Step-by-step explanation:
Quadratic Equation
Quadratic equation is in the form
ax2+bx+c=0
Where
a, b, & c = real-number constants
a & b = numerical coefficient or simply coefficients
a = coefficient of x2
b = coefficient of x
c = constant term or simply constant
a cannot be equal to zero while either b or c can be zero
Examples of Quadratic Equation
Some quadratic equation may not look like the one above. The general appearance of quadratic equation is a second degree curve so that the degree power of one variable is twice of another variable. Below are examples of equations that can be considered as quadratic.
1. 3x2+2x−8=0
2. x2−9=0
3. 2x2+5x=0
4. sin2θ−2sinθ−1=0
5. x−5x−−√+6=0
6. 10x1/3+x1/6−2=0
7. 2lnx−−−√−5lnx−−−√4−7=0
For us to see that the above examples can be treated as quadratic equation, we take example no. 6 above, 10x1/3 + x1/6 - 2 = 0. Let x1/6 = z, thus, x1/3 = z2. The equation can now be written in the form 10z2 + z - 2 = 0, which shows clearly to be quadratic equation.
Roots of a Quadratic Equation
The equation ax2 + bx + c = 0 can be factored into the form
(x−x1)(x−x2)=0
Where x1 and x2 are the roots of ax2 + bx + c = 0.
Quadratic Formula
For the quadratic equation ax2 + bx + c = 0,
x=−b±b2−4ac−−−−−−−√2a
See the derivation of quadratic formula here.
The quantity b2 - 4ac inside the radical is called discriminat.
• If b2 - 4ac = 0, the roots are real and equal.
• If b2 - 4ac > 0, the roots are real and unequal.
• If b2 - 4ac < 0, the roots are imaginary.
Sum and Product of Roots
If the roots of the quadratic equation ax2 + bx + c
= 0 are x1 and x2, then
Sum of roots
x1+x2=−ba
Product of roots
x1x2=ca
You may see the derivation of formulas for sum and product of roots here.
A Toy Story poster is enlarged. The new length is 5 feet and the width is 3 feet. The original length was 6 inches what was the width?
bob can draw 14 shapes in 7 minutes how long does it take bob to draw 28 shapes at the same rate
Answer: 14 minutes
Step-by-step explanation:
Because 28 ÷ 2 is 14.
We have to divide the number Bob has to draw by the number of minutes.
We multiply the number of minuted by 2.
Answer is 14
Answer:
14 minutes
Step-by-step explanation:
We can use ratios to solve
14 shapes 28 shapes
---------------- = ----------------
7 minutes x minutes
Using cross products
14x = 28*7
Divide each side by 14
14x/14 = 28*7/14
x = 14
14 minutes
Able has a younger sister and an older brother.
- Able’s age can be represented by x.
- Able’s sister is 4 years younger than him.
- Able’s older brother is twice as old as he is.
- The combined age of all three siblings is 32.
How old is Able’s younger sister?
9 years
13 years
5 years
3 years
Answer:
5 years
Step-by-step explanation:
1. if able's age is x, then his sister's is x-4, and his brother's is 2x
2. if these sum to 32, then we can formulate the equation x+(x-4)+2x=32
3. now solve for x, 4x-4=32, 4x=36, x=9
4. if able's sister is x-4 years old, she is 9-4, or 5 years old
Is -3/4 rational or irrational
Answer:
Rational
Step-by-step explanation:
The fraction -3/4 can be written as a ratio, and is a finite amount, making it rational.
Calculate (2.2 x 10^2 g^3) (2.8 x 10^3 g) put it into standard notation please
Answer:
5
Step-by-step explanation:
Whats 0.52 / 0.0013?
Answer:
400
Step-by-step explanation:
Use a calculator if you don’t believe me
Please help giving 10 points!
Which statements about the graphs of the equations y = 2x + 4 and y = −x + 4 are true? Select all that apply.
A. The graphs intersect the x-axis at the same point.
B. The graphs intersect the y-axis at the same point.
C. The graphs have different slopes.
D. The graphs are parallel lines.
Answer:
The answer is B and c.
Step-by-step explanation:
first thing you need to do is look at slopes
the slopes are different then look at the y intersects there the same
and finally they both intersect at the same point.
the correct answer is B and C.
Will give brainliest will give brainliest will give brainliest and 60 think point
Answer:
∠3 and ∠2
Step-by-step explanation:
Adjacent angles are angles that have a common side and common vertex which each other.
The first option is incorrect because they don't share a common side. They do share a vertex but that isn't enough to call them adjacent.
The second option is correct because they share a common side and vertex.
The third option is incorrect because they don't share a common side.
The fourth option is incorrect because they don't share a common side. These two angles are congruent and opposite angles.
Best of Luck!
Answer:
3
Step-by-step explanation:
Can someone help me? It's only 2 questions and I will give you 20 points and brainliest!
Answer:
Dont worry about me, I just added this answer so the other person can get their brainliest because they definetly deserve it
Step-by-step explanation:
Proving Triangles congruent: ASA, AAS, SAS SSS
Cate:
For each problem give the correct naming order of the congruent triangles Write that name in order on the
lines for the problem number (see box at bottom) Aso indicate which postulate or theorem is being used
2
AVAVAV
N
ASC.
ABC a
by
LABCO
Answer:
WIR by SAS
EHS by AAS
GTN by SSS
What is the slope of this graph?
A. −4
B. −14
C. 14
D. 4
(picture down below)
5) 2-X = 15
Find the value of x
Answer:
x= -13
Step-by-step explanation:
-x= 13
x=-13
Answer:
13 urgupieux8ttc9y d6 og
Is the difference of 18 and 3 a rational number?
Answer:
it is a whole number but because rational numbers include all intergers and whole numbers it is also a rational number
Step-by-step explanation:
Plz help
2.
The midpoint of AB is M. If the
coordinates of M are (,-2) and
the coordinates of B are (6,1),
what are the coordinates of A?
a) (-5,-5)
b) (2, -10)
c) (-10, 2)
d) (-13/4,-3/2
e) (-5,5)
Answer:
A
Step-by-step explanation:
the distance between M and point be is 5.5 for the x coordinate and 3 for the y coordinate. to find point b you added 5.5 to to the x and 3 to the y so if you subtract this from point M you get (-5,-5).
Evaluate the function f(x) = sec(x - ) for x = 0.
Can someone please help me with these 50 points I just don't get it I need help?
Answer: I think the first one is A. and the next one is B
Step-by-step explanation:
4x-6>6x-20 solve for the inequality
Answer:
x < 7
Step-by-step explanation:
4x - 6 > 6x - 20
Add 6 to both sides.
4x - 6(+6) > 6x -20(+6)
Simplify.
4x > 6x - 14
Subtract 6x from both sides.
4x(-6x) > 6x(-6x) - 14
Simplify.
-2x > -14
Multiply both sides by -1 (reverse the inequality).
(-2x)(-1) < (-14)(-1)
Simplify.
2x < 14
Divide both sides by 2.
2x/2 < 14/2
Simplify.
x < 7
5(2x-3)=24
Help me in this pleasee
Answer:
x = 3.9
Step-by-step explanation:
5(2x-3)=24
Distribute
10x -15 = 24
Add 15 to each side
10x-15+15 = 24+15
10x = 39
Divide each side by 10
10x/10 = 39/10
x = 3.9
OK, this question is a little complicated. Solve v, 5/v=7.25
Answer:
Hope this helps you .....
Answer:
[tex]v=\frac{145}{8}[/tex]
Step-by-step explanation
[tex]\frac{5}{v}=\frac{2}{7.25}[/tex]
[tex]\frac{5}{v}=\frac{2}{\frac{725}{100}}[/tex]
[tex]v=\frac{2}{\frac{5^2*29}{2^2*5^2}}[/tex]
[tex]v=\frac{145}{8}[/tex]
what is 2.6 divided by 0.4
Answer:
6.5
Step-by-step explanation:
Jeff earns money mowing lawns. His earnings and hours worked represent a direct variation. He worked for 5 hours and earned $37.50. Determine the constant of proportionality for dollars earned per hours worked and for hours worked per dollars earned.
Answer:
Jeff earns $7.50 dollars per hour
Step-by-step explanation: Just divide $37.50 and 5.
Which table shows a proportional relationship ?? Pls help
Answer:
Option 2
Step-by-step explanation:
If you multiply 2 by 2 you get 4. If you multiply 3 by 2 you get 6. If you multiply 4 by 2, you get 8. If you multiply 5 by 2 you get 10. A proportional relationship is where you can multiply all the numbers by a certain number to get the answer. In this case, all the numbers in the left column could get multiplied by 2 to get the number in the right column.
The next train will arrive in 32 minutes and 30 seconds.
In how many seconds will the next train arrive?
Answer:
1950 seconds
Step-by-step explanation:
if sixty seconds are in a minute, then you just multiply 32, the number of minutes by the number of seconds in a minute and add 30.
Need help ASAP
Please
Answer:
area:[tex]16x^2+24x+9[/tex] Perimeter: 16x+12
Step-by-step explanation:
area :[tex](4x+3)^2[/tex]
thats [tex]16x^2+24x+9[/tex]
P: 4(4x+3)
thats 16x+12
Hope this helped you
<3
Red
Answer:
Perimeter is all sides added together, while Area is one side height times length
Step-by-step explanation:
Since your shape is a square all sides are equal so the equation is the same for all sides
Perimeter = 4z+3+4z+3+4z+3+4z+3 or (4z+3)4
14z+12 <= answer for perimeter
Area = (4z+3) (4z+3)
16z^2+12z+12z+9
16z^2+24z+9 <= answer for area
You typed a 600 word essay in 12 minutes. Let w be the number of words you can type in one minute. Can w be 60?
Answer:
w = 50
Step-by-step explanation:
600 = 12w
600/12 = 12/12w
w = 50
An Ice cream machine fills cartons at a rate of 1440 pints per hour. How many gallons are filled per minute? 1 gal is equal to 8 pints.
Answer:
that will be 3 gallons per minute
Step-by-step explanation:
just took it on a test
Suppose you had two circular objects. Let the first circular object have a diameter of 26 cm and let second circular object have a diameter that is half as long as the diameter of the first. What would the circumference be for the second item in centimeters?
Answer:
its sonar
Step-by-step explanation:
h bug
I HAVE 5 MINUTES PLZ HELP ! (its a slope problem)
Answer:
-1/4
Step-by-step explanation:
Simply draw a slope triangle
Answer:
its -1/4 which is the third option
Step-by-step explanation:
negative because it's going down, 1/4 because every four blocks to the right it goes down by only one block
Which of the following can you add/subtract?
A) 5√4 + 6√4
B) 3√7 − 3√5
C) 9 √ + 39√
Answer:
A
Step-by-step explanation:
you can only +/- an equation like this with the same square root
John purchased a carr in 1961 for $12,000. Experts estimate that its value will increase by 5% per year. How much will be the cost of the car after 22 years
A- 35103$ B- 27600$
C- 10000$ D- 30105$
Answer:
A- 35103$
Step-by-step explanation: