**30 points*** PLEASE ASSIST WILL GET BRAINIEST I REALLY NEED HELP!!!
Describe how you can use a double-angle formula or a half-angle formula to derive the formula for the area of an isosceles triangle. Use a labeled sketch to illustrate your derivation. Then write two examples that show how your formula can be used.

Answer:

Step-by-step explanation:

if you can pick the same card 3 times the probability of winning is

[tex](\frac{5}{10})^{3} = \frac{1}{8}[/tex]

but if you remove each card after you've picked them it's :

[tex]\frac{5}{10}.\frac{4}{9}.\frac{3}{8}= \frac{60}{720}[/tex]

notice if you remove an odd card every time you pick one of them you are also removing one of the overall cards

and if you subtract these two you get : [tex]\frac{1}{8} - \frac{60}{720} =0.0417[/tex]

which is like 4 percent

Answer:

y = 10x - 3

Step-by-step explanation:

We have the point (0, -3), which is the y-intercept. In slope-intercept form,

y = mx + b,

that is the b.

Now we find the slope between the other 2 points:

[tex]\frac{18-8}{3-2}=10[/tex]

So m = 10.  Therefore, the equation is

y = 10x - 3

Explanation:

Any function that has a derivative that changes sign will have an extreme value (maximum or minimum). If the derivative never changes sign, the function will not have any extreme values.

__

Logarithmic, exponential, and certain trigonometric, hyperbolic, and rational functions are monotonic, having a derivative that does not change sign. Odd-degree polynomials may also have this characteristic, though not necessarily. These functions will not have maximum or minimum values.

__

Certain other trigonometric, hyperbolic, and rational functions, as well as any even-degree polynomial function will have extreme values (maximum or minimum). Some of those extremes may be local, and some may be global. In the case of trig functions, they may be periodic.

Composite functions involving ones with extreme values may also have extreme values.

Answer:

This is because √-1 is i, which is an extension of real numbers called complex numbers.

Step-by-step explanation:

A real number is one that can be expressed in decimal form.Real numbers are those that appear on the number line.In mathematics, √-1 is i which is an extension of real numbers to represent complex numbers.

Answer:

there is no number than can be multiplied by itself it give a negative answer.

Step-by-step explanation:

Eg. 1 X 1 = 1

     -1 X -1 = 1

Answer:

The answer would be C. 1,926.97 :)

Answer:

Option C

Step-by-step explanation:

Principal,P = $8180

Time = 10 years

Rate,R = 5.3% compounded monthly

Formula: [tex]P(1+\frac{R}{n} )^{nt}[/tex], where n is the number of times interest is compounded that is monthly, quarterly, yearly.

Now, we have to calculate the interest by the time Sebastian has graduated that is the time now is 4 years, t = 4 and n = 12, because the interest is compounded monthly.

Puttin all the values in the formula

Amount = [tex]8180(1+ \frac{5.3}{1200} )^{48}[/tex] = 10106.9707$

Also, Interset = Amount - Principal

Interest = 10106.9707$ - 8180$ = 1926.97074$

Option C

Answer:

Step-by-step explanation:

Divide 1 7/10 by 3/5 to see if the quotient is greater than 2.  If it's not, you can't get 2 scarves out of it.  If it is, then you can get 2 scarves out of it and have whatever the remainder is as left-over.  Before we divide, let's change that 1 7/10 into an improper fraction since it will be easier to work with.

1 7/10 = 17/10

Now we can divide:

[tex]\frac{\frac{17}{10} }{\frac{3}{5} }[/tex]

The rule for dividing fractions is that you bring up the lower fraction and flip it to multiply, so that looks like this:

[tex]\frac{17}{10}[/tex]×[tex]\frac{5}{3}[/tex]

To simplify before we multiply, we can reduce between the 5 and the 10 and have smaller numbers to deal with:

[tex]\frac{17}{2}[/tex]×[tex]\frac{1}{3}[/tex]

The product there is [tex]\frac{17}{6}=2\frac{5}{6}[/tex]

So the answer you want from your choices is

"Yes, because the quotient of Fraction 1 and 7 over 10 [division sign]Fraction 3 over 5 is 2 and 5 over 6", third choice

Answer:

Yes, because the quotient of Fraction 1 and 7/10 [division sign]Fraction 3/5  is 2 and 5/6", third choice

Step-by-step explanation:

Divide 1 7/10 by 3/5 to see if the quotient is greater than 2.  If it's not, you can't get 2 scarves out of it.  If it is, then you can get 2 scarves out of it and have whatever the remainder is as left-over.  Before we divide, let's change that 1 7/10 into an improper fraction since it will be easier to work with.

1 7/10 = 17/10

Now we can divide:

The rule for dividing fractions is that you bring up the lower fraction and flip it to multiply, so that looks like this:

×

To simplify before we multiply, we can reduce between the 5 and the 10 and have smaller numbers to deal with:

×

The product there is  

So the answer you want from your choices is

"Yes, because the quotient of Fraction 1 and 7 over 10 [division sign]Fraction 3 over 5 is 2 and 5 over 6", third choice

B

3+5=8

8-2=6

6-1=5

Answer 5

Answer:

The correct option is C.

Step-by-step explanation:

We need to find the problem that could be solved with the expression 3(5-2)-1.

The solution of given expression is

[tex]3(5-2)-1=8[/tex]

1. Ralph's problem

His 5 toy cars, he gave two to his sister = 5 - 2

After that he found one more toy car = 5-2+1

Then, he decided to go to the store and triple his number of cars, therefore the total number of toys = 3(5-2+1) =12

2. Stephanie's problem

Stephanie had 3 apples. Then, she found 5 more = 3+5

but immediately ate 2 of them = 3+5-2

Several minutes later, she ate 1 more, therefore the total number of apples = 3+5-2-1 = 5

3. Orlando' problem

Orlando had 5 action figures but decided to give 2 of them to his younger brother = 5-2

His parents were so impressed with his kindness that thy tripled the action figures he had left = 3(5-2)

Since he got so many new action figures, then he gave 1 more to his brother, therefore the total number of action figures = 3(5-2)-1 = 8

Orlando' problem could be solved with the expression 3(5-2)-1. Therefore the correct option is C.

The number of ways to distribute five identical fruits into three bowls is solved using the stars and bars technique in combinatorics, resulting in 21 different ways.

The student is asking about the number of ways to distribute five identical fruits into three bowls, where bowls can be left empty.

This problem is a classic example of a combinatorial problem in mathematics, often approached using the stars and bars method.

The stars and bars technique is a way to solve problems related to distributing indistinguishable items into distinguishable groups.

To solve this, think of the five identical fruits as stars (*) and the separations between bowls as bars (|).

We need to place two bars to create three sections (bowls) among the five stars.

The question then becomes: In how many ways can we arrange five stars and two bars?

This is equivalent to choosing two places for bars out of seven possible positions (five stars plus two bars).

The number of ways we can choose two positions out of seven for the bars is given by the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items and k is the number of items to choose.

In this case, C(7, 2) = 7! / (2!5!) = 21 ways.

Therefore, there are 21 different ways to distribute five identical fruits into three bowls.

[tex](x-(-2))(x-(-3))(x-(3-6i)(x-(3+6i))=\\(x+2)(x+3)(x-3+6i)(x-3-6i)=\\(x^2+3x+2x+6)((x-3)^2+36)=\\(x^2+5x+6)(x^2-6x+9+36)=\\(x^2+5x+6)(x^2-6x+45)=\\x^4-6x^3+45x^2+5x^3-30x^2+225x+6x^2-36x+270=\\x^4-x^3+21x^2+189x+270[/tex]

Answer:

1st line

Step-by-step explanation:

Should be z=11-3x-2y, then solve from there.

Answer:

A  f(x) = 1/3x^3

Step-by-step explanation:

g(x) = x^3

We want f(x) to be vertically compressed

f(x) = ag(x )    

a is vertical stretch/compression

|a| > 1 stretches  

|a| < 1 compresses

so we need to multiply by a number less than between 0 and 1

If a is negative it is a reflection, which was not asked for

f(x) = 1/3 x^3

Answer:

A  f(x) = 1/3x^3

Step-by-step explanation:

g(x) = x^3

We want f(x) to be vertically compressed

f(x) = ag(x )    

a is vertical stretch/compression

|a| > 1 stretches  

|a| < 1 compresses

so we need to multiply by a number less than between 0 and 1

If a is negative it is a reflection, which was not asked for

f(x) = 1/3 x^3

Answer:

B

Step-by-step explanation:

This is the difference of perfect squares, which follows a pattern of

(A+B)(A-B)

We have 64, which is 8-squared,

we have A squared, which is A squared ( :/ )

we have 81, which is 9-squared, and

we have B-squared, which is B squared.

We can factor this then following the pattern into:

(8A+9B)(8A-9B)

Choice B only matches one of our binomials.

Answer:

B. 8A + 9B.

Step-by-step explanation:

The general form is

a^2 - b^2 = (a - b)(a + b) so here we have:

a = square root of 64A^2 = 8A and b = square root of 81B^2 = 9B and therefore:

64A^2 - 81B^2

= (8A - 9B)(8A + 9B).

Answer:

$352

Step-by-step explanation:

Simple interest (I) is calculated as

I = [tex]\frac{PRT}{100}[/tex]

where P is the principal ( investment), R is the rate of interest and T is time in years, thus

I = [tex]\frac{275(8)(16)}{100}[/tex] = $352

Answer:

$352

Step-by-step explanation:

Answer:

[tex]\theta=\frac{\pi}{2},\frac{3\pi}{2}\frac{2\pi}{3}\frac{4\pi}{3}[/tex]

Step-by-step explanation:

You need 2 things in order to solve this equation:  a trig identity sheet and a unit circle.

You will find when you look on your trig identity sheet that

[tex]cos(2\theta)=1-2sin^2(\theta)[/tex]

so we will make that replacement, getting everything in terms of sin:

[tex]sin(\theta)+1=1-2sin^2(\theta)[/tex]

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

[tex]2sin^2(\theta)+sin(\theta)=0[/tex]

We can factor out the sin(theta), since it's common in both terms:

[tex]sin(\theta)(2sin(\theta)+1)=0[/tex]

Because of the Zero Product Property, either

[tex]sin(\theta)=0[/tex] or

[tex]2sin(\theta)+1=0[/tex]

Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi.  They are:

[tex]\theta=\frac{\pi}{2},\frac{3\pi}{2}[/tex]

The next equation needs to first be solved for sin(theta):

[tex]2sin(\theta)+1=0[/tex] so

[tex]2sin(\theta)=-1[/tex] and

[tex]sin(\theta)=-\frac{1}{2}[/tex]

Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval.  They are:

[tex]\theta=\frac{2\pi}{3},\frac{4\pi}{3}[/tex]

Answer:

The answer is 0.067.

Step-by-step explanation:

Let the entire sample size be = s

Now there are 2 laptops in sample size, hence these can be chosen in one way only.

The required probability that both selected setups are for laptop computers can be found as:

[tex]p(two laptops)=\frac{s(two laptops)}{s}[/tex]

= [tex]\frac{1}{15}[/tex] or 0.067.

So, the probability is 0.067.

The probability of both selected setups being for laptop computers is 2/15.

The probability of both selected setups being for laptop computers can be calculated as the ratio of favorable outcomes to total outcomes. Out of the six computers, two have been selected to be laptops. The first laptop can be any of the two laptops, and the second laptop can be any of the remaining one laptop. Therefore, the probability of both selected setups being for laptop computers is 2/15.

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Answer:

They are both the same at 3/4 of an hour

Step-by-step explanation:

We have a system of equations here.  The first one is for Friday:

3A + 5B = 6, which says that 3 people at the number of hours for plan A plus 5 people at the number of hours for plan B equals 6 hours total.

The second equation is for Saturday:

9A + 7B = 12, which says that 9 people at the number of hours for plan A plus 7 people at th number of hours for plan B equals 12 hours total.

We can solve this easily using the addition/elimination method.  Begin by multipying the first equation through by a -3 to eliminate the A's.  That gives you a new first equation of:

  -9A  -  15B  =  -18

  9A  +    7B  =  12

You can see that the A's are eliminated, and adding what remains leaves us with

-8B = -6 so

B = 3/4 hour

Now we can sub that back in for B in either one of our original equations to solve for A.  I changed the 3/4 to .75 for ease of multiplying:

9A + 7(.75) = 12 and

9A + 5.25 = 12 and

9A = 6.75 so

A = .75 which is also 3/4 of an hour

Let Tony's age = x

He is 4 years younger than his brother Josh, so Josh's age would be x + 4

He is 2 years older than his sister, so her age would be x - 2

He has a twin, which would be the same age, so the twins age is also x

They all add together to equal 66, so you get:

x  + x + x+4 + x-2 = 66

Simplify:

4x +2 = 66

Subtract 2 from both sides:

4x = 64

Divide both sides by 4:

x = 64/4 = 16

Tony is 16 years old.

Final answer:

By setting up an equation with Tony's age as T, and considering the ages of his siblings, we find that Tony is 16 years old.

Explanation:

Tony is 4 years younger than his brother Josh and two years older than his sister Cindy. Additionally, Tony has a twin brother, Evan. If we add the ages of Tony, Josh, Evan, and Cindy, the total is 66 years. To solve for Tony's age, we need to set up an equation. Let's assume Tony's age is T years.

Since Tony is 4 years younger than Josh, Josh is T + 4 years old. As Tony has a twin brother, Evan, Evan is also T years old. Cindy, being two years younger than Tony, is T - 2 years old. So, the sum of all their ages is:

T + (T + 4) + T + (T - 2) = 66

Combining like terms, we get:

4T + 2 = 66

Subtracting 2 from both sides gives us:

4T = 64

Dividing both sides by 4 results in:

T = 16

Therefore, Tony is 16 years old.

Answer:

  a)  t = 2 seconds

  b)  6.05 meters

Step-by-step explanation:

I prefer a graph for questions like this, but I have attached a table, too. Here, the table is created using a graphing calculator to evaluate the function. A spreadsheet can do this nicely, too.

The maximum height occurs at t=0.9 seconds, and the ball hits the ground at a time that is slightly more than double that, 2.0 seconds.

The maximum height is 6.05 meters.

Step-by-step explanation:

f(x) = x² − 6x + 9

f(½) = (½)² − 6(½) + 9

f(½) = ¼ − 3 + 9

f(½) = 6¼

The value is 6¼, or as an improper fraction, 25/4.

Answer:   The correct answer is:   " 6 [tex]\frac{1}{4}[/tex] " ;  

_______________________________________________                  

                                 or;  write as:   " 6.25 " .

______________________________________________

     " f([tex]\frac{1}{2})[/tex] =  6 [tex]\frac{1}{4}[/tex] " ;

                                             =  6.26 " .

______________________________________________

Step-by-step explanation:

______________________________________________

Given the function:

______________________________________________

      " f(x)  =  x² − 6x + 9 " ;

______________________________________________

What is:   " f([tex]\frac{1}{2}[/tex]) " ?

______________________________________________

Plug in "([tex]\frac{1}{2}[/tex])"  for all values of "x" in the equation;  

                →  to solve for:  " f([tex]\frac{1}{2}[/tex]) " ;   as follows:

______________________________________________

→     " f([tex]\frac{1}{2}[/tex]) " ;  

     =  ([tex]\frac{1}{2}[/tex])² −  6*([tex]\frac{1}{2}[/tex]) + 9  ;

    =   ([tex]\frac{1^{2} }{2^{2}}[/tex])  −  ([tex]\frac{6*1}{2}[/tex]) + 9 ;

     =        ([tex]\frac{1}{4}[/tex]) −  ([tex]\frac{6}{2}[/tex])   +  9    ;

     =       ([tex]\frac{1}{4}[/tex])  −  3    +  9    ;

Note:   " - 3 + 9 "  =  9 + (-3)  =  9 −  3 =  " 6 " ;  

So:  Rewrite as:

______________________________________________

      →  " ([tex]\frac{1}{4}[/tex]) + 6 "  ;

______________________________________________    

      →   which equals:  " 6 [tex]\frac{1}{4}[/tex] " ;  

_______________________________________________                  

                         or;  write as:  " 6.25 " .

_______________________________________________

Hope this answer —and lengthy explanation — is helpful to you!

       Wishing you the best in your academic endeavors

                 — and within the "Brainly" community!

_______________________________________________

Explanation:

Polygons are classified by ...

The number of coordinate pairs will define the number of vertices.

The differences between "adjacent" coordinate pairs can be used to find side lengths and relationships (angles, parallel, perpendicular).

_____

If the differences between adjacent coordinate pairs are ...

  (∆x, ∆y) = (x2 -x1, y2 -y1)

then the slope of the line joining those coordinates is ∆y/∆x. (This may be "undefined" if ∆x = 0.) Two line segments with the same slope are parallel. Two line segments with slopes that have a product of -1 are perpendicular. (Two segments with slopes of 0 and "undefined" are also perpendicular.)

It can be useful on occasion to know that the angle (α) a line segment makes with the x-axis can be found from ...

  α = arctan(slope)

The length of a line segment (d) can be found from the Pythagorean theorem:

  d = √((∆x)² +(∆y)²)

Answer:

I think the answer is 23

Answer:

  the resulting error is about 0.754 in²

Step-by-step explanation:

  A(r) -A(r0) ≈ dA/dr·(r -r0)

The area of a circle is given by ...

  A(r) = πr²

so the derivative is

  dA/dr = 2πr

and the area error is ...

  dA/dr·(r -r0) = 2π(12 in)(0.01 in) = 0.24π in² ≈ 0.754 in²

Answer:

[tex]\large\boxed{A).\,x^2+3x+5}[/tex]

Step-by-step explanation:

In this question, we're trying to figure out what f(x) + g(x)  equals to.

We are going to be plugging in the equations they gave to us and solve.

Equations we're going to use:

Now, lets get to solving.

We would plug the equations in the appropriate spot. In other words, we're pretty much plugging them in to the right variable.

Your expression should look like this:

[tex]3x+5+x^2[/tex]

Now we solve.

[tex]3x+5+x^2\\\\x^2\,\text{can't combine with 3x because of the exponent, so we will eave it as is}\\\\\text{There is nothing else we can combine, so it would stay as:}\\\\x^2+3x+5[/tex]

You should end up with x²+3x+5.

This means that your final answer would be A) x^2 +3x+5

Answer:

[tex]\large\boxed{Q5.\ x=45\sqrt2}\\\boxed{Q6.\ x=8\sqrt2,\ y=4\sqrt6}[/tex]

Step-by-step explanation:

Q5.

x it's a diagonal of a square.

The formula of a length of diagonal of a square:

[tex]d=a\sqrt2[/tex]

a - side of a square

We have a = 45.

Substitute:

[tex]x=45\sqrt2[/tex]

Q6.

Look at the first picture.

In a triangle 45° - 45° - 90°, all sides are in ratio 1 : 1 : √2.

In a triangle 30° - 60° - 90°, all sidea are in ratio 1 : √3 : 2.

Look at the second picture.

from the triangle 45° - 45° - 90°

[tex]a\sqrt2=8[/tex]        multiply both sides by √√2  (use √a · √a = a)

[tex]2a=8\sqrt2[/tex]      divide both sides by 2

[tex]a=4\sqrt2[/tex]

from the triangle 30° - 60° - 90°

[tex]x=2a\to x=2(4\sqrt2)=8\sqrt2[/tex]

[tex]y=a\sqrt3\to y=(4\sqrt2)(\sqrt3)=4\sqrt6[/tex]

Answer:

6. [tex]\displaystyle 4\sqrt{6} = y \\ 4\sqrt{2} = x[/tex]

5. [tex]\displaystyle 45\sqrt{2} = x[/tex]

Step-by-step explanation:

30°-60°-90° Triangles

Hypotenuse → 2x

Short Leg → x

Long Leg → x√3

45°-45°-90° Triangles

Hypotenuse → x√2

Two identical legs → x

6. You solve the shorter triangle first:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ \\ x^2 + x^2 = 8^2 \\ \\ \frac{2x^2}{2} = \frac{64}{2} → \sqrt{x^2} = \sqrt{32} \\ \\ 4\sqrt{2} = x[/tex]

Now that we know our x-value, we can solve the larger triangle:

[tex]\displaystyle 4\sqrt{6} = 4\sqrt{2}\sqrt{3} \\ \\ 4\sqrt{6} = y[/tex]

5. This exercise is EXTREMELY SIMPLE since two congruent isosceles right triangles form that square, so all you have to do, according to the rules for 45°-45°-90° triangles, is attach [tex]\displaystyle \sqrt{2}[/tex]to 45, giving you [tex]\displaystyle 45\sqrt{2}.[/tex]

I am joyous to assist you anytime.

Answer:

False

Step-by-step explanation:

Correct me if I'm wrong but this suppose to be a true or false question.

The measure of angle of B is going to be half the arc measure of AC so they don't have the same measurement. If they don't have the same measurement, then they can't be congruent.

Answer:

so  equation for the temperature in terms of t is D = 5 sin [tex]\pi[/tex] / 12 (t) + 45

Step-by-step explanation:

Given data

temperature = 45 degrees

high temperature = 50 degrees

low temperature = 40 degrees

to find out

an equation for the temperature in terms of t

solution

first we find the amplitude i.e.

Amplitude (A) = ( high temperature - low temperature )  / 2

Amplitude (A) = (50 - 40)  / 2

Amplitude (A)  = 5

here we know in a day 24 hours so

2[tex]\pi[/tex] /K = 24

K = [tex]\pi[/tex] / 12

so we have temperature equation is

temperature D = amplitude sinK (t) + avg temperature midnight

D = 5 sin [tex]\pi[/tex] / 12 (t) + 45

so  equation for the temperature in terms of t is D = 5 sin [tex]\pi[/tex] / 12 (t) + 45

The temperature over a day can be modeled as a sinusoidal function. The equation for the temperature, D, in terms of t is: D = 5cos((pi/12)t) + 45.

The temperature over a day can be modeled as a sinusoidal (sine or cosine) function. To find an equation for the temperature, we can use the cosine function because it starts at its maximum value at t = 0, which corresponds to midnight. The equation for the temperature, D, in terms of t is:

D = 5cos((pi/12)t) + 45

Here, t represents the number of hours since midnight, and D represents the temperature in degrees. The amplitude of the sinusoidal function is 5, which represents the difference between the high and low temperatures. The cosine function is scaled and shifted to match the given data: it is multiplied by 5 to match the amplitude, and 45 is added to shift the function vertically so that it starts at 45 degrees at t = 0.

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Answer:

C is correct as well as D.

Step-by-step explanation:

The rhombus also shares the common traits that the picture shows

Answer:

So the probability that the city won't receive rain on none of these days is [tex]\frac{2}{15}[/tex]

Step-by-step explanation:

From the question we know that the probability of rain on June 1 is [tex]\frac{1}{2}[/tex], on July 1 is [tex]\frac{1}{5}[/tex] and in August 1 is [tex]\frac{2}{3}[/tex], So the probability of no rain at any of these days is calculate as:

For June 1:

[tex]P(no-rain)=1-\frac{1}{2} =\frac{1}{2}[/tex]

For July 1:

[tex]P(no-rain)=1-\frac{1}{5} =\frac{4}{5}[/tex]

For August 1:

[tex]P(no-rain)=1-\frac{2}{3} =\frac{1}{3}[/tex]  

So the probability that the city won't receive rain on none of these days is the multiplication of the probabilities of no rain for every one of these days. Then:

[tex]P=\frac{1}{2} *\frac{4}{5} *\frac{1}{3} =\frac{4}{30}[/tex]

Simplified the value of P, we obtain: [tex]P=\frac{2}{15}[/tex]

Answer:

C. is your answer

Step-by-step explanation:

In order to determine the line of symmetry, it would help to put this standard form parabola into vertex form, which is

[tex]y=a(x-h)^2+k[/tex],

where x = h is the equation of the line of symmetry.

To get this into vertex form we will complete the square.  The first couple of steps I will combine into 1.  We will set the quadratic equal to zero, then move the constant over to the other side:

[tex]88x^2-264x=-300[/tex]

The next rule is that the leading coefficient HAS to be a positive 1.  Ours is a positive 88, so we have to factor it out:

[tex]88(x^2-3x)=300[/tex]

Now we can perform the process of completing the square.  The rule is to take half the linear term, square it, and add it to both sides.  Our linear term is 3.  Half of 3 is 3/2, and 3/2 squared is 9/2.  We will add 9/2 inside the parenthesis on the left, but don't forget about that 88 sitting out front which refuses to be ignored.  It serves as a multiplier into the parenthesis.  What we actually added in, then, was 88(9/2) which is 198:

[tex]88(x^2-3x+\frac{9}{4})=-300+198[/tex]

The purpose of completing the square is to give us a perfect square binomial which serves as the axis of symmetry of the parabola and also gives us the h coordinate of the vertex.  We will state that binomial and at the same time do the addition on the right:

[tex]88(x-\frac{3}{2})^2=-102[/tex]

Now we can move the constant back over and set it back equal to y:

[tex]y=88(x-\frac{3}{2})^2+102[/tex]

From that form you can see that the equation of the line of symmetry is x = 1.5.  The coordinates of the vertex are (1.5, 102).  If we move 1 unit to the left of the vertex, or 1 unit to the right of the vertex, we will be at the same height.

C then is your answer.

The solution is : C. is the answer.

C. The trajectory of the airplane is symmetric about the line x = 1.5 km, which indicates that the height of the airplane when it moves a horizontal distance of 0.5 km is the same as the height of the airplane when it moves a horizontal distance of 2.5 km.

The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.

here, we have,

In order to determine the line of symmetry, it would help to put this standard form parabola into vertex form, which is

y = a (x-h)^2 + k

,where x = h is the equation of the line of symmetry.

To get this into vertex form we will complete the square.  The first couple of steps I will combine into 1.  We will set the quadratic equal to zero, then move the constant over to the other side:

88x^2 - 264x = -300

The next rule is that the leading coefficient HAS to be a positive 1.  Ours is a positive 88, so we have to factor it out:

88( x^2 - 3x) = 300

Now we can perform the process of completing the square.  The rule is to take half the linear term, square it, and add it to both sides.  Our linear term is 3.  Half of 3 is 3/2, and 3/2 squared is 9/2.  We will add 9/2 inside the parenthesis on the left, but don't forget about that 88 sitting out front which refuses to be ignored.  It serves as a multiplier into the parenthesis.  What we actually added in, then, was 88(9/2) which is 198:

88( x^2 - 3x + 9/4 ) = -300 + 198

The purpose of completing the square is to give us a perfect square binomial which serves as the axis of symmetry of the parabola and also gives us the h coordinate of the vertex.  We will state that binomial and at the same time do the addition on the right:

88( x - 3/2)^2 = -102

Now we can move the constant back over and set it back equal to y:

y = 88( x - 3/2)^2 + 102

From that form you can see that the equation of the line of symmetry is x = 1.5.  The coordinates of the vertex are (1.5, 102).  If we move 1 unit to the left of the vertex, or 1 unit to the right of the vertex, we will be at the same height.

C then is the answer.

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Answer:

Step-by-step explanation:

Both x and y are inscribed angles.  The value of an inscribed angle is half the measure of its intercepted arc.  This means that x has a value of 33°, and y has a value of 48°.  That means that, according to the triangle angle sum theorem, the third angle has to equal 180 - 33 - 48 = 99°.

This angle is vertical with angle z, so angle z also equals 99°

Answer:

graph 1

Step-by-step explanation:

Let's look at graph 1:

The first vertex (the left hand top corner) has a degree 3 because there are 3 line segments coming from it.

Let's check to see if the other vertices have degree 3.

The second vertex (the middle top) has degree 3 because again it has 3 line segments coming from it.

The third vertex (the top right) has degree 3 because it has 3 line segments coming from it.

The fourth vertex (the bottom left) has degree 3 because it has 3 line segments coming from it.

The fifth vertex (the middle bottom) has degree 3 because it has 3 line segments coming from it.

The last vertex (the bottom right) has degree 3 because it has 3 line segments coming from it.

Let's look at graph 2:

The first vertex (top left) has degree 1 because it has one line segment coming from it.

The second vertex( middle top) has degree 2 because it has 2 line segments coming from it.

Graph 2 doesn't have the same degree per vertex.

Looking at graph 3:

The first vertex (top left) has degree 1 while the second (top middle) has degree 2.

Graph 3 doesn't have the same degree per vertex.

Looking at graph 4:

The top left has degree 1.  Looking at one of the middle vertices there, they have degree 4 each because they have 4 line segments coming from it. So graph 4 doesn't have the same degree per vertex.

The answer is only graph 1.