How can you use factoring to solve quadratic equations in standard form?
Step-by-step explanation:
The roots or the zeroes of a quadratic equation are its x-intercepts, which are the points on the graph where it crosses the x-axis. When a quadratic equation is in standard form, ax² + bx + c, the usual goal is to find the binomial factors that could help us determine the roots or solutions to the given equation. Once you find the factors, then you will use the Zero-Product Property to solve for the solutions.
For example, if you were given the following quadratic equation in standard form, x² + 6x + 8 = 0, and were tasked to find its factors.
x² + 6x + 8 = 0
where a = 1, b = 6, and c = 8:
In order to find the factors of the given quadratic equation, we must find the factors with a product ac, and sum b.
Using 2 and 4 as possible factors produce a product that is equal to
product of ac: 2 × 4 = 8
sum of b: 2 + 4 = 6.
Therefore, the factors of the given quadratic equation, x² + 6x + 8 = 0 are:
(x + 2) (x + 4).
Using the Zero-Product Property, where it states that for any real numbers, u and v, if uv = 0, then u = 0 or v = 0.
Thus, setting the binomial factors of the given quadratic equation to zero will provide the solutions.
(x + 2) (x + 4)
x + 2 = 0
x + 2 - 2 = 0 - 2
x = -2
x + 4 = 0
x + 4 - 4 = 0 - 4
x = -4
Therefore, the solutions to the quadratic equation, x² + 6x + 8 = 0 are x = -2, and x = -4.
Write the inequality.
The sum of negative 3 and a number is no more than two
Answer: -3+x<2
Step-by-step explanation: can't be greater than 2.
HELP!!
Lenor and Juan go to school together after leaving school Lenor drove 12 miles to get to his house and Juan drove 35 mile
get to his house. Based on the picture below what is the shortest distance from Lenor's house to Juan's house. (show your
for full credit)
a= distance Lenor drove
Lenor
b distance Juan drove
c=distance between
Lenor and Juan
Juan
graph using the slop and y intercept
Answer:
the slop is -1/2 and they y intercept 2
Identify the vertex of the parabola represented by the equation y=−2x2+8x−1.
(−4, −65)
(4, −1)
(2, 7)
(−2, −25)
Answer:
it is correct but -65 is not correct
Second derivative of -2x^2+2/(x^2+1)^2
Answer:
\frac{-2x^2+2}{x^4+2x^2+1}
2x^2+2
-------------
x^4+2x^2+1
You rent an apartment that costs $1000 per month during the first year, but the rent
is set to go up $160 per year. What would be the monthly rent during the 10th year of
living in the apartment?
Answer: In the tenth year your rent would be 2440 a month.
Hope this helps!
15. Describe and correct the error in finding the intercepts of the graph of the equation.
Х
6x + 9y
= 18
6x + 9(0) = 18
6x = 18
6x + Oy 18
6(0) + 9y = 18
9y =
= 18
X = 3
y = 2
The x-intercept is at (0,3), and the y-intercept is at (2, 0).
Answer:
Wrong order!
Step-by-step explanation:
There's a reason why coordinates are called an "ordered pair", and for every point (a, b) a is the x coordinate and b is the y coordinate. The calculations are correct, the way reporting them are not: the point should be (3.0) and (0,2) - in fact, all points on the x axis are of the form (p, 0) and all points on the y axis of the form (0,q)
please help solve for RN
Answer:
I guess...
Step-by-step explanation:
Since QR and PN are parallels, I think what happens in MN and MP is proportional, so:
RN = x
8 is to 10 as
5 is to x
8 * x = 5 * 10
8x = 50
x = 50 / 8
x = 6.25
RN = 6.25
What have you learned about geometric relationships?
PLEASE HELP 15 POINTS
Answer:
that you can define a tangent relationship between a line and an arc. If the adjoining elements change, the tangent relationship is maintained between the elements. Geometric relationships control how a sketch changes when edits are made.
Step-by-step explanation:
i took this i guess and it was gud
Work out the nth term of the following sequence:
7, 16, 31, 52, 79
its a quadratic sequence and i worked out the second difference (6) so know its 3n² but i don't know the rest
Answer:
Step-by-step explanation:
Since it is given that it is quadratic it is of the form f(n)=an^2 + bn+c.
Since we know a few terms we can plug in to get some equations:
f(1)= a +b+c = 7
f(2)=4a+2b+c = 16
f(3)=9a+3b+c = 31
Now you've got yourself a system of three equations which I trust you can solve.
I will say that I'm not sure that this is the most efficient solution(check out the link below which might have a better solve).
Here are some nice explanations with the "real" math notation for a slightly different but related problem:
https://math.stackexchange.com/questions/2345256/how-to-find-the-nth-term-of-quadratic-sequences
Good luck!
If the circumference of full circle is equal to 2 cm, find the length of the arc of the composing semicircle
Answer:
it is 1 cm because semi means half
If the length of each side of a cuboid decreases by 20%, find the percentage decrease in its volume.
Solution : (Identify the ratio of the length of one edge of the original cuboid and the length of one edge of the new cuboid)
Answer:
Step-by-step explanation:
(1+25 /100) (1-20/100) (1-50/100) <1
5/4 x 4/5 x 1/2 <1
Decrease in volume (in percent)
(1+25 /100) (1-20/100) (1-50/100) x 100
=48.8%
Which of the following describes the transformation from Figure 1 to Figure 2? On a coordinate plane, figure A B C D E has points (negative 3, 5), (negative 2, 5), (negative 1, 4), (negative 2, 3), (negative 5, 3). Figure A prime B prime C prime D prime E prime has points (2, 2), (3, 2), (4, 1), (3, 0), (0, 0). CLEAR CHECK translation 2 units to the right and 3 units down translation 3 units to the left and 2 units up translation 5 units to the right and 3 units down translation 5 units to the left and 3 units up
Answer:
a
Step-by-step explanation:
The transformation from Figure 1 to Figure 2 is:
The transformation of 5 units to the right and 3 units down.
Option C is the correct answer.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
A B C D E has points (-3, 5), (-2, 5), (-1, 4), (-2, 3), and (-5, 3).
A' B' C' D' E' has points (2, 2), (3, 2), (4, 1), (3, 0), and (0, 0).
Now,
A = (-3 + 5, 5 - 3) to A' = (2, 2)
B = (-2 + 5, 5 - 3) to B' = (3, 2)
C = (-1 + 5, 4 - 3) to C' = (4, 1)
D = (-2 + 5, 3 - 3) to A' = (3, 0)
E = (-5 + 5, 3 - 3) to E' = (0, 0)
We see that,
There is a translation of 5 units to the right and 3 units to the down.
Thus,
The transformation of 5 units to the right and 3 units down.
Learn more about translation here:
https://brainly.com/question/12463306
#SPJ1
On an airplane the passengers may have chicken vegetable or tomato soup
Half of the passengers choose the Chicken soup
A third of the passengers choose tomato soup
What fraction of the passengers chose soup?
There are 240 passengers on the airplane
How many passengers chose vegetable soup?
How many 2 digit numbers have unit digit 6 but are not perfect squares
9514 1404 393
Answer:
7
Step-by-step explanation:
Of the 9 2-digit numbers ending in 6, only 2 are perfect squares: 16 and 36. The other 7 are not perfect squares.
There are 5 boxes and each box weighs x pounds. Write the expression for the total weight of the
boxes.
Answer:
5x pounds
Step-by-step explanation:
Here's the solution if you need, hope it's help
HELP WILL GIVE THE MOST POINTS IT LETS ME NEED ANSWER SOON
Answer:
c. -5x - 2 = -42
Step-by-step explanation:
Have a nice day! :-)
Answer:
-5x-2 = -42
Step-by-step explanation:
less than means you do this after what comes next
Product of a number and -5
-5x
Two less than
-5x -2
is means equals
-5x-2 = -42
When determining domain it is important to work from
Answer:
use graphs
Step-by-step explanation:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
ABCD is a parallelogram and X and Y are any point on CD and AD respectively. Prove that triangle AXB and triangle BYC are equal in area. Prove that
Answer:
See answer below
Step-by-step explanation:
ABCD is a parallelogram Given
BC ≅ AD; AB ≅ DC opposite sides of a parallelogram ≅
Δ AXB = 1/2 (AB)(AD) Formula for the area of a Δ
Δ BYC = 1/2 (BC) (DC) Formula for the area of a Δ
1/2 (AB)(AD)= 1/2(BC)(DC) Substitution
∴ Area of Δ AXB = Area of ΔBYC
FInd the value of T - triangle measerments
JK=JH
[tex]\\ \sf\longmapsto 10t=7t+15[/tex]
[tex]\\ \sf\longmapsto 10t-7t=15[/tex]
[tex]\\ \sf\longmapsto 3t=15[/tex]
[tex]\\ \sf\longmapsto t=15/3=5[/tex]
Write the equation of the line with x-intercept 3 and passing through the point (5.4)
Answer: y=(1/5)m+3
Step-by-step explanation:
Start with the standard form of an equation of a straight line: y=mx+b, whre m is the slope and b the y-intercept (the value of y when x=0).
y=mx+b
We know b (3), so:
y=mx + 3
To find the slope, m, we can use the one given point, (5,4):
y=mx + 3 for (5,4) would be:
4 = m*5+3
1 = 5m
m = (1/5)
y=(1/5)m+3
A box of cereal states that there are 84 calories in a 3/4
-cup serving. What is the unit rate for calories per cup?
Answer:
It is 112 calories per cup of cereal.
Step-by-step explanation:
multiply 3/4 by 4 and youll get 3 and them multiple 84 by 4 and you'll get 336. Divide 336 by 3 and youll get your answer.
the ball started at the 5 yard line. what is the position of the ball after these two plays
Answer:
you have to show a diagram or I can't help you
$4 is what percent of 50
Answer:
8%
Step-by-step explanation:
4/50 = 0.08 = 8%
Steps to solve "what percent is 4 of 50?" If you are using a calculator, simply enter 4÷50×100 which will give you 8 as the answer.
Plz help fast.
I will mark Brainlyist
solve pls brainliest
Answer:
y=15x
Step-by-step explanation:
Plug in the numbers given and the equation works.
answer please help me out
Answer:
Hey just search up an algebraic calculator I finished my homework with it lol
Step-by-step explanation:
A line passes through point A (12,18). A second point on the line has an x-value that is 125% of the x-value of point A and a y-value that is 75% of the y-value of point A . Use point A to write an equation of the line in point-slope form.
The answer is 18, 0
You gotta trust me
Please help asap! I will give brainliest for correct answer!
Answer:
0.01miles/day
Step-by-step explanation:
1: Convert 9cm to miles
[tex]9cm*(\frac{1m}{100cm})*(\frac{1km}{1000m})*(\frac{1mile}{1.609km})=0.000055935miles[/tex]
2: Convert 5.5 minutes to days
[tex]5.5minutes*(\frac{1hour}{60minutes})*(\frac{1day}{24hours})=0.003819444 days[/tex]
3. Set miles over days
[tex]\frac{0.000055935miles}{0.003819444days}[/tex]
4: Divide to get the answer
0.014644 miles/day
5: Round to get the final answer
0.01 miles/day
