The Reed High School basketball program earned $7,115.03 in profits over the current season. Based on game attendance, it is determined that the girls' basketball team will receive 7% of the profits, while the boys' basketball team will receive 11% of the profits. Which is the best estimate of how much more the boys' team will receive in profits than the girls' team?

 A. 

$770

 B. 

$490

 C. 

$280

 D. 

$1,260



​

Answer:

scalene and obtuse all sides are different and bigger than 90 degree angle

Answer:

The simplified form of √100 is 10

Step-by-step explanation:

We have given√100

We know that if we multiply 10 two times than it will give us 100 as  an answer

So,

√100 =√10*10

√100 = 10

The simplified form of √100 is 10....

Answer:

none

Step-by-step explanation:

Hi, I hope this helps, I'm in high school LOL.

Use these, they help to figure this out:

a + b > c

b is the longest side, or hypotenuse. c would be the base.

We have to make sure that c is less than what a + b is.

Plug the numbers in:

2.7 + 4.8 > 8.6

4.8 plus 2.7 is 7.5 cm.

So, 7.5 > 8.6

Obviously, 7.5 is less than 8.6 so 7.5 > 8.6 does not work at all.

That tells you that no triangles can be formed. So, it's none.

Answer:

C   2x^2 + 3/2x -5

Step-by-step explanation:

f(x)=x/2-2

g(x)=2x^2+x-3

(f+g) (x)=x/2-2+2x^2+x-3

Combine like terms

           2x^2 + 3/2x -5

Answer:

True.

Step-by-step explanation:

Let's use the picture I made.

I used degrees instead...

tan(90-x)= b/a   .  I did opposite over adjacent for the angle labeled 90-x which is that angle's measurement.

cot(x)=b/a    .  I did adjacent over opposite for the angle labeled 90 which is that angle's measurement.

Now this is also known as a co-function identity.

[tex]\tan(\frac{\pi}{2}-x)[/tex]

Rewrite using quotient identity for tangent

[tex]\frac{\sin(\frac{\pi}{2}-x)}{\cos(\frac{\pi}{2}-x)}[/tex]

Rewrite using difference identities for sine and cosine

[tex]\frac{\sin(\frac{\pi}{2})\cos(x)-\sin(x)\cos(\frac{\pi}{2})}{\cos(\frac{\pi}{2})\cos(x)+\sin(\frac{\pi}{2})\sin(x)}[/tex]

sin(pi/2)=1 while cos(pi/2)=0

[tex]\frac{1 \cdot \cos(x)-\sin(x) \cdot 0}{0 \cdot \cos(x)+1 \cdot \sin(x)}[/tex]

Do a little basic algebra

[tex]\frac{\cos(x)-0}{0+\sin(x)}[/tex]

More simplification

[tex]\frac{\cos(x)}{\sin(x)}[/tex]

This is quotient identity for cotangent

[tex]\cot(x)[/tex]

Answer:

True

Step-by-step explanation:

tan( pi/2 -x)

We know that tan (a-b) = sin (a-b) / cos (a-b)

tan (pi/2 -x) = sin (pi/2 -x)

                       --------------

                      cos (pi/2 -x)

We know that

sin (a-b) = sin(a) cos(b) - cos(a) sin(b)

and cos (a-b) = sin(a) sin(b) + cos(a) cos(b)

tan (pi/2 -x) = sin (pi/2) cos (x) - cos (pi/2) sin (x)

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

                      sin(pi/2) sin(x) + cos(pi/2) cos(x)

We know sin (pi/2)=1

                cos (pi/2) = 0

tan (pi/2 -x) = 1 cos (x) - 0 sin (x)

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

                      1 sin(x) +0 cos(x)

tan (pi/2 -x) =  cos (x)

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

                      1 sin(x)

We know cos(x)/ sin (x) = cot(x)

tan (pi/2 -x) = cot(x)

[tex]\huge{\boxed{1}}[/tex]

This statement can be represented as [tex]2*\frac{3}{6}[/tex], since the quotient is the answer to a division problem.

Divide. [tex]2*\frac{1}{2}[/tex]

Multiply. [tex]2*\frac{1}{2}=\frac{2}{1}*\frac{1}{2}=\frac{2*1}{1*2}=\frac{2}{2}[/tex]

Simplify.  When the numerator and denominator are the same, the fraction is equal to 1. [tex]\frac{2}{2}=1[/tex]

Step-by-step explanation:

The answer is attached.

Probability helps us to know the chances of an event occurring. The given symbols can be matched with their description as shown below.

Probability helps us to know the chances of an event occurring.

The given symbols can be matched with their description as shown below, therefore,

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The expression will be x=y-4

The less than expression implies that one number x is lower than another number b by some constant d i.e. it implies that b is greater than a. If we subtract a from b it will give the constant d.

Here, given that,

x is 4 lesser than a number,

let's assume that number is y

from the above, it is clear that As y is greater than x, if we subtract 4 from y we will get x.

so the expression can be written as

y-x=4

⇒x=y-4

Therefore The expression will be x=y-4.

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The expression 'x is 4 less than a number' can be represented algebraically by the equation 'x = n - 4', where n is the unknown number.

If you're asked to represent a situation involving x as an algebraic expression, you should analyze all the provided facts. According to the question, x is 4 less than a certain number. This situation can be represented by the expression x = n - 4, where n is the number being referred to. In this expression, we made sure to account for the fact that x is 4 less than this number, so we subtract 4 from n to find the value of x.

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Answer:

  x = {-8/3, 7/2}

Step-by-step explanation:

To use the zero product property, you need the equation in the form of a product that is equal to zero. We can get that by subtracting 56 and factoring the resulting equation.

  6x^2 -5x -56 = 0

  (3x +8)(2x -7) = 0

The zero product property tells us this product is zero only when the factors are zero:

  3x +8 = 0   ⇒   x = -8/3

  2x -7 = 0   ⇒   x = 7/2

The solution is x = {-8/3, 7/2}.

_____

Comment on factoring

Consider the product ...

  (ax +b)(cx +d) = (ac)x^2 +(ad +bc)x +(bd)

Now consider the product of first and last term coefficients compared to the coefficient of the middle term:

  acbd = (ad)(bc)  vs.  ad+bc

We see that the coefficient of the middle term is the sum of two of the factors of the first·last product. This means we want factors of 6·(-56) that have a sum of -5.

  6(-56) = -(2^4)(3)(7) . . . . has 20 divisors.

We're looking for factors that are nearly equal. The clue is given by simplifying the above factoring:

  = -(16)(21) = (16)(-21) . . . . the sum of these factors is -5, as we need.

Again considering the first-last product and the middle coefficient, we see that we can choose ...

  ad = -21, bc = 16; ac = 6, so a=3, c=2, and ...

  (a, b, c, d) = (3, 8, 2, -7)

These values give us the factors we used above.

Note this process gets easier with practice and familiarity with multiplication tables.

Answer:

9(sqrt)2 (B)

Step-by-step explanation:

1. 18(sqrt)2/2=12.727

2. 9(sqrt)2=12.727

3. 12.727=12.727

They match! So the final answer is B

Hope this helps :)

your question is incomplete. please read below to find the missing content.

A. 9 cm

B. 9[tex]\sqrt{2}[/tex] cm

C. 18 cm

D. 18[tex]\sqrt{2}[/tex] cm

The answer is option B. 9[tex]\sqrt{2}[/tex] cm

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios.

Calculations:-

given length=18 cm (hypoteneuse)

angle = 45°

⇒sin 45°=perpendicular/hypoteneuse

⇒1/[tex]\sqrt{2}[/tex]=perpendicular/hypoteneuse

⇒perpendicular =1/[tex]\sqrt{2}[/tex]*hypoteneuse

⇒perpendicular = 18/[tex]\sqrt{2}[/tex] = 12.727

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Answer:

the volume of a cube by 5cm is going to be a 5x6=30

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

The median from B intersects the midpoint of AC

Find the midpoint using the midpoint formula

midpoint = [ 0.5(1 - 5), 0.5(- 1 + 3) ] = (- 2, 1 )

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = - 2, 1 ) and (x₂, y₂ ) = (0, 4 )

d = [tex]\sqrt{(0+2)^2+(4-1)^2}[/tex]

  = [tex]\sqrt{2^2+3^2}[/tex]

  = [tex]\sqrt{4+9}[/tex] = [tex]\sqrt{13}[/tex] ≈ 3.6 ( to 1 dec. place )

The value of x will be equal to 3.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

We know that the  exterior angles are equal to the opposite interior angles

So the equation would be:

25x  +  57  +  x   =   45x

26x  +  57   =   45x

57  =   19x

x    =    3

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Answer:

Mary has 72 breads and Sue has 72 breads....Total they have 144 breads.

Step-by-step explanation:

Let the bread of Sue be x and Mary be y.

y=x

Later , Sue has x- 54 breads and Mary has y+ 54 breads.

As per question,

y+54=7(x-54)

y+54= 7x-378

y+54=7y- 378

6y= 378+54

y=432/6

y=72

Answer:

2 and 7/25

Step-by-step explanation:

Trust me dude.

let's firstly convert the mixed fractions to improper fractions, also recall PEMDAS, multiplication is done before any additions or subtractions.

[tex]\bf \stackrel{mixed}{1\frac{1}{5}}\implies \cfrac{1\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{6}{5}}~\hfill \stackrel{mixed}{2\frac{2}{5}}\implies \cfrac{2\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\mathbb{P~E~M~D~A~S}}{\cfrac{6}{5}\cdot \cfrac{12}{5}-\cfrac{3}{5}}\implies \cfrac{6\cdot 12}{5\cdot 5}-\cfrac{3}{5}\implies \cfrac{72}{25}-\cfrac{3}{5}\implies \stackrel{\textit{using the LCD of 25}}{\cfrac{(1)72~~-~~(5)3}{25}} \\\\\\ \cfrac{72-15}{25}\implies \cfrac{57}{25}\implies 2\frac{7}{25}[/tex]

2(5x+4)+3(2x-1)

Use the distributive property for both sets of parenthesis:

2(5x+4) = 2*5x + 2*4 = 10x+8

3(2x-1) = 3*2x - 3*1 = 6x-3

Now you have:

10x+8 + 6x-3

Now combine like terms:

10x + 6x = 16x

8-3 = 5

The final answer is 16x+5

Algebraic expression includes at least one unknown variable and at least one mathematics operation. The simplified way to represent the given equation is [tex]16x+5[/tex].

The given algebraic expression is,

[tex]2(5x+4)+3(2x-1)[/tex]

An algebraic expression is the mathematical expression of variable which is the combination of variables, coefficients of variables and constants.Algebraic expression includes at least one unknown variable and at least one mathematics operation.

Let [tex]f(x)[/tex] is equal to the given expression. Thus,

[tex]f(x) =2(5x+4)+3(2x-1)[/tex]

The above equation consist one unknown variable x.

Solve the equation using the BODMOS rule. According to the BODMOS to solve a equation first open its bracket. Thus,

[tex]f(x) =2(5x+4)+3(2x-1)[/tex]

[tex]f(x) =10x+8+6x-3[/tex]

Arrange the equation with same power of the variables,

[tex]f(x) =10x+6x+8-3[/tex]

[tex]f(x) =16x+5[/tex]

Hence the simplified way to represent the given equation is [tex]16x+5[/tex].

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Answer:

30

Step-by-step explanation:

[tex]\sin^{-1}(\theta)[/tex] is going to output a number in between [tex]\frac{-\pi}{2}[/tex] and [tex]\frac{\pi}{2}[/tex].

Luckily you are looking for [tex]\theta[/tex] in the 1st quadrant which is contained in the given interval above, so the answer just comes down to what the calculator returns from entering [tex]\sin^{-1}(\frac{1}{2})[/tex] in your calculator.

You may also use the unit circle.  sine value refers to the y-coordinate on there.

So you are looking for when the y-coordinate is 1/2 in the fist quadrant which is at 30 degrees.

Answer: 6

Step-by-step explanation: 8 times 3/4 equals to 6.

Answer:

6 teaspoons

Step-by-step explanation:

Number of teaspoon in 1 batch = 3/4

Number of teaspoon in 8 batches = ?

We know the quantity of teaspoon of  vanilla for one batch. To find the quantity for 8 batches we will simply multiply the quantity of teaspoon  of vanilla for one batch by 8

=3/4 * 8

=3*2

=6

Therefore 6 teaspoons will be needed....

Both of these are linear equations with different y-intercepts and different slopes.

Let's analyze the lines:

y = 2x:

This is a linear equation with a slope of 2 and a y-intercept at the origin (0,0). This means that for every unit increase in x, y increases by 2. The graph is a straight line that passes through the origin.

y = 2 - x:

This is also a linear equation, but with a slope of -1 and a y-intercept at (0,2). This means that for every unit increase in x, y decreases by 1. The graph is a straight line that intersects the y-axis at the point (0,2).

Now, let's consider their relationship:

Both equations are linear, so their graphs are straight lines.

Therefore, the graphs of these two equations are lines with different slopes. The line represented by y = 2x slopes upwards, while the line represented by y = 2 - x slopes downwards.

The formula h=2A/b indicates a combined variation. As the values of A and B change, the value of H also changes accordingly. Understanding its concept helps in solving related problems.

The formula h=2A/b is a representation of combined variation. Combined variation, or joint variation, occurs when a quantity varies directly with the product of two or more other quantities. In other words, as the values of A and B change, the value of h will also adjust accordingly. Let's break it down:

By understanding the concept of combined variation, solving problems involving such formula will become much easier.

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The equation h=2A/b represents combined variation where h varies directly with area (A) and inversely with width (b). The formula indicates how changing one variable affects another in the context of proportional relationships. The mention of molecular cohesion and size pertains to a different scientific context and is not directly related to this mathematical formula.

The formula h=2A/b describes a scenario of combined variation, where h varies directly as the area A and inversely as the width b. Direct variation means that as one variable increases, the other variable increases as well, while inverse variation indicates that as one variable increases, the other decreases. In this case, if the area doubles, h will also double if b remains constant, and if b is halved, h will double, assuming A stays constant.

The provided information about the parameter a describing inter-molecular cohesion and the parameter b describing the effect of molecular size seems to be associated with a completely different context, likely a scientific or chemical formula, rather than the combined variation formula presented in the question. This formula might be relevant to the Born-Oppenheimer surfaces as depicted in Figure 3.1c, which describes a chemical interaction.

Answer:

the answer is 15

Step-by-step explanation:

Answer:

27) 18 < P ≤ 18 + 6√2 ⇒ answer D

28) The sum of the degree measures these angles is 1080° ⇒ answer B

29) 3E minutes before A ⇒ answer B

30) The difference between the greatest possible values is 0 ⇒ answer E

31) r divided by s = 1/3 ⇒ answer A

Step-by-step explanation:

* Lets explain each problem

27)

∵ BE is a quarter circle

∵ The radius of the circle is 6

∵ Point c is on the arc BE

∴ The distance from D to C = 6 ⇒ not depends on the position of c

   because DC is a radius in the quarter circle BE

- In Δ BDE

∵ m∠ D = 90°

∵ DB = DE = 6 ⇒ radii of the quarter circle

- By using Pythagoras Theorem

∴ BE = √ (6² + 6²) = √(36 + 36) = √72 = 6√2

- The perimeter of the quadrilateral ABCD is the sum of the sides

∵ AB = 6 , AD = 6 , CD = 6

- Point C can move from B to E

∴ The length of side BC can b greater than 0(it can not be 0

   because the quadrilateral has 4 sides

∴ The length of BC can not exceed the length of BE because the last

   position of point C to be on the arc BE is point E

∴ The length of BC ⇒ 0 < BC ≤ 6√2

  equal 6√2

∵ P is the perimeter of the quadrilateral ABCD

∴ P = 6 + 6 + 6 + (0 < BC ≤ 6√)

∴ P = 18 + (0 < BC ≤ 6√)

- Add 18 to 0 and 18 to 6√2

∴ 18 < P ≤ 18 + 6√2

28)

- In the figure we have a quadrilateral

- All the arrows represent the exterior angles of the figures

- Use the fact that:

 The sum of all angles around a points is 360°

∵ There are 4 vertices (points) on the quadrilateral

∴ The sum of the all angles around the 4 vertices = 4 × 360 = 1440°

- Use the fact that:

 The sum of the interior angles of any quadrilateral is 360°

∵ The sum of the angles represented by the arrows is the difference

  between the sum of all angles around the 4 vertices and the sum

  of the interior angles of the quadrilateral

∴ The sum of these angles = 1440° - 360° = 1080°

* The sum of the degree measures these angles is 1080°

29)

- In any watch the short arrow-hand represents the hours and the long

 arrow-hand represents the minutes

- The numbers of the hours in the watch from 1 to 12

- The number of minutes between each two hours is 5 minutes, then

  at 1 o'clock the minutes number is 5 , at 6 o'clock the number of

  minutes is 30 , at 9 o'clock the number of minutes is 45 , so we can

  find the number of minutes at any number of hour by multiply the

  number of hour by 5

∵ The number of hours have been replaced by letters

∵ The time on the watch is 45 minutes after 12 o'clock OR

  15 minutes before 1 o'clock

∵ The short arrow-hand pointed between L and A

∵ L is the replacing of 12 o'clock and A is the replacing of 1 o'clock

∵ The long arrow-hand pointed at I

∵ I is the replacing of  9 o'clock

∵ The hour number 9 means 5 × 9 = 45 minutes

∴ The hour hand I has 5I minutes

∴ The time in letter is 5I minutes after L

- This answer is not in the choices

- But the answer of 3E minutes before A means:

∵ E is the replacing of 5 o'clock

∴ 3E = 3 × 5 = 15 minutes

∵ A is the replacing of 1 o'clock

∴ 3E minutes before A means 15 minutes before 1 o'clok

* The answer is ⇒ 3E minutes before A

30)

∵ r² = 9

∴ r = ± √9 = ± 3

∴ r has two values -3 and 3

∵ s² = 25

∴ s = ± √25 = ± 5

∴ s has two values -5 and 5

- To find the greatest value of s - r put s greatest and r smallest

∵ The greatest value of s is 5

∵ The smallest value of r is -3

∴ The greatest value of s - r = 5 - (-3) = 5 + 3 = 8

- To find the greatest value of r - s put r greatest and s smallest

∵ The greatest value of r is 3

∵ The smallest value of s is -5

∴ The greatest value of r - s = 3 - (-5) = 3 + 5 = 8

∴ The difference between the greatest possible values of s - r

   and r - s = 8 - 8 = 0

* The difference between the greatest possible values is 0

31)

- There are 27 cubes each of side length r

- The 27 cubes are arranged to form on single large cube of side

  length s

∵ The volume of any cube is V = L³ , where L is the length of its side

∵ The large cube formed from the 27 small cubes

∴ The volume of the large cube = the volume of the 27 small cubes

∵ The side of the small cube is r

∴ The volume of the small cube is r³

∵ The side of the large cube is s

∴ The volume of the large cube is s³

∴ s³ = 27 r³

- Divide both sides by s³ and 27

∴ s³/(27 s³) = (27 r³)/(27 s³)

∴ 1/27 = r³/s³

- Take ∛  for both sides

∴ ∛(r³/s³) = ∛(1/27)

- The cube root canceled by the power 3 and the cube root of

  1/27 is 1/3

∴ r/s = 1/3

* r divided by s = 1/3

Answer:

a = 162

Step-by-step explanation:

9 = 1/27 a +3

Subtract 3 from each side

9-3 = 1/27 a +3-3

6 = 1/27 a

Multiply each side by 27

6*27 = 1/27 a *27

162 = a

Answer:

a = 162.

Step-by-step explanation:

1/27 a + 3 = 9

1/27 a = 9 - 3 = 6

Multiply both sides by 27:

a = 6 * 27

a =  162.

Answer:

-12x+54

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{In order for you to simplify, you need to}[/tex] [tex]\huge\text{ distribute}[/tex]

[tex]\huge\text{The formula is: a(b + c) = a(b) + a(c) = ab + ac}[/tex]

[tex]\huge\text{Simplify: -6(2x - 9)}[/tex]

[tex]\huge\text{-6(2x) = -12x}\\\huge\text{-6(-9) = 54}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: -12x + 54}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

The answer is 183.

When you estimate that it is 200.

So the answer is (C) 200

Step-by-step explanation:

The explanation is shown in the picture.

The answer is 183.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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Answer:

Step-by-step explanation:

Look at the picture.

Mark points (0, 2) and (8, -4) in the coordinate system.

Plot the line going through these points.

Read the coordinates of the intersection of the line (solution).

The solution of the system of linear equation is (4,-1) and this can be determined by using the arithmetic operations.

Given :

Equations  ---  y = x - 5   --- (1)

                       [tex]\rm y = -\dfrac{3}{4}x+2[/tex]    --- (2)

The system of linear equations can be determined by substituting the value of y in terms of x in another equation in order to determine the value of 'x' and by finding the value of 'x', the value of 'y' can also be determined.

Substitute the value of 'y' in equation (2) that is:

[tex]\rm x-5 = -\dfrac{3}{4}x+2[/tex]

Further, simplify the above equation.

[tex]4x - 20 = -3x +8[/tex]

7x = 28

x = 4

Now, substitute the value of 'x' in equation (1) that is:

y = 4 - 5

y = -1

So, the solution of the system of linear equation is (4,-1).

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Answer:

1.45

Step-by-step explanation:

Percent is the same as putting the number over 100. In this case that would be 145/100 which as a decimal is 1.45.

Answer: is 1.45

Step-by-step explanation:

first you would take 145 percent and divide it by 100 then the answer would be 1.45 or 145/100=1.45

hope this helps

Answer:

x= -4 and x=-2

Step-by-step explanation:

Using a graphing calculator (See picture attached) we find that the solution to the equation are the x-values at which the graph of the function intercepts the x-axis. It ocurrs at x= -4 and x=-2.

Given that exact roots were found, there's no need to state the consecutive integers between which the roots are located.

Answer:

Step-by-step explanation:

because :

when : x = 2        y = 3(2)-4 =6-4 =2   non 3

Answer:

Part 1) The smallest x-intercept is x=-1

Part 2) The largest x-intercept is x=6

Part 3) The y-intercept is y=-6

Part 4) The vertex is the point (2.5,-12.25)

Part 5) The equation of the line of symmetry is x=2.5

Step-by-step explanation:

we have

[tex]f(x)=x^{2}-5x-6[/tex]

step 1

Find the x-intercepts

we know that

The x-intercept is the value of x when the value of the function is equal to zero

so

equate the function to zero

[tex]x^{2}-5x-6=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-5x-6=0[/tex]

so

[tex]a=1\\b=-5\\c=-6[/tex]

substitute in the formula

[tex]x=\frac{-(-5)(+/-)\sqrt{-5^{2}-4(1)(-6)}} {2(1)}[/tex]

[tex]x=\frac{5(+/-)\sqrt{49}} {2}[/tex]

[tex]x=\frac{5(+/-)7} {2}[/tex]

[tex]x=\frac{5(+)7} {2}=6[/tex]

[tex]x=\frac{5(-)7} {2}=-1[/tex]

therefore

The x-intercepts are

x=-1 and x=6

The smallest x-intercept is x=-1

The largest x-intercept is x=6

step 2

Find the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]f(0)=(0)^{2}-5(0)-6[/tex]

[tex]f(0)=-6[/tex]

therefore

The y-intercept is y=-6

step 3

Find the vertex

we know that

The equation of a vertical parabola into vertex form is equal to

[tex]f(x)=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex

Convert the function into vertex form

[tex]f(x)=x^{2}-5x-6[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)+6=(x^{2}-5x)[/tex]

Complete the square, Remember to balance the equation by adding the same constants to each side

[tex]f(x)+6+2.5^{2}=(x^{2}-5x+2.5^{2})[/tex]

[tex]f(x)+12.25=(x^{2}-5x+6.25)[/tex]

Rewrite as perfect squares

[tex]f(x)+12.25=(x-2.5)^{2}[/tex]

[tex]f(x)=(x-2.5)^{2}-12.25[/tex]

The vertex is the point (2.5,-12.25)

step 4

Find the equation of the line of symmetry

we know that

In a vertical parabola the equation of the line of symmetry is equal to the x-coordinate of the vertex

we have

vertex (2.5,-12.25)

The x-coordinate of the vertex is 2.5

therefore

The equation of the line of symmetry is x=2.5