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3 years ago

What is the range of the function f(x) = 3x2 + 6x – 8?

1 answer:

5 0

Find minimum and max y value because that is what range is
we see it opens up becasue 3 is positive
x value of vertex is -b/2a when you have f(x)=ax^2+bx+c

f(x)=3x^2+6x-8
vertex is -6/(2*3)=-6/6=-1
find y value by subsituiong it for x
f(-1)=3(-1)^2+6(-1)-8
f(-1)=3(1)-6-8
f(-1)=3-14
f(-1)=-11

range is from -11 to infinity

You might be interested in

Twice the difference of a number and 4 is equal to three times the sum of the number and 4.

Delvig [45]

Answer:

2(x-4)=3(x+4)

Step-by-step explanation:

that's easy.

6 0

3 years ago

Find the slope between these two points:<br> (-5, 8), (-5,-9)

Elena L [17]

Answer:

The slope is undefined.

Step-by-step explanation:

The slope of a line is its relationship between its change in verticalness and its change in horizontalness. In layman's terms, we call it rise over run. Slope can be useful for many things: to show how steep a line is, to write a line in slope-intercept form (y = mx + b), etc.

Recall that a line only needs two points to be formed. That's why slope matters so much. With lines, we only care about its steepness and its position on the coordinate plane, so slope knocks out one of those criteria.

One way to find slope is to use the definition of slope, the change in verticalness (y) divided by the change in horizontalness (x):

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

where m is the slope of the line;

and x1, y1, x2, and y2 are coordinates for points (x1, y1) and (x2, y2).

So let's use what we now know to solve the problem.

Since (-5,8) and (-5,9) are two points, they can form a line. So I can say that x1 = -5, y1 = 8, x2 = 5, and y2 = 9. Now, let's plug these numbers into the formula.

$m=\frac{-9-8}{-5-(-5)}$

$m = \frac{-17}{0}$

"Wait, what's going on? I thought I can't divide by 0." - You

Yes, exactly. But what we have here is a special case of a line, nothing more. Let me explain.

Lines don't always have a natural number for a slope, like m = 1. There are two special lines that deviate from the norm: horizontal lines and vertical lines.

Horizontal lines have a slope of zero. This is because they change in x, but not in y. So y appears as 0 in the formula: 0/x = 0. That's why horizontal lines have a slope of zero. They are usually written as y = C where C is some constant.

Vertical lines have an undefined slope. We're dealing with this type of line for our problem. They change in y, but not in x. So x appears as 0 in the formula: y/0 = undefined. We simply cannot divide by zero. That's why vertical lines have undefined slopes. They are usually written as x = C where C is some constant.

So there you go. (-5, 8) and (-5, -9) form a vertical line that has an undefined slope. And if you really want to know the equation for this line, it's x = -5.

6 0

2 years ago

Given a sequence is defined by the explicit definition tn=n^2+n.... (questions attached)

s2008m [1.1K]

Question 1: The correct answer is Option 3: 20

Question 2: The correct answer is Option 3: 27

Step-by-step explanation:

We put the term number as value of n in explicit formula to find the term.

<u>Question 1:</u>

Given

$t_n=n^2+n$

To find t4, we will put t=4 in explicit formula

$t_4=(4)^2+4\\t_4=16+4\\t_4=20$

The correct answer is Option 3: 20

<u>Question 2:</u>

Given, the explicit formula

$t_n=2^n-n$

We have to find the 5th term, putting n=5 in the explicit formula

$t_5=2^5-5\\=32-5\\=27$

The correct answer is Option 3: 27

Keywords: Explicit formula, arithmetic sequence

Learn more about arithmetic sequence at:

#LearnwithBrainly

5 0

3 years ago

The design pattern on a blanket has 3 circles followed by 4 triangles. this pattern repeats across the entire blanket. move a nu

maxonik [38]

The ratio between the circle and triangle is described as 3:4.

<h3>What is ratio?</h3>

An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.
In this section, the terms ratio and proportion are defined. Both ideas play a significant role in mathematics. Numerous examples where the concept of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.
An equation for proportion establishes the equality of the two provided ratios.
Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol
A fraction, like 2/5, can be used to represent a ratio. In our daily lives, we come across many comparisons, or ratios.
As a result, the ratio can be expressed in three distinct ways, including:

a to b
a : b
a/b

Know more about ratio and proportion numerical

brainly.com/question/12024093

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5 0

2 years ago

2x-y=10 <br> X+3y=-9 <br> I need to find the intersecting points but i dont know how

Vera_Pavlovna [14]

Answer:

x=3, y=-4

Step-by-step explanation:

The intersection points of these two equations are the values of x and y. You can use graphical method for solving it or mathematical equation.

The equations given are;

2x-y=10 Equation 1

x+3y=-9 Equation 2

Multiplying equation 1 by 3 and equation 2 by -1 ie the figures before the y

6x-3y=30 Equation 3

-x-3y=9 Equation 4

Subtracting the values of x, y and RHS for both equations 3 and 4

(6- -1)x=7x

(-3- -3)y=0

(30-9)=21

Therefore,

7x=21

Solving for x

x=21/7=3

x=3

To find y, substitute the value of x in equation 1 hence

2(3)-y=10

y=6-10=-4

y= -4

7 0

3 years ago