All categories

2 years ago

Solve the system of linear equations by substitution. 3x + y = -9 y=5x+7

Mathematics

1 answer:

11Alexandr11 [23.1K]2 years ago

8 0

Answer:

The solution is x = -2, y = -3

Step-by-step explanation:

Let's start with the equation 3x + y = -9

Substitute the y for 5x+7 seen in the second equation

Now you have 3x + (5x+7) = -9

Lets solve:

Let's add the x's

Now we have 8x + 7 = -9

Substracy seven from each side

Now we have 8x = -16

Now let's divide 8 on each side

Now we have x = -2

Now lets plug in -2 to the second equation

The second equation is y = 5x+7

When we plug in -2 we get y=5(-2)+7

We multiply

We now have y = -10+7

Add

y = -3

The solution is x = -2, y = -3

You might be interested in

3/5÷33/5 find the quotient

defon

Flip 33/5

3/5 times 5/33
3 times 5 /5 times 33
15/165
Reduce
1/11

7 0

3 years ago

What is the solution to the equation below? Round your answer to two decimal places? (apex) 5+8*In x=15.8

Sliva [168]

Option A : $x=3.86$ is the solution of the equation.

Explanation:

The equation is $5+8 \ln x=15.8$

To determine the value of x, let us simplify the equation.

Subtracting 5 from both sides of the equation, we have,

$5+\ 8 \ ln \ x-5=15.8-5$

Simplifying, we get,

$8 \ ln \ x= 10.8$

Now , dividing both sides of the equation by 8, we get,

$\ ln \ x=1.35$

Using the logarithmic definition that if $\log _{a}(b)=c$ then $b=a^{c}$

Thus, rewriting the above expression $\ ln \ x=1.35$ using the logarithmic definition, we have,

$\ln \ x =1.35$ ⇒ $x=e^{1.35}$

Substituting the value of $e^{1.35}$=3.85742...$ , we get,

$x=3.85742 \ldots$

Rounding off the answer to two decimal places, we get,

$x=3.86$

Hence, the solution of the equation is $x=3.86$

Therefore, Option A is the correct answer.

8 0

2 years ago

[PROBABILITY] THERE ARE FOUR PEOPLE IN A ROOM THAT HAVEN'T MET BEFORE. THEY ARE TOLD TO SHAKE HANDS, EXACTLY ONCE, OF EVERY OTHE

Ivahew [28]

Answer:

Step-by-step explanation:

Let the 4 people be A, B, C and D. If each of them shakes hands with another person exactly one time then that means

A shakes with B, C and D. So 3 handshakes

B already shakes with A. So B shakes with C and D. 2 handshakes

C already shakes with A and B. So C shakes with D only. 1 handshake.

D already shake hand with all above.

Total handshakes: 3 + 2 + 1 = 6

8 0

3 years ago

A hemisphere has an area of 256 pi cm^2. What is its volume?

Amanda [17]

$\bf \begin{array}{llll}
\textit{surface area of a sphere}\\\\
A=4\pi r^2
\\\\\\
\textit{a hemisphere is half that}\\\\
A=\cfrac{4\pi r^2}{2}\implies A=2\pi r^2
\end{array}\qquad r=radius
\\\\\\
\textit{now, we know the area is }256\pi \implies 256\pi =2\pi r^2
\\\\\\
\cfrac{256\pi }{2\pi }=r^2\implies \sqrt{128}=r\implies \boxed{8\sqrt{2}=r}
\\\\
-----------------------------\\\\$

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4}{3}\pi r^3\qquad r=radius
\\\\\\
\textit{a hemisphere is half that}\\\\
V=\cfrac{\frac{4}{3}\pi r^3}{2}\implies V=\cfrac{\frac{4\pi r^3}{3}}{\frac{2}{1}}\implies V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{2}
\\\\\\
V=\cfrac{2\pi r^3}{3}
\\\\\\
\textit{now, we know the radius is }8\sqrt{2}\implies V=\cfrac{2\pi (8\sqrt{2})^3}{3}
\\\\\\
V=\cfrac{2\pi (8^3\sqrt{2^3})}{3}\implies V=\cfrac{2\pi \cdot 512\cdot 2\sqrt{2}}{3}
\\\\\\
\boxed{V=\cfrac{2048\pi \sqrt{2}}{3}}$

7 0

3 years ago

What’s the rational number has -0.875 as its decimal equivalent

Fynjy0 [20]

Get rid of the decimal first.
-0.875*1000
-875/1000=-0.875
Simplify it since both denominator and numerator is divisible by 5
1/5(-875/1000)
-175/200
Still divisible by 5
1/5(-175/200)
-35/40
Keep going
-7/8
There, now it can’t be more simplified.

8 0

3 years ago