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4 years ago

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If seven times a number is added to the squares of the number and the result is negative twelve, what are the numbers?

1 answer:

AleksAgata [21]4 years ago

6 0

Let's name the number 'n'. Now write an equation. 7*n +n^2 =12Now you can form a quadratic. n^2 +7n-12=0. Now you can use a myriad of methods to solve it. If you still need help, just message me.

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Intersection point of Y=logx and y=1/2log(x+1)

GalinKa [24]

Answer:

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

The Problem:

What is the intersection point of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ ?

Step-by-step explanation:

To find the intersection of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ , we will need to find when they have a common point; when their $x$ and $y$ are the same.

Let's start with setting the $y$ 's equal to find those $x$ 's for which the $y$ 's are the same.

$\log(x)=\frac{1}{2}\log(x+1)$

By power rule:

$\log(x)=\log((x+1)^\frac{1}{2})$

Since $\log(u)=\log(v)$ implies $u=v$ :

$x=(x+1)^\frac{1}{2}$

Squaring both sides to get rid of the fraction exponent:

$x^2=x+1$

This is a quadratic equation.

Subtract $(x+1)$ on both sides:

$x^2-(x+1)=0$

$x^2-x-1=0$

Comparing this to $ax^2+bx+c=0$ we see the following:

$a=1$

$b=-1$

$c=-1$

Let's plug them into the quadratic formula:

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

$x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$x=\frac{1 \pm \sqrt{1+4}}{2}$

$x=\frac{1 \pm \sqrt{5}}{2}$

So we have the solutions to the quadratic equation are:

$x=\frac{1+\sqrt{5}}{2}$ or $x=\frac{1-\sqrt{5}}{2}$ .

The second solution definitely gives at least one of the logarithm equation problems.

Example: $\log(x)$ has problems when $x \le 0$ and so the second solution is a problem.

So the $x$ where the equations intersect is at $x=\frac{1+\sqrt{5}}{2}$ .

Let's find the $y$ -coordinate.

You may use either equation.

I choose $y=\log(x)$ .

$y=\log(\frac{1+\sqrt{5}}{2})$

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

6 0

3 years ago

Which set of data does not have a mode?

Y_Kistochka [10]

Answer:

FIRST ONE

Step-by-step explanation:

NO NUMBER REPEATS ITSELF

4 0

3 years ago

Read 2 more answers

When drawing the arcs in order to bisect a line segment, why must the width of the compass be more than half of the length of

Aleonysh [2.5K]

Answer: Choice A

If the compass isn't open wide enough, then the arcs won't intersect forming the points we need to create the perpendicular bisector.

Check out this link to see my response to the identical question answered 2 days ago

brainly.com/question/17191122

feel free to ask any questions you have if you're still stuck

8 0

3 years ago

One number is 10 more than the other. Their product is 299. Which of the following are the representations?

Talja [164]

Answer:

A.

Step-by-step explanation:

the second number is just 10 more than the first

6 0

3 years ago

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Find the gradient of the line passing through (6,8) and (4,10)

Mariulka [41]

Question:

Find the gradient of the line passing through (6,8) and (4,10).

Answer:

-1 is the right answer.

Step-by-step explanation:

Slope of the line = The gradient of the line

Gradient of the line is known as change in the value of y-axis by change in the value of x-axis

Gradient = ∆y\∆x

$Gradient = \frac{y_ 2 - y_1}{x_2 - x_1} = \frac{(10 - 8)}{(4 - 6)} = \frac{(2)}{(- 2)} =\boxed{- 1}\\$

7 0

3 years ago