What is the length of the diameter of a circle inscribed in a right triangle with the length of hypotenuse c and the sum of the legs' lengths equal to m?

Answer:

c = 25, d = 65

Step-by-step explanation:

∠d + 90 = 155 ( vertical angles )

Subtract 90 from both sides

d = 65

The angle above 155 = 180 - 155 ( straight angle ) = 25

Hence c = 25 ( corresponding angles )

Answer:

<d = 65 degrees.

<c = 25 degrees.

Step-by-step explanation:

<d + 90 = 155 since vertically opposite <'s are equal. Therefore <d = 155-90

= 65 degrees.

The angle adjacent to <d is 180-155= 25 degrees since <'s on a line = 180 degrees.

Therefore <c= 25 degrees since corresponding <'s on parallel lines are equal.

The volume of the solid is 8/3 cubic units.

Visualization:

Imagine a right triangle with one leg on the x-axis and the other on the y-axis. The hypotenuse of the triangle intersects the line x + y = 2 at a point (x, y). The solid is formed by stacking square cross-sections perpendicular to the base triangle, with each square having a side length equal to the distance between the line x + y = 2 and the triangle's hypotenuse at that point.

Volume Calculation:

Let x be the distance from the origin to the point where the hypotenuse intersects the line x + y = 2. Then, the length of the side of each square cross-section is (2 - x). The area of each cross-section is therefore (2 - x)^2.

As we move from the origin to the vertex of the triangle where the hypotenuse intersects the line, the distance x increases from 0 to 2. Thus, the volume of the solid can be calculated by integrating the area of the cross-sections over the range of x:

Volume = ∫(2 - x)^2 dx from x = 0 to x = 2

Integration:

Solving the integral using the power rule, we get:

Volume = [4/3 * x^3 - 2x^2 + x] from x = 0 to x = 2

Evaluating the expression at the limits of integration:

Volume = (32/3 - 8 + 2) - (0 - 0 + 0) = 32/3 - 6 = 8/3 cubic units

Therefore, the volume of the solid is 8/3 cubic units.

Answer:

  a)  y = x+1

  b)  The transformation shifts the graph 1 unit to the left

Step-by-step explanation:

a) Put (x+1) where (x) is in the function definition:

  y = f(x+1)

  y = x+1

__

b) This transformation has the effect of shifting the graph one unit to the left. Any point (x, f(x)) on the original curve, will now be (x-1, f(x)), shifted one unit to the left.

Answer: A C and E

Step-by-step explanation:

-4+6 (x-2x)^2 36x^2yz-3

(A) (C) (E)

There's a screenshot of the answers below

Answer:

  Wet Suit Willy

Step-by-step explanation:

To find boxes per dive, divide boxes by dives:

  Sam: 33/11 = 3 . . . boxes per dive

  Willy: 81/18 = 4.5 . . . boxes per dive

  Dan: 104/26 = 4 . . . boxes per dive

Wet Suit Willy found the most treasure boxes per dive: 4.5.

Answer:

  {4}

Step-by-step explanation:

It is helpful to let a calculator or spreadsheet perform the function evaluations for you. The two functions have the same value only for x=4 in the domain.

  f(4) = 13 = g(4)

_____

The functions also have the same value for x=-2, but that is not in the domain given.

Explanation:

When the points are plotted on a graph, it is easy to see that the slope of AC is -2 and the slope of BC is 1/2. These slope values have a product of -1, so the corresponding line segments are perpendicular to each other.

___

If you have studied vectors, you can find the dot product of AC with BC:

  AC = (-5, 3) -(-2, -3) = (-3, 6)

  BC = (6, 1) -(-2, -3) = (8, 4)

The dot product is ...

  (-3, 6)·(8, 4) = (-3)(8) + (6)(4) = -24+24 = 0

When the dot product of vectors is zero, they are perpendicular.

The answer is:

The correct answer is c.

[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]

To calculate the slugging average or slugging percentage, we need to divide the number of total bases by the total times at bat.

[tex]SluggingAverage=\frac{TotalBases}{TimesAtBat}[/tex]

We know that:

A single means 1 base.

A double means 2 bases.

A triple means 3 bases.

A homerun means 4 bases.

So, we know that:

[tex]Singles=25=25bases\\Doubles=2*10=20bases\\Triples=3*3=9bases\\Homeruns=10*40=40bases\\TimesAtBat=140[/tex]

Then, substituting and calculating we have:

[tex]SluggingAverage=\frac{25bases+20bases+9bases+40bases}{140}[/tex]

[tex]SluggingAverage=\frac{94bases}{140times}=0.671[/tex]

Hence, the correct answer is c.

[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]

Have a nice day!

Answer:

1. C. 8000 - 24x; 2 A. x + 2x + 2 = 40; 3. C. Step 3

Step-by-step explanation

1. Desmond  

[tex]\begin{array}{rcl}\text{Value of car two years ago} & = & 8000\\\\\text{Less depreciation = 24 mo} \times\dfrac{x}{\text{1 mo}} & = & -24 x\\\\\text{Current value} & = & \mathbf{8000 - 24x}\\\end{array}[/tex]

2. Avi and Sergi  

[tex]\begin{array}{rcl}\text{Sergi's money} & = & x\\\text{Double Sergi's money} & = & 2x\\\text{Avi's money} & = & 2x + 2\\\text{Avi's money + Sergi's money} & = & x + 2x + 2\\\text{Avi's money + Sergi's money} & = & 40\\x + 2x + 2 & = & 40\\\end{array}[/tex]

3. Isabella  

[tex]\begin{array}{crl} \textbf{Step} & \textbf{Work} & \textbf{Justification} \\ & 4x - 2x + 8 = 6(x + 4) & \\ 1 & 4x - 2x + 8 = 6x + 24 & \text{Distributive Property} \\ 2 & 2x + 8 = 6x + 24 & \text{Combine like terms} \\ 3 & -4x + 8 = 24 & \textbf{Subtraction Property of Equality}\\ 4 & -4x = 16 & \text{Subtraction Property of Equality} \\ 5 & x = -4 & \text{Division Property of Equality} \\ \end{array}[/tex]

Step 3 has the incorrect justification. Isabella subtracted 6x from each side, so she should have used the Subtraction Property of Equality

Answer:

60

Step-by-step explanation:

Sam is 5, Tom is 3 times as old, 5 times three is 15, so tom is 15, 20 is 4 times 5, so you take 15, and multiply it by 4, and that's your answer

Answer:

Step-by-step explanation:

In the third quadrant, sine and its inverse, cosecant, are negative. In that quadrant, tangent and its inverse, cotangent, are positive. The sine function always has a magnitude less than or equal to 1, while the cosecant function always has a magnitude at least 1.

The negative numbers on your list can be assigned to sin(x) and csc(x) based on their magnitudes. 2√6 = √24 < 5, so 2(√6)/5 < 1. The number with this magnitude is the sine; its inverse is the cosecant.

The tangent is the ratio of sine to cosine, so is ...

  tan(x) = ((-2√6)/5)/(-1/5) = 2√6

and the cotangent is the inverse of that:

Of course, the secant is the inverse of the cosine, so would be -5. That is not one of the number choices, so sec(x) can be ignored.

No, because AB is 2/5 the length MN but CD is 1/3 the length QP.  

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Given:

As, Comparing the corresponding sides, the length of AB is 4.  

The length of MN is 10.  This makes their ratio 4/10 = 2/5.

and, the CD length is 2.

QP has a length of 6. Consequently, their ratio is 2/6 = 1/3.

Therefore, because the side ratios differ, the figure is not proportionate and is not a dilation.

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Trapezoid ABCD is not the result of the dilation of trapezoid MNPQ by a scale factor of 2/5 because AB is 2/5 the length MN but CD is 1/3 the length QP.

Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.

Given a trapezoid ABCD and another trapezoid MNPQ.

From the figure,

length of AB = 2 + 2 = 4

Length of MN = 5 + 5 = 10

Scale factor = 4/10 = 2/5

Now,

Length of CD = 1 + 1 = 2

Length of QP = 3 + 3 = 6

Scale factor = 2/6 = 1/3

That is, the scale factor differs.

Hence the correct option is C.

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WHERE IS THE QUESTION ??

Answer:

A. 6i

Step-by-step explanation:

Apply by the radicial rule.

[tex]\sqrt{-36}=\sqrt{-1}\sqrt{36}[/tex]

[tex]\sqrt{-1}\sqrt{36}[/tex]

Imaginary number.

[tex]\sqrt{36 i}[/tex]

Square root the numbers from left to right.

[tex]6^2=36[/tex]

[tex]\sqrt{6^2}=6[/tex]

6i is the correct answer.

I hope this helps you, and have a wonderful day.

Answer:

A

Step-by-step explanation:

Answer:

The true statements are:

The y-variable will be eliminated when adding the system of equations

There is only one solution to the system of equations is

Step-by-step explanation:

* Lets explain how to solve the problem

- We use the elimination method to solve the system of the

  linear equation

- The solution is one of three cases

# Exactly one solution ⇒ the 2 lines which represented the equations

  intersect each other at one point

# No solution ⇒ the 2 lines which represented the equations are

  parallel to each other

# Infinite solutions ⇒ the two lines are coincide

- In the system of the linear equations of the problem we have two

 linear equations  -x + 6y = 16 and 8x - 6y = -2

- To solve we must to eliminate one of the two variables

∵ The y's in the two equations have the same coefficients and

   different signs

∴ We add the equations to eliminate y

∴ (-x + 8x) + (6y - 6y) = 16 + -2

∴ 7x = 14 ⇒ divide both sides by 7

∴ x = 2

- Substitute the x in any one of the two equations by 2

∴ -2 + 6y = 16 ⇒ add 2 to both sides

∴ 6y = 18 ⇒ divide both sides by 6

∴ y = 3

∴ The solution of the system of the equations is (2 , 3) ⇒ only one

   solution

- Lets check the statements to find the true statements

# The x-variable will be eliminated when adding the system of

   equations is not true

# The y-variable will be eliminated when adding the system of

   equations is true

# The sum of the system of equations is - x + 6y is not true

# There is only one solution to the system of equations is true

Statements 1 and 2 are true, while statements 3 and 4 are false.

Let's analyze each statement:

1. The x-variable will be eliminated when adding the system of equations.

  - When adding the equations, the x-variables are eliminated because (x) in one equation cancels with (-8x) in the other equation. So, this statement is true.

2. The y-variable will be eliminated when adding the system of equations.

  - When adding the equations, the y-variables are also eliminated because (6y) in one equation cancels with (-6y) in the other equation. So, this statement is true.

3. The sum of the system of equations is -x + 6y.

  - The sum of the two equations is indeed (-x + 6y). Adding the equations directly gives ( -x + 6y = 14), not ( 16). So, this statement is false.

4. There is only one solution to the system of equations.

  - Since the system of equations represents two equations with two variables, the solution can either be a unique solution, no solution, or infinitely many solutions. To determine this, we need to solve the system of equations. We can do this by eliminating one variable and solving for the other. However, from the given equations, we can't determine the nature of the solution without further analysis. So, this statement is indeterminate based solely on the provided equations.

Therefore, statements 1 and 2 are true, while statements 3 and 4 are indeterminate based on the given information.

Answer:

  1/4 of the credit

Step-by-step explanation:

The problem statement tells you n=5. Putting that into the expression for lost credit, you get ...

  1/(5-1) = 1/4

of the credit is lost for a question with 1 wrong answer.

You will lose 1/4 of the credit.

Answer:

The credit will you lose for the part of question is 1/4 or 25%.

Step-by-step explanation:

Consider the provided information.

It is given that, if you submit an incorrect answer to a multiple-choice question with n options, you will lose 1/(n−1) of the credit for that question.

Suppose the given multiple choice question has 5 answer. So for one wrong answer the loss will be:

Substitute the value of n=5 in above formula.

[tex]\frac{1}{n-1} \\\frac{1}{5-1} \\\frac{1}{4}=0.25[/tex]

That means you will lose 1/4 or 0.25credit.

Now convert it into %.

[tex]\frac{1}{4}\times 100=25\%[/tex]

Hence, the credit will you lose for the part of question is 1/4 or 25%.

Answer:

270 degrees

Step-by-step explanation:

180 would be diagonal from original, 360 would be where the original is and 90 would be in the second quadrant so therefore its 270

Answer:

B) 270°

Step-by-step explanation:

it was correct for me

Answer:

So a point is (-3,-5) and the vertex is (-4,-3)

Step-by-step explanation:

This is in vertex form. Vertex form is y=a(x-h)^2+k where (h,k) is the vertex.

The vertex here is (-4,-3)... now just use a value of x to plug in (any value besides -4)

I will choice -3.  This gives -2(-3+4)^2-3

f(-3)=-2(1)^2-3

f(-3)=-2-3

f(-3)=-5

So a point is (-3,-5) and the vertex is (-4,-3)

Answer:(-4,-3)

Step-by-step explanation:

Volume = 9in • 9in • 9in

Volume = 729 in^3

Now multiply the volume by 6 grams.

Let H = total weight of the cube in terms of grams.

H = V • 6

H = 729 • 6

H = 4,374 grams

Answer:

Step-by-step explanation:

Add all the students: 4+6+2+2+3+4+6+3 = 30

Add all the male students = 14

divide : 14/30=0.466666

multiply by 100

0.466*100=4.66

round

Answer = 5

Answer:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side ⇒ answer B

Step-by-step explanation:

* Lets explain the triangle inequality theorem

- The triangle Inequality Theorem is the sum of the lengths of any two

  sides of a triangle is greater than the length of the third side.

- That means when we add the lengths of the shortest two sides,

  the answer will be greater than the length of the longest side.

- Examples:

# Is the set of {4 , 5 , 9} could form a triangle

- Add 4 , and 5 because they are the shortest sides

∵ 4 + 5 = 9

∵ The third side is 9

∵ In any triangle the sum of the lengths of any two sides of a triangle

  must be greater than the length of the third side

∴ The set {4 , 5 , 9} couldn't form a triangle

# Is the set of {4 , 5 , 8} could form a triangle

- Add 4 , and 5 because they are the shortest sides

∵ 4 + 5 = 9

∵ The third side is 8

∵ In any triangle the sum of the lengths of any two sides of a triangle

  must be greater than the length of the third side

∴ The set {4 , 5 , 8} could form a triangle

# Is the set of {3 , 5 , 9} could form a triangle

- Add 3 , and 5 because they are the shortest sides

∵ 3 + 5 = 8

∵ The third side is 9

∵ In any triangle the sum of the lengths of any two sides of a triangle

  must be greater than the length of the third side

∴ The set {3 , 5 , 9} couldn't form a triangle

* Lets solve the problem

∵ The triangle inequality theorem is the sum of the lengths of any two

  sides of a triangle is greater than the length of the third side

- It talks about the relation between the lengths of the sides

∴ The right answer is B. The sum of the lengths of any two sides of

   a triangle is greater than the length of the third side

Answer:

B

Step-by-step explanation:

A cannot be correct as it is measuring angles, and the theorem is not abt the angles.

B is correct because the theorem is abt triangle sides.

C is incorrect because that is just ridiculous.

D is incorrect because is not always true and the theorem once again, is not abt angles.

Answer:

  D.  60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relationship of interest is ...

  Sin = Opposite/Hypotenuse

  sin(M) = ON/OM = 4(√3)/8 = (√3)/2

  M = sin⁻¹((√3)/2) = 60°

Answer: [tex](-2,1)[/tex]

Step-by-step explanation:

It is important to remember that a rotation is a transformation in which the shapes and sizes do not change, but the object can be turned in different directions.

By definition, the rule for 180° counterclockwise rotation is this:

[tex](x,y)[/tex]→ [tex](-x,-y)[/tex]

Therefore, we know that the image of the point [tex]P=(2,-1)[/tex] under a 180° counterclockwise rotation is:

 [tex](2,-1)[/tex]→ [tex](-2,1)[/tex]

Answer:

  32°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the trig function relating angles to the opposite and adjacent sides of the triangle is ...

  Tan = Opposite/Adjacent

The side opposite the angle x is shown as having measure 5; the side adjacent has measure 8. Putting all this in the above equation gives ...

  tan(x) = 5/8

To find the angle from the value of the tangent, you use the inverse of the tangent function. The name of that is the arctangent function. It is often written as tan⁻¹(x) and often accessible on your calculator using a "second function" key. Some calculators, like the one shown in the attachment, recognize the arctan function name.

  x = arctan(5/8) ≈ 32°

The value of x rounded to the nearest whole degree is 32°.

Answer:

  √17

Step-by-step explanation:

The distance formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

Filling in the point values, we have ...

  d = √((-1-3)² +(9-8)²) = √(16 +1)

  d = √17

Answer:

Yes, because the P(A) · P(B) = P(A and B) ⇒ last answer

Step-by-step explanation:

* Lets study the meaning independent and dependent probability

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events

 is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)

* Lets solve the question

∵ P(A) =  watching a movie

∵ P(B) =  going out to dinner

∵ The probability that a person will watch a movie is 62%

∴ P(A) = 62% = 62/100 = 0.62

∵ The probability of going out to dinner is 46%

∴ P(B) = 46% = 46/100 = 0.46

∵ The probability of watching a movie and going out to dinner

  is 28.52%

∵ P(A and B) = 28.52% = 28.52/100 = 0.2852

- Lets find the product of P(A) and P(B)

∵ P(A) = 0.62

∵ P(B) = 0.46

∵ P(A and B) = 0.2852

∴ P(A) · P(B) = 0.62 × 0.46 = 0.2852

∴ P (A and B) = P(A) · P(B)

∴ Watching a movie and going out to dinner are independent events

  because the P(A) · P(B) = P(A and B)

The probability of drawing a blue marble will be 1/3.

Blue marbles = 3

Red marbles = 2

Yellow marbles = 4

Total marbles = 3 + 2 + 4 = 9

The probability of drawing a blue marble will be:

= 3/9

= 1/3

The probability of drawing a marble that isn't red will be:

= 3/9 + 4/9

= 7/9

The probability of drawing a red and yellow marbles will be:

= 2/9 + 4/9

= 2/3

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Answer:

41

Step-by-step explanation:

plug in each number with the corresponding variable so

5*2-(-3)^2+2*4(2-(-3))

the use pemdas and you get 41

It is best to graph the function when searching for the range.

For the function f(x) = (x + 5)(x + 1), the range is ALL REAL NUMBERS when y is greater than or equal to -4.

Get it?

Answer:

45.71 - 6x

Step-by-step explanation:

If Heather bought markers to donate, the amount she donates is subtracted from her balance of 45.71.  We know she bought 6 packs of markers, but we do not know how much each pack cost.  We will make this our unknown "x".  The expression for  packs of markers costing "x" is 6x.  Because she buys them from her account, which takes aways from her balance, the expression that represents this donation is:

45.71 - 6x

(Notice that the question asks for the EXPRESSION after she buys the markers, not the EQUATION.  The difference between an expression and an equation is the lack of an equals sign in the expression.)

Answer:

M= 45.71 - 6x

Step-by-step explanation:

M represents money and x is how much each pack of markers cost. 45.71, which is the original amount, minus 6x will give the correct amount.