Question 32:
Write an equation in Slope-Intercept form for the
line that passes through (1,-3) and is parallel to
y+2 = 4(x-1)

Answer:

4x+6y = 46

Step-by-step explanation:

you just add by column

2x+2x

y+5y

9+37

Answer:

Small jet seat capacity: 73

Large jet seat capacity = 90

Step-by-step explanation:

Let x be the number of seats on the small jet

Let y be the number of seats on the large jet

From the word description for last week:

Last week, she worked on flights on 1 small jet and 2 large jets, which could seat a total of 253 passengers

we can formulate the equation
1x + 2y = 253  .............(1)

For the week before:
The week before, she was assigned to flights on 5 small jets and 4 large jets, which could seat a total of 725 passengers

5x + 4y = 725 ...............(2)

Equation (1)  x 2 ==>
2x + 4y = 2(253)

2x + 4y = 506  ..............(3)

So our two equations are:

5x + 4y = 725 . .............(2)
2x + 4y = 506  ..............(3)

Equation (2) - Equation (3) will eliminate the y terms making it possible to solve for x
(5x + 4y) - (2x + 4y) = 725 - 506

5x + 4y - 2x - 4y = 219

5x -2x +4y - 4y = 219

3x = 219

x = 219/3

x = 73

Plugging this value back into equation (1): 1x + 2y = 253 we get
1(73) + 2y = 253

73 + 2y = 253

2y = 253 - 73

2y = 180

y = 180/2

y = 90

Answer
Small jet seat capacity: 73

Large jet seat capacity = 90

Answer

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Step-by-step explanation:

Answer:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To find the equation of a line passing through two given points, we can use the slope-intercept form, and use the slope formula:

slope = (y2 - y1) / (x2 - x1)

Given the points (2, -4) and (2, -5), we can see that the x-coordinates are the same, which means that the line is a vertical line.

Since the line is vertical, the slope is undefined, and we can say the line can be represented by the equation x = 2

This is the equation of the line passing through the given points (2, -4) and (2, -5) in slope-intercept form.

Answer:

66?

Step-by-step explanation:

18+18= 36

15+15= 30

30+36= 66

According to Isabella transactions, her present balance in bank statement is -$9.45

The term called transaction in math is defined as  a finalized agreement between a seller and a buyer for transferring goods, services, or financial assets in exchange for money

Here let us consider that Isabella's present balance be X.

According to the problem statements regarding her deposits, there is withdrawals, auto-payments, direct deposit and service charge are also done on the account.

Then those transaction values are calculated as,

=> (1/2)x - (1/3)x -(1/4)x +(1/10x) -$9.29 = x

Here by finding the LCM of common terms, then we get

=> (1/60)x - $9.29 = x

When we solve it for x, then we get the equation like the following,

=> 59x = -$9.29 × 60

=> 59x = -$557.4

Therefore the value of x is -$9.45.

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Answer:

$62.50

Step-by-step explanation:

We multiply 0.25(25% as a decimal) by $250 to get $62.50.

Answer:300 tires

Step-by-step explanation: I set it up like this 100:45

X : 135

Then I am trying to find x. I cross multiplied. (100 times 135) and (45 times x) which is 45x= 13500 then if you know simple algebra then you get x by itself so you divide 13500 and 45 which equals 300.

The length of string will be used to hang each pennant is 3.9 meters.

The term length in math is defined as the measurement or extent of something from end to end and it is used to identifying the size of an object or distance from one point to the other.

Here we have given that Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school.

And here we have also know that she needs 0. 65 meter of string for the banner and the same length string for each pennant.

the length of the string needed for 5 pennants is calculated as,

=> 0.65 x (5 + 1)

=> 3.9 meter.

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Answer:

a) the triangles are similar triangles because they are the same shape. The angles in both triangles have the same value.

b) The similarity ratio between the two triangles is 0.5, because the lengths of the sides of the triangle on the right are double the value of the lengths of the sides of the triangle on the left.

c) angle U = angle G. angle V = angle H. angle T = angle F.

UV/GH = VT/HF = TU/FG = 0.5

The experimental probability that a person selected at random is going to City C is 4/25.

Number of responses from destination A = 22

Number of responses from destination B = 40

Number of responses from destination C = 16

Number of responses from destination D = 14

Number of responses from destination E = 8

As we know, the formula of experimental probability is

Probability of an Event P(E) = Total Number of times an event occurs/Total number of trials.

Number of responses from destination C = 16

Total number of responses from all destinations = 100

∴ Probability of an Event P(C) = 16/100 = 4/25

--The given question is incorrect; the correct question is

"The table shows the results of a survey of 100 people selected at random at an airport. Find the experimental probability that a person selected at random is going to City C."--

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The solution to the equation is described as follows:

The equation says that a number was divided by 5 and that 3 was then subtracted from the quotient, giving the result 2. So, working backward, first add 3 to 2, giving 5. Then multiply that result by 5, giving x = 25.

The equation for this problem is described as follows:

x/5 - 3 = 2.

We must isolate the variable x, hence the first step is adding 3 to 2, as follows:

x/5 = 2 + 3

x/5 = 5.

Then we apply cross multiplication, multiplying the result by 5, as follows:

x = 5(5)

x = 25.

Which is the solution to the equation.

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The error is that the student did not distribute the -3 to the x and 2 inside the parentheses.

The correct answer is 3x - 6

Simplification of an algebraic expression is defined as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression.

The student's error is that the student did not distribute the -3 to the x and 2 inside the parentheses when simplifying the expression.

The correct simplification of the expression is:

-3(x + 2) + 6x = -3x - 6 + 6x = -3x + 6x - 6 = 3x - 6

Therefore, the student's answer is 3x + 2, but the correct answer is 3x - 6.

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The student made error when removing the bracket. The correct simplification of the expression is 3x - 6

We can spot the error of the student by carefully observing the student's answer. This is illustrated below:

-3(x + 2) + 6x = -3x + 2 + 6x = 3x + 2

From the student's work, we can see that the student made an error when removing the bracket.

We can correct the student's error by carefully removing the bracket as shown below:

-3(x + 2) + 6x

Remove bracket by multiplying through by -3

-3x - 6 + 6x

Rearrange by bring the numbers with x variables together

-3x + 6x - 6

3x - 6

Thus, the correct answer to the simplification is 3x - 6

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Answer:

The function rule for this set of ordered pairs is y = 2x + 1.

This can be determined by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) can be calculated by using the formula:

m = (change in y) / (change in x)

For the ordered pair (1, 3) and (3, 7), we can see that change in x = 3 - 1 = 2 and change in y = 7 - 3 = 4, so m = 4/2 = 2.

Then, using any of the point we can find the b which is y-intercept. let's take the point (-2, -3) and substitute the values in the function y = 2x + b

-3 = 2(-2) + b

-3 = -4 + b

b = 1

So, the function rule is y = 2x + 1

Answer: 10 I'm not sure ok

Step-by-step explanation: divide 50 and 5 you get 10

When I run 5280 feet in 5.00 minutes my speed is 12 miles per hour

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this exercise is:

v = x /t

Where:

Information about the problem:

Applying the velocity formula, we get:

v = x /t

v = 5280 feet / 5 minutes

v = 1056 feet/ minutes

By converting the unit from feet to miles and from hours to minutes, we have:

1056 feet/ minutes * (1 miles / 5280 feet) * (60 minutes / 1 hour) = 12 miles/hour

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The length of the base is 3.1 cm when you subtract 12.6 from btohs ides b is15.7.

There are two equal sides and two equal angles in an isosceles triangle. The word is a combination of the Greek words iso (same) and skelos (leg). Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.

Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.

The equal sides of an isosimple triangle are longer than the base's length.

We know that identical sides are greater, thus 6.3 is one of the identical sides in the perimiter=15.7 equation, which is 2a+b=15,7.

2a denotes the two identical sides: 2(6.3) + b = 15.7

The answer is base=3.1 cm when you subtract 12.6 from btohs ides b=15.7.

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Let x be the cost price of an entertainment system.

The selling price is x+800

The number of systems sold is 60-((x+800-x)/20) = 60-((800)/20) = 60-40 = 20 systems

The revenue is the product of the number of systems sold and the selling price.

R = 20(x+800) = 20x+16000

To maximize the revenue, we need to differentiate the above equation with respect to x and set it to 0 and solve for x.

dR/dx = 20 = 0

20x = 0

x = 0

Therefore, the cost price of an entertainment system is 0 and the store should sell the system at x+800 = 800

This means that the store should sell the system at $800 more than the cost price to maximize the revenue.

Answer: y=-2x-19

Step-by-step explanation:

First, you should arrange the equation in the form of y=mx+c (that is the standard form of this type of equation)

10x+5y=15

       5y=-10x+15

       [tex]\frac{5y}{5} =\frac{-10x}{5}+\frac{15}{5}[/tex]

         y=-2x+3 (now you got the equation in the simple form)

now you should substitute the given point (-10,1) into the simplified equation

y= 1 & x=-10

1=-2(-10)+c  (the y-intercept must be taken as c )

c= 1 - 20

c= -19

therefore the equation will be : y=-2x-19

it will be the same gradient as the other line for this line too as the lines are parallel, you should only find the y-intercept. The gradient of the other line will stay the same as long as they are parallel lines.

For the definition "An angle is 2 collinear rays with a common endpoint" , then

(a) the contradictory example is "When two rays are collinear having a  common end point; then the rays do not form an angle instead they form a line."

(b) the changed definition is , "An angle is formed at the intersection of two non-collinear rays that have the same endpoint " ;

(c) the example is "the Plane" .

The Angles are formed when the two straight lines or rays meet at a common endpoint.

Part(a) ;

An example which contradicts this definition of angles is "When two rays are collinear with a common endpoint; the rays do not form an angle ,instead  they form a line" because when all the points of two lines are collinear then all the points of the two lines will be overlapping .

Part(b) ;

The change that need to be made in the definition of angle is "An angle is formed at intersection of two non-collinear rays which have same endpoint ".

Part(c) ;

The Example of the undefined term is :

Undefined terms do not have a formal definition; an example of this is "the plane" . The plane pertains to the angles because the plane determines the parameter to be measured.

The given question is incomplete , the complete question is

An angle is two collinear rays with a common endpoint.

(a) Find an example that contradicts this definition.

(b) How would you change the definition to make it more accurate ?

(c) Give an example of an undefined term and how it pertains to angles .

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Answer:

150

Step-by-step explanation:

90/0.6 = 150

Check:

150*0.6 = 90

Then:

90 is 0.6 of 150

The HCF of the numbers 114, 138 and 234 is 6.

The term HCF in math is also know as the greatest common factor or highest common factor of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder.

Here we have given the numbers 114, 138 and 234.

And we need to find the HCF of the numbers.

By using the prime factorization method, here we have identified the factors of the numbers, and it can be written as

The factors of 114 are: 1, 2, 3, 6, 19, 38, 57, 114

The factors of 138 are: 1, 2, 3, 6, 23, 46, 69, 138

The factors of 234 are: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234

While we looking into the given number we have identified that the the greatest common factor is 6.

Complete Question:

Find the HCF of the numbers 114, 138, and 234 by using the prime factorization method.

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[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-6)}) \implies y +7= \cfrac{1}{3} (x +6) \\\\\\ y+7=\cfrac{1}{3}x+2\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-5 \end{array}}[/tex]

Answer:

I think it is y=1/3x -7

Step-by-step explanation:

It should be noted that the rate will be gotten by dividing the distance by the time taken.

A rate in mathematics is a ratio that contrasts two distinct quantities with dissimilar units. Typically, a rate is defined as the ratio of two quantities expressed in different units. The first quantity is typically written as the numerator of a fraction, and the second quantity is written as the denominator

By reducing them to their simplest form, we can express the rate. By way of illustration, if a person walks 30 steps in 20 seconds, their walking speed is 30 steps/20 seconds, or 3 steps/2 seconds.

The information above was given as your information is incomplete. The table wasn't shown.

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Correct answer is parallelogram and rhombus.

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.

Rhombuses are a particular sort of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal. This is a rhombus' fundamental characteristic. A rhombus has a diamond-shaped form. As a result, it is also known as a diamond.

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rectangle, rhombus

got it wrong on my test and was given the correct answers, so here they are.

The percent of the gas in the tank remaining is equals to the 53.6..

The capacity of Wilon's car's gas tank

= 15 gallons

The amount of gas in Wilon's car's tank

= 8.4 gallon

The amount of gas in tank used on a recent trip = 3.9 gallons

The remaining amount of gas in tank

= amount of gas in Wilon's car's tank before trip - amount of gas in tank used on a recent trip.

= 8.4 gallons - 3.9 gallons

= 4.5 gallons

Percent is calculated as the value diving by total value and then multiply with hundred. Now, the percent of the gas in the tank remaining = (4.5/8.4)× 100

=( 45/84)100

= 4500/84

= 53.57 ~ 53.6 %

Hence, the percent of the gas in the tank remaining is 53.6 .

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Complete question:

Wilon’ car hold 15 gallon of gaoline in it tank. Wilon had 8.4 gallon of gaoline in the tank. He used 3.9 gallon on a recent trip. What is the percent of the gas in the tank remaining?

There is a 0.17 percent chance that a student spent 4 hours in class.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. Probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

To determine the probability.

The number of students that has 5 hours is 6

The total number of students are 35.

P(5 hours) = 6/35

P(5 hours) = 0. 17

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The ways they can fall are 4,8 and 36

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Given;

Two coins, three coins and two dices are tossed

Probability of two coins;

=2x2=4

Probability of three coins;

=2x2x2=8

Probability of two dices;

=6x6=36

Therefore, the probability of coins and dice will be 4,8 and 36

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The solution to the given inequality expression is; x < 5

We want to solve the inequality expression;

8 - 4x > -12

Add 4x + 12 to both sides using addition property of equality to get;

8 - 4x + 4x + 12 > -12 + 4x + 12

20 > 4x

Divide both sides by 4 using division property of equality to get;

20/4 > 4x/4

x < 5

That expression is what we will have as our final solution to the inequality expression .

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Answer:

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