Express each ratio as a fraction in lowest terms.
1) 55 cents to 66 cents :
2) 21 inches to 3 feet:
3) 2 weeks to 14 days :​

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:

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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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:

Step-by-step explanation:

From the table

f(a) = 11 → a = 7

a - 2 = 5

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

Answer:

Total cost spent on supplies = 5 dollars

Lemonade will be sold at 0.5 dollars.

Let the total glasses of lemonade sold be x

So, revenue generated will be = 0.5x

To get the break even we will equal both.

[tex]0.5x=5[/tex]

[tex]x=5/0.5[/tex]

x = 10

Hence, number of glasses to be sold are 10.

The profit or y can be found as;

[tex]y=0.5x-5[/tex]

So, putting x = 11

[tex]y=0.5(11)-5[/tex]

y = 0.5

Putting x = 12

[tex]y=0.5(12)-5[/tex]

y = 1

Putting x = 13

[tex]y=0.5(13)-5[/tex]

y = 1.5

The slope is 0.5.

The y-intercept is -5. This means if 0 glasses of lemonade are sold then there is a loss of $5.

The y intercept is obtained when x=0.

[tex]y=0.5(0)-5[/tex]

y = -5

The x-intercept is 10 or the number of glasses I must sell to break even.

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:

x = -1223, y = -629, and z = -31.

Step-by-step explanation:

This question can be solved using multiple ways. I will use the Gauss Jordan Method.

Step 1: Convert the system into the augmented matrix form:

•  1    -2    1       |  4

•  3   -5   -17     |  3

•  2   -6   43     |  -5

Step 2: Multiply row 1 with -3 and add it in row 2:

•  1    -2    1       |  4

•  0    1   -20     |  -9

•  2   -6   43     |  -5

Step 3: Multiply row 1 with -2 and add it in row 3:

•  1    -2    1       |  4

•  0    1   -20     |  -9

•  0   -2   41      |  -13

Step 4: Multiply row 2 with 2 and add it in row 3:

0 2 -40 -18

•  1    -2    1       |  4

•  0    1   -20     |  -9

•  0    0     1      |  -31

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• x - 2y + z = 4

• y - 20z = -9

• z = -31

Step 6: Since we have calculated z = -31, put this value in equation 2:

• y - 20(-31) = -9

• y = -9 - 620

• y = -629.

Step 8: Put z = -31 and y = -629 in equation 1:

• x - 2(-629) - 31 = 4

• x + 1258 - 31 = 4

• x = 35 - 1258.

• x = -1223

So final answer is x = -1223, y = -629, and z = -31!!!

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:

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:

Shii ion kno... Ong I don't

Answer:

The coefficient of xy^4 is 10

Step-by-step explanation:

to solve the questions we proceed as follows:

(2x+y)^5

=(2x+y)²(2x+y)²(2x+y)

We will solve the brackets by whole square formula:

=(4x²+4xy+y²)(4x²+4xy+y²)(2x+y)

By multiplying the brackets we get:

=32x^5+32x^4y+8x³y²+32x^4y+32x³y²+8x²y³+8x³y²+4x²y³+2xy^4+16x^4y+

16x³y²+4x²y³+16x³y²+16x²y³+4xy^4+4x²y³+4xy^4+y^5

=32x^5+80x^4y+80x³y²+40x²y³+10xy^4+y^5

Therefore the coefficient of xy^4 is 10

The answer is 10....

Answer: 10

Step-by-step explanation: a p e x

Answer:

A. f and h

Step-by-step explanation:

For a linear function the First Differences of the y-values must be a constant. i.e. if we take the difference between any two consecutive y values or values of f(x) it should be the constant. For this rule to work, x values must change by the same number every time, which is true for all three given functions.

For function f:

The values of f(x) are: 5,8,11,14

We can see the difference in consecutive two values is a constant i.e. 3, so the First Difference is the same. Hence, function f is a linear function.

For function g:

The values of g(x) are: 8,4,16,32

We can see the difference among two consecutive values is not a constant. Since the first differences are not the same, this function is not a linear.

For function h:

The values of h(x) are: 28, 64, 100, 136

We can see the difference among two consecutive values is a constant i.e. 36. Therefore, function h is a linear function.

To identify the linear relationships in the tables, we need to look for constant rates of change. Functions f and g have this property, while h does not.

In order to identify which functions represent linear relationships, we need to look for patterns in the tables. A linear relationship is characterized by a constant rate of change.

Looking at the tables, we can see that functions f and g have a constant difference between the values in the input column (x) and the output column (y). However, function h does not have a constant rate of change, so it does not represent a linear relationship.

Therefore, the correct answer is A. f and h, as these two functions represent linear relationships.

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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.

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:

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:

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:

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:

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: 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

I believe it should be A

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

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:

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:

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:

A - 48,96, -192

Step-by-step explanation:

Given:

geometric sequence:

-3, 6, -12, 24,

geometric sequence has a constant ratio r and is given by

an=a1(r)^(n-1)

where

an=nth term

r=common ratio

n=number of term

a1=first term

In given series:

a1=-3

r= a(n+1)/an

r=6/-3

r=-2

Now computing next term a5

a5=a1(r)^(n-1)

    = -3(-2)^(4)

   = -48

a6=a1(r)^(n-1)

    = -3(-2)^(5)

   = 96

a7=a1(r)^(n-1)

    = -3(-2)^(9)

   = -192

So the sequence now is -3, 6, -12, 24,-48,96,-192

correct option is A!

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:

The real zeroes are -√5 , 0 , √5

Step-by-step explanation:

* Lets explain how to solve the problem

- The function is y = x^5 + x³ - 30x

- Zeros of any equation is the values of x when y = 0

- To find the zeroes of the function equate y by zero

∴ x^5 + x³ - 30x = 0

- To solve this equation factorize it

∵ x^5 + x³ - 30x = 0

- There is a common factor x in all the terms of the equation

- Take x as a common factor from each term and divide the terms by x

∴ x(x^5/x + x³/x - 30x/x) = 0

∴ x(x^4 + x² - 30) = 0

- Equate x by 0 and (x^4 + x² - 30) by 0

∴ x = 0

∴ (x^4 + x² - 30) = 0

* Now lets factorize (x^4 + x² - 30)

- Let x² = h and x^4 = h² and replace x by h in the equation

∴ (x^4 + x² - 30) = (h² + h - 30)

∵ (x^4 + x² - 30) = 0

∴ (h² + h - 30) = 0

- Factorize the trinomial into two brackets

- In trinomial h² + h - 30, the last term is negative then the brackets

 have different signs (     +     )(     -     )

∵ h² = h × h ⇒ the 1st terms in the two brackets

∵ 30 = 5 × 6 ⇒ the second terms of the brackets

∵ h × 6 = 6h

∵ h × 5 = 5h

∵ 6h - 5h = h ⇒ the middle term in the trinomial, then 6 will be with

  (+ ve) and 5 will be with (- ve)

∴ h² + h - 30 = (h + 6)(h - 5)

- Lets find the values of h

∵ h² + h - 30 = 0

∴ (h + 6)(h - 5) = 0

∵ h + 6 = 0 ⇒ subtract 6 from both sides

∴ h = -6

∵ h - 5 = 0 ⇒ add 5 to both sides

∴ h = 5

* Lets replace h by x

∵ h = x²

∴ x² = -6 and x² = 5

∵ x² = -6 has no value (no square root for negative values)

∵ x² = 5 ⇒ take √ for both sides

∴ x = ± √5

- There are three values of x ⇒ x = 0 , x = √5 , x = -√5

∴ The real zeroes are -√5 , 0 , √5

Answer:

82.8 degrees

Step-by-step explanation:

The information given here SSS.  That means side-side-side.

So we get to use law of cosines.

[tex](\text{ the side opposite the angle you want to find })^2=a^2+b^2-2ab \cos(\text{ the angle you want to find})[/tex]

Let's enter are values in.

[tex]12^2=10^2+8^2-2(10)(8) \cos(B)[/tex]

I'm going to a little simplification like multiplication and exponents.

[tex]144=100+64-160 \cos(B)[/tex]

I'm going to some more simplification like addition.

[tex]144=164-160\cos(B)[/tex]

Now time for the solving part.

I'm going to subtract 164 on both sides:

[tex]-20=-160\cos(B)[/tex]

I'm going to divide both sides by -160:

[tex]\frac{-20}{-160}=\cos(B)[/tex]

Simplifying left hand side fraction a little:

[tex]\frac{1}{8}=\cos(B)[/tex]

Now to find B since it is inside the cosine, we just have to do the inverse of cosine.

That looks like one of these:

[tex]\cos^{-1}( )[/tex] or [tex]\arccos( )[/tex]

Pick your favorite notation there.  They are the same.

[tex]\cos^{-1}(\frac{1}{8})=B[/tex]

To the calculator now:

[tex]82.81924422=B[/tex]

Round answer to nearest tenths:

[tex]82.8[/tex]

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.