if m<1=40 and m<2=80, what is m<3?

Step-by-step explanation:

[tex]\text{The distributive property:}\ a(b+c)=ab+ac\\\\\dfrac{1}{2}(10x+20y+10z)=\dfrac{1}{2\!\!\!\!\diagup_1}\cdot10\!\!\!\!\!\diagup^5x+\dfrac{1}{2\!\!\!\!\diagup_1}\cdot20\!\!\!\!\!\diagup^{10}y+\dfrac{1}{2\!\!\!\!\diagup_1}\cdot10\!\!\!\!\!\diagup^5z\\\\=5x+10y+5z[/tex]

Answer:

5x+10y+5z

Step-by-step explanation:

I did it on Khan Academy :)

Answer:

C.

Step-by-step explanation:

(6^7)^3 means (6^7)(6^7)(6^7).

When multiply numbers with same base, add the exponents.

6^(7+7+7)=6^(3*7)=6^(21).

In the beginning you could have just multiply 7 and 3 so the answer is 6^(21).

Answer: The Answer to this question is C bc of the brackets it multiplies the exponents if that makes sense, hope this helps

Step-by-step explanation:

Answer:16-3v

Step-by-step explanation:

Take off the brackets by multiplying the terms inside the bracket by 4,

4v+16-7v

Simplify

16-3v

Answer:

16-11v

Step-by-step explanation:

4(v+4)-7v    - Question

4v+16-7v     - Distribute the 4 with the digits inside the parenthesis

        -4v      - Subtract 4 from both sides

   16 -11v      - Answer

Hello!

Answer:

Out of all the options, the following apply: B. Equilateral, D. Isosceles, and F. Acute.

Explanation:

An equilateral triangle is one where all sides and angles are equal. All three angles are the same in this triangle, so it is equilateral.

An isosceles triangle is one where at least 2 sides are equal. In this triangle, all three sides are equal, so it's isosceles.

An acute triangle is one where there are 3 angles that are less than 90 degrees. All angles are 60 degrees, so it is acute.

Have a fabulous day! :)

The equation 15x-5+x=-47 simplifies to x=-2.625.

The student has provided the equation 15x - 5 + x = -47 and is looking to simplify it. To simplify this equation, we can combine like terms by adding 15x and x together, resulting in 16x - 5 = -47. The next step is to isolate the variable x by adding 5 to both sides of the equation, which gives us 16x = -42. Finally, we divide both sides by 16 to solve for x: x = -42 / 16.

It seems that there might be confusion with the typos and irrelevant parts in the question; the solution presented does not result in x = 3 or x = -7, as suggested by the incorrect context provided. The proper solution using the equation given leads to x = -42 / 16, which simplifies to x = -2.625. This is the correct solution for the presented equation.

As a check, we can substitute the value of x back into the original equation and confirm that the left side equals the right side, thus verifying our solution.

Answer:

Shii ion kno... Ong I don't

Answer:

slope = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x + 5 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2

Answer:

Triangles ABD and CBD are congruent by the SSS Congruence Postulate

⇒ Answer A is the best answer

Step-by-step explanation:

* Lets revise the cases of congruence  

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ  

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ  

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  

 ≅ 2 angles and the side whose joining them in the 2nd Δ  

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles  

 and one side in the 2ndΔ

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse  

 leg of the 2nd right angle Δ

* Lets solve the problem

- In ΔADC

∵ DA = DC

∵ DB is a median

- The median of a triangle is a segment drawn from a vertex to the

 mid-point of the opposite side of this vertex

∴ B is the mid-point of side AC

∴ AB = BC

- In the two triangles ABD and CBD

∵ AD = CD ⇒ given

∵ AB = CB ⇒ proved

∵ BD = BD ⇒ common side in the two triangles

∴ The two triangles are congruent by SSS

* Triangles ABD and CBD are congruent by the SSS Congruence

  Postulate.

HELLO :)

Triangles ABD and CBD are congruent by the SSS Congruence Postulate, this is because both  of the triangles have the same angle and the have the same sides. Therefore they are congruent by the SSS Congruence Postulate.

you're absolutely correct.

each system is sold for $2150, that includes cost + markup, namely the markup is the surplus amount otherwise called "profit".

they sold 12 of those, 2150 * 12 = 25800

they had $4824.36 in profits from it, so if we subtract that from the sale price, we'll be left with the cost of all 12 systems

25800 - 4824.36 = 20975.64

that's the cost for all 12 systems sold, how many times does 12 go into 20975.64?  20975.64 ÷ 12 = 1747.97.

Answer:

Not sure exactly which equivalent expression you are looking for but my goal would be to write it without the negative exponent.

[tex]\frac{1}{28^2}[/tex]

Step-by-step explanation:

They have the same exponent and it is multiplication.

There is a law of exponent that says [tex](a \cdot b)^x=a^x \cdot b^x[/tex] .

So we have [tex]4^{-2} \cdot 7^{-2}[/tex] equals [tex](4 \cdot 7)^{-2}[/tex].

Let's simplify (4*7)^(-2).

Since 4*7=28, we can say [tex](4*7)^{-2}=(28)^{-2}[/tex].

Some people really hate that negative exponent. All that - in the exponent means is reciprocal. So [tex]28^{-2}=\frac{1}{28^2}[/tex].

Answer:

Step-by-step explanation:

From the table

f(a) = 11 → a = 7

a - 2 = 5

f(a - 2) = f(5) = 7

I believe it should be A

Answer:

f (x) = (x+5) is linear

Step-by-step explanation:

We are given the following function and we are to determine if it is a linear function or not:

[tex] f ( x ) = ( x + 5 ) [/tex]

For a function to be linear, it must be written in the standard form [tex]y=mx+c[/tex] and its graph gives a straight line.

Whereas, when an equation is squared, its graph becomes a curved one which is not linear.

Therefore, the given function f (x) = (x+5) is linear.

Answer: Yes, it is a linear function.

Step-by-step explanation:

The linear function in Slope-Intercept form is:

[tex]f(x)=mx+b[/tex]

Where m is the slope and b the y-intercept.

In this case, given the following function:

 [tex]f(x)=(x+5)[/tex]

You can observe that it has the form  [tex]f(x)=mx+b[/tex]

You can identify that:

[tex]m=1\\b=5[/tex]

Therefore, you can conclude that it is a linear function.

Answer:

The box office sold 34 general admission tickets and 24 student tickets.

Step-by-step explanation:

2.5 dollars for students and 3 dollars for general admission.

58 people attended and 162 dollars was collected.

We are asked to find the number of general admission tickets and number of student tickets sold. Let's call the number of general admission tickets sold g and the number of student tickets sold s.

So we are going to make a money equation and a how many equation.

Let's being the money equation:  2.5 per student means you have 2.5*s

and 3 dollars per general admission ticket means you have 3*g.  You are given total collected was 162 dollars so 162 is the sum of whatever 2.5s and 3g is.  That setup as an equation in symbol form is 162=2.5s+3g

Let's do the how many equation:  There are only 2 kinds of tickets, s and g. And we know that the sum of these should be 58 since that is how many people attended.  So the equation in symbol form is 58=s+g.

This is our system of equations:

162=2.5s+3g

58=     s+   g

------------------I'm going to set this up for elimination by multiplying both equation by -3 which gives:

  162=2.5s+ 3g

 -174=  -3s+-3g

------------------------Now I'm going to add.

   -12=-0.5s+0

   -12=-0.5s

Divide both sides by -0.5

   24=s

Or s=24.

Now we know that s+g=58 and s=24 so g=58-24=34.

The box office sold 34 general admission tickets and 24 student tickets.

Answer:

24 tickets for students

34 tickets for general admission

Step-by-step explanation:

Let's call x the number of students admitted and call z the number of Tickets for general admission

Then we know that:

[tex]x + z = 58[/tex]

We also know that:

[tex]2.50x + 3z = 162[/tex]

We want to find the value of x and z. Then we solve the system of equations:

-Multiplay the first equation by -3 and add it to the second equation:

[tex]-3x - 3z = -174[/tex]

[tex]2.50x + 3z = 162[/tex]

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

[tex]-0.50x = -12[/tex]

[tex]x =\frac{-12}{-0.50}\\\\x=24[/tex]

Now we substitute the value of x in the first equation and solve for the variable z

[tex]24 + z = 58[/tex]

[tex]z = 58-24[/tex]

[tex]z = 34[/tex]

Answer:

The coordinates of point P are (3.5 , 7) ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

- If the point (x , y) divide a line whose endpoints are (x1 , y1) , (x2 , y2)

 at ratio m1 : m2 from the point (x1 , y1), then the coordinates of the

 point (x , y) are [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}},y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]

* Lets solve the problem

∵ A is (5 , 8) and B is (-1 , 4)

∵ P divides AB in the ratio 1 : 3

∴ m1 = 1 and m2 = 3

- Let A = (x1 , y1) and B = (x2 , y2)

∴ x1 = 5 , x2 = -1 and y1 = 8 , y2 = 4

- Let P = (x , y)

∴ [tex]x=\frac{(5)(3)+(-1)(1)}{1+3}=\frac{15+(-1)}{4}=\frac{14}{4}=3.5[/tex]

∴ [tex]y=\frac{(8)(3)+(4)(1)}{1+3}=\frac{24+4}{4}=\frac{28}{4}=7[/tex]

∴ The coordinates of point P are (3.5 , 7)

Answer:

The value of cos C = 15/17

Step-by-step explanation:

* Lets revise the cosine rule

- In Δ ABC

# AB opposite to angle C

# BC opposite to angle A

# AC opposite to angle B

# ∠A between AB and AC

# ∠B between BA and BC

# ∠C between CA and CB

- Cosine rule is:

# AB² = AC² + BC² - 2(AC)(BC) cos∠C

# BC² = AC² + AB² - 2(AC)(AB) cos∠A

# AC² = AB² + BC² - 2(AB)(BC) cos∠B

* Lets solve the problem

∵ AB = 8 units

∵ BC = 15 units

∵ CA = 17 units

∵ AB² = AC² + BC² - 2(AC)(BC) cos∠C

- Add 2(AC)(BC) cos∠C to both sides

∴ AB² + 2(AC)(BC) cos∠C = AC² + BC²

- Subtract AB² from both sides

∴ 2(AC)(BC) cos∠C = AC² + BC² - AB²

- Divide two sides by 2(AC)(BC)

∴ cos∠C = (AC² + BC² - AB²)/2(AC)(BC)

- Substitute the values of AB , BC , AC to find cos∠C

∴ cos∠C = (17)² + (15)² - (8)²/2(17)(15)

∴ cos∠C = (289 + 225 - 64)/510

∴ cos∠C = 450/510 = 15/17

* The value of cos C = 15/17

Answer:

Step-by-step explanation:

Yes, "If the slopes of two lines are negative reciprocals,the lines are perpendicular" is correct.

Answer:

True

Step-by-step explanation:

a p e x

Answer:

Step-by-step explanation:

f(x) = x3 - 6x2 + 8x

     = x(x²- 6x+8)

f(x) = x (x-2)(x-4)

Answer:

640

Step-by-step explanation:

The maximum force required to stretch the spring that distance is 640N. This is calculated by dividing the work done (8J) by the distance (0.025m) to find the force, and then doubling this figure because the maximum force is needed at maximum extension of the spring.

In this question, we are asked to find the maximum force required to stretch a spring by a certain amount. The work done on an object, in this case, the spring, is equal to the force applied times the distance over which the force is applied. This is expressed in the formula Work = Force x Distance. We are given that the work done is 8 Joules and the distance is 2.5 cm (or 0.025 m, converting centimeters to meters).

So, to find the force, we re-arrange the formula to be Force = Work/Distance. Plugging in the given values, we find Force = 8J/0.025m = 320N. However, the maximum force required to stretch it that distance happens at the maximum extension of the spring, so we have to double that force (because for a spring, force is linear with displacement until it reaches maximum extension). Hence, the maximum force is 2 x 320N = 640N, thus making the correct option the second one.

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Answer:

prove that:

Sin²A/Cos²A + Cos²A/Sin²A = 1/Cos²A Sin²A - 2

LHS = \frac{Sin^2A}{Cos^2A} + \frac{Cos^2A}{Sin^2A}

Cos

2

A

Sin

2

A

+

Sin

2

A

Cos

2

A

= \begin{lgathered}= \frac{Sin^4A + Cos^4A}{Cos^2A . Sin^2A}\\\\Using\: a^2 + b^2 = (a+b)^2 - 2ab\\\\a = Cos^2A \: \& \:b = Sin^2A\\\\= \frac{(Sin^2A + Cos^2A)^2 - 2Sin^2A Cos^2A}{Cos^2A Sin^2A} \\\\Sin^2A + Cos^2A = 1\\\\= \frac{1 -2Sin^2A Cos^2A}{Cos^2A Sin^2A}\end{lgathered}

=

Cos

2

A.Sin

2

A

Sin

4

A+Cos

4

A

Usinga

2

+b

2

=(a+b)

2

−2ab

a=Cos

2

A&b=Sin

2

A

=

Cos

2

ASin

2

A

(Sin

2

A+Cos

2

A)

2

−2Sin

2

ACos

2

A

Sin

2

A+Cos

2

A=1

=

Cos

2

ASin

2

A

1−2Sin

2

ACos

2

A

\begin{lgathered}= \frac{1}{Cos^2A Sin^2A} - 2\\\\= RHS\end{lgathered}

=

Cos

2

ASin

2

A

1

−2

=RHS

LHS=RHS

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

sin²A + cos²A = 1

Consider the left side

[tex]\frac{sin^2A}{cos^2A}[/tex] + [tex]\frac{cos^2A}{sin^2A}[/tex]

= [tex]\frac{sin^2A}{1-sin^2A}[/tex] + [tex]\frac{cos^2A}{1-cos^2A}[/tex]

= [tex]\frac{sin^2A(1-cos^2A)+cos^2A(1-sin^2A)}{(1-sin^2A)(1-cos^2A)\\}[/tex]

= [tex]\frac{sin^2A-sin^2Acos^2A+cos^2A-sin^2Acos^2A}{1-sin^2A-cos^2A+sin^2Acos^2A}[/tex]

= [tex]\frac{sin^2A+cos^2A-2sin^2Acos^2A}{1-(sin^2A+cos^2A)+sin^2Acos^2A}[/tex]

= [tex]\frac{1-2sin^2Acos^2A}{sin^2Acos^2A}[/tex]

= [tex]\frac{1}{sin^2Acos^2A}[/tex] - [tex]\frac{2sin^2Acos^2A}{sin^2Acos^2A}[/tex]

= [tex]\frac{1}{sin^2Acos^2A}[/tex] - 2 = right side ⇒ proven

Answer:

s = √(3V/[8 in])

Step-by-step explanation:

Where are "the following functions" that were mentioned in this problem statement?  Please share them.  Thanks.

The volume of a right square pyramid is V = (1/3)(area of base)(height).  In more depth, V = (1/3)(s²)(h).  We want to solve this for s.

Multiplying both sides by 3 to eliminate the fractional coefficient, we get:

3V = s²(h), and so s² = 3V/h.

Taking the square root of this, we get:

s = √(3V/h).

Now let's substitute the given numerical value for the height:

s = √(3V/[8 in]).  We could also label this as a(V) as is done in the problem statement.

Answer:

143

Step-by-step explanation:

17300=.965(125X)

17927.46=125X

143.41=X

To calculate the number of software licenses the department manager can purchase, we first find the discounted price of a single license, then divide the total budget by this single license price. In this case, the manager can purchase approximately 143 licenses with a budget of $17,300.

The subject of this question is a typical real-life application of Mathematics, specifically in percentages and budgeting. Given the scenario, the Information Services Manager plans to buy word-processing software licenses for each cost of $125. However, a volume discount of 3.5% is offered for large purchases.

Firstly, we need to figure out the discounted price of one license, which can be calculated as 96.5% (100% - the 3.5% discount) of $125, leading to $120.63 approximately (rounding the number to two decimal places).

With a total budget of $17,300, the number of licenses she can purchase can be found by dividing the total budget by the price of a single license after the discount: $ 17,300 divided by $120.63, which gives us approximately 143.

Therefore, the department manager can buy approximately 143 licenses when considering the volume discount.

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Answer: Option B

[tex]k> 0[/tex]

Step-by-step explanation:

The graph shows a radical function of the form [tex]f(x)=a(x+k)^{\frac{1}{n}}+c[/tex]

Where n is a even number.

This type of function has its vertex at the origin when [tex]k = 0[/tex] and [tex]c = 0[/tex]

If [tex]k> 0[/tex] the graph moves horizontally k units to the left

If [tex]k <0[/tex] the graph moves horizontally k units to the right.

Note that in this case the vertex of the function is horizontally shifted 5 units to the left. Therefore we know that [tex]k = 5> 0[/tex]

The correct answer is option B

Answer:

14.35 ft.

Step-by-step explanation:

We have 2 right-angled triangles so we can apply the Pythagoras theorem to each one:

14^2 = 12^2 + BC^2

BC^2 = 14^2 - 12^2 =  52

BC = √52 = 7.21.

10^2 = 7^2 + CD^2

CD^2 = 100 - 49 = 51

CD = √51 = 7.14.

So the distance between the 2 poles = BC + CD

= 14.35 ft.

The distance between B and D is 14.35 ft if two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC option (C) is correct.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

From the right angle triangle ABC:

14² = 12² + BC²

BC = √52 = 7.21 feet

In right angle triangle DCE

10² = 7² + CD²

CD = √51 = 7.14 feet

BD = BC + CD = 7.21 + 7.14

BD = 14.35 ft

Thus, the distance between B and D is 14.35 ft if two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC option (C) is correct.

Learn more about the right angle triangle here:

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Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 0 ) and (x₂, y₂ ) = (0, - 3)

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

Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = - [tex]\frac{3}{2}[/tex] x - 3 ← equation in slope- intercept form

Answer:

y=-3(x-1)^2+5

Step-by-step explanation:

The vertex form of a parabola is y=a(x-h)^2+k where (h,k) is the vertex.

We are given the vertex (h,k) is (1,5) so that makes the equation we have

y=a(x-1)^2+5.

We still need to find a.

We do have the point (0,2) on our parabola.

So replace (x,y) with (0,2) and solve for a.

2=a(0-1)^2+5

2=a(-1)^2+5

2=a(1)+5

2=a+5

-3=a

So the equation is

y=-3(x-1)^2+5

Answer:

2c

Step-by-step explanation:

c is a common factor of both terms

Consider the factors of the coefficients 4 and 18

factors of 4 : 1, 2, 4

factors of 18 : 1, 2, 3, 6, 9, 18

The common factors are 1, 2

The greatest common factor is 2

Combining with c gives

Greatest common factor of 2c

To find the greatest common factor of 4c and 18c, the common factor is 2c.

To find the greatest common factor of 4c and 18c, you need to identify the largest factor that both numbers share. In this case, the common factor is 2c. Here's how you can determine it:

Write the numbers as a product of their prime factors: 4c = 2 * 2 * c and 18c = 2 * 3 * 3 * c.

Identify the common factors: The common factors are 2 and c.

Multiply the common factors together: 2 * c = 2c.

Answer:

Lara's average speed :

average speed = total distance / total time

                         => 8 miles / 2.5 hours

                         => 3.2 mph

Tim's average speed :

= total distance / total time

= 12 miles / 3.5 hours

= 3.43 mph

therefore,

Tim's average speed (3.43 mph) is greater.

After calculating the average speeds for Lara (3.2 mph) and Tim (3.43 mph), it is evident that Tim's average speed is greater than Lara's on their respective routes from Point A to Point C.

To answer the question of which person's average speed is greater, we need to calculate the speeds of Lara and Tim on their respective routes from Point A to Point C.

Lara's route from A to B is 6 miles taking 1.5 hours, and from B to C is 2 miles taking 1 hour. To find her average speed, we sum up the distances and times, which gives us 8 miles over 2.5 hours, resulting in:

Average speed of Lara = Total Distance / Total Time = 8 miles / 2.5 hours = 3.2 miles per hour.

Tim's route from A to E is 2 miles taking 0.5 hours, from E to D is 4 miles taking 1.5 hours, and from D to C is 6 miles taking 1.5 hours. Summing Tim's distances and times, we have 12 miles over 3.5 hours, which means:

Average speed of Tim = Total Distance / Total Time = 12 miles / 3.5 hours = 3.43 miles per hour.

Comparing both average speeds, Tim's average speed is greater than Lara's.

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Answer:

The numbers are 19,20 and 21

Step-by-step explanation:

Let

x -----> the first consecutive number

x+1 ---> the second consecutive number

x+2 --> the third consecutive number

we know that

x+(x+1)+(x+2)=60

Solve for x

3x+3=60

3x=57

x=19

so

x+1=19+1=20

x+2=19+2=21

therefore

The numbers are 19,20 and 21

Answer:

The numbers are 1, 20, and 21

Step-by-step explanation:

Let n, n+1 and n+2 be the three consecutive numbers.

To find the numbers

It is given that, the sum of 3 consecutive numbers is 60

n + (n + 1) + (n + 2) = 60

n + n + 1 + n + 2 = 60

3n + 3 = 60

3n = 60 - 3 = 57

n = 57/3 = 19

Therefore the numbers are 1, 20, and 21