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3 years ago

Which of the following (x,y) pairs is the solution for the system of equations x+2y=4 and -2x+y=7

Mathematics

1 answer:

kakasveta [241]3 years ago

3 0

Answer:

(-2 ,3)

Step-by-step explanation:

Step 1: Rewrite first equation

x = 4 - 2y

-2x + y = 7

Step 2: Substitution

-2(4 - 2y) + y = 7

Step 3: Solve y

-8 + 4y + y = 7

-8 + 5y = 7

5y = 15

y = 3

Step 3: Plug in y to find x

x + 2(3) = 4

x + 6 = 4

x = -2

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Lincoln went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 250 mg of sodium and each

Ludmilka [50]

We can solve with a system of equations, and use c for the amount of cans of soup and f for the amount of frozen dinners.

The first equation will represent the amount of sodium. We know the (sodium in one can times the number of cans) plus (sodium in one frozen dinner times the number of dinners) is the expression for the total sodium. We also know the total sodium is 4450, so:

250c + 550f = 4450

The second equation is to find how many of each item are purchased:

c + f = 13

Solve for c in the second equation:

c = 13 - f

Plug this in for c in the first equation:

250(13-f) + 550f = 4450

3250 - 250f + 550f = 4450

300f = 1200

f = 4

Now plug the value for f into the second equation:

c + 4 = 13

c = 9

The answer is 9 cans of soups and 4 frozen dinners.

6 0

3 years ago

Read 2 more answers

How would you teach something you have learned this year in Math to someone younger than you? Write more than 5 sentences

rewona [7]

Answer:

ok here ya go

Step-by-step explanation:

A way that I would teach someone something that I learned in math this year to someone else is simple. I would start by writing everything out so that they have a visual of what I am teaching them. I would also use a visual of a real world situation so that it relates to something they would understand. Teaching someone younger than you means they probably will not understand as easy as you understood it so, I would be very slow and make sure if they are confused to help them. I would also make sure not to be too bossy, understanding that they may not understand and that is ok.

5 0

2 years ago

Wich expression can be used to find the slope of a line containing the points (-3,2) and (7,-1)

docker41 [41]

$A(x_1;\ y_1);\ B(x_2;\ y_2)\\\\\text{The slope:}\ m=\dfrac{y_2-y_1}{x_2-x_1}$

$\text{We have:}\\(-3;\ 2)\to\ x_1=-3;\ y_1=2\\(7;\ -1)\to x_2=7;\ y_2=-1$

$\text{substitute}\\\\m=\dfrac{-1-2}{7-(-3)}=\dfrac{-3}{10}=-\dfrac{3}{10}$

6 0

3 years ago

Graph the following lines and write the equation in slope-intercept form. With y intercept of −3 and an x intercept of −4.5.

makvit [3.9K]

Answer:

$y=-\frac{2}{3}x-3$

Step-by-step explanation:

To write the equation of a line we need 2 points. We know:

If the y-intercept of the line is -3 then the point is (0,-3).

If the x-intercept of the line is -4.5 then the point is (-4.5,0).

Using these two point, we will find the slope and then substitute it into the point slope form $y-y_1=m(x-x_1)$ with a point.

Slope: $m=\frac{0--3}{-4.5-0}=\frac{0+3}{-4.5}=\frac{3}{-4.5}=-0.6667$

This decimal is -2/3. We will now substitute -2/3 and (0,-3) into the point slope form.

$y--3=-\frac{2}{3}(x-0)\\y+3=-\frac{2}{3}(x)\\y+3=-\frac{2}{3}x\\y=-\frac{2}{3}x-3$

6 0

3 years ago

Fifteen years ago, you deposited $12,500 into an investment fund. Five years ago, you added an

True [87]

Answer:

a) 8.16%

b) $65,762.50

c) $39,701.07

Step-by-step explanation:

Given:

15 years ago, Initial investment = $12500

5 years ago, Investment = $20000

Nominal interest = 8% semi annually for first 10 years

Interest2= 6.5% compunded annually for last five years

a) for the effective annual interest rate (EAR) in the first 10 years, let's use the formula:

[1+(nominal interest rate/number of compounding periods)]^ number of compounding periods-1

$EAR = [1 + (\frac{0.08}{2})]^2 - 1$

$= (1 + 0.04)^2 - 1$

$= (1.04)^2 - 1$

= 1.0816 - 1

= 0.0816

= 8.16%

The effective annual interesting rate, EAR = 8.16 %

b) To find the amount in my account today.

Let's first find the amount for $12500 for 10 years compounded semi annually

= 12,500 +( 12,500 * 8.160% * 10)

= $ 22,700

Let's also find the amount for $32,500($12,500+$20,000) for 5 Years compoundeed annually

$32,500 + ($32,500 * 6.5% *5)

= $ 43,062.50

Money in account today will be:

$22,700 + $43,062.50

= $65,762.50

c) Let's the amount I should have invested to be X

For first 10 years at 8.160%, we have:

Interest Amount = ( X * 8.160% * 10 ) = 0.8160 X

For next 5 years at 6.5%, we have:

Interest Amount = (X * 6.5% * 5) = 0.325 X

Therefore the total money at the end of 15 Years = 85000

0.8160X + 0.3250X + X = $85,000

= 2.141X = $85,000

X = 85,000/2.141

X = 39,701.074 ≈ $39,700

If I wish to have $85,000 now, I should have invested $39,700 15 years ago

7 0

3 years ago