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3 years ago

2. Solve for x: 2(x - 5) = x + 3(x + 2)

Mathematics

2 answers:

MrMuchimi3 years ago

5 0

Answer:

x=-8

Step-by-step explanation:

Artist 52 [7]3 years ago

5 0

Answer:

x = -8

Step-by-step explanation:

Firstly, distrubute 2 to our parentheses (2x - 10). Now, let's add our like terms, 2x - 10 = 4x + 6 since x alone is one we add this to 3x, equaling 4x. Then we're going to move our variable and sign, 2x - 10 - 4x = 6. Alright, now combine like terms and calculate (2x - 4x), we know when we subtract two and four, it's a negative 2, -2x = 6 + 10 = 16. Now divide both sides of the equation by -2, 16 divided by -2 is -8. Therefore, x = -8, hope this helped! Have a great day!

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The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm. What is the smallest possi

Veronika [31]

The longest side in the triangle is opposite to the largest angle of this triangle. If triangle is acute, then all angles are acute. Acute angle has cosine that is positive.

Use cosine theorem to determine the cosine of the largest angle:

$15^2=x^2+(2x)^2-2\cdot x\cdot 2x\cdot \cos \alpha,$ where $\alpha$ is the largest angle.

Then

$225=x^2+4x^2-4x^2\cos \alpha,\\ \\\cos \alpha=\dfrac{225-5x^2}{-4x^2}=\dfrac{5x^2-225}{4x^2}.$

Since $\cos \alpha>0,$ then

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Divide this inequality by 5:

$x^2-45>0,\\ \\(x-3\sqrt{5})(x+3\sqrt{5})>0,\\ \\x\in (-\infty,-3\sqrt{5})\cup (3\sqrt{5},\infty).$

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Answer: correct choice is B

6 0

3 years ago

Read 2 more answers

Ariyonne claims (3,6) that is the point of intersection of the lines y=4x-2 and y=1/2x+5 Is she correct? How do you know?

yan [13]

Answer:

The point of intersection of the lines is $(2,6)$ .

Thus, Ariyonne's claim is incorrect.

Step-by-step explanation:

Given equations:

1) $y=4x-2$

2) $y=\frac{1}{2}x+5$

To find the point of intersection, we need to solve the given system of equations.

In order to solve the system we will use substitution method.

We will substitute value of $y$ from first equation in the second equation and solve for $x$

So, we have

$4x-2=\frac{1}{2}x+5$

Multiplying both sides by 2 to remove fraction.

$2\times(4x-2)=2\times(\frac{1}{2}x+5)$

Using distribution.

$8x-4=x+10$

Subtracting both sides by $x$

$8x-4-x=x+10-x$

$7x-4=10$

Adding 4 to both sides.

$7x-4+4=10+4$

$7x=14$

Dividing both sides by 7.

$\frac{7x}{7}=\frac{14}{7}$

$x=2$

We can find value of $y$ by plugging in $x=2$ in the first equation.

$y=4(2)-2$

$y=8-2$

$y=6$

So, the point of intersection of the lines is $(2,6)$ .

Thus, Ariyonne's claim is incorrect.

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Dvinal [7]

Answer:

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Step-by-step explanation:

Multiplication is really just repeated addition. In multiplication, the 2 terms are the number being added and the number of times it is added. In this case, the number being added is -8 and it is being added 4 times. Therefore, the multiplication expression must be -8 x 4.

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3 years ago

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2. Solve for x: 2(x - 5) = x + 3(x + 2)​

2. Solve for x: 2(x - 5) = x + 3(x + 2)