All categories

3 years ago

Algebra

2 answers:

6 0

2x + 3y = 12
2*3 6 x = 3 because 2 times 3 equals 6y = 2 because 3 times 2 equals 6. 6+6=12.
4(3) - 3(2) = 6\/ \/12 6 = 6

(I'm copy-pasting from the work I just did on another tab. I know the page would reload)

vladimir2022 [97]3 years ago

5 0

(2x + 3y = 12) x (-2)
(4x - 3y = 6) x 1

-4x - 6y = -24
4x - 3y = 6

You can cancel out the x values by adding the two equations together.
(-4x + 4x) + (-6y - 3y) = (-24 + 6)
-9y = -18
y = 2

Solve for x now...
4x - 3(2) = 6
4x - 6 = 6
4x = 12
x = 3

Check... (x = 3, y = 2)
2(3) + 3(2) = 12
6 + 6 = 12
12 = 12 <- this works!

4(3) - 3(2) = 6
12 - 6 = 6
6 = 6 <- this works!

You might be interested in

Julie got 21 of the 23 questions

maw [93]

No because they do not have a common d
21/23 ( ) 29/32 (divide the two fractions)
0.9130434783 ( > ) 0.90625

5 0

4 years ago

What is the approximate area of the circle shown below?

svet-max [94.6K]

Answer:

A. 804 cm²

Step-by-step explanation:

Formula :

$\boxed{A = \pi r^2}$

A = 3.14 × 16²

A = 3.14 × (16 × 16)

A = 3.14 × 256

A = 803.84 cm²

A = 804 cm² (rounded)

So, the approximate area of the shown below is 804 cm² (A)

#CMIIW ^^

3 0

4 years ago

Find the value of X.20,40,x

Mazyrski [523]

Step-by-step explanation:

267:(;»«=:3688865)):;(645789

6 0

3 years ago

"Select the equation of the least squares line for the data: (34.0, 1.30), (32.5, 3.25), (35.0, .65), (31.0, 6.50), (30.0, 5.85)

yulyashka [42]

Answer:

$y=-1.055 x +37.643$

And the best option would be:

a. ŷ= 37.643-1.0543x

Step-by-step explanation:

We assume that the data is this one:

x: 34.0, 32.5, 35.0, 31.0, 30.0, 27.5, 29.0

y: 1.30, 3.25, 0.65, 6.50, 5.85, 8.45, 6.50

Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 34.0+ 32.5+ 35.0+ 31.0+ 30.0+ 27.5+ 29.0
=219$

$\sum_{i=1}^n y_i =1.3+3.25+0.65+6.5+5.85+8.45+6.5=32.5$

$\sum_{i=1}^n x^2_i = 34.0^2+ 32.5^2+ 35.0^2+ 31.0^2+ 30.0^2+ 27.5^2+ 29.0^2
=6895.5$

$\sum_{i=1}^n y^2_i =1.3^2+3.25^2+0.65^2+6.5^2+5.85^2+8.45^2+6.5^2=202.8$

$\sum_{i=1}^n x_i y_i =34*1.3 + 32.5*3.25+ 35*0.65+ 31*6.5+30*5.585 +27.5*8.45 +29*6.5=970.45$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6895.5-\frac{219^2}{7}=43.929$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=970.45-\frac{219*32.5}{7}=-46.336$

And the slope would be:

$m=-\frac{46.336}{43.929}=-1.055$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{219}{7}=31.286$

$\bar y= \frac{\sum y_i}{n}=\frac{32.5}{7}=4.643$

And we can find the intercept using this:

$b=\bar y -m \bar x=4.643-(-1.055*31.286)=37.643$

So the line would be given by:

$y=-1.055 x +37.643$

And the best option would be:

a. ŷ= 37.643-1.0543x

5 0

4 years ago

Vincent earns $258 on Monday, $105 on Tuesday, and $312 on Wednesday. He spends $299 on Thursday. How much money does he have le

Inessa05 [86]

Estimated amount : 375.

Exact amount : 376.

3 0

4 years ago