The rise and run of the line, state the slope in simplest form

For the given quadratic equation:

y = x² - 6x - 7

The vertex is (3, -16) and the axis of symmetry is at x = 3.

For a quadratic equation of the form:

y = a*x² + b*x + c

The x-value of the vertex (h, k) is:

h = -b/2a

And the axis of symmetry is the vertical line x = h.

In this case, the quadratic equation is:

y = x² - 6x - 7

The x-value of the vertex is at:

h = -(-6)/2*1 = 3

And the y-value of the vertex is at:

y = (3)² - 6*3 - 7

y = 9 - 18 - 7

y = -16

Then the vertex is at (3, -16)

And the axis of symmetry is x = 3

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Answer:

Step-by-step explanation:

u

Answer:

105

Step-by-step explanation:

1. x = mushroom he gather

2. he dry 2/5 from he gather, 2/5 from x

3. he pickled 5/9 of remaining mushroom

find the remaining mushroom value first, x-2/5x = 3/5x

then multiply with 5/9, 5/9(3/5x) = 15/45x

4. total mushroom - dry - pickled, he still have 28 to fry

5. write the equation like this

x - 2/5x - 15/45x = 28

45/45x - 18/45x -15/45x = 28

12/45x = 28

x = 28(45) / 12

x = 105

The values of x and y which are the missing terms of the given triangle have their values as; x = ⁵/₂ and y = ⁹/₄

From the given triangle, we can see that the transverse line intersects both side lengths at their midpoints. Thus, we can say that;

3x - 4 = x + 1   ------(1)

⁴/₃y + 2 = 4y - 4   ------(2)

Let us solve equation 1 by rearranging to get;

3x - x = 1 + 4

2x = 5

x = ⁵/₂

Similarly, we can say that for equation 2;

4y - ⁴/₃y =  2 + 4

4y - ⁴/₃y = 6

Multiply through by 3 to get;

12y - 4y = 18

8y = 18

y = 18/8

y = ⁹/₄

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the slope of the given point is m=−7/2

The equation (D) y - 6 = 4(x+8) represents the line passing through the points (-8, 6) and (-11, -6).

The point-slope form can be used to get the equation of a straight line that traverses a specified point and is inclined at a particular angle to the x-axis. A line exists if and only if each point on it fulfills the equation for the line. This suggests that a linear equation in two variables can represent a line.

The given points are

(x₁, y₁) = (-8, 6)

(x₂, y₂) = (-11, -6)

So, the slope is given by

m = (y₂- y₁)/ (x₂- x₁)

= (-6 -6)/ (-11 -(-8)

= -12/ -3

= 4

Put (x₁, y₁) = (-8, 6) in the equation (y - y₁) = m (x- x₁)

y - 6 = 4(x-(-8)

y - 6 = 4(x+8)

So, the correct option is (D).

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Answer: MARK  ME BRAINLIEST I WORK HARD Soda consumption among children and teens is a health concern for a number of reasons. Drinking soda contributes to childhood weight issues, can lead to tooth decay,1 and can contribute to sleep problems. Some studies also suggest that kids who consume soda may have an increased risk for behavioral issues and mental health problems.

This article discusses the potential connection between soft drinks and behavioral problems, the limitations of this research, and other reasons to limit soft drink consumption in kids. It also covers some of the steps you can take if you are dealing with behavior issues and aggression in children.

Health Problems Associated Soft Drinks

Americans have some of the highest consumption rates of soda per capita worldwide.2 And many of those people consuming soda are very young children.

Over the years, there has been a big push to eliminate soft drinks from school vending machines and to educate parents about the risks associated with sugary drinks. Physicians and nutritionists have made it clear that soda provides children with empty calories and contributes to childhood obesity.

Dentists advise parents not to let children drink soda as well. Sugary drinks aren't good for children's teeth and may cause cavities.3

Most soft drinks also contain caffeine. Caffeine can cause headaches, upset stomach, jitteriness, and sleep problems. It’s also been associated with some behavioral problems and nervous system disorders in children.4

In children, it doesn’t take much caffeine to produce unwanted side effects. The American Academy of Pediatrics (AAP) discourages caffeine intake for kids of all ages.4

Recap

Soda and other sugary soft drinks pose a number of health risks including weight problems, dental cavities, headaches, and sleep problems.

Behavior Problems and Soft Drinks

If the health risks aren’t enough to dissuade parents from giving kids soda, the potential mental health concerns that might be associated with soft drink consumption might be a deterrent.

Research suggests that children who consume soda tend to have slightly higher scores on measures of aggression than do children who do not drink soda beverages. It's important to note, however, that the research only suggests that there is a correlation between soda consumption and aggressive behaviors; research has not proven a causal relationship, meaning that more research is needed to determine whether drinking soda causes this type of behavior.

In one 2013 study published in The Journal of Pediatrics found that aggression, withdrawal behavior, and attention problems are associated with soft drink consumption in young children.5

The researchers assessed 2,929 5-year-old children from 20 different U.S. cities. Even after adjusting for factors such as maternal depression, paternal incarceration, and domestic violence, soft drink consumption was still linked to aggressive behavior.

Children who drank four or more soft drinks per day were more than twice as likely to destroy other people's belongings, get into fights, and physically attack people.

However, it is important to note some flaws in the study that make it difficult to make assumptions about the potential impact of drinking soda. The study did not consider serving size, the type of soda, or what beverages specifically count as soft drinks.

While the study suggests there may be a correlation between drinking soda and behavioral aggression, it isn't enough to conclude that there is a causal connection.

One concerning point that this study indicates is that it is quite common for young children to consume soda. Forty-three percent of five years olds were reported to drink one serving of soda per day, while 4% reported drinking four servings per day.

Why Soda Might Affect Mental Health and Behavior

It’s unclear why soda consumption might be connected to aggressive behavior and other mental health issues. Soft drinks are highly processed, and there is not much research on how certain ingredients impact children. Some studies have linked aspartame to irritability6 and sodium benzoate to ADHD-related symptoms.7

Caffeine has also been linked to some behavior problems in children, so researchers suspect the caffeine content may play a role.

An underlying physical condition, such as low blood glucose levels, could also explain the link. Low blood glucose may cause children to crave soda while also causing them to become withdrawn or aggressive.8

However, further research is needed to understand how soda and mental health issues might be connected.

Recap

Soda may contain sugar, aspartame, sodium benzoate, and caffeine, and these ingredients may play a role in triggering negative side effects in kids.

MARK ME BRAINILEST I WORK SUPER HARD  PLEASE!!! YOU ARE WELCOME  FOR THE ANSER MARK ME BRAINIEST NOW THANKS. IF YOU NEED MORE ANSWER MORE QUESTION COME TO ME.

Step-by-step explanation:

Each worker looked 40 passengers

From the question, we have

On a plane there were 6 airline workers and 240 passengers.

each worker looked after the same number of passengers

number of passengers = 240/6

=40

Each worker looked 40 passengers

Divide:

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

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If DB and BC are congruent, then AB must be a perpendicular bisector. We conclude that AB is congruent to AB by the reflexive characteristic because DB and BC are congruent.

ADB is congruent to ACB according to the Side-Side-Side, or SSS, congruency rule because the sides AD, AB, and DB in triangle ADB are congruent to the equivalent sides AC, BC, and AB in triangle ACB.

As a result, CPCTC ABD = ABC according to the notion of congruency, where Congruent Parts of Congruent Triangles are Congruent.

Due to the fact that ABD and ABC are linear pair angles,

ABD + ABC = 180°,

ABD + ABD = 2, and ABD = 180°

by virtue of the substitution feature,

ABD = 180°/2 = 90°.

As AB is perpendicular to CD and AB is a perpendicular bisector of CD, ABD = 90° = ABC.

Therefore, the option; DB and BC are congruent is what Kiran needs to know in order to demonstrate that AB is a perpendicular bisector of segment CD.

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(a) she land to minimize the total travel time is 2.4min

(b) the minimum speed at which she must row so that the quickest way to the restaurant is to row directly is 6

(a)

T(x) = time rowing + time walking

     = [tex]\frac{\sqrt{x^{2} +16} }{2}[/tex] +[tex]\frac{6 - x}{3}[/tex]

T(x) = 1/2[tex]\sqrt{(x^{2} + 16)}[/tex]  + 2 - [tex]\frac{x}{3}[/tex]

  first derivation

T'(x) = 1/4[tex]\sqrt[-1/2]{(x^{2} + 16)}[/tex] .2x - 1/3

       = [tex]\frac{x}{2\sqrt{(x^{2} + 16)} }[/tex] - 1/3

T'(x) = 3x - 2 [tex]\sqrt{(x^{2} + 16)}[/tex] / 6[tex]\sqrt{(x^{2} + 16)}[/tex]

T'(x) = 0

3x - 2 [tex]\sqrt{(x^{2} + 16)}[/tex] / 6[tex]\sqrt{(x^{2} + 16)}[/tex]  = 0

3x - 2 [tex]\sqrt{(x^{2} + 16)}[/tex] =0

3x/2 = [tex]\sqrt{(x^{2} + 16)}[/tex]

9[tex]x^{2}[/tex]/4 = [tex]x^{2}[/tex] + 16

9[tex]x^{2}[/tex] = 4 [tex]x^{2}[/tex] + 64

5 [tex]x^{2}[/tex] = 64

[tex]x^{2}[/tex] =64/5

x = [tex]\sqrt{64/5}[/tex]

x = 8/[tex]\sqrt{5}[/tex]

x = 8[tex]\sqrt{5}[/tex]/5

total travel time = 6 - 8[tex]\sqrt{5}[/tex]/5 = 2.4 min

she land to minimize the total travel time is 2.4min

(b) T(x) = time rowing

           = [tex]\frac{\sqrt{x^{2} +16} }{2}[/tex]

first derivation

T'(x) = 1/4[tex]\sqrt[-1/2]{(x^{2} + 16)}[/tex] .2x

      = [tex]\frac{x}{2\sqrt{(x^{2} + 16)} }[/tex]

T'(x) = 0

[tex]\frac{x}{2\sqrt{(x^{2} + 16)} }[/tex] =0

x = 0

minimum speed = 6-x = 6-0=6

the minimum speed at which she must row so that the quickest way to the restaurant is to row directly is 6

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The cat ate 3/7 of a bag per week when the food lasted for 7/4 week.

According to the question,

We have the following information:

Amira had 3/4 of a bag of cat food. The food lasted 7/4 weeks.

Now, we can easily find how much food Amira's cat ate in one week by dividing the total number of bags of food by the number of weeks the food lasted.

So, we have the following expression:

3/4 of a bag = 7/4 weeks

1 week = 3/4 ÷ 7/4

1 week = 3/4 * 4/7 of a bag

1 week = 3/7 of a bag

Hence, the cat ate 3/7 of a bag per week when the food lasted for 7/4 week.

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The equation of the line passing through the given point and parallel to the given line (-1, 2), 2y = 6x + 13 will be y=3x+3.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that, the equation of the line passing through the given point and parallel to the given line.(-1, 2), 2y = 6x + 13

The slope of the given line is,

2y = 6x + 13

y=3x+13/2

m=3

The equation of the line passing through the (-1, 2) and slope equal to 3 is,

y-2=3(x+1)

y-2=3x+1

y=3x+3

Thus, the equation of the line passing through the given point and parallel to the given line (-1, 2), 2y = 6x + 13 will be y=3x+3.

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Answer:

-32

Step-by-step explanation:

Given expression,

→ 7s + (c/-3)

Solving the given expression,

→ 7s + (c/-3)

→ 7(-5) + (-9/-3)

→ -35 + 3 = -32

Hence, the answer is -32.

Answer:

[tex]-32[/tex]

Step-by-step explanation:

[tex]When[/tex] [tex]c=-9, s=-5[/tex]

[tex]7s+\frac{c}{-3} = 7(-5) +\frac{-9}{-3}[/tex]

            [tex]= -35+3\\\\=-32[/tex]

The angle 1 is 88 degree, 2 is 42 degree and the 3 is 113 degree.

We know that the sum of the angles of the triangle is 180, so in one triangle where the 3 angle is missing we can write as:

42 + 25 +  ∠3 = 180

∠3 + 67 = 180 ,

∠3 = 113°

now in the triangle where 1 and 2 angles are missing, we can say that ∠2 = 42° because of transversely equal angles:

so, ∠ 2 = 42°

now again for a triangle,

∠1 + 42 + 50 = 180

∠1 + 92 = 180

∠1 = 88°

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The volume of gas consumed by the first and second cars is 25 gallons and 30 gallons, respectively.

A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas, and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars travelled a combined total of 1525 miles, for a total gas consumption of 55 gallons.

Let the volumes of gas consumed by the first car and the second car be denoted by the variables "x" and "y". We can form the given two equations using the given data.

x + y = 55

25x + 30y = 1525

We will substitute the value of "x" from the first equation into the second equation.

x = 55 - y

25x + 30y = 1525

25(55 - y) + 30y = 1525

1375 - 25y + 30y = 1525

5y = 150

y = 30

x = 55 - y = 55 - 30 = 25

Hence, the gas consumed by the first and second cars is 25 gallons and 30 gallons, respectively.

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Answer:

Step-by-step explanation:

hope it helps

The equation for the line of best fit for a woman's height, y, based on her shoe size, x is y = 1.36x + 55.6.

From the given table:

To find the equation we need to insert the points (x,y) in calculator.

Points are:

Sum of X = 91

Sum of Y = 624.5

Mean X = 10.1111

Mean Y = 69.3889

Sum of squares (SSX) = 42.8889

Sum of products (SP) = 57.6111

Regression Equation = ŷ = bX + a

b = SP/SSX = 57.61/42.89 = 1.34326

a = MY - bMX = 69.39 - (1.34*10.11) = 55.80699

y = 1.34326X + 55.80699

aproximate:

y = 1.36 + 55.6.

Therefore The equation for the line of best fit for a woman's height, y, based on her shoe size, x is y = 1.36x + 55.6.

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Answer:

10 72

Step-by-step explanation:

The recursive formula which correctly represents the given formula; g ( n ) = g ( n − 1 ) + 5.

It follows from the task content that the expression which represents the recursive formula.

By observation, the common difference, d of the arithmetic progression is; 5.

On this note, the recursive formula can be written as follows;

g ( n ) = g ( n − 1 ) + 5.

Consequently, the required recursive formula for the given arithmetic progression is; g ( n ) = g ( n − 1 ) + 5.

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By using distance formula the following results are obtained

a) Other value of k = 14

b) For k = 4, the equation of bisector of [tex]\angle ABC[/tex] is

[tex]y = \frac{1}{3}x + 4[/tex]

What is distance formula?

Distance formula is used to find the distance between two coordinates.

If the coordinates of one point be ([tex]x_1, y_1[/tex]) and coordinates of other point is  ([tex]x_2, y_2[/tex]), then  distance between the two points is

[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]

The points A, B and C have coordinates A(2, 8), B(9, 7) and C(k, k-2).

Length of AB =

[tex]\sqrt{(9 - 2)^2 + (7 - 8)^2}\\\\\sqrt{49 +1}\\\\\sqrt{50}[/tex]

Length of BC =

[tex]\sqrt{(k - 9)^2 + (k - 2 - 7)^2}\\\\\sqrt{(k - 9)^2 + (k - 9)^2}\\\\\sqrt{2(k-9)^2}\\\\(k-9) \sqrt{2}[/tex]

By the problem,

[tex](k-9)\sqrt{2} = \sqrt{50}\\k - 9 = \sqrt\frac{50}{2}}\\k - 9 = \sqrt{25}\\k - 9 = \pm 5\\k - 9 = 5 \ or \ k - 9 = -5\\k = 5 + 9 \ or \ k = 9 -5\\k = 14 \ or \ k = 4[/tex]

The other value of k is 14

b) When  k = 4

Coordinate of C = (4, 2)

Since AB =AC , the bisector of [tex]\angle ABC[/tex] passes through the midpoint of AC

Midpoint of AC =

[tex](\frac{2 + 4}{2} , \frac{8+2}{2})\\(3, 5)[/tex]

The line also passes through (9, 7)

Slope of the  bisector of [tex]\angle ABC[/tex] = [tex]\frac{7 -5}{9 - 3}[/tex]

                                                    = [tex]\frac{1}{3}[/tex]

Equation of the bisector of [tex]\angle ABC[/tex]

[tex]y - 5 = \frac{1}{3}(x - 3)\\\\y - 5 = \frac{1}{3}x -1\\\\y = \frac{1}{3} x - 1 + 5\\\\y = \frac{1}{3} x + 4[/tex]

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The median for a particular set is one less than the mean.

Given;

List of order for goals scored by a soccer team in 9 matches

= 0, 0, 1, 1, 1, 3, 3, 4, 5

To find the relation between mean and median;

The obtained mean = Sum of observations/number of observations

                                 = 0 + 0 + 1 + 1 + 1 + 3 + 3 + 4 + 5

                                 = 18/9

                                 = 2

Mean = 2

For median;

let us write the given observations in ascending order;

⇒  0, 0, 1, 1, 1, 3, 3, 4, 5

Here no. of observations is r = 9 which is an odd number.

Therefore observation at 5th is a middle position which has 1 as a value.

Median = 1

Therefore, the median is less than the mean by 1.

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Answer:

It will take 8 days

Step-by-step explanation:

Mixed numbers in equations

1 3/4 * d = 14

Change the mixed number to an improper fraction

1 3/4 = ( 4*1 + 3) /4 = 7/4

7/4 * d = 14

Multiply each side by 4/7

4/7 * 7/4  *d = 14 * 4/7

d = 8

It will take 8 days.

The initial value of f(x) is -36.

The initial value of g(x) is -44

The range of f(x) is {y | -36 ≤ y ≤ -20}

The range of g(x) is {y | -44 ≤ y ≤ -20}

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

{x | -6 ≤ x ≤  -2}

g(x) = 6x - 8

From the table, we get that,

The initial value of f(x) is -36.

The initial value of g(x).

g(x) = 6 x (-6) - 8 = -36 - 8 = -44

The range of f(x).

= {y | -36 ≤ y ≤ -20}

g(x) = 6x - 8

g(x) = 6 x (-6) - 8 = -36 - 8 = -44

g(x) = 6 x (-2) - 8 = -12 - 8 = -20

The range of g(x)

= {y | -44 ≤ y ≤ -20}

Thus,

The initial value of f(x) is -36.

The initial value of g(x) is -44

The range of f(x) is {y | -36 ≤ y ≤ -20}

The range of g(x) is {y | -44 ≤ y ≤ -20}

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The equation of line v is y - x = 7 and The equation in slope-intercept form is y = x + 7.

Given:

y = -x + 7

Compare it to Slope-intercept form y = mx + c (∵ m = slope or gradient)

The gradient (m₁) is -1.

The gradient of the perpendicular line v is given by

m₂= -1/m₁

m₂=-1/-1

m₂=1

To find the duration of the perpendicular line v use the formula

y- y₁ = m(x-x₁)   (i.e., one slope, one point formula)

y₁=-1, x₁ =-8 , m₂ =1

y-(-1) = 1[x-(-8)]

y + 1 = x + 8

y - x = 8 - 1

y - x = 7

So, The equation of line v is y - x = 7 and The equation in slope-intercept form is y = x + 7.

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a)An expression for the value of the account at the end of three years will be:

$1000[tex]x^3[/tex] +300[tex]x^2[/tex] + 500x

b) The amount in the account at the end of three years if the interest rate is 4% will be:

= 1000 × [tex]1.04^3[/tex] + 300 × [tex]1.04^2[/tex] + 500 × 1.04

= $ 1969.344

Given,

In the question:

A growth factor of x = 1+r. $1,000 is deposited at the start of the first year,

An additional $300 is deposited at the start of the next year, and $500 at the start of the following year.

To find the:

a) Write an expression for the value of the account at the end of three years in terms of the growth factor x.

b) Determine (to the nearest cent) the amount in the account at the end of three years if the interest rate is 4%.

Now, According to the question:

a) Growth factor x = 1 + r

Based on the given conditions:

An expression for the value of the account at the end of three years will be:

$1000[tex]x^3[/tex] +300[tex]x^2[/tex] + 500x

b) The amount in the account at the end of three years if the interest rate is 4% will be:

1 + 4% = 1 + 0.04 = 1.04

= 1000 × [tex]1.04^3[/tex] + 300 × [tex]1.04^2[/tex] + 500 × 1.04

= $ 1969.344

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Answer:

Hence, he booked 19 tickets for Airlines A, 12 tickets for Airline B, and 41 tickets for Airlines C.

Step-by-step explanation:

Suppose the office manager booked a+b+c = 72 tickets.

a = b + 7

c = 3b + 5.

So, we have (b + 7) + b +(3b + 5) = 72, or

5b + 12 = 72, or

5b = 60, or

b = 12.

Answer:

the greatest number I guess is 2

Step-by-step explanation:

18÷2= 9male to the 2group

24÷2=12female to the 2group

The amount of money Rita will get after 5 year with interest rate compounds monthly is $4,420.

The formula for the calculation of the compound interest is-

A = P(1 + r/100n)∧nt

In which,

A  = amount after compounding

P = principal amount (  $20,000 )

n = number of time principal amount compounded in a year. ( 12 )

t = total time in years. (5 )

r = rate of interest (4%)

Put the value in eq.

A = 20,000(1 + 4/1200)∧5×12

A = 20,000×1.22

A = 24420

CI = A - P

CI = 24420 - 20000

CI = 4,420.

Thus, the amount of money Rita will get after 5 year with interest

rate compounds monthly is $4,420.

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