Plot the data points on the graph below. Make sure you use the corresponding color dot for the point according to the following: 1st point - yellow dot, 2nd point - blue dot, 3rd point - green dot, 4th point - red dot, 5th point - pink dot, 6th point - purple dot. x values y values 1 18 2 9 3 6 6 3 9 2 18 1 (Inverse relationship, k = 18)

To find the general form of the equation of the quadratic function given a vertex and a point, we can proceed as follows:

The vertex form of the equation for a quadratic function can be expressed as:

\[ f(x) = a(x - h)^2 + k \]

where
- \( a \) is a coefficient that affects the width and direction of the parabola,
- \( (h, k) \) is the vertex of the parabola.

We've been given the vertex \( (h, k) = (-6, -1) \) and a point on the graph \( (x, y) = (-9, 8) \).

Let's use the vertex form and plug in the values of the vertex and the given point to solve for \( a \).

\[ 8 = a(-9 + 6)^2 - 1 \]
\[ 8 + 1 = a(-3)^2 \]
\[ 9 = a(9) \]
\[ a = 9 / 9 \]
\[ a = 1 \]

Now we know that \( a \) equals 1, and our vertex form equation becomes:

\[ f(x) = 1(x + 6)^2 - 1 \]

To write the equation in general form \( f(x) = ax^2 + bx + c \), we need to expand the equation:

\[ f(x) = 1(x + 6)^2 - 1 \]
\[ f(x) = (x^2 + 12x + 36) - 1 \]  (Expand the square)
\[ f(x) = x^2 + 12x + 36 - 1 \]

Finally, combine the constants:

\[ f(x) = x^2 + 12x + 35 \]

So the general form of the equation of the quadratic function given the vertex \( (-6, -1) \) and the point \( (-9, 8) \) is:

\[ y = x^2 + 12x + 35 \]

Here, \( a = 1 \), \( b = 12 \), and \( c = 35 \).

Answer-

Quadratic regression equation  [tex]y=0.392x^2 - 5.583x + 21.167}[/tex]

Solution-

Quadratic Regression  Equation,

[tex]ax^2+bx+c[/tex]

[tex]a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}[/tex]

Where,

[tex]\sum xx=\sum x^2-\frac{(\sum x)^2}{n}[/tex]

[tex]\sum xy=\sum xy-\frac{\sum x\sum y}{n}[/tex]

[tex]\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}[/tex]

[tex]\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}[/tex]

[tex]\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}[/tex]

Calculating the values from the table,

a= 0.392

b= -5.583

c= 21.167

∴ Quadratic regression equation,

[tex]y=0.392x^2 - 5.583x + 21.167[/tex]

If i understand the question correctly the plane will fly 6 trips of 500 miles each trip.

Number of minutes it takes the plane to fly 500 miles

= 500 / 11

= 45.45 minutes

For 6 trips this = 45.45 * 6 = 272.73 minutes

=  4.55 hours to nearest hundredth.

Put 124m over 29s. Distance/Time = Speed. The answer is 4.27 mps.

Using the formula:

The  speed would be the result of  = distance divided by time

distance= 124m

time. =29 s

= 124 \div 29

= your speed

total speed = 4.27

The ratio is 2:3 puppies to adult dogs, which means for every 2 puppies, there is 3 adult dogs.

Add the ratio together: 2+3 = 5

Divide total dogs by that total: 50 dogs / 5 = 10

Now multiply each number of the ratio by that to find the total number of each:

2 puppies x 10 = 20 total puppies.

3 adults x 10 = 30 total adult dogs.

J(1 , 0); N(5, 0) ; M(5 , -3) and P(2 , -5)

Translation (x,y) -->(x-4, y+4)

J'(-3,4), N'(1, 4) ; M'(1 , 1) and F'(-2 , -1)

Answer is C)

J'(-3,4), N'(1, 4) ; M'(1 , 1) and P'(-2 , -1)

[tex]7x > -35\qquad|\text{divide both sides by 7}\\\\x > -5\\------------------------------------\\\\3x\leq30\qquad|\text{divide both sides by 3}\\\\x\leq10\\\\Answer:\ b)\ -5 < x\leq10[/tex]

Answer:

 [tex]x^2-12x+36= -6+36[/tex]

Step-by-step explanation:

Equation : [tex]x^2-12x = -6[/tex]

General equation : [tex]ax^2+bx+c=0[/tex]

So,we need to add and subtract [tex](\frac{b}{2})^2[/tex] for completing square.

So, next step of completing square :

 [tex]x^2-12x+6^2-6^2= -6[/tex]

 [tex]x^2-12x+36= -6+36[/tex]

Hence Step 2 shows lamar's next step and the solution to the equation

The solution to the equation after completing the square is:

(x - 6)² = 30

Lamar starts with the equation x² - 12x = -6.

Step 2: To complete the square, Lamar takes the coefficient of the x term, which is -12, divides it by 2, and then squares it. In this case, (-12/2)² = 36.

Lamar adds 36 to both sides of the equation to maintain its balance. By doing so, he effectively creates a perfect square trinomial on the left side of the equation.

x² - 12x + 36 = -6 + 36

Simplifying the right side, -6 + 36 equals 30.

The equation now becomes:

x² - 12x + 36 = 30

Now, Lamar can rewrite the left side of the equation as a perfect square. The left side is (x - 6)² because (x - 6)(x - 6) equals x² - 12x + 36.

(x - 6)² = 30

Thus, the solution to the equation x² - 12x = -6, after completing the square, is (x - 6)² = 30.

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answer : D

A. (6 × 7) + 6 = 48

Associative property of multiplication . Here we have +6 . there is a + sign inbetween.  so it does not comes under Associative property of multiplication

B. 6 × (4 + 2) = 36

Here we have 4 +2 . there is a + sign inbetween.  so it does not comes under Associative property of multiplication

C. (6 + 4) × 2 = 20

Here we have 6 + 4 . there is a + sign inbetween.  so it does not comes under Associative property of multiplication

D. (6 × 4) × 2 = 48

Here we have 6 times 4 times 2.  so it comes under Associative property of multiplication

x= 5 that is what x =

First you had to expanded form.

[tex]-3(x-5)-2x=-5x+15[/tex]

[tex]=-5x+15=-10[/tex]

Then you subtract by fifteen from both sides of equation form.

[tex]-5x+15-15=-10-15[/tex]

Simplify.

[tex]-5x=-25[/tex]

Next, divide by negative five from both sides of equation form.

[tex]\frac{-5x}{-5}= \frac{-25}{-5}[/tex]

And finally simplify by equation.

[tex]x=5[/tex]

Final answer: [tex]\boxed{x=5}[/tex]

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

That would  be (40 + 110) / 2

= 150 / 2

= 75 degrees   answer

Final answer:

The equation that demonstrates the additive inverse property is B. 6 + (-6) = 0, where 6 and -6 are additive inverses of each other.

Explanation:

The equation that illustrates the additive inverse property is B. 6 + (-6) = 0. The additive inverse property states that for any number 'a', there is a number '-a' such that 'a' plus '-a' equals zero. This is because adding a number to its additive inverse (which is the negative of the number) will result in zero.

Examples demonstrating the additive inverse include subtracting a positive number and changing its sign before operating the addition, for instance, 5-(+3) results in 5-3, which equals 2. Conversely, if you subtract a negative number, like subtracting -6 from 2, you would perform 2-(-6) which equals 2+6, resulting in 8.

Let's assume

reference angle =B

so,

opposite =b

adjacent=a

now, we can use tan

[tex]tan(B)=\frac{b}{a}[/tex]

now, we can solve for b

Multiply both sides by a

[tex]a*tan(B)=a*\frac{b}{a}[/tex]

[tex]b=a*tan(B)[/tex]

so, option-A...............Answer

This question is about evaluating the solutions of two students, Alisha and Brianna, for a number puzzle involving sets and probabilities. Without specific puzzle instructions, it's hard to determine whose solution is correct. The correctness would depend on the puzzle's directions and the application of mathematical principles.

The question is a mathematical one, involving the solving of number puzzles by two students, Alisha and Brianna. The requirements are to evaluate their solutions for correctness based on given parameters or steps. However, without the specific steps or guidelines of the puzzles presented, it's difficult to provide a definitive assessment or explanation of whose solution would be correct.

From the provided resources, we can infer that we're dealing with a problem-solving scenario involving sets, probabilities, problem analysis, and solution refinement. An example scenario might be: Alisha and Brianna are solving a magic number puzzle where they need to calculate the probability of specific outcomes from a set of numbers. Alisha identifies sets S and A and calculates P(A) as the number of outcomes in A divided by outcomes in S, while Brianna might approach the puzzle differently. The correctness of their results will depend on the puzzle's instructions and the maths principles applied.

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GIVEN: y = -5/6x + 6

slope of given line = -5/6

--> Because the line you are trying to find is perpendicular to the given line, you must find the opposite reciprocal of the slope

opposite reciprocal of the slope = 6/5

You need to find what "b" is for your equation

Plug "b" back into the slope-intercept form along with your equation's slope

y = mx + b

(if your teacher doesn't want any decimals, then write: y = 6/5x + 89/5)

The equation of the line that is perpendicular to y=-5/6x+6 and cross through the point (-9,7) is y = 6/5x + 29.8, found by using the slope-intercept form and the concept of negative reciprocal slopes.

To find the equation of the line that is perpendicular to y=-5/6x+6 and crossing through the point (-9,7), we first need to find the slope of that line. We can determine that by knowing that the slopes of perpendicular lines are negative reciprocals of each other. So, if the slope of given line is -5/6, the slope of the line perpendicular to it will be the negative reciprocal, which is 6/5.

Now we have a point (-9,7) and a slope (6/5) and can use the slope-intercept form of a line to write the equation of a line.

We use the formula y = mx + b:

 Where 'y' and 'x' are coordinates of a point on the line, 'm' is the slope, and 'b' is the y-intercept. We know 'm', 'y' and 'x', so we can solve for 'b'. Substituting, we get: 7 = (6/5)(-9) + b, which simplifies to b = 29.8.

The equation of the line in slope-intercept form is: y = 6/5x + 29.8

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It will take 120 minutes to fill up

The pump will take 120 minutes to fill the tank.

To answer the question of how many minutes it will take to fill an 800-unit tank that is already 1/4 full using a pump that can supply 5 units of water per minute, we must first determine the amount of water needed to fill the tank completely.

Since the tank is 1/4 full, it already contains 800 units * 1/4 = 200 units of water. Therefore, the remaining volume to fill is 800 units - 200 units = 600 units. Next, we divide this remaining volume by the rate at which the pump supplies water:

600 units / (5 units/minute) = 120 minutes.

It will take 120 minutes to fill the tank to its full capacity.

The polynomial degree relates to the number of "zeros" or points of intersection of the polynomial function (curve in the (x,y) plane) with the x axis (that is, points where y=0). These zeros can sometimes be coinciding but that phenomenon aside, you will see N such intercepts with the x axis for a polynomial expression of N-th degree.

Example of a polynomial of 3rd degree is: x^3 + 2 x^2 - x - 2

You can factor it to (x-1)(x+1)(x+2) to see that the zeros are +1, -1, and -2. The plot is attached as an image - note the intercepts. Lmk if you have questions.

A degree in a polynomial function is the greatest exponent of that equation, which determines the most number of solutions that a function could have and the most number of times a function will cross the x-axis when graphed or we can  also say that degree of polynomial determines the number of  zeroes of that polynomial  function.

Let us take an example of polynomial expression of degree three,

For e.g.  [tex]x^{3}+2x^{2} -x-2=0[/tex]              ...(1)

By hit  and trial method we have to solve it .

Firstly, we put [tex]x = +1[/tex] in above equation ,

We get , [tex]1+2-1-2=0[/tex]

Thus, x = +1 is  first zero of the equation.

Now ,we put [tex]x = -1[/tex] in equation...(1) ,

We get,

[tex]-1+2-(-1)-2=0[/tex]

i.e. x = -1 is also  second zero of the equation.

Then, we put [tex]x = -2[/tex] in equation...(1) ,

We get ,

[tex]-8+8-(-2)-2=0[/tex]

Thus, the third zero of the equation is x = -2.

Therefore there are three zeroes of the polynomial function  are x = -1, +1 and -2.

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1/2 inch…………4.5 feet

x inches……….54 feet

x=(54•1/2)/4.5

x=27/4.5

x=6 inches

Final answer:

To calculate the growth of a coral reef over 5 weeks at a rate of 0.12 meters per week, you multiply the weekly growth by 5, resulting in a total growth of 0.6 meters.

Explanation:

If a coral reef grows 0.12 meters every week, we can calculate its growth over 5 weeks by multiplying the weekly growth rate by the number of weeks.

Perform the calculation: 0.12 m/week × 5 weeks = 0.6 meters.

Therefore, a coral reef grows 0.6 meters in 5 weeks.

capacity of the stadium=23564

no.of seats occupied=3/4 of 23564

no.of people in the stadium=23564*3/4

=17673

Answer:

17673

Step-by-step explanation:

Answer:

31.5 minutes only

Inverse proportion

Step-by-step explanation:

It takes 45 minutes for Laura to mow the lawn.

For Kelly it takes 1 hour 45 minutes or 60+45 = 105 minutes

In one minute Laura can mow 1/45 of the lawn.

Similarly in one minute Kelly can mow 1/105 of the lawn

Together in one minute they can mow the sum

= [tex]\frac{1}{45} +\frac{1}{105}[/tex]

Take lcd for 45 and 105 and make them equivalent fractions with same denominator

LCD of 45 and 105 is 15(3) (7) = 315

[tex]\frac{1}{45} +\frac{1}{105}=\frac{7+3}{315}=\frac{10}{315}\\=\frac{2}{63}[/tex]

In other words it would take 63/2 = 31.5 minutes only to lawn if they work together.

The situation here is the problem on inverse proportion.  If no of people increase, work time would decrease.

If each couple rests for [tex] k [/tex] minutes every hour, the time spent resting, [tex] r [/tex], after [tex] h [/tex] hours is given by

[tex] r = kh [/tex]

We know that a couple spent 25 minutes resting in 5 hour. So, the rate is

[tex] 25 = 5k \iff k = \dfrac{25}{5}=5 [/tex]

So, every couple rests 5 minutes per hour.

This means that, after 8 hours, the couples rest

[tex] r = 5\cdot 8 = 40 [/tex]

minutes.

The definitions of the labels are:

Since RQU is the sum of RQS, SQT and TQU, it measures 19+71+18 degrees, i.e. 108 degrees, and thus it's obtuse

Similarly, SQU is the sum of SQT and TQU, so it measures 71+18 = 89 degrees, so it's acute.

Finally, RQT is the sum of RQS and SQT, so it measures 19+71=90 degrees, and it's a right angle.

obtuse, acute and right

∠RQU = 19° + 71° +18° = 108° ⇒ obtuse angle

∠SQU = 71° + 18° = 89° ⇒ acute

∠RQT = 19° + 71° = 90° ⇒ right

Answer:

2

Step-by-step explanation:

Answer:

d. 50 m

Step-by-step explanation:

1. You have the following information given in the problem above:

- The speed of the puck is 20 [tex]\frac{m}{s}[/tex] and experiences no frictional force.

- The time is 2.5 seconds.

2. Then, to calculate the distance, you must apply the following formula:

[tex]d=Vt[/tex]

Where [tex]d[/tex] is the distance, [tex]V[/tex] is the speed and [tex]t[/tex] is the time.

3. Now, you must substitute values into the formula, as below:

[tex]d=(20\frac{m}{s})(2.5s)[/tex]

4. Therefore, the result is:

[tex]d=50m[/tex]

Using the physics equation of distance = speed x time, it can be calculated that an ice-hockey puck moving at a constant speed of 20 ms^-1 for 2.5s would cover a distance of 50 m.

In Physics, the equation for distance can be expressed as distance = speed x time. In this case, the speed of the ice-hockey puck is given as 20 ms^-1 and the time is 2.5 s. By plugging these values into the formula, we get:
Distance = 20 ms^-1 x 2.5 s = 50 m. As a result, the ice-hockey puck will travel a distance of 50 meters in 2.5 seconds if it continues at a steady speed of 20 ms^-1 without any interference from frictional forces. Therefore the correct answer to this question is option d) 50 m.

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she has 40 nickels because: 80-40 = 40. this is equal to 40 nickels

Answer:

Option C, 18/24 = 75%

Step-by-step explanation:

Patients who were addicted to cocaine were divided into 3 groups of 24.

Each group was treated with three different drugs. One group of 24 patients were put on Lithium for treatment out of 24 patients who relapsed were 18.

So conditional relative frequency for relapse among patients who took Lithium would be :

Relative frequency of patients = (patients relapsed) / (total number of patients)

Relative frequency = [tex]\frac{18}{24}[/tex] = 75%

Option C, 18/24 = 75% would be the answer.