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2 years ago

What is the solution of the system y=-3x 3x+2y=6

Mathematics

2 answers:

RSB [31]2 years ago

8 0

You have 3x+2(-3x)=6. First you multiply using distributive property. Your new equation is 3x+-6x=6. Next you would add 3x+-6x, giving you -3x. now you have -3x=6. Lastly you would divide 6 by -3. This will give you that x is equal to -2.

irinina [24]2 years ago

7 0

I like to solve these by graphing, so if you graph both of these functions (as shown in the picture below), you look for the intersection between the two graphs, which in this case is (-2,6).

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I need help ASAP. If TU=10 and ST=15, What is the measure of the radius of the circle?

Svetach [21]

Answer:

5.6

Step-by-step explanation:

Use pythag to get SU. 10^2 + x^2 = 15^2, this will give you x = 11.2. 11.2 is the diameter of SU so divide it by 2 to get the radius. 11.2/2= 5.6.

3 0

2 years ago

The graphs of f(x) and g(x) are shown below:

rosijanka [135]

<h2>Answer:</h2>

Option: C is the correct answer.

C.) x = −3.8, 3

<h2>Step-by-step explanation:</h2>

The function f(x) is given by:

$f(x)=x^2-x-12$

and the function g(x) is given by:

$g(x)=-1.8x-0.6$

Now, we are asked to find the solution of the equation:

$f(x)=g(x)$

i.e. we have to find the value of x such that both the functions are equal i.e.

$x^2-x-12=-1.8x-0.6\\\\i.e.\\\\x^2-x+1.8x-12+0.6=0\\\\i.e.\\\\x^2+0.8x-11.4=0\\\\i.e.\\\\10x^2+8x-114=0\\\\i.e.\\\\5x^2+4x-57=0$

Now, on solving the equation using the quadratic formula i.e. the solution of the equation:

$ax^2+bx+c=0$

is given by:

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here we have:

$a=5,\ b=4\ and\ c=-57$

Hence, the solution is given by:

$x=\dfrac{-4\pm \sqrt{4^2-4\times 5\times (-57)}}{2\times 5}\\\\i.e.\\\\x=\dfrac{-4\pm \sqrt{16+1140}}{10}\\\\i.e.\\\\x=-3.8\ and\ x=3$

6 0

3 years ago

Willie left the mall and traveled toward the town hall at an average speed of 40 km/h. Gabriella left two hors later and travele

mezya [45]

Answer:

<em>3 hours</em>

Step-by-step explanation:

Given that:

Average speed of Willie = 40 km/h

After 2 hours, Gabriella traveled in opposite direction at an speed of 70 km/h.

After some time, they are 410 km apart.

To find:

Number of hours = ?

Solution:

For the first two hours, Willie traveled alone.

Formula for distance:

$Distance = Speed \times Time$

Distance traveled in two hours by Willie = $40 \times 2 = 80\ km$

Now, they both travel in opposite directions.

So the relative speed is = 40 + 70 = 110 km/h

The distance traveled by them = 410 - 80 = 330 km

$Time\ taken = \dfrac{330}{110} = 3\ hours$

Therefore, the time taken is <em>3 hours.</em>

5 0

2 years ago

5.03+13.7+108 what is the answer an how do u solve it

jarptica [38.1K]

Answer:

126.73

Step-by-step explanation:

5.03+13.7+108

5.03+13.7= 18.73

18.73 +108=

126.73

5 0

2 years ago

What is the 6th term of the geometric sequence where a1 = -4096 and a4 = 64?

Akimi4 [234]

$\bf \begin{array}{llccll}
term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
a_1&-4096\\
a_2&-4096r\\
a_3&-4096rr\\
a_4&-4096rrr\\
&-4096r^3\\
&64
\end{array}\implies -4096r^3=64
\\\\\\
r^3=\cfrac{64}{-4096}\implies r^3=-\cfrac{1}{64}\implies r=\sqrt[3]{-\cfrac{1}{64}}
\\\\\\
r=\cfrac{\sqrt[3]{-1}}{\sqrt[3]{64}}\implies \boxed{r=\cfrac{-1}{4}}\\\\
-------------------------------$

$\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=-\frac{1}{4}\\
a_1=-4096\\
n=6
\end{cases}
\\\\\\
a_6=-4096\left( -\frac{1}{4} \right)^{6-1}\implies a_6=-4^6\left( -\frac{1}{4} \right)^5$

4 0

2 years ago

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