Solve for x: x²−9=5(x−3).

Nadusha1986 [10]

We can eliminate choice C because our parabola is not upside down. The way I determined which one it was was by picking a point on the graph and testing the x value of the point in the equation. If the y value on the graph was the same as the y value on my calculator, then I chose the right one. Let me give you an example of what doesn't work first. Let's pick (3, 2) from the graph. Let's test that point in choice D. Filling in x = 3, y should = 2 if that's the right equation. $\frac{1}{2}(3^2)-3+2= \frac{7}{2}$ . Our y coordinate is not 7/2, it's 2. Let's try A: $\frac{1}{3}(3^2)-3-2=-2$ . Again, our y value is 2, not -2. Let's try B: $\frac{1}{3}(3^2)-3+2=2$ . See how that works? Your choice is B.

7 0

3 years ago

Use the augmented matrix method to solve the following system of equations. Your answers may be given as decimals or fractions.

Alexandra [31]

Answer:

$x\ =\ \dfrac{21}{5}$

$y\ =\ \dfrac{3}{5}$

z = 2

Step-by-step explanation:

Given equations are

x - 2y - z = 2

x + 3y - 2z = 4

-x + 2y + 3z = 2

from the given equations the augmented matrix can be written as

$\left[\begin{array}{ccc}1&-2&-1:2\\1&3&-2:4\\-1&2&3:2\end{array}\right]$

$R_2=>R_2-R_1\ and\ R_3=>R_3+R_1$

$=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&5&-1:2\\0&0&2:4\end{array}\right]$

$R_2=>\dfrac{R_2}{5}$

$=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\0&0&2:4\end{array}\right]$

$R_1=>R_1+2.R_2$

$=\ \left[\begin{array}{ccc}1&0&-1-\dfrac{2}{5}:2+\dfrac{4}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]$

$=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]$

$R_3=>\dfrac{R_3}{2}$

$=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&1:2\end{array}\right]$

$R_1=>R_1+\dfrac{7}{5}R_3\ and\ R_2+\dfrac{1}{5}R_3$

$=\ \left[\begin{array}{ccc}1&0&0:\dfrac{14}{5}+\dfrac{7}{5}\\\\0&1&0:\dfrac{2}{5}+\dfrac{1}{5}\\\\0&0&1:2\end{array}\right]$

So, from the above augmented matrix, we can write

$x\ =\ \dfrac{21}{5}$

$y\ =\ \dfrac{3}{5}$

z = 2

7 0

3 years ago

The ravens won three more games than they lost.they played 96 games.how much games did they win?

balandron [24]

$x-the \ number \ of \ games \ won \ \\\\ y-the \ number \ of \ games \ lost \\\\ x= y+3 \\\\ x+y=96 \\\\ 3+y+y=96 \\\\ 3+2y=96 \\\\2y=96-3\\\\2y=93 \\\\ \boxed{y=\frac{93}{2}=46.5\approx46\ games \ lost} \\\\ x=3+46 \\\\ \boxed{x=49 \ games \ win}$

4 0

3 years ago

The price of a toaster increase 10% to $40. What is the original price of the toaster before the increase?

tresset_1 [31]

Answer:

36.36

Step-by-step explanation:

We can express 10% as a decimal by multiplying it by (1/100), resulting in 0.1. Therefore, adding 0.1 of the original price, or x, to the price will result in 40, so x+0.1*x=40

= 1.1x

Dividing both sides by 1.1, we get that x, or the original price, is $36.36 (approximately).

8 0

3 years ago

There is a box with 6 marbles: 3 red, 1 blue, 1 green, and 1 yellow. What is the probability of picking yellow marble, keep it,

fiasKO [112]

Answer:

1:6

Step-by-step explanation:

you have one out of 6 chances to pick the yellow marble

6 0

3 years ago

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