellation is created by repeating a regular polygon. The first and third diagrams show multiple regular polygons of different sizes and shapes. The second diagram has no regular polygons in it.

The last diagram shows a regular tessellation.

Answer:

Step-by-step explanation:

Your equation comes out to x + 3 = x/3.  Multiplying all three terms by 3 results in 3x + 9 = x, which simplifies to 2x = -9, so that x = -9/2.

Unsure of what you're asking for by "model."

Answer:

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

Step-by-step explanation:

The given expression is:

[tex]\frac{3m-6}{4m+12} \cdot \frac{m^2+5m+6}{m^2-4}[/tex]

We factor to get:

[tex]\frac{3(m-2)}{4(m+3)} \cdot \frac{(m+2)(m+3)}{(m-2)(m+2)}[/tex]

Cancel out the common factors to get:

[tex]\frac{3(m-2)}{4(m+3)} \cdot \frac{(m+3)}{(m-2)}[/tex]

We cancel further to get:

[tex]\frac{3(m-2)}{4(m+3)} \cdot\frac{(m+3)}{(m-2)}=\frac{3}{4}[/tex]

The correct chice is B.

Answer:

Step-by-step explanation:

Answer: Option B and option D.

Step-by-step explanation:

We know that a quadrilateral is a 2-dimensional closed shape that has four sides.

By definition the diagonals of a quadrilateral are the lines that connect two non-adjacent vertices.

The following quadrilaterals have diagonals that are perpendicular to each other (also known as perpendicular bisector diagonals), which means that they form four angles of 90 degrees (right angles): Rhombus and Square.

Therefore the answers are: the option B and the option D.

The quadrilaterals that have diagonals perpendicular to each other are:

a. Rectangle

b. Rhombus

d. Square

In a rectangle, the diagonals are always perpendicular to each other. The same applies to a rhombus, which is a special case of a parallelogram with all sides equal.

Similarly, a square is a special type of rectangle and rhombus, so its diagonals are also perpendicular. However, in a general parallelogram, the diagonals are not necessarily perpendicular. Therefore, the correct options are a, b, and d.

Therefore, The quadrilaterals that have diagonals perpendicular to each other are:

a. Rectangle

b. Rhombus

d. Square

Learn more about quadrilaterals here

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Answer:

  B.  49:9

Step-by-step explanation:

The ratio of surface areas is the square of the ratio of edge lengths:

  7² : 3² = 49 : 9

Answer:

  C.  population; students

Step-by-step explanation:

Since every member of the population is asked, the survey is not a sample. If opinions are given equal weight, there are more students than staff, so we expect students to have more influence on results.

Answer:

C population, students

Step-by-step explanation:

Since everyone is asked the question, a population is used  (sample only uses part).  There are more students than staff, so students will have a bigger influence on the results

Answer:

No;  the angle of elevation of the front bottom of the dump truck body will be only 31°, much smaller an angle than the required 50°

Step-by-step explanation:

Let the body of the truck rest upon the x-axis with the rear body at (0, 0).  The front of that body is located at (15, 0).  The dump body is elevated to 9 ft.

We thus have a right triangle with base 15 ft and height 9 ft, and want to know what the angle is.  The angle is at (0, 0).  The front of the body is at (0, 15), and when elevated that point will be located at (15, 9).

The tangent function relates the angle to the opposite side (length 9 ft) and the adjacent side (length 15 ft):

tan Ф = opp / hyp = 9 / 15 = 31 degrees.

NO:  the elevation of the front of the dump truck body is only 31° approx.  The clay will not easily dump from the body.

Answer:

r = 15.2

Step-by-step explanation:

Where AB meets the circle creates a right angle.  This is a right triangle problem involving missing sides.  This means that we will use Pythagorean's theorem to find the length of the radius.  Pythagorean's theorem applies this way:

[tex]10^2+r^2=(r+3)^2[/tex]

Foiling the right side gives us the equation:

[tex]100 + r^2=r^2+6r+9[/tex]

When we combine like terms, we find the squared terms cancel each other out, leaving us with

100 = 6r + 9 and

91 = 6r so

r = 15.2

Answer:

  y = 45,121,040×1.027^t

Step-by-step explanation:

An exponential growth equation is generally of the form ...

  value at time t = (initial value)(growth factor)^t

where the growth factor is the multiplier for a period equal to one time unit.

Here, the initial value (in 2014) is 45,121,040. The growth factor is given as 1.027 (2.7% added per year), and we can define t as the number of years after 2014. Then our equation is ...

  y = 45,121,040×1.027^t . . . . where t = years after 2014

A = bh

A = (3.5)((0.75)

A = 2.625

A = 2_5/8 ft^2

Answer:

x=6.5 cm

Step-by-step explanation:

The tangent meets the circle at right angles.

Therefore the triangle formed is a right triangle.

From the Pythagorean Theorem;

[tex]x^{2} +20.2^2=(x+14.7)^2[/tex]

We expand to obtain:

[tex]x^{2} +408.4=x^2+29.4x+216.04[/tex]

We group like terms to get:

[tex]x^{2} -x^2+408.4-216.04=29.4x[/tex]

We simplify now to get:

[tex]192.36=29.4x[/tex]

We divide both sides by 29.4 to get:

x=6.5 to the nearest tenth.

Answer:

  It is not a function

Step-by-step explanation:

The plot shows (1, 1) and (1, 3) are both defined by the relation. It does not pass the "vertical line test", which requires the relation be single-valued everywhere.

Answer:

This is not a function

Step-by-step explanation:

To determine whether a relation is a function, we can use the vertical line test.  If a vertical line touches the relation in more than one point, it is not a function.

Since a vertical line will touch the relation at two points at x=1

(1,1) and (1,3)  this is not a function

Answer:

GCF is 5

Step-by-step explanation:

The factors of 35 are: 1, 5, 7, 35

The factors of 50 are: 1, 2, 5, 10, 25, 50

Aubrey's total earnings over 20 years, given a starting salary of $45,000 and a 2% annual increase, would be approximately $1,157,357, calculated using the formula for an increasing annuity.

The subject of this question is compound interest, which is a mathematical concept used to calculate the future value of an investment or loan. In this case, Aubrey's salary is subject to an annual increase of 2%, which is compounded yearly.

To calculate the total amount earned over 20 years, we need to use the formula for the future value of a salary subject to yearly increases: Future Value = Salary * ((1 + Rate)^Years). Substitute the given values into the equation: Future Value = $45,000 * ((1 + 0.02)^20). Calculating this gives a value of approximately $66,207.11, which would be Aubrey's salary in the 20th year.

To find the total earnings over 20 years, you would add each year's salary together. However, it is much more complex due to the increasing salary. In this case, an annuity formula can be used.

The formula is: Total Earnings = Pmt * ((1 - (1 + r) ^ -n) / r). 'Pmt' is the first period payment, 'r' is the interest rate, and 'n' is the number of payments. Here, Pmt = $45,000, r = 2% or 0.02, and n = 20 years. After substituting everything in, the result should be around $1,157,357 rounded to the nearest whole number.

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Answer:

i agree

Step-by-step explanation:

The answer is in the attachment below!

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I don’t understand. Explain mate

Answer:

Given in the problem , as ΔBEC is an equilateral triangle , ∠GCD=90°,m∠ECD=30°

Step-by-step explanation:

Step1:

Statement 2:

as ΔBEC is an equilateral triangle

statement 3:

BG ≅ GC as FG  is perpendicular bisector given in the problem.

Statement 4.

∠CFG =60° as as ΔBEC is an equilateral triangle

Staement 5 : Reason : All the angles of an equilateral triangle are 60°

step 2 :-

Statement 1.

as ΔBEC is an equilateral triangle is given in the fourth statement of the problem.

Statement 2.

m∠GCE = 60° as it is contained in ΔBEC which is an equilateral triangle. All the angles of an equilateral triangle are 60°.

Statement 3:

∠GCD =90° as ABCD is a square

Statement 4:

m∠ECD=∠GCD-m∠GCE

            =90°-60°

            =30°

Hence Proved

Answer:

3:5

Step-by-step explanation:

The areas of two similar octagons are 9m² and 25m²

The scale factor of their areas is [tex]\frac{25}{9}[/tex] or 9:25

The scale factor of their side lengths is [tex]\sqrt{25/9}[/tex] or 3:5

ANSWER

3:5

EXPLANATION

The given similar octagons have areas 9 m² and 25m² .

Let the scale factor of their side lengths be in the ratio:

m:n

[tex] {( \frac{m}{n}) }^{2} = \frac{9}{25} [/tex]

We take square root of both sides to get;

[tex] \frac{m}{n} = \sqrt{ \frac{9}{25} } [/tex]

We simplify the square root to get

[tex] \frac{m}{n} = \frac{3}{5} [/tex]

Therefore the scale factor of their side lengths is 3:5

Answer: second option.

Step-by-step explanation:

Given the transformation [tex]T:(x,y)[/tex]→[tex](x-5,y+3)[/tex]

 You must substitute the x-coordinate of the point A (which is [tex]x=2[/tex]) and the y-coordinate of the point A (which is [tex]y=-1[/tex]) into [tex](x-5,y+3)[/tex] to find the x-coordinate and the y-coordinate of the image of the point A.

Therefore, you get that the image of A(2,-1) is the following:

[tex](x-5,y+3)=(2-5,-1+3)=(-3,2)[/tex]

You can observe that this matches with the second option.