Answer:
Lets say there's a quadratic equation → ax² + bx = -c
Lets make one side zero which gives → ax² + bx + c = 0
From the above equation ,
if you can split b into 'p' & 'q' (some real numbers) such that p + q = b & pq = ac ; then the quadratic equation can be easily solved by using factorisation method. Here the easiest way to guess the values of 'p' & 'q' is to find out the prime factors of 'ac' and taking any two prime numbers in random , just check whether the sum of those two primes is equal to 'b' (excluding their signs).if you can't split b into 'p' & 'q' (some real numbers) such that p + q = b & pq = ac ; then try solving quadratic equation by completing the squares method.For example :- x² - 12x = -35.
Lets make one side zero → x² - 12x + 35 = 0 . Now, lets break -12x into two real numbers 'p' & 'q' such that p + q = -12x & pq = 35. Prime factors of 35 are 1 , 5 & 7. If we take 5 & 7 as 'p' & 'q' then p + q = 5 + 7 = 12. but as we need -12 , the values of 'p' & 'q' are -5 & -7.
⇒ [tex]x^2 -5x - 7x + 35 = 0[/tex]
⇒ [tex]x(x - 5) - 7(x - 5) = 0[/tex]
⇒ [tex](x - 5)(x - 7) = 0[/tex]
⇒ [tex]x = 5 \: or \: 7[/tex]
Lets take another example :- x² + 4x = 1.
Lets make one side zero → x² + 4x - 1 = 0 . Now , lets split +4x into into two real numbers 'p' & 'q' such that p + q = +4x & pq = -1 . Prime factors of 4 are 1 & 2 only. But there's no such combination of its primes such that their sum would be equal to 4. So, the quadratic equation can't be solved by factorisation method. Now, lets bring -1 to Right Hand Side & try solving by completing squares method.
⇒ [tex]x^2 + 2 \times x \times 2 + 2^2 = 1 + 2^2[/tex]
⇒ [tex](x + 2)^2 = 1 + 4 = 5[/tex]
⇒ [tex]x + 2 = +\sqrt{5} \: \: or \: -\sqrt{5}[/tex]
⇒ [tex]x = (\sqrt{5} - 2) \: or \: (-\sqrt{5} -2)[/tex]
Conclusion:
First try making one side zero and try to solve the equation by factorisation method. If it got factorised , then you are done and if it didn't get factorised , then solve it by completing squares method.
Answer:
I'm assuming we're asking about the difference between:
[tex]ax^2 + bx + c = 0[/tex]
and
[tex]ax^2 + bx = -c[/tex]
Let's preface this by stating the obvious: there's no actual difference. Both equations are equivalent.
Now, it has a lot to do with our goal. Sometimes our goal is to write an equation concisely (then the "no-zero" way uses less characters), and sometimes we're dealing with a quadratic function of
[tex]y = ax^2 + bx + c[/tex]
in the second case, we wouldn't write
[tex]y - c = ax^2 + bx[/tex]
because it'd be confusing. That means that when we're looking for y=0 points of a quadratic equation, the way to convey that goal is that we're looking for the point where [tex]ax^2 + bx + c = 0[/tex] - so we preserve the structure of the quadratic function.
Round your answer to the nearest hundredth.
Answer:
take 20 degree as reference angle
let hypotenuse be x
using cos rule
cos 20=adjacent/hypotenuse
0.93=7/x
0.93*x=7
x=7/0.93
x=7.5
Step-by-step explanation:
Which of the following best describes Y on the scatter plot below?
A.
positive association
B.
outlier
C.
cluster
D.
nonlinear association
Solve the following system of equation using any method.
3x+3y=12
2x+4y=16
X = and Y=
Answer:
X=0
Y=4
Step-by-step explanation:
3x=12-3y
x=4-y
Plug 4-y in for x in the other equation:
2(4-y)+4y=16
8-2y+4y=16
2y=8
y=4
If x=4-y and y=4, x=4-4=0
#6. Find the volume of the cone. Use 3.14 for Pi and round to the nearest
tenth. *
DO NOT PUT A LINK!!!
Answer: D
Step-by-step explanation:
Plug in 0 for each variables in the equation and see which one holds true
Hope this helps
On three successive plays, a quarterback was sacked for a total loss of more than 19 yards. What describes the number of yards gained
A. more than B. less than
please help answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!! ASAP !!!!!!!
Answer:
16.9°
Step-by-step explanation:
tan x = 1.7/5.6
tan^-1 x = 16.9°
Which equation has a graph that is a parabola with a vertex at (-2, 0)?
O y=-22²
O y = (x + 2)2
O y = (x - 2)2
Oy=x²-2
Answer: y = (x+2)^2
Aka: B
Step-by-step explanation:
Did it on edge just now !
The equation y = (x + 2)² has a graph that is a parabola with a vertex at
(-2, 0).
Option B is the correct answer.
What is a parabola?A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.
The equation of a parabola:
y = a(x-h)^2 + k
We have,
The equation that has a graph that is a parabola with a vertex at (-2, 0) is
y = (x + 2)².
The general equation for a parabola is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Comparing this general equation to y = (x + 2)²,
We can see that h = -2 and k = 0, which means that the vertex of the parabola is (-2, 0).
Therefore,
The equation y = (x + 2)² has a graph that is a parabola with a vertex at
(-2, 0).
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Give me authentic answers please.
Find the volume (and show work)
Please help will mark brainliest
Answer:
D,C,E IS CORRECT
Step-by-step explanation:
Hi! Does anyone know the answer to this question? I’m bad at geometry and I’m struggling to get the answer. Please help!
if i understand the question it's 25
Step-by-step explanation:
6/21 equal 10/10+x
info x is GJ
6x=150
x=25
i used the similarity in trangle formula because he sayed that FG is parelel to HJ
Which transformation produces another triangle that has the same area as the one shown?
A clockwise rotation of 180' about the origin, then a
dilation by scale factor 2
3
2
A reflection in the line y = -2, then a translation of
2 units right.
1
Р
-4 -3
-2
11
Z
-10
-1
Q4%
A clockwise rotation of 90 about the origin, then a
dilation by scale factor 4.
-2
R
-3
A dilation by scale factor then a translation of
4 units up.
Answer:
A reflection in the line y = -2, then a translation 2 units right.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Rigid transformation are transformation that preserves the shape and size of the object. Rotation, reflection, translation are rigid transformation whereas dilation is not a rigid transformation.
Any transformation regarding dilation changes the side length of the object and hence the area.
From the question, only one option is right. The rest options are not right because they involve dilation. The correct option is:
A reflection in the line y = -2, then a translation 2 units right.
A fish tank, shaped as a cube, has a volume of 36 liters, or 2, 197 in What are the dimensions of the fish
tank in inches? Use paper to show your work.
Alex bought some crayon pens and sketch pens in the ratio of 7:4.
Each crayon pen cost $2.
Each sketch pen cost $2 more than each crayon pen.
He spent a total of $360 on these crayon pens and sketch pens.
How much did he spend on the crayon pens he bought?
Answer:
$168.
Step-by-step explanation:
1 group of 7 crayon pens and 4 sketch pens = 7 x 2 + 4 x (2 + 2) = 14 + 4 x 4 = $30
Number of groups = 360/30 = 12
12 x 7 x 2 = 168
He spent $168 on the crayons.
Jenny needs 1/2 of a stick of butter for a recipe. She cuts the half stick of butter into four equal pieces what portion of the whole stick of butter is each of the pieces I need to show my work plz
Answer:
1/16
Step-by-step explanation:
1/2 of 1/2 is 1/4 then 1/4 of 1/4 is 1/16
If Janie cuts half a stick of butter into four equal pieces, one-eighth (1/8) portion of the whole stick of butter is in each of the pieces.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
It is given that Jenny needs 1/2 of a stick of butter for a recipe. She cuts the half stick of butter into four equal pieces.
The portion of the whole stick of butter in each of the pieces is found as,
= (1/2) / 4
=1/8
Thus, if Janie cuts half a stick of butter into four equal pieces, one-eighth (1/8) portion of the whole stick of butter is in each of the pieces.
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how do you give bainlist
The Image below show kite ABCD that lie on E
Answer:
[tex]m(DAB)=228^o[/tex]
[tex]m[/tex]∠[tex]BCD=48^o[/tex]
[tex]m[/tex]∠[tex]ABC=123^o[/tex]
Step-by-step explanation:
[tex]Given:[/tex]
m∠BAD=66°
m BD =2(m∠BAD)
= 2(66)
m BD=132°
m DAB= 360° - 132°
m(DAB) = 228°
-------------------
m∠BCD= 1/2(m DAB -m BD)
= 1/2(228- 132)
m∠BCD= 48°
-------------------
m∠ABC= 360-(66+48)/2
= 360 -114/2 = 246/2
m∠ABC=123°
----------------------------------
hope it helps...
have a great day!!
7 students have 8 books each. Which helps you find the total number of books?
Answer:
21 Books in total
Step-by-step explanation:
If you just want the total number of books, here:
If each student has 3 books, and there are 7 students, we can create the equation: 7 * 3 :because this is showing that 7 people each have 3 books
7 * 3 = 21 so There are 21 books in total
Another we could write it is 3 + 3 + 3 + 3 + 3 + 3 + 3 because there are 7 students with 3 books each. Adding this up would equal 21.
A company models its net income, in thousands of dollars, with the function f(x)=9x2−54x−144 , where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0?
The company needs to sell 8 units in order for the net income to equal $0
The net income function is given as:
[tex]f(x) = 9x^2 - 54x - 144[/tex]
When the net income is 0, then f(x) = 0.
So, we have:
[tex]9x^2 - 54x - 144 = 0[/tex]
Divide through by 9
[tex]x^2 - 6x - 16 = 0[/tex]
Expand the above equation
[tex]x^2 +2x- 8x - 16 = 0[/tex]
Factorize the above equation
[tex]x(x +2)- 8(x + 2) = 0[/tex]
Factor out x + 2 in the above equation
[tex](x - 8)(x + 2) = 0[/tex]
Split and solve for x
[tex]x = 8[/tex] or [tex]x =-2[/tex]
The units of product cannot be negative.
So, the value of x is [tex]x = 8[/tex]
Hence, the company needs to sell 8 units
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DETERMINE WHICH OF THE ANGLE MEASURES BELOW CORRECTLY
SATISFY THE MISSING VALUE, X, IN EACH DIAGRAM.
Each day, Robert eats 40% of the pistachios left
in his jar at that time. At the end of the second
day, 27 pistachios remain. How many pistachios
were in the jar at the start of the first day?
Answer:
At the beginning of the first day there were 75 pistachios in the jar.
Step-by-step explanation:
Given that each day, Robert eats 40% of the pistachios left in his jar at that time, and at the end of the second day, 27 pistachios remain, to determine how many pistachios were in the jar at the start of the first day you must perform the following calculations:
100 - 40 = 60
60 = 27
100 = X
100 x 27/60 = X
2700/60 = X
45 = X
60 = 45
100 = X
100 x 45/60 = X
4500/60 = X
75 = X
Therefore, at the beginning of the first day there were 75 pistachios in the jar.
Find the image of the given point
under the given translation.
P(-3,-3)
T(x,y) = (x -8, y-3)
P' = ([?], [])
Answer:
Step-by-step explanation:
p(-3,-3)
here x is -3 and y is also -3 so
p(-3,-3)=p'(x-8,y-3
=p'(-3-8,-3-3)
=p'(-11,0)
what is 434 miles in 7 hours as a rate
Answer:
420 miles/7 hours = 60 miles per hour.
Answer:
62 miles and hour
Step-by-step explanation:
Find the value of 7w-2 given that - 2w-4=6 .
Simplify your answer as much as possible.
(help me out :|)
Answer:
w= -5
Step-by-step explanation:
-2w - 4 = 6-2w - 4 + 4 = 6 + 4-2w = 10Isolate "w":
[tex]\frac{-2w}{-2} = \frac{10}{-2}[/tex] w = -5Given:BK=CH Which additional congruence statement could you use to prove that ∆BJK ≅ ∆CFH by the HL Theorem?
Answer:
B
Step-by-step explanation:
The hl theorem says that if we have two right triangles that have a congruent hypotenuse and a congruent leg, the two triangles are congruent
in this case the exercise says the two leg are congruent, so we have to say that the two hypotenuse are congruent
So
JB congruent to FC
PLZZZ HURRY!!
What is the series in summation notation?
Answer:
A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum. The series 4+8+12+16+20+24 can be expressed as 6∑n=14n . The expression is read as the sum of 4n as n goes from 1 to 6 .
Step-by-step explanation:
I hope it's help u
Answer:
the answer is B
Step-by-step explanation:
i got your back
Researchers give one group a new cold medicine and compare them with to a group that takes no medicine. what is the group that is not given any medicine?
A. the control group in an experiment
B. the experimental group in a survey study
C. the experimental group in an experiment
D. the control group in an observational study
Answer:
A. the control group in an experiment
Step-by-step explanation:
Researchers give one group a new cold medicine and compare them with to a group that takes no medicine. The group that is not given any medicine is the control group in an experiment.
Who are researchers?Researchers are those who do research on something i.e. systematics and deep investigation into something.
What is control group?Control Group is that group in research which does not take any medication or untreated group.
During the research while a new type of medicine is to be tested, the group that receives the medication or being tested is called the experimented group and the group that does not receive the treatment is called the control group.
Hence, we can say that the group that is not given any medicine is the control group in an experiment.
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NO IDEA HELP PLS SO CONFUSING
Answer:
1. slope formula?
2. (0,6)
3. y= -3x+6
Step-by-step explanation:
because the original formula to make a like is y=mx+b.
just plug the values you have into the equation knowing that m is the slope and b is the y intercept.
the slope would be rise/run which in this case the rise is -6 and the run is 2.
so m= -6/2 = -3
and b = 6 because x is 0 when y is 6 for this graph.
(btw I put -6 as the rise because you are going down 6 units instead of going up)
Need help with #6
Find the missing angles
Answer:
p = 95
q = 95
r = 85
s = 85
Step-by-step explanation:
85 deg & p are same-side int angles & are supplementary.
p = 180 - 85 = 95
p & q are vertical & congruent.
q = 95
p & s are supplenmentary.
s = 85
s & r are alt int angles & congruent.
r = 85