Hello:

5 What is the range of y = -x2 - 2x + 3?<br> Ax<4<br> B x2-4<br> c y<4<br> Dy2-4

Vesnalui [34]

Answer:

$y\leq 4$

Step-by-step explanation:

we have

$y=-x^{2}-2x+3$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex is a maximum

The vertex is the point (h,k)

The range of the function is the interval (-∞,k]

so

$y\leq k$

Convert the quadratic equation in vertex form

Factor -1 leading coefficient

$y=-(x^{2}+2x)+3$

Complete the square

$y=-(x^{2}+2x+1)+3+1$

$y=-(x^{2}+2x+1)+4$

Rewrite as perfect squares

$y=-(x+1)^{2}+4$

The vertex is the point (-1,4)

therefore

The range is $y\leq 4$

7 0

3 years ago

What integer is having 3 dollats

faust18 [17]

Answer:

Why is 3 an integer?

They are the numbers you usually count and they will continue on into infinity. Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4… Integers include all whole numbers and their negative counterpart e.g. … -4, -3, -2, -1, 0,1, 2, 3, 4

8 0

3 years ago

Alaska has a Land area of about 1,700,000 square kilometers. Florida has a land area 1 10 the size of Alaska. What is the land

xenn [34]

The answer to your question is: 187,000,000 because 110 x 170,000,000

6 0

3 years ago

Please help with 8.???

IRINA_888 [86]

Answer:

They are inverse functions

Step-by-step explanation:

A property of inverse functions is that if $f(x) = a, g(a) = x$

We can plug in x = 3

$f(1) = 3(3) - 2 = 7$

That means that, supposing they are inverse functions, g(7) should equal 3

$g(7) = \frac{7+2}{3} =3$

It checks out

Another way to see if two functions are inverse is to swap the x and y of one of the functions.

ex. $y = 3x-2\\-> x = 3y - 2\\-> x+2 = 3y\\-> y = \frac{x+2}{3}\\ \\$

Since, after the swap, the functions are equal, we know it is an inverse function

5 0

3 years ago

A positive integer is twice another.the sum of the reciprocal of the two positive integer is 3/14. Find the integers

icang [17]

Answer:

$\huge\boxed{14\ \text{and}\ 7}$

Step-by-step explanation:

$n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right$

$\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}$

$\text{Substitute it to (1):}\\\\n=2\cdot7\\\\\boxed{n=14}$

8 0

3 years ago