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4 years ago

Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution?

Mathematics

2 answers:

BlackZzzverrR [31]4 years ago

8 0

Answer: B. (2,1)

Step-by-step explanation:

The given system of equation :

$y=2x-3...........................(1)\\\\y=-2x+5.............................(2)$

Adding equation (1) and (2), we get

$2y=-3+5\\\\\Rightarrow\ 2y=2\\\\\Rightarrow\ y=1$

Substitute the value of y in the first equation , we get

$1=2x-3\\\\\Rightarrow\ 2x=1+3\\\\\Rightarrow\ 2x=4\\\\\Rightarrow\ x=2$

Therefore, the solution to the given system of equations = (2,1)

Nataly [62]4 years ago

7 0

Answer:

B (2,1)

Step-by-step explanation:

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Alekssandra [29.7K]

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3 years ago

Two number cubes are tossed. What is P(4, 6)? O.1/6 O.1/12 O.1/3 O.1/36

Bezzdna [24]

The value of P(4, 6) when the two number cubes are tossed is 1/36

<h3>How to determine the probability?</h3>

On each number cube, we have:

Sample space = {1, 2, 3, 4, 5, 6}

The individual probabilities are then represented as:

P(4) =1/6

P(6) =1/6

The value of P(4, 6) when the two number cubes are tossed is:

P(4, 6) = P(4) * P(6)

This gives

P(4, 6) = 1/6 * 1/6

Evaluate

P(4, 6) = 1/36

Hence, the value of P(4, 6) when the two number cubes are tossed is 1/36

Read more about probability at:

brainly.com/question/24756209

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6 0

1 year ago

Show work please \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

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2 years ago

Circle two addends to add first. write the sum 7,3,3

Hitman42 [59]

7 + 3 = 10 those are the 2 addens

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3 years ago

Write an algebraic rule to describe the translation c (5,-4) c'(-2,1)

Sauron [17]

We can solve this by using the formula:
(x, y) (x + a, y + b) = (5,-4) (-2,1)

So, plugging in the values and solving for a and b,
5 + a = -2
a = -8

-4 + b = 1
b = 5

Therefore, the translation is
(x,y) (x - 8, y +5)

5 0

3 years ago