What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)? y = Negative one-thirdx − One-third y = Negative one-thirdx − Five-thirds y = 3x − 3 y = 3x − 7

The variable expression is;

Here, we want to select an option that represents the phrase

The quotient of a number x and 8 means that we divide x by 8

That means we have a fraction, with x as the numerator and 8 as the denominator

We have this as;

5 more than this quotient means that we are to add 5 to the result

We have this as;

The greatest possible value of n is -5

From the question, the given parameters are:

The second highlight above can be represented as

n < -3.25

Since n is an integer, then the possible values of n are

n = -4, -5, -6, -7, -8....

Remove the even integers from the above list of numbers because n is an odd integer

So, we have

n = -5, -7, -9....

The greatest value above is n

This means that n can have the highest value of -5

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two lines are parallel if their slope is equal

equation of line is

y=mx+c

where m=slope

for y=2x-5

m=2

for -x+2y=-5

2y=-5+x

y=-5/2+x/2

m=1/2

lines are nor parallel becuase m (slope) is not equal

now we will test for perpendicularity

perpendicular lines have slopes that are reciprocal of each other

first line , m=2

second line, m=1/2

2 and 1/2 are reciprocals

therefore, the lines are perpendicular

To question 16, we see that for every change of plus 2 drinks, they pay an additional value of $2.50. It means that each drink does cost half of this value.

This way, the equation that will give the value of the total cost will be:

Where X stands for the number of drinks, and 1.25 is the value of a single drink.

From the solution presented above, we are able to conclude that the rate of change represents the value of a unitary drink, in the present situation.

Answer:

912

Step-by-step explanation:

the assumption is that this is an arithmetic progression

the nth term of an arithmetic progression is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

use this to find which term 120 is in the sequence

with a₁ = 32 and d = a₂ - a₁ = 40 - 32 = 8 , then

32 + 8(n - 1) = 120 ( subtract 32 from both sides )

8(n - 1) = 88 ( divide both sides by 8 )

n - 1 = 11 ( add 1 to both sides )

n = 12

given the first and last terms in the sequence then sum is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first + last)

S₁₂ = [tex]\frac{12}{2}[/tex] (32 + 120) = 6 × 152 = 912

EXPLANATION :

The cost of a 12 nights camp accommodation is 6720.

We need to divide the cost by 12 to get the cost per day.

Now, we are asked to find the cost of 7 nights and 4 nights.

We just need to multiply the daily rate by the number of nights.

a. 7 nights :

7 x 560 = 3920

b. 4 nights :

4 x 560 = 2240

ANSWER :

a. 3920

b. 2240

The probability that the sample proportion will differ from the population proportion by less than 0.03 exists 0.9909.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Let the true proportion exists 0.07

number of samples exists 492 then we get

√(0.07)(1−0.07)/492 ≈ 0.01150291586

Since the true value of the population proportion exists 0.07, the value of p^ must fall between 0.04 and 0.10 in order for the error of estimation to be less than 0.03.

Therefore, the probability that the sample proportion will differ from the population proportion by less than 0.03 exists 0.9909.

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Let's find the unit price of each store

Store A : $8.16 /4 = $2.04 per pound

store B: $6.51 / 3 = $2.17 per pound

store c: $2.66 / 2 = $1.33 per pound

store D : $11.40 / 4 = $ 2.85 per pound

Therefore, store A, store B, store C and store D sells at a lower unit price than Corner grocery store.

Answer:

2.5

Step-by-step explanation:

$12.50 ÷ 5 bags = $2.5 per bag

Answer:

2.50

Expination:

devide 12.50 by the total amount of dog food purchased (5 bags)

12.50/5 = 2.50

the price per bag is $2.50

The rate at which the base of the triangle is changing is equal to,

dB = -6.3 cm/minutes.

From the data given in the question.

The rate of increase in the area of the triangle, dA = 4.5 cm/minute

The rate of increase in the altitude of the triangle, dH = 3.5 cm/minute

The Area of the triangle, A = 87 square centimeters

The altitude of the triangle, H = 7.5 centimeters

The equation for the area of a triangle is equal to

A = 0.5×B×H

Plug in A and H to solve for B at that point:

87 = 0.5×B×7.5

B = 23.2

Differentiate the equation for the area of a triangle to find the rate of change of the area of a triangle (dA):

dA = 0.5× dB× H + 0.5×B × dH.

Plug in known variables to solve for the rate of change of the base dB

dA = 0.5 × dB × H + 0.5 × B × dH

4.5 = 0.5 × dB × 7.5 + 0.5 × 23.2 × 3.5

The rate at which the base of the triangle is changing is equal to,

dB = -6.3 cm/minutes.

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Answer:

Step-by-step explanation:

First, graph your first point at (-1,3) Then, take your slope which is 1/2 and use rise over run. So from your point of (-1,3) go up 1 in your y coordinate, and 2 in your x coordinate. So your next point should be at (1,4)

Answer:

Slope is 1 and y-intercept is 9

Step-by-step explanation:

y=mx+b

The slope is the coefficient of x in this case it would be 1

The y-intercept is whatever b is and it is +9 so it is 9

y = 2x - 12

here's your answer hope it helps

The total number of files after 16 days using the function P(t) = 3t² + 5t + 8 is 856.

A relationship between a group of inputs having different outputs is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output.

The function P(t) represents the population of a collection of fruit flies at a particular time in days.

P(t) is the number of flies and t is the time in days.

Now, consider the function:

P(t) = 3t² + 5t + 8

Therefore, the number of flies after 16 days will be:

When t = 16,

P(t) = 3t² + 5t + 8

P(16) = 3(16)² + 5(16) + 8

P(16) = 3 × 16 × 16 + 5 × 16 + 8

P(16) = 768 + 80 + 8

P(16) = 856

Hence, the number of flies after 16 days will be 856 flies using the function P(t).

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The value of a in the equation (3x869)+(19x528)+428(3)(1049)=a is 1359555

From the question, the equation to evaluate is given as

(3x869)+(19x528)+428(3)(1049)=a

Rewrite the above equation to make it legible

So, we have the following equation

(3 x 869) + (19 x 528) + 428(3)(1049) = a

Evaluate the products in the expression

So, we have the following equation

2607 + (19 x 528) + 428(3)(1049) = a

Evaluate the other products in the expression

So, we have

2607 + 10032 + 428(3)(1049) = a

Remove the brackets in the equation

So, we have the following equation

2607 + 10032 + 1346916 = a

Evaluate the sum

1359555 = a

Rewrite as

a = 1359555

Hence, the solution to the equation is 1359555

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Option C, 59° is correct answer, The angle JIL is equal to 59 degree.

What is angle?

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.

Given information in the question,

∠HIL = (6x-7)°

∠JIL = (5x+4)°

The ray IL bisects the ∠HIJ

Since, IL bisects angle HIJ then, angle HIL = angle JIL

So,

6x - 7 =  5x + 4

x = 11

Putting the value of x in given value of JIL to get the angle JIL

∠JIL = (6x-7)°

∠JIL = (6(11)-7)°

∠JIL = 59°

Therefore angle JIL is equal to 59 degrees.

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Answer:

x = -9

6x + 42 = -12

6x = -54

x = -9

Since the speed of the turbopropeller plane was 200 mph faster than the speed of the car, the speed of the turbopropeller plane is equal to 70 mph.

In order to solve this word problem, we would assign variables to the distance and speed of both Mattie's car and the turbopropeller plane, and then translate the word problem into algebraic equation as follows:

Translating the word problem into an algebraic equation, we have;

v₂ = v₁ + 200

Since Mattie and the turbopropeller plane travled at the same time, we have:

Time = distance/speed

Time = d₁/v₁ = d₂/v₂

Time = 140/v₁ = 540/v₁ + 200

Cross-multiplying, we have:

140(v₁ + 200) = 540v₁

140v₁ + 28,000 = 540v₁

Next, we would rearrange the equation by collecting like terms as follows:

540v₁ - 140v₁ = 28,000

400v₁ = 28,000

Speed of plane, v₁ = 28,000/400

Speed of plane, v₁ = 70 mph.

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Given the following question:

We are given the repeating decimal of 0.45

We will use the formula:

The resulting sample space of the given situation is S = {PQ, QP, PR, RP, QR, RQ}

Sample space:

Sample space refers the collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.

Given,

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.

Here we need to find the sample space for the event.

Let us consider,

P represents Patty

Q represents Quinlan

R  represents Rashad

And through the question we have know that, the teacher drawn two card at a time,

So we have consider that the teacher is going to draw out of the hat one first, without replacement, and then draw another one.  

The first chosen one will be the president, and that could be P, Q or R, Now, the chosen second one is the Vice president, and already one has already being drawn, that could only be two fellows.

Therefore, the total of likely outcomes is PQ,QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.

So, the resulting sample space is

S = {PQ, QP, PR, RP, QR, RQ}

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Answer:

[tex]x=\frac{-m-n+p}{-y+1}[/tex]

Step-by-step explanation:

Answer:

A' = (0, 0)

B' = (-5, -2)

C' = (2, 4)

Step-by-step explanation:

Vertices of triangle ABC:

Given mapping rule:

(x, y) → (x - 2, y + 3)

This notation tells you that the x-coordinate is translated 2 units to the left, and the y-coordinate is translated 3 units up.

Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':

⇒ A' = (2 - 2, -3 + 3) = (0, 0)

⇒ B' = (-3 - 2, -5 + 3) = (-5, -2)

⇒ C' = (4 - 2, 1 + 3) = (2, 4)

1) Considering that the slant height of those pyramids is 4 and 6, we can find the scale factor by dividing their slant heights:

So we can state that the bigger pyramid is larger than the 1st pyramid by a scale factor of 1.5.

2) For the Volume of the Pyramid, we can write out the formula below:

Since the scale factor is 1.5 Then we can state that

the Volume of the smaller one is by similarity 1.5 or 3/2 times smaller than the larger one.

3) Hence, the answers are:

1.k=1.5

2. 32 m³

Answer:

Explanation:

Given the function f(x)

A translation of 2 units up = f(x)+2

Next, a translation of 2 units right = f(x-2)+2

When we reflect the result above in the x-axis, we have:

A rule for g is therefore:

We will have the following:

We can see that the shape of the head can be subdivided in smaller shapes, that is:

Now, we calculate the 5 areas, that is:

Now, the total area is:

So, the total area is 108 mm^2-

Answer: 126

Step-by-step explanation:: 90 ÷ 10 = 9 (10%) 9 × 4 = 36 (40%) 90 + 36 = 126