PLEASE HELP
Can someone please help, my teacher wants this done a certain way and I don't know how to do it.

Answer:

Price per large envelope = $1.42 (option A)

Price of each postcard = $0.35 (not asked for in this specific question)

Step-by-step process for solution given below

Step-by-step explanation:

The first thing to do for this problem and other similar problems is to set up the system of linear equations to be solved

We start with the unknowns and provide variable names for these unknowns

There are two unknowns here - the cost of each postcard and the cost of each large envelope

Let
x = cost of one postcard

y = cost of one large envelope

Customer 1 bought 14 postcards(cost = 14x) and 5 envelops(cost = 5y) for a total cost of $12

We can set up this as an equation:
12x + 5y =  12    ............ [1]

Customer 2  bought 10 postcards(cost = 10x) and 15  envelops(cost = 15y) for a total cost of $24.80
This translates to the following equation:
10x + 15y = 24.80 .... [2]

Let's re-write these equations one below the other for easier solution:

[tex]\begin{amatrix}14x+5y=12\dots[1]\\ 10x+15y=24.8\dots[2]\end{amatrix}[/tex]

Solving by substitution:
From any one of the above equations, express one variable in terms of the other variable and substitute for that variable in the other equation to solve.

Take equation [1]
[tex]14x+5y=12[/tex]

Let's express x in terms of y.

Move 5y to the right:
[tex]14x=12-5y[/tex]

[tex]x =\dfrac{12-5y}{14}[/tex]

Use this expression in y for x in equation [2]

[tex]10x + 15y = 24.8\\\\\implies 10 \cdot \dfrac{12-5y}{14}+15y=24.8\\\\\implies \dfrac{\left(12-5y\right)\cdot \:10}{14} + 15y = 24.8\\\\\implies \dfrac{\left(12-5y\right)\cdot \:10}{14} + 15y = 24.8\\\\[/tex]

Multiply throughout by 14:
[tex]14 \cdot \dfrac{\left(12-5y\right)\cdot \:10}{14} + 14\cdot 15y = 14 \cdot 24.8\\\\(12-5y)10 + 210y = 347.2\\\\120 - 50y + 210y = 347.2\\\\120 + 160y = 347.2\\\\160y = 347.2- 120\\\\160y = 227.2\\\\y = \dfrac{227.2}{160}\\\\y = 1.42[/tex]

Substitute y = 1.42 in equation [tex]x=\dfrac{12-5y}{14}[/tex]
[tex]x=\dfrac{12-5\cdot \:1.42}{14}\\\\x = 0.35\\\\[/tex]

So the cost of each large envelope was $1.42 and cost of each postcard was $0.35

Answer is option A

Solve by elimination

The idea here is to get the coefficients of one of the variables the same in both equations by multiplying / dividing one or both of the equations by some factor and then add/subtract to isolate the other variable and solve

For equations 1 and 2 do the following

Subtract the equations:
[tex]70x+105y=173.6\\-\\70x+25y=\;\;\;\;\;60\\\\[/tex]
-------------------------------
[tex]80y=113.6[/tex]

y = 113.6/80 = 1.42 as before

Substitute for y in equation 1 and solve for x
14x + 5y = 12 => 14x + 5(1.42) = 12

=> 14x + 7.1 = 12

=> 14x = 12 - 7.1

=> 14x = 4.9

=> x = 4.9/14 = 0.35 as before

I personally prefer solving by elimination since solving by substitution involves heavy duty fractional expressions

Answer: 2x2+4x−30

Step-by-step explanation:

Answer: D) 2x² + 4x - 30. Step-by-step explanation: Follow the FOIL method: FOIL = First. Outside. Inside. Last ...and is the order you multiply to solve

Step-by-step explanation:

Answer:Top question:Table =0.8
Constant of proportionality is 1.25?


a)The speed they are going at?
b)187.5(units which are being used)
c)0.4 hours=24 minutes

Step-by-step explanation:

a)The formula is distance=speed x time. Speed is only one missing
b)Substitute into the formula 75 x 2.5=187.5
c) Re-arrange the formula so it becomes time = distance/speed
Substitute into it so it become time=30/75
=0.4
=24 minutes





I think...

Answer:

Step-by-step explanation:

Top question:Table =0.8

Constant of proportionality is 1.25?

a)The speed they are going at?

b)187.5(units which are being used)

c)0.4 hours=24 minutes

Step-by-step explanation:

a)The formula is distance=speed x time. Speed is only one missing

b)Substitute into the formula 75 x 2.5=187.5

c) Re-arrange the formula so it becomes time = distance/speed

Substitute into it so it become time=30/75

=0.4

=24 minutes

Answer:

total area of the given figure is 126

step by step guide:

1) 14×6+1/2×14×6

2) 84+42

3) =126

Answer: A=2cm

Step-by-step explanation:

All the sides of a regular hexagon are equal. SO PQ is the same as MN

Answer: It's A) 2 cm

Step-by-step explanation: All the sides are the same length.

Good luck!

Answer:

Ribeye (ea) = $18.54

Salmon (ea) = $9.78

Step-by-step explanation:

x is the price for each ribeye steak

y is the price for each grilled salmon

15x + 28y  = $551.97 (a)

24x + 14y = $581.91 (b) -----(x2)------> 48x + 28y = 1163.82 (c)

Subtract c with a

48x + 28y = 1163.82 (c)

15x + 28y  = $551.97 (a)

===================  -

33x           = 611.85

x = 18.54

Put the value of x into a

15 · 18.54 + 28y = 551.97

278.1 +28y = 551.97

28y = 273.87

y = 9.78

In conclusion, the price of 1 ribeye is $18.54, and the price of 1 salmon is $9.78.

Answer:

16,49 and 121 are perfect squares

Step-by-step explanation:

hope it helps :)

Answer:50.24 is the closest its really 50.26

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

20*6*8=960

960/(12*8)=10

Answer:

10

Step-by-step explanation:  volume=l*w*h   20*6*8=960       12*8*10=960

Answer:

Use the 'Keep, Change, Flip/Reciprocal' (KCF) method.

• 6/3 × 4/2

Then, multiply both numerators together and both denominators together.

• 24/6

Simplified: 4

Answer: 6t = 9

Step-by-step explanation:

What is visually explicable is that the 2 tape diagrams are equal.

One tape diagram equals 9, one is divided into 6 equal parts, each equals t.

6t's make up a diagram that is equal to a diagram equal to 9.

therefore 6t=9

Answer:

I believe the answer is B.

Step-by-step explanation:

Explanation:

30/5=6

6*3=18

Therefore, she can ride approximately 18 miles in 3 hours.

"Pure mathematics is, in its way, the poetry of logical ideas" -Albert Einstein

Answer: D for Q 1. A for Q 2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

-7 2/6>-13

is true because when u calculate the denominator by the numerator its the only real number

Answer: 350

Step-by-step explanation:

Divide it by the centimeter

Answer:

350  (*^▽^*)

Step-by-step explanation:

Answer:

I haven't done anything like this for many years, but i think the answer is 900

Step-by-step explanation:

5000/ 150 = 33.33333333

33.3333333 X 27 = 900

Again, I haven't done this in forever, but I'm 99% sure it is 900. :)

Answer: 540 degrees! :D

Step-by-step explanation:

So you can see, there is a little angle on the inside of the pentagon already. How many letters are there on each of the little corners? 5.

You would multiply 108 times 5. That comes out to 540 degrees!

Hope this helps! :)

Answer: It's B) 540°

Step-by-step explanation: I just multiplied 108 by 5 since there are 5 angles on that pentagon.

Hope It Helped! :D

Answer:

t = 5 kilometers

Step-by-step explanation:

From the given figure,

Perimeter = 18 kilometers

Now, the formula for perimeter of a rectangle = 2(l + b)

Where,

'l' is the length of the rectangle

and

'b' is the breadth of the rectangle.

Since length is the longest side of a rectangle, therefore from the given figure

=> l = t kilometers

and

=> b = 4 kilometers

Substituting values in the formula,

18 = 2(t + 4)

=> 18/2 = t + 4

=> 9 = t + 4

=> 9 - 4 = t

=> t = 5 kilometers

Answer:

5 km

Step-by-step explanation:

We know that the perimeter of this rectangle is 18km.

We also know that 1 side is 4km.

Given the perimeter formula:

[tex]P=2(l+w)[/tex]

We can substitute our given values:

18=2(4+w)

Solve the right side

18=8+2w

subtract 8 from both sides

10=2w

divide both sides by 2

5=w

This means that z, the width, is 5 km.

Hope this helps!

Answer:b

Step-by-step explanation:

Answer:

#3 points are
(-4, 2)
(4, 2)

(-4, -2)

(4, 0)

#4 scale factor = 1/4

#5 scale factor = 1/2

Step-by-step explanation:

#3

take the given points and multiply the x and y by 2/3

#4 take any point and compare it to a similar point on the dilated graph. for example, you take a point from the original graph (-2, 4) and a point from the dilated graph (-1/2, 1) since you multiply -2 by 1/4 to get -1/2, that is your scale factor.

#5 same as #4 but with different points

Answer:

13

13

Step-by-step explanation:

-7+6= 7+6= 13

-7+6= 7+6= 13

Answer:

To find the x-intercept, substitute in

0 for y

and solve for x. To find the y-intercept, substitute in

0 for x

and solve for y.

x-intercept(s): (−5,0)

y-intercept(s): (0,10)

Step-by-step explanation:

90 30 + 50 +(2x+10)=90

Answer: C

Step-by-step explanation:

32/4 = 8 ( the unit rate )

And then if you do 128/8 you get 16

Answer: $82.35

Step-by-step explanation:

For every 3 you buy, you get 2 free. This means out of every 5 twelve-packs, you pay for 3 of them, or 60%.

3/5 = 0.6 or 60%

So, if you buy 25 of them, you pay for 60% of 25 twelve-packs, or 15 of them.

25 x 0.6 = 15

If you are paying for 15 twelve-packs, and each one is $5.49, then the total would be $82.35.

15 x 5.49 = 82.35

Answer:82.35

Step-by-step explanation:

For every 3 you buy, you get 2 free. This means out of every 5 twelve-packs, you pay for 3 of them, or 60%.

3/5 =  60%

if you buy 25 of them, you pay for 60% of 25 twelve-packs, or 15 of them.

25 x 0.6 = 15

15 twelve-packs,  each one is $5.49, then the total would be $82.35.

15 x 5.49 = 82.35