Answer:
[tex]f(x)=2x^{2}-3[/tex]
[tex]D=(-\infty,\infty)[/tex]
[tex]R=[-3,\infty)[/tex]
x-intercepts: [tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]
y-intercept: (0,-3)
f(3)=15
Step-by-step explanation:
A quadratic function is any polynomial function whose greatest power is a 2, so [tex]f(x)=2x^{2}-3[/tex] is a nice example of it.
For the domain, as a rule, polynomial functions that have positive whole degrees will be defined for all real numbers, so:
[tex]D=(-\infty,\infty)[/tex]
When talking about quadratic functions, its range will happen from the lowest point (in this case the vertex) to it's highest point (in this case infinity)
In order to find the vertex, we can use the following formula:
[tex]x=-\frac{b}{2a}[/tex]
which is used for quadratic equations in standard form:
[tex]y=ax^{2}+bx+c[/tex]
In this case a=2, b=0 and c=-3, so we get:
[tex]x=-\frac{0}{2(2)}=0[/tex]
Now we know that the range will happen at x=0, so we substitute:
[tex]f(0)=2(0)^{2}-3=-3[/tex]
so the range will be:
[tex]R=[-3,\infty)[/tex]
For the x-intercepts we need to set the given function equal to zero so we get:
[tex]2x^2-3=0[/tex]
and solve for x:
[tex]2x^{2}=3[/tex]
[tex]x^{2}=\frac{3}{2}[/tex]
[tex]x=\pm \sqrt{\frac{3}{2}}[/tex]
which can be rationalized to:
[tex]x=\frac{\sqrt{6}}{2}[/tex] and [tex]x=-\frac{\sqrt{6}}{2}[/tex]
so the x-intercepts are located at:
[tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]
For the y-intercept, we need to set x=0 so we get:
[tex]f(0)=2(0)^{2}-3[/tex]
[tex]f(0)=-3[/tex]
So the y-intercept is located at:
(0,-3)
and finally, in order to get f(3) we must substitute x for 3 so we get:
[tex]f(3)=2(3)^{2}-3[/tex]
f(3)=15
means to find the only possible answer.
9. Whats is the equivalent fraction for 0.625
Answer:
5/8
Step-by-step explanation:
You need to convert to a simplified fraction by placing the numbers to the right of the decimal over 1000. Then reduce the fraction.
The distance between the paralled lines 3x + 4y +15 = 0 and 3x + 4y -10 = 0 is equal to: pls help ASAP
Answer:
5 units
Step-by-step explanation:
Please see attached pictures for the full solution.
(This distance is the perpendicular distance between the 2 parallel lines, which is the shortest distance between them.)
Answer:
D 21/5
Step-by-step explanation:
edge
How is the graph of y = (x + 1)^2- 5 transformed from the graph of y=x^2?
[tex]\text{Hi there! :D}[/tex]
[tex]\boxed{\text{There is a horizontal shift of 1 unit left and 5 units down.}}[/tex]
[tex]\text{Recall that the transformations form of a quadratic function is:}\\\\y = \pm a(b(x-h))+k \text{ where:}\\\\a = \text{ vertical stretch/compression}\\\\b = \text{ horizontal stretch/compression}\\\\h = \text{ shift left/right}\\\\k = \text{ shift up/down}\\\\\text{Therefore, in this instance:}\\\\h = -1\\\\k = -5, \text{ so:}\\\\\text{There is a horizontal shift of 1 unit left and 5 units down.}[/tex]
Suppose that J and K are points on the number line.
If JK = 10 and J lies at -17, where could K be located?
If there is more than one location, separate them with commas.
Answer:
-7, -27
Step-by-step explanation:
J is at -17. K is 10 units from J.
Start at point J, -17:
a) If you go 10 units to the right, you end up at -17 + 10 = -7
b) If you go 10 units to the left, you end up at -17 - 10 = -27
J can be at -7 or at -27
Answer: -7, -27
Aliaa uses deductive reasoning to identify the number angles that fit inside a circle based on her knowledge that obtuse angles have measures greater than and that there are at the center of the circle. Aliaa wants to partition the circle in 3 congruent angles, what is the angle measurement that best fits Aliaa's circle partition?
Answer:
The best angle measurement that best fits Aliaa's circle partition is three angles of 120° each.
Step-by-step explanation:
The sum of angles at the center of the circle = The sum of angles at a point = 360°
Therefore, to partition the circle into three congruent angles, the measurement of each of the partition should be 360°/3 = 120°
The steps to partition a circle into three are;
1) Draw the diameter of the circle, to intersect the circumference of the circle at points A and B
2) Mark a point, C, at a distance of half the radius from the center of the circle, O, to the point, B, on the circumference, using a straight edge
3) Draw a perpendicular line to the diameter of the circle, through the point, C, to intersect the circle circumference at points D and E)
4) Draw radial lines from the circle center, O, to the points D and E
5) The segments OA, OB, and OE, are segment lines partitioning the segment into three congruent angles.
Can anyone help me with this? (I took a picture of it too)
11. STEM To convert a temperature in degrees Celsius to degrees
Fahrenheit, multiply the Celsius temperature by 9/5 and then add 32°. Is a
temperature in degrees Celsius proportional to its equivalent temperature in
degrees Fahrenheit?
Degrees Celsius
0
10
20
30
Degrees Fahrenheit
132
Answer:
no
Step-by-step explanation:
Whenever a linear equation is something other than
y = kx
the relation is not proportional.
__
Here, you have ...
y = (9/5)x +32
The added constant ensures the relation is not proportional.
Examine the diagrams below. What is the angle pair
relationship between the labeled angles? Use the
relationship to write an equation and solve for x. Then
confirm your answer by calculating the angle measures
of the labeled angles. Show your work in the text box.
✓
a.
3x + 5°
5x - 57°
Answer:
b
Step-by-step explanation:
3
— of -60 please help me!
4
Answer:
-45
Step-by-step explanation:
Rey baked 144 desserts in 6 1/4 months. Find reys dessert making rate in desserts per month.
Answer:
23 1/25 desserts per month
Which equation represents the data: m = -3, b = 5
O y = -3x + 5
O y = x
Oy= 5x - 3
Zero
Answer:
y=-3x+5
Step-by-step explanation:
In the form of y=mx+b
can someone pleaseee help me with explaination
2-3a / 4 >5
THE DASH IS FOR DIVISION SO 2- 3a OVER 4
Answer:
a < -4
I apologise if it is wrong.
3(1 + 7r) + 7r <— please help! :)
Answer: 28r+3
Step-by-step explanation:
3(1+7r)+7r
distributive property
3+21r+7r
combine like terms
28r+3
Answer:
4r/7 is the answer 4r over 7
HELP PLEASE
what is the slope of the function
Answer:
1/2 probably
Step-by-step explanation:
helppp fast!!!10 points!!
Write this series in sigma notation: 5+9+13+17+21+ 25 + 29+ 33.
Answer:
5+9+13+17+21+25+29+33= 152
Answer:
5+9+13+17+21+25+29+33=148
Is 1/2 an irrational number?
Answer:
Yes, 1/2 is a irrational number
Step-by-step explanation:
This is the answer because (Google research):
A number is rational if we can write it as a fraction where the numerator and denominator are both integers. However, numbers like 1/2, 46485928/2628242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.
Hope this helps!
one of the displays at a botanical garden is a koi pond with a walk away around it. The figure who’s the dimensions of the pond and the walkaway?
a) area of pond
b) area of walkaway
GEOMETRY HELP!!
Find the midpoint of AB
It’s Q right?
Answer:yes it’s q
Step-by-step explanation:
8.3 + x= 12.1
I will love you if you can help me!
Answer: x= 3.8
Step-by-step explanation:
21.1 - 8.3 = 3.8
x= 3.8
Answer:
X = 3.8
Explanation: 12.1 minus 8.3 equals the missing value
9x^2 - 16 = (px+t)(px-t) both p and t are constants. Which of the following could be the value of p
Answer:
p = 3
Step-by-step explanation:
9x² - 16 ← is a difference of squares and factors in general as
a² - b² = (a + b)(a - b)
Thus
9x² - 16
= (3x)² - 4²
= (3x + 4)(3x - 4)
Compare with (px + t)(px - t)
then p = 3
can anyone help me it’s algebra 2
Answer:
2.5
Step-by-step explanation:
4x+1=11
4x=11-1
4x=10
x=10/4
=2.5
What is the value of √23
Answer:
Step-by-step explanation:
If you looking for square and square root:
Square: 529
Square root: 4.796 and the longer one,4.79583152331
Which letter represents the first number in an ordered pair?
Step-by-step explanation:
Example: (5,2)
On a graph, the 5 goes on the x-axis and the 2 goes on the y-axis.
Also, in the world of variables, and the alphabet, x is before y.
So x represents the first number in an ordered pair.
hope it helps!
A rectangle has an area of 102cm2. The length of the rectangle is 17 cm. What is the perimeter of the rectangle
Answer:
36
Step-by-step explanation:
To find the with divide 102 by 17, we get 6. Then add 6+6+17+17 because we know this is a rectangle and it has 2 with sides and 2 length sides. We get the answer of 36.
A number múltiple by 0.5 is 12.25. Find the number.
Answer:
24.5
Step-by-step explanation:
n0.5=12.25
n/0.5=12.25/0.5
n=24.5
540 repeated is equal to x/37
Is this true?
Answer:
The answer is x= 19980
Step-by-step explanation:
You do 540 = x/37 ---> then divide by 1/37 on each side and you get --> 19980 = x ---> you can plug it back in and get the right answer. 540 = 19980/37 = --------> 540=540
Find two consecutive odd integers such that seven times the first equals five times the second.
Answer:
Odd integers are always one more that an even integer:
1st: 2n+1
2nd: 2n+3
Step-by-step explanation:
14n+7 = 10n+15
4n = 8
n = 2
------------
1st: 2n+1 = 5
2nd: 2n+3 = 7
7x=5*(x+2)
7x=5x+10
7x-5x=10
2x=10
x=5
5 and 7 are the two consecutive odd integers such that seven times the first equals five times the second.
What are Integers?Integers are the numbers consisting of whole numbers and the negatives of natural numbers.
Let 2n + 1 and 2n + 3 be the two consecutive odd integers.
We have the relation seven times the first integer equals five times the second.
7 (2n + 1) = 5 (2n + 3)
By distributive property,
(7 × 2n) + (7 × 1) = (5 × 2n) + (5 × 3)
14n + 7 = 10n + 15
Taking the terms containing unknowns on one side and constants on other side,
14n - 10n = 15 - 7
4n = 8
n = 8 / 4
n = 2
So the first number = 2n + 1 = (2 × 2) + 1 = 5
and the second number = 2n + 3 = (2 × 2) + 3 = 7
Hence the two consecutive odd integers such that seven times the first equals five times the second is 5 and 7.
To learn more about Integers, click :
https://brainly.com/question/15276410
#SPJ2
Tell me the linear equation for point-slope form?
solve for the equation 6x+14=7x+8
Answer:
x = 6
Step-by-step explanation:
For this problem, we simply will isolate the x to find the value of x:
6x + 14 = 7x + 8
6x + -6x + 14 = 7x + -6x + 8
14 = x + 8
14 + -8 = x + 8 + -8
6 = x
Hence, x = 6.
Cheers.
Answer:
x=6
Step-by-step explanation:
First, subtract 6x from both sides to get:
14=x+8
Now, subtract 8 from both sides to get x alone:
6 = x