Equations and Inequalities: Tutorial
Each year, the junior class at East High School sells discount cards as a fundraiser. Each $20 discount card is valid for a year
and provides discounts at many area businesses.
This year's juniors are analyzing the revenue, or earnings, from past years and this year. If n represents the number of cards
that students sold last year, match each algebraic expression to what it represents.
Drag the tiles to the correct boxes. Not all tiles will be used.
Tiles
20n
n + 200
20n + 200
20(n + 200)
200n
Pairs
revenue from last year
number of cards sold this year if students sell 200 more cards than last year
revenue this year if students sell 200 more cards than last year

Answer:

(4,4)

Step-by-step explanation:

We can solve this system of equations using the elimination method.

In order to use the elimination method there must be two variables with the same coefficient. Note that the coefficients don't have to have the same sign ( eg. 6 and -6 would work ). If there are two similar variables with similar coefficients then you can add or subtract, depending on the signs of the coefficients, the two equations "eliminating" the variable. There would then be one variable left over in which you can solve for.

For this case, both equations have 7x, one negative 7 and one positive 7. When the signs are different you add the two equations. So our first step is to add the two equations

7x - 4y = -44

+ (-7x -3y = 16 )

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

Remove parenthesis

7x -4y = -44

-7x -3y = +16

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

0x - 7y = -28

We are left with -7y = -28.

Because there is now only one variable, we can solve for it.

-7y = -28

divide both sides by -7

y = 4

Now we want to find the value of x. We can do this by plugging in the value of y into one of the equations and then solving for x. Note that we can plug in 4 for y into either equation and solve for x and we would get the same answer.

7x - 3y = 16

y = 4

7x - 3(4) = 16

multiply 4 and -3

7x - 12 = 16

add 12 to both sides

7x = 28

divide both sides by 7

x = 4

So x = 4 and y = 4 so the solution to the system of equations is (4,4)

Answer:

It is 4

Step-by-step explanation:

Answer:

a= 0.84m

b= 7m

i tried my best but im not sure of the answer

Step-by-step explanation:

5x+3y=4.2

2x=3y

x = 4.2-3y/5

2*(4.2-3y/5) = 3y

=1.68/3 = 0.56

y=0.56

2x = 3*0.56

x = 0.84

a) The length of one belt (b) is 0.6 meters, or 60 centimeters.

b) The total length of 7 belts and 2 shoe laces is: 5 meters.

Let the length of one belt be "b" meters, and the length of one shoe lace be "s" meters.

a) Find the length of a belt:

According to the given information, the total length of 5 belts and 3 shoe laces is 4.2 meters. We can express this information as an equation:

5b + 3s = 4.2

b) Find the total length of 7 belts and 2 shoe laces:

The total length of 3 shoe laces is equal to the length of 2 belts. We can express this information as another equation:

3s = 2b

Now, we can use these two equations to solve for the values of "b" and "s."

Step 1: Solve the second equation for "s":

3s = 2b

Divide both sides by 3:

s = (2/3)b

Step 2: Substitute the value of "s" from the second equation into the first equation:

5b + 3((2/3)b) = 4.2

5b + 2b = 4.2

7b = 4.2

Step 3: Solve for "b":

b = 4.2 / 7

b = 0.6

Now that we have the value of "b," we can find the value of "s" using the second equation:

s = (2/3)b

s = (2/3) * 0.6

s = 0.4

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Camila puso 30 botellas de cada sabor en la estantería.

Dado que Camila ubicó 90 botellas en una estantería de un supermercado, y los jugos sin azúcar tienen tres sabores diferentes y Camila puso la misma cantidad de cada sabor en la estantería, para determinar la cantidad de botellas de jugo sin azúcar de cada sabor que puso Camila en la estantería se debe realizar el siguiente cálculo:

Por lo tanto, Camila puso 30 botellas de cada sabor en la estantería.

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Answer: No

Step-by-step explanation:

It should be 2x-4 (2*×=2x and 2*2=4)

No, the simplified expression is not correct.

Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.

Given expression

2(x - 2) - 2(3)

so 2(x - 2) = 2x - 2(2)

= 2x - 4

and 2(3) = 6

substitute the value

2(x - 2) - 2(3) = 2x - 4 - 6

= 2x - 10

and equation of Marty is  2x - 8

Hence the equation of marty is incorrect.

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Answer:

38 minutes per day

Step-by-step explanation:

Divide 114 to 3

114 ÷ 3 = 38

Divide 304 to 8

304 ÷ 8 = 38

Answer:

1 day = 38 minutes

Step-by-step explanation:

3 days = 114 minutes

=> 1 day = 38 minutes

=> 8 days = 38 x 8 minutes.

Her rate is 1 day = 38 minutes. Hoped this helped.

Answer: C) y = -1

Step-by-step explanation:

A horizontal line is represented by y = a constant.  As such, the line must be    y = -1, because the given point is (-3, -1), which has a y-coordinate of -1.

Answer:

D y=-1

Step-by-step explanation:

In horizontal lines, the equation is y=b. B is the location of the y-axis where the line crosses through it. Hope this helps :)

Answer:

  10. (-1, 7), (-7, 1)

  11.  (8, 4), (16, 2)

Step-by-step explanation:

Let x and y represent the two missing factors. Then you have ...

  -3xy = 21

  xy = -7 . . . . . . . divide by -3

Integer divisors of -7 are ±1, ±7, so possible factor pairs are (-1, 7), (-7, 1) and their reverse.

Of course, the only requirement is that the values be rational, so we could have (-1/4, 28), for example. One of the above factors can be multiplied by any rational number, and the other multiplied by its inverse.

__

If the two factors of interest are x and y, then the product of the three factors is ...

  (-3/4)xy = -24

  xy = (-4/3)(-24) = 32

Integer divisors of 32 are 1, 2, 4, 8, 16, 32. So, any of those, positive or negative, could be one of the (integer) factors you're looking for. On the attached graph, we have shown (x, y) pairs ...

  (8, 4), (16, 2), (-4, -8)

There are an infinite number of possibilities.

Answer:

100 days

Step-by-step explanation:

You know that you write at a speed of 5 pages every 2 days. In order to write a 250 page novel, you're going to have to to write 250/5 = 50 *2 = 100 days.

Answer:

72

Step-by-step explanation:

If it wrong i'm sorry

Answer:

i. Rs6,000

ii. Rs6,900

Step-by-step explanation:

i. FV = PV(1 + r)^d

FV = 40,000(1 + 0.15)^1

FV = 40,000(1.15)

FV = 46, 000

46, 000 - 40,000

Interest = Rs6, 000

ii. FV = PV(1 + r)^d

FV = 46,000(1 + 0.15)^1

FV = 46, 000(1.15)

FV = 52, 900

52, 900 - 46, 000

Interest = Rs6, 900

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Answer is on the attachment...

☆...hope this helps...☆

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Answer:

3x-4y=19

Step-by-step explanation:

Hi there!

We want to write the equation of the line in standard form that passes through the point (1, -4) and has the slope of 3/4

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negative

First, in order to find ax+by=c, we'll need to get slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

Since we already know the slope (3/4), we can substitute it into the formula for y=mx+b.

y=3/4x+b

Now we need to solve for b

Since the equation passes through the point (1, -4), we can use it to solve for b

Substitute 1 as x and -4 as y.

-4=3/4(1)+b

Multiply

-4=3/4+b

Subtract 3/4 from both sides

-19/4=b

Now substitute -19/4 as b into the equation

y=3/4x-19/4

Now we have the equation in slope-intercept form, but remember, we want it in standard form

Since x and y are on the same side in standard form, subtract 3/4x from both sides

-3/4x+y=-19/4

Remember that a cannot be negative, and the coefficients are integers (they cannot be fractions)

So in order to clear the fractions and change the sign of the equation, multiply both sides by -4

-4(-3/4x+y)=-4(-19/4)

Multiply

3x-4y=19

Hope this helps!

Answer: Option 2

Step-by-step explanation: the slope is -3 so option 4 is wrong. Y intercept is 5 so the equation is y=-3x+5. Move the 5 to the left side and you get y-5=-3x which is option 2.

Answer:

B) (-8, -6, 1)

There are a lot of steps and I don't want to spend the time writing it all out... sorry. :')

Hope this helps :)

Answer:

x≤5/3

So any number at 5/3 or above is a solution

Step-by-step explanation:

Subtract 4 on both sides:

5≤3x

Divide 3 on both sides

x≤5/3

So any number at 5/3 or above is a solution

Hope this helps!

Answer:

i dont k if my explanation will help or not

Step-by-step explanation:

but it goes through the crosshairs in the 2nd quadrant at -10 on the y axis and up 6 on the x axis and then you go down 5 over 2

[tex]\\ \sf\longmapsto 2x+11=3x-9[/tex]

[tex]\\ \sf\longmapsto x=11+9[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

And

[tex]\\ \sf\longmapsto y+10=2y-40[/tex]

[tex]\\ \sf\longmapsto 2y-y=10+40[/tex]

[tex]\\ \sf\longmapsto y=50[/tex]

Step-by-step explanation:

2x + 11 = 3x - 9

2x - 3x = -9 - 11

x = -20

[tex] \: [/tex]

y + 10 = 2y - 40

y - 2y = -40 - 10

-y = -50

y = 50

Answer:

150 Miles

Step-by-step explanation:

Let's say it takes x time to get there.

X x 30=(8 - 6) x 50 (The distance is the same)

30X=400 - 50X=7 X=5 hours.

So the distance is 5 x 30=150 miles.

3x + 2 > x + 8

3x - x > 8 -2

2x > 6

x > 3

ok done. Thank to me  :>

Answer:

26,530,000

Step-by-step explanation:

this is quite easy, first you can write this question differently

Just view this problem as 7 x 379 which is 2653, now count how many zeros 70,000 has, which is 4 and add it to the answer 2653, which will give you 26,530,000

The multiplication or products of 70,000 and 379 is 26,530,000

Given:

70,000 × 379

= 26,530,000

Where from the left,

In words, 26,530,000 is written as twenty six million, five hundred and thirty thousand.

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Answer:

D

4th option is correct

............

Answer:

7.9

Step-by-step explanation:

Volume = side · side · side

∛496 = 7.915783219

Answer:

3 years.

Step-by-step explanation:

Answer

3 years

Step by step explanation

Interest = 1740 - 1200

= 540

SI = prt/100

540 = 1200*15*t/100

540 = 12*15*t

540 = 180*t

t = 540/180

t = 3 yrs

Answer:C

Step-by-step explanation: The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04

The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04.

Given that, Diya regrouped 2 as 20 tenths and regrouped 0.8 as 7 tenths plus 10 hundredths.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point.

According the given question, the numerical expression is

20/10 + 7/10+12/100

= 2+0.7+0.1

= 2.8

She divided all of the tenths and hundredths into three equal groups.

That is, 2.82/3

=0.94

Hence, the quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04.

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Answer:

The cost price 49,359

Step-by-step explanation:

To find the loss, turn 5% to decimal then multiply it to the selling price

5% = 0.05

47,180 * 0.05 = 2,359

The loss is 2,359.

Now add it to the selling price to find the cost price.

47,180 + 2,359 = 49,539

Answer:

its 19 ur welcome byeeee

Step-by-step explanation:

Answer:

v is -8

Step-by-step explanation:

The form of a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

We are given the slope, so let's write:

  y = -(2/9)x + b

We can find b by using the one fully given point, (-4, -6).

y = -(2/9)x + b

-6 = -(2/9)(-4) + b

b = -6 - (8/9)

b = -(62/9)

Now we have   y = -(2/9)x - (62/9)

We want the value of y when x is 5 to find v in (5,v):

y = -(2/9)x - (62/9)

y = -(2/9)(5) - (62/9)

y = -(10/9) - (62/9)

y = -(72/9)

y = -8

v is -8

Answer: x=1

Add 1 to both sides x-1=0 x-1+1=0+1

Answer:

0.21

Step-by-step explanation: