The product of a number and 4 increased by 7 is 5. What is the number?

Mathematics

1 answer:

yanalaym [24]3 years ago

6 0

Answer: x = -1/2 = -0.5

Step-by-step explanation:

set up an equation

4x + 7 = 5 subtract 7 from both sides

4x = - 2 divide both sides by 4

x = -2/4

x = -1/2 = -0.5

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What is lim x→3 x^2 - x - 6/ x - 3

Kisachek [45]

<h3>Answer: D) 5</h3>

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Explanation:

If we plugged x = 3 into the expression, then we'd get x-3 = 3-3 = 0 in the denominator. That's not allowed. But we can simplify first

x^2-x-6 factors to (x-3)(x+2). The key here is that (x-3) is a factor. It cancels with the x-3 in the denominator

So, $\frac{x^2-x-6}{x-3} = \frac{(x-3)(x+2)}{x-3} = x+2$

Allowing us to say,

$\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}\frac{(x-3)(x+2)}{x-3}\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}(x+2)\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 3+2\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 5\\\\\\$

5 0

4 years ago

A circle has the equation x2 + (y−7)2 = 121. What is the length of the diameter of the circle?

Reika [66]

Answer:

Step-by-step explanation:

The standard form for an equation of a circle is $(x-h)^2+(y-k)^2=r^2$ , where h is the x coordinate of the center of the circle, k is the y coordinate, and r is the radius of the circle. Therefore, the radius of this circle squared is 121, meaning that the radius of the circle is 11. Since the diameter of a circle is twice the radius, the radius of this circle is 22. Hope this helps!