Janelys has a points card for a movie theater. She receives 20 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs at least 165 points for a free movie ticket.

I WILL TAKE THE POINTS (0,7) AND (2,1) FROM THW GRAPH AND USE THEM TO GET THE GRADIENT.

[tex]m \frac{y2 - y1}{x2 - x1} \\ = \frac{1 - 7}{2 - 0} \\ m = \frac{ - 6}{2} \\ m = - 3[/tex]

I WILL USE THE POINT (0,7) TO FIND THE VALUE OF C IN THE GENERAL EQUATION.

[tex]7 = - 3(0) + c \\ c = 7[/tex]

THE EQUATION IS

[tex]y = - 3x + 7[/tex]

ATTACHED IS THE SOLUTION

To solve this question, find the 4 first terms of the sequence.

The first term is a₁

a₁ is given and a₁ = 7

The second term is a₂

Given:

Then, let's find a₂ using the value of a₁

The third term is a₃

let's find a₃ using the value of a₂

The fourth term is a₄

let's find a₄ using the value of a₃

Answer:

The four first terms are:

a₁ = 7

a₃ = 12

a₃ = 17

a₄ = 22

[tex]6 {x}^{2} - 5x - 6 = 0 \\ 6 {x}^{2} - 9x + 4x - 6 = 0 \\ (6 {x}^{2} - 9x) + (4x - 6) = 0 \\ 3x(2x - 3) + 2(2x - 3) = 0 \\ (3x + 2)(2x - 3) = 0 \\ 3x + 2 = 0 \\ \\ \\ or \\ 2x - 3 = 0 \\ x = \frac{ - 2}{3} \\ \\ or \\ \\ x = \frac{3}{2} [/tex]

I FACTORISED THE EQUATION FIRST WITH A SIMPLE METHOD OF MULTIPLYING THE COEFFICIENT OF

[tex] {x}^{2} [/tex]

and the constant number then find the factors that will give me the coefficient of x.

ATTACHED IS THE SOLUTION

Step-by-step explanation:

are you sure this is the whole information ?

because

6² = 5x + 6

is not called a quadratic equation.

it is a quadratic equation, when there is one term in x² involved.

I assume therefore, that your problem is

6x² = 5x + 6

that is then as basic quadratic equation

6x² - 5x - 6 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 6

b = -5

c = -6

x = (5 ± sqrt((-5)² - 4×6×-6))/(2×6) =

= (5 ± sqrt(25 + 144))/12 = (5 ± sqrt(169))/12 =

= (5 ± 13)/12

x1 = (5 + 13)/12 = 18/12 = 3/2

x2 = (5 - 13)/12 = -8/12 = -2/3

so, the 2 solutions for the quadratic equation are

x = 3/2 and x = -2/3

Applying the slope formula, we have:

16. Slope = -9/4; Parallel slope = -9/4; Perpendicular slope = 4/9.

17. Slope = -4; Parallel slope = -4; Perpendicular slope = 1/4.

See explanation below for the rest answers.

Slope of a line = change in y / change in x.

The slope of parallel lines are the same, while the slopes of two lines that are perpendicular to each other are negative reciprocals of each other, i.e. 1/a and -a can be the slopes of two lines that are perpendicular to each other.

In an equation given in slope-intercept form, y = mx + b, the slope is represented as "m".

16. Given, (3, 7) and (7, -2):

Slope (m) = (-2 - 7)/(7 - 3)

Slope = -9/4

Parallel slope = -9/4

Perpendicular slope = 4/9.

17. Given, y = -4x + 2,

Slope = -4

Parallel slope = -4

Perpendicular slope = 1/4.

18. Rewrite 5x - 2y = 8 in slope-intercept form:

-2y = -5x + 8

y = 5/2x - 4

Slope = 5/2

Parallel slope =  5/2

Perpendicular slope = -2/5.

19. Rewrite  4x + 3y = 2 in slope-intercept form:

3y = -4x + 2

y = -4/3x + 2/3

Slope (m) = -4/3

Substitute (a, b) = (2, -5), and m = -4/3 into y - b = m(x - a):

y - (-5)) = -4/3(x - 2)

y + 5 = -4/3(x - 2) [point-slope form]

20. Given, y = -5x + 2

Slope (m) = -5

Substitute (a, b) = (-4, -6), and m = -5 into y - b = m(x - a):

y - (-6) = -5(x - (-4))

y + 6 = -5(x + 4) [point-slope form]

21. Rewrite 9x - 3y = 6 in slope-intercept form:

-3y = -9x + 6

y = 3x - 2

The slope of y = 3x - 2 (9x - 3y = 6) is 3.

The slope of -3x - 5 is -3.

Therefore, the lines are neither parallel nor perpendicular.

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I WILL USE THE LAWS OF EXPONENTS WHEN WE MULTIPLY POWERS OF THW SAME BASES WE KEEP ONE POWER AND ADD THE EXPONENTS.

[tex] = 7^{ - 5} \times 7^{2} \\ = {7}^{ - 5 + 2} \\ = {7}^{ - 3} \\ = \frac{1}{ {7}^{3} } \\ = \frac{1}{343} [/tex]

ATTACHED IS THE SOLUTION

Let Bailey drive x miles.

So, Kacie drove 2x miles.

Kaiden drove 2x + 10 miles.

According to the question,

x + 2x + 2x + 10 = 50

x = 8

Therefore, Bailey drove 8 miles and Kacie drove 16 miles, while Kaiden 36 miles.

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The angle whose supplement is 12 degrees less than twice its measure is 64 degrees.

supplementary angles are angles that add up 180 degrees.

Given the data in the question;

Let x represent the first angle.

Since the angle are supplementary, sum of angles = 180°

First angle + second angle = 180

x + ( 2x - 12 ) = 180

Solve for x

x + 2x - 12 = 180

3x - 12 = 180

3x = 180 + 12

3x = 192

x = 192/3

x = 64

Therefore, the measure of the angle 64 degrees.

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The domain and the range pf the curve was solved and the correct answer to the question is the last option which is

The domain are the input values and are represented in the x axis while the range are the output values and represented in the y axis

From the graph

We can conclude that the last option is the correct answer

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Answer:

1/4^3

Step-by-step explanation:

US$ the tourist received finally is US$985.

BD$2000 is there.

BD$1 = US$0.50

Bank charged a commission of 1.5%.

Solution:

For one BD i.e., BD$1 he gets US$0.50.

It is half the value of BD$.

By cross multiplication technique, you can find this.

Then for,

BD$2000 he will get US$ 1000.

Bank charges =  1.5%.

That is,

1.5/100*1000 = $15

US$ the tourist received finally = 1000-15

= $985

US$ the tourist received finally is US$985.

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The percentage of the tip that Serena's father paid was 20%.

Mathematically, a percentage is a numerical ratio, usually expressed as a fraction of 100 and denoted by the percent sign (%).

Percentages show the proportional relationship between two fractions, like proportions and ratios.

The amount of the tip = $5

The cost of the ride = $25

The total amount paid by Serena's father = $30 ($5 + $25)

The percentage of tip to the ride's cost = The amount of the tip divided by the cost of the ride.

= 20% ($5/$25 x 100)

Thus, in percentage terms, the amount that Serena's father tipped the taxi driver is 20% of the ride's actual cost.

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0.020 is a probability for student selects at least 6 .

What is a probability simple definition?

There are two ways to do it. You can either interpret this as

One minus the probability that the student will guess 5 or fewer

correct answers with a probability of a correct answer being = 1/4  ⇒      

0.0197277069

The probability that the student will guess 4 or fewer wrong answers

with a probability of a wrong answer being = 3/4

  binomcdf (10,3/4,4)

     = 0.0197277069

Either way it rounds to 0.020

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Answer:

perpendicular

Step-by-step explanation:

The equations represent a vertical and horizontal line, respectively, which are perpendicular to each other.

Answer:

I see a right angle, so the transversal is perpendicular to the parallel lines. Therefore, x and y are supplementary and congruent, and so we have x = 90 and

y = 90.

Answer:

207/4 some other forms are 51 3/4 or 51.75

Step-by-step explanation:

Answer:

24  3/4 gal

Step-by-step explanation:

2 3/4 gal / bucket    *   9 bucket   = 24 3/4 gal

The most appropriate choice for exponent will be given by-

Keiko is not correct because the exponent [tex](-1)^n[/tex] does not always give -1

What is exponent?

Exponent denotes how many times a number is multiplied by itself.

For example in [tex]2^4[/tex] = [tex]2 \times 2 \times 2 \times 2[/tex], here 2 is multiplied 4 times.

Suppose [tex]a^m = a \times a \times a \times a[/tex][tex].....[/tex] (m times), here a is the base and m is the power.

Here,

The given exponents are[tex](1)^n[/tex] and [tex](-1)^n[/tex]

[tex](1)^n = 1 \times 1 \times 1\times.....\times 1[/tex] (n times)

      = 1

For [tex](-1)^n[/tex]

If n is even,  [tex](-1)^n[/tex] = 1

If n is odd ,  [tex](-1)^n[/tex] = -1

But Keiko told that [tex](-1)^n[/tex] always results in -1

So, Keiko is not correct.

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Answer:

x = 1 +sqrt(5)

x = 1 -sqrt(5)

Step-by-step explanation:

y= x^2 -2x -3

Let y = 1

1= x^2 -2x -3

Subtract 1 from each side

1-1= x^2 -2x -3-1

0 = x^2 -2x -4

Using the quadratic formula

x = - (-2) ±sqrt( (-2) ^2 -4(1)(-4))

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

                      2(1)

x = 2 ±sqrt( 4 +16)

     ------------------------

                      2

x = 2 ±sqrt( 20)

     ------------------------

                 2

x = 2 ±sqrt( 4*5)

     ------------------------

                 2

x = 2 ±sqrt(5)

     ------------------------

                 2

x = 1 ±sqrt(5)

The solution for the inequality is x < 11/130.

The problem we dealing with is related to inequality which is referred to as An inequality in mathematics could be a relationship that produces a non-equal comparison between two integers or other numerical expressions.

Since we are provided with inequality which is 81 - 11/5x < 55

Now multiplying both by 5x we get

81 × 5x - (11/5x) × 5x < 55 × 5x

=> 405x - 11 < 275x

=> 405x - 275x < 11

=> 130x < 11

=> x < 11/130

so it is the solution for the inequality 81 - 11/5x < 55

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The simplified form of like terms in -3(u+6) -4(u+5) is 7u = -38.

Similar variables and powers are defined as like terms. It is not necessary for the coefficients to agree. When two or more terms do not share the same variables or powers, they are said to be unlike terms. Unless there is a power, the variables' order is irrelevant.

Two expressions joined by an equal sign form a mathematical statement known as an equation.

Given that,

Expression is -3(u+6) -4(u+5)

Simplifying the equation,

-3u-18-4u–20 = 0

-7u -38 = 0

-7u = 38

7u = -38

Therefore 7u = -38 is the simplifief form of like term in -3(u+6) -4(u+5).

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Answer:

2.5

Step-by-step explanation:

if it is divison then the answer would be 2.5

if its additin is  35

if subtraction it is 15

if multipcation  250

The function to show how quickly the weeds grow each day is "f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily. Option B

f(x) = 4(1.15)x = 4(1+ 0.15)x ................... (1)

Given that there are seven days in a week, the daily growth rate of the weeds may be estimated using equation (1) by dividing 0.15 (which stands for the 15% weekly growth rate) in the following manner:

f(x) = 4(1.15)x = 4(1+ 0.15/7)x

f(x) = 4(1 + 0.02)x

f(x) = 4(1.02)x

Since 0.02 is the same as 2%, this implies that the rate at which the weeds grow each day is 2%.

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Answer:

5

Step-by-step explanation:

he needs $85 and he has $25,

so it will be 85-25=60

that means he would need $60 more. if he saves $13 every week, it will 60÷13= 4.6 weeks or approximately 5.

If the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units

The length of the hypotenuse = 13.5 units

The angle = 41 degrees

Here we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

In this question hypotenuse and angles are given and we have to find the opposite side.

sin θ= opposite side /  Hypotenuse

Substitute the values in the equation

sin 41 = Opposite side / 13.5

Opposite side = sin 41×13.5

= 8.86 units

Hence, if the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units.

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The rate/speed at which one must travel to cover 227.5 miles in 3.5 hours is 65 miles per hours.

Speed or rate is simply referred to as distance traveled per unit time.

It is expressed as;

r = d / t

Where r is the speed/rate, d is the distance and t is time elapsed.

Given the data in the question;

To determine the rate at which one must travel to cover 227.5 miles in 3.5 hours, plug the given values into the equation above and solve for r.

r = d / t

r = 227.5 miles / 3.5 hours

r = 65m/h

r = 65mph

Therefore, the speed/rate one must travel is 65mph.

Option A)65mph is the correct answer.

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By using the Unitary method, $468 was spent on newspapers in 52 weeks.

Unitary method is a method used for finding the unit cost in which we divide the total cost by the total number of articles and to find the cost of more than one article, we multiply the unit cost by the number of articles required.

Cost of newspapers in a week from monday to saturday = $(1 x 6) = $6

Cost of newspaper only on sunday of a week = $3

Cost of newspapers in a week = $(6 + 3) = $9

Therefore, the cost of newspapers in 52 weeks = $(52 x 9) = $468.

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Scientific notation of the given expression divided -6.5 × 10^-7 by

9.88 ×10^-8 with two decimal places is equal to  6.58 × 10^0.

As given in the question,

Divided  -6.5 × 10^-7 by  9.88 ×10^-8 we have,

= ( -6.5 × 10^-7 ) /( 9.88 ×10^-8 )

= ( -6.5 / 9.88) × 10^(-7 +8)

= 0.65789 × 10^1

Express above quotient in scientific notation form with two decimal is equal to

= 6. 58 × 10^0

Therefore, scientific notation of the given expression divided -6.5 × 10^-7 by  9.88 ×10^-8 with two decimal places is equal to 6.58 × 10^0.

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Because the angles on the first quadrant of the bottom horizontal line are equal, we conclude that the two parallel lines are FM and GB,

We know that two lines are parallel if when intersected by the same line, the two give the same angles.

In the image, we can see only one pair of equal angles, which are the two ones represented by a red quarter circle.

Both of these angles are on line MB, this means that the two parallel lines are the ones that intersect MB (in this case are the two vertical lines).

Then we can conclude that the two parallel lines are FM and GB.

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Diameter = 13.93771776 cm