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3 years ago

12

For this graph mark the statements that are true

1 answer:

Nitella [24]3 years ago

7 0

For the graph in the figure

we know that

the function is a quadratic equation ( vertical parabola) open up

so

The vertex is a minimum

the vertex is the point $(1,0)$

The domain x of the function is all real numbers-------> (-∞,∞)

The range is the interval--------> [0,∞)

$f(x)\geq 0$

therefore

Statements

A) The range is the set of all real numbers

Is false

B) The domain is the set of all real numbers

Is true

C) The domain is the set of all real numbers greater than or equal to zero

Is false

D) The range is the set of all real numbers greater than or equal to zero

Is true

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What is the suplementary of 75 3/5 degrees

belka [17]

I hope this helps you

180- 75 3/5

180-378/5

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3 years ago

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

Carrie is buying bulk candy for a high school fundraiser. She buys 1000 candy bars for $350. What is the unit cost per candy bar

Darina [25.2K]

B. $0.35
since to find the unit rate of one candy bar, you have to divide $350 by 1000 and you get $0.35
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6 0

3 years ago

Is 76 pounds of Christina's body weight comes from water about how much does Christina weigh

Ghella [55]

If 90% of bodies are water weight, then we have 10% left.

76+10% = 83.6.

83.6 total.

8 0

3 years ago

I need help pls, i would appreciate it !!

kramer

Answer:

a. x = 1.2, b. A = 32.1°

Step-by-step explanation:

1.41²-.75²=x²

a. x = 1.2

sin A = 0.75/1.41

b. A = 32.1°

5 0

3 years ago