What is the equation of the line in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

The equation of the line that is parallel to the line y = -x + 10 is y = -x - 13.

Given table:

x            y

0           10

4           6

8           2

12         -2

slope m = 6 - 10 / 4 - 0

= -4/4

m = -1

substitute in y=mx+c

y = -x+c passes through (0,10)

10 = -0 + c

c = 10.

y = -x + 10.

here m = -1 and passes through (-3,-10)

y = mx +c

-10 = -1(-3)+c

-10 = 3 + c

c = -13

y = -x + (-13)

y = -x - 13.

Therefore the equation of the line that is parallel to the line y = -x + 10 is y = -x - 13.

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Answer:

the domain is the x values: -5,-4,-2,0,1

The range is the y values: -1, 1, 3, 4

Step-by-step explanation:

Step-by-step explanation:

they are parabolas.

their line of symmetry is exactly in the middle between their x-intercepts (when y = 0).

these x-intercepts we get from the factors : y can only be 0, when at least one of the factors is 0.

y = (x + 14)(x + 16)

means y = 0, when x = -14 or x = -16.

so, the line of symmetry is

x = -15

y = (x - 12)(x - 18)

y = 0, when x = 12 or x = 18

line of symmetry is

x = 15

y = (x + 13)(x - 17)

x = -13 or x = 17

line of symmetry

x = 2 (again, the middle between -13 and +17)

y = (x - 10)(x + 20)

x = 10 or x = -20

line of symmetry

x = -5

Answer:75

Step-by-step explanation:

since there are 15 students and they each need 5 plates you just do 15x5 and get 75

Answer:

y = [tex]\frac{1}{5}[/tex] x - 5

Step-by-step explanation:

y = mx +b  You have to find the slope and the y intercept

slope:

I used the two points on the graph (0,-5) and (5,-4)  The slope is the change in y over the change in x.  An ordered pair is given in the form (x,y)

[tex]\frac{- 4 - - 5}{5-0}[/tex] = [tex]\frac{-4 + 5}5}[/tex] = [tex]\frac{1}{5}[/tex]

or you could just look at the two points.  If you start at (0,-5) and go straight up one and the then go right 5 spaces, you will be at the point (5,-4) [tex]\frac{1}{5}[/tex]

The y intercept for the b is where the line crosses the x axis.  It crosses at the point (0,-5)  The -5 is the b part.

The unit rate for the given situation is 29 students per classroom.

What is the unit rate?

A unit rate is described as a ratio comparing the first quantity to one unit of the second quantity.

Given situation is 87 students in 3 classrooms.

So, the unit rate  [tex]= \frac{87}{3}[/tex]  students/classroom

                            [tex]= 29[/tex] students per classroom

Hence, the unit rate for the given situation is 29 students per classroom.

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Answer:

6CO2 + 6H2O → C6H12O6 + 6O2.

Step-by-step explanation:

That's the equation for photosynthesis. let me know if you have any questions.

The height of the triangle is 15 feet.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the interior angles of a triangle add up to 180 degrees. It is the polygon with the fewest sides.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest side of the three sides, known as the hypotenuse, is the third side.

The formula for the area of a right-angle triangle is A = (½)×b×h square units.

Let the height of the triangle be h

Given:- The area (A) of the triangle is 120 ft^2.

            The base (b) of the triangle is 16 feet.

From the formula, we know that area of the triangle is:-

A = (½)×b×h

By substituting the values of A and b

[tex]120=\frac{1}{2}*16*h\\ h=(120*2)/16\\h=15[/tex]

Hence the height of the triangle is 15 feet.

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Elena will need 180 more bats

Let she bats  b more needs

Total bats =  110 + b

Base hits = 24 + 0.35 b

From the question, we have

( 24 + 0.35b) / (110 + b) = 0.300

24 + 0.35b = 33 + 0.3 b

0.05 b = 9

b = 9 / 0.05 = 180

Subtraction:

The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.

The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.

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The solution to the inequality 6 + t ≤ 13 is given as follows:

t ≤ 7.

An inequality is solved similarly to an equality, isolating the variable of which the solution we want to find.

The difference, of the inequality compared to an equality, is that the solution contains an infinity number of values, instead of a finite number of values. This is because the solution of an inequality is composed by a range of values in one of the infinity number sets.

For this problem, the inequality is given as follows:

6 + t ≤ 13

Hence the solution for variable t is found isolating it as follows:

t ≤ 13 - 6 (moving every term that is not the variable to the opposite side)

t ≤ 7.

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The curve -3[tex]x^{2}[/tex] + 18x +3 has a maximum value of 30 at x = 3

In mathematics, a point at which a function’s value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum. if it is merely greater than any nearby point, it is a relative, or local, maximum. In calculus, the derivative equals zero or does not exist at a function’s maximum point.

Differentiate f(x) =  -3[tex]x^{2}[/tex] + 18x +3 ,

we have dy/dx = -6x + 18.

at turning point, dy/dx = 0

-6x + 18 = 0

6x = 18

x =18/3

x = 3

to check if x = 3 is a minimum or maximum point, we take the second derivate

which is  [tex]\frac{d^{2}y }{dx^{2} }[/tex] = -6

since  [tex]\frac{d^{2}y }{dx^{2} }[/tex] < 0

F(x) is a maximum,

so maximum value of x, we substitute x = 3 into the function

f(x)  = -3[tex](3)^{2}[/tex] + 18(3) + 3

f(x) = 30

In conclusion, the maximum value for the function is 30 at x = 3

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The number of pages read by her will be 36.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Marion read 616 pages in 14 days, The number of pages each day will be calculated as,

N = 616 / 17

Divide the number 616 by 17,

N = 36.23

N = 36

Therefore, the number of pages read by her will be 36.

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The value of the expression when z = -19 is 25.

Here we have the expression:

(33 + 2z)²

And we want to evaluate this on z = -19

Evaluating just means that we need to replace the variable in the expression by the given number.

By doing that we will get:

(33 + 2*(-19))^2

(33 - 38)^2

(-5)^2 = 25

The expression is equal to 25.

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Yes, it is correct. (a) congruent by SSS

                             (b) congruent by SAS

                             (c) congruent by ASA

(a) Given in figure,

    MN = OP

    ∠MNO = ∠NOP

    ON = ON (Common)

   Hence, ΔMNO ≅ ΔNOP by SAS.

(b) Given in figure,

     UV = XY

    ∠UVW = ∠XYZ

    UW = XZ

   Hence, ΔUVW ≅ ΔXYZ by SAS.

(C) Given in figure,

     ∠ABC = ∠EDF

     BC = DE

    ∠ACB = ∠DEF

   Hence, ΔABC ≅ ΔDEF by ASA.

Therefore, all are congruent.

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Answer:

7 cents:$0.45

Step-by-step explanation:

(whatever you do to one side you do the same to the other)

35 divided by 5= 7

2.25 divided by 5= 0.45

Answer:

The first measurement is known as the "P-R interval" and is measured from the beginning of the upslope of the P wave to the beginning of the QRS wave. This measurement should be 0.12-0.20 seconds, or 3-5 small squares in duration.

Step-by-step explanation:

...

Answer:  81

Step-by-step explanation:

Let's start with what we know:

Time spent each evening = 1/3 of an hour

Time spent: 27

We need to turn the time spent into minutes so We will do

27 * 60 = 1620 minutes

As well as we need to turn the 1/3 of an hour into minutes so we will do

1/3 * 60 = 20 minutes

So now we have these numbers

You can pick any letter but I will pick x

We can do 20x = 1620 (Time spent times number of evenings equals time spent)

Then after that you just divide 20x/20 and 1620/20

Then getting x = 81.

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Answer: [tex]h=\frac{S}{2πrh}[/tex]

Step-by-step explanation:

= Solve S = 2πrh:

= [tex]h=\frac{S}{2πrh}[/tex]

Step-by-step explanation:

2.

it is a square !

what do we know about squares ?

first of all, they are a special rectangle, where length = width, and therefore all 4 sides are equally long.

and secondly, as they are a form of rectangle, every inner angle is 90°.

so,

6x - 12 = 90

6x = 102

x = 102/6 = 17

therefore,

CD = x + 15 = 17 + 15 = 32

many greetings to your teacher, CD is a side, a length, and NOT an angle, so it is NOT measured in degrees (°).

since it is a square and all sides are equally long,

AD = CD = 32

3.

it is a rectangle.

so, it has 4 sides consisting of 2 pairs of equally long sides. that means there are 2 equally long side we call length, and 2 equally long sides we call width.

these equally long sides are always opposite of each other.

that means

2x - 52 = x - 2

x - 52 = -2

x = -2 + 52 = 50

Using the concepts of statistics, we got that at least 79 is the minimum size of the sample needed in order to have a margin of error of two minutes or less, when we need to construct a 95% confidence interval for the mean length of time.

We have mean as  357.9minutes and standard deviation as 20.18 minutes.

To have the margin error 2 minutes or less than it we need to take

Z-score of the given sample distribution which is given by:

                Z=(X-μ)/σ

Here ,μ=357.9,σ=20.18,X=?,Z=95/100

=>95/100=(X-357.9)/20.18

=> -0.95×20.18=X-357.9

=>X=-357.9+0.95×20.18

=>X=-357.9+19.171

>X=-338.729

When X=-338.729,the p score is around 79.

Hence, when I want to construct a 95% confidence interval for the mean length of time of the flight in 2018 based on a sample of flights in 2018., the minimum size of the sample needed in order to have a margin of error of two minutes or less is 79.

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The correct option is B "Models n independent replications of a Bernoulli experiment each with a probability p of success".

It is a frequency distribution of the number of successful outcomes that could occur in a set number of trials with an equal chance of success. In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p. When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The probability of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

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Dan has money left is £30.

Given:

Dan spends 3/4 of his wages on rent and 1/8 on food.

If he makes £240 per week.

Money left =  240 - 240* 3/4 - 240 * 1/8

= 240 - 60*3 - 240/8

= 240 - 180 - 30

= 60 - 30

= 30.

Therefore Dan has money left is £30.

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The angle amount of m is 128⁰

Angle can also refer to the length of a rotation or an angle. The Greek word , which means "crooked, curled," and the English word "ankle," are related words. Both stem from the Proto-Indo-European root  which means "to bend" or "bow," in some way.

A plane angle, according to Euclid, is the inclination to each other of two intersecting lines in a plane that are not perpendicular to one another. Proclus asserts that an angle must be either a quality, a number, or a connection. Eudemus used the first idea, viewing an angle as a departure from a straight line; Carpus of Antioch used the second idea, viewing an angle as the distance or space between intersecting lines; and Euclid used the third idea. Vertical angles, opposing angles, or vertically opposite angles refer to a pair of angles that are directly across from one another and are created by two straight lines meeting to form a "X". Vert is the shorthand for them. opp.

The vertical angle theorem states that angles that are vertically opposing are equal. The assertion shown that since both of a pair of vertical angles are supplementary to both of the neighboring angles, the vertical angles are equal in measure, according to Eudemus of Rhodes' attribution of the proof to Thales of Miletus. When Thales visited Egypt, it is recorded in history[9] that he noticed the Egyptians measuring the vertical angles whenever two intersecting lines were drawn to ensure that they were equal. Thales came to the conclusion that one might establish

4x+6=7x-21

3x=27

x=9

x+x+42+42=360

2x+84=360

x=128⁰

Therefore, the angle amount of m is 128⁰

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The expression that represents the statement "the product of a number and eight" is 8x.

Expression:

Expression means the mathematical statement that consists of  minimum of two numbers/variables and at least one math operation(addition, subtraction, multiplication and division) in it.

Given,

The given statement is "the product of a number and eight".

Now, we have to find the suitable expression for this statement.

In order to find the suitable expression, we have to divide the given statement and then we have to identify the keyword in it.

By using those keywords, we have to solve it.

In the given statement we have identify the following:

product

number

eight

Here the product refers the multiplication

number is any unknown number that is x.

eight refers the number 8.

When we combine these keywords we can get the expression 8x.

Therefore, the resulting expression is 8x.

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The probability that a card drawn randomly from a standard deck of 52 cards is a red queen is 1/26 or 0.038461. The result is obtained from the ratio of the number of red queen to 52 cards.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

In case a card drawn randomly from 52 cards, what is the probability that it is a red queen?

The four suits for a standard deck of 52 cards are hearts, diamonds, clubs, and spades of 13 cards each. The hearts and diamonds are red. While, the clubs and spades are black. The 13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

From that information, the number of red queen in a standar deck of 52 cards is 2 cards. So,

The probability of drawing a red queen is

P(A) = n(A) / n(S)

P(A) = 2/52

P(A) = 1/26

P(A) = 0,038461

Hence, the probability that a card drawn is a red queen is 1/26 or 0,038461.

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The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.

This is a plane figure which is referred to as a quadrilateral and has four right angles. The area is calculated by the following below:

Area = Length × breadth.

In cases where the algebra tile rectangles is used , it is ideal to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 7cm and the breadth is 6cm then the area will be  7cm × 6cm = 42cm²

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The height of the tower is 9.24 feet. That is, the tower is 9.24 feet tall

From the question, we are to determine how tall the tower is

From the given information,

From a distance of 10 feet, the angle of elevation of the tower at a height 5 feet from the ground is 23 degrees.

Let x represent the length of the tower from a point 5 feet from the ground.

Thus,

The height of the tower will 5 + x feet

Now, we will determine x

Using SOH CAH TOA

tan 23° = x / 10

x = 10 × tan 23°

x = 4.24 feet

Height of the tower is 5 + x feet

Therefore,  

Height of the tower = 5 + 4.24 feet

= 9.24 feet

Hence,

The height is 9.24 feet

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Answer:

To do percentages with fractions,

divide the numerator by denominator to get a decimal,

so for example, your question 56/80.

56/80 is 0.7 decimal, and then to make it percent,

we multiply by 100,

how does that work?

you move two places to the right because 100 has two zeros

so 0.7 would be 70,

therefore the percent of 56/80 would be 70%

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The function g(-1) has its value to be (c) g(-1) =  1

The definition of the function is given as

g(x)=x³+6x² + 12x+8

Rewrite the above function properly

So, we have the following representation

g(x) = x³ + 6x² + 12x + 8

To find the function g(-1), we set the value of x in the equation g(x) = x³ + 6x² + 12x + 8 to -1

This is represented by

Calculate g(x), when x = -1

Substitute -1 for x in the equation g(x) = x³ + 6x² + 12x + 8

So, we have the following equation

g(-1) = (-1)³ + 6(-1)² + 12(-1) + 8

Evaluate the exponents

This gives

g(-1) = -1 + 6(1) + 12(-1) + 8

Evaluate the products

This gives

g(-1) = -1 + 6 - 12 + 8

Evaluate the sum

g(-1) =  1

Hence, the value of the function is g(-1) =  1

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