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enyata [817]
4 years ago
6

Two lines have the given equations. Use the Linear Combination Method to solve.

Mathematics
1 answer:
Rasek [7]4 years ago
5 0

Answer:

\large{\textbf{(x,y) = (-7, -15)}\\}

Step-by-step explanation:

\large{\textup{The given equations represent two straight lines.}}\\\\ \large{\textup{To solve them is to find the \textbf{point of intersection} of the two lines.}}\\

\begin{align*}\\2x - y &= 1  \hspace{25mm} (1) \\3x - y &= -6 \hspace{24mm} (2) \\\end{align*}

\large{ \textup{We start by eliminating one variable.}}\\

\textup{In this case, $y$ can be eliminated by subtracting (1) \& (2).}}}

\large{\textup{We get}\\}

\begin{align*}2x - y &= 1   \\-3x + y &= 6 \\\implies -x &= 7\\\implies x &= -7\end{align*}

\large{\textup{Substituting $x = -7$ in $(1)$, we get:}$ 2(-7) - 1 = y \\ $$\implies y = -15 $\\\textup{Therefore, $x= -7, y = -15$}\\\textup{Simply put, $(x,y) = (-7,-15) $ is the point of intersection of $(1)$ \& $(2)$}.}

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NemiM [27]
The answer is 63. 9 times 7 is 63
7 0
3 years ago
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The equation of the graphed line in point-slope form is _______, and its equation in slope-intercept form is .
Ivenika [448]

Answer:

Point-slope form equation line

(y-3)=(-0.6)\times (x+2)

Slope-intercept form is:

y=-0.6x+1.8

Step-by-step explanation:

Point-slope form equation line passing through points (x_1,y_1)(x_2,y_2)

Slope = m  =\frac{y-2-y_1}{x_2-x_1}

slope-intercept form is:

y = mx +c

where : c = intercept of on axis

(y-y_1)=m\times (x-x_1)

Equation of line passing through (-2,3) and (3,0).

m=\frac{0-3}{3-(-2)}=-0.6

(y-3)=-0.6\times (x-(-2))

Point-slope form equation line

(y-3)=(-0.6)\times (x+2)

For slope-intercept form open the brackets of Point-slope form equation l:

y-3=-0.6x-1.2

So, the slope-intercept form is:

y=-0.6x+1.8

7 0
3 years ago
a tool set is on sale for $280. the original price of the tool set was $400. what percent of the original price is the sale pric
Marianna [84]

70%

Hope this helps! :)

______________

5 0
4 years ago
Read 2 more answers
You’ve bought a cylindrical thermos 8 in. high with a base 6 in. across. How much coffee can you put in the thermos?
lana66690 [7]

Answer:

3.706 liters

Step-by-step explanation:

Hello

assuming that these measures correspond to the internal measures of the thermos,

we can calculate the volume as, the volume of a cylinder, which is given by

V=\pi r^{2} h

where r is the radius of the base, and h the height

also

Diameter=2r

r=Diameter/2

Step 1

let

h=8 in

base = diameter = 6 inch

r=diameter/2

r=6/2 inch,r=3 inch

Step 2

Put the values into the equation

V=\pi r^{2} h\\V=\pi (3in)^{2} (8 in)\\V=\pi *72 \ in^{3} \\\\V=72\pi\ in^{3} \\\\

Step 3

Now, the unit (cubic inches) is not an usual unit for measuring coffee, let´s convert cubic inches into liters by knowing

1 inch = 2.54 cm

1 litro =  1000 cubic centimeters

if\ 1\ inch\ = 2.54\ cm\\(1\ inch)^{3} =(2.54\ cm)^{3}\\\\1\ inch^{3}=16.3870\ cm^{3}

1 cubic inch = 16.3870 cubic centimeters

1\ cubic\ inch\ = 16.3870\ cubic\ centimeters\\\\\\72\pi =x?\ cubic\ centimeters\\\\x=\frac{72\pi \cubic \ inch\ \*16.3870 }{1\ cubic\ inch} \\\\x=3706.65\ cubic\ centimeters

Step 4

Finally, convert cubic centimeters into liters1000\ cubic\ centimeters =1\ liter \\\\\\3706.65\ cubic\ centimeters = x?\ liters\ centimeters\\\\x=\frac{3706.65 \cubic \ centimeters\ \*1 liter}{1000 cubic centimeters} \\\\x=3706.65\ cubic\ centimeters\\x=3.706 Liters

I can put 3.706 liters in the thermos

Have a good day

4 0
4 years ago
HELP ME PLEASE :(
Alina [70]

Correct option D) 1,185.6 inches cubed .

<u>Step-by-step explanation:</u>

Here we have , A triangular prism. The triangular base has a base of 12 inches and height of 10.4 inches. The height of the prism is 19 inches. We need to find  the volume of the triangular prism .Let's find out:

We have following parameters :

b=12 inches\\h=10.4inches\\l=19inhes

We know that , Volume of triangular prism is :

⇒ Volume = \frac{1}{2}b(h)(l)

⇒ Volume = \frac{1}{2}12(10.4)(19)

⇒ Volume = 6(10.4)(19)

⇒ Volume = 1,185.6in^3

Therefore , Correct option D) 1,185.6 inches cubed .

5 0
3 years ago
Read 2 more answers
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