Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*x^2+2*x^2+4-(-6*x)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
(((3 • (x2)) + 2x2) + 4) - -6x = 0
STEP
2
:
Equation at the end of step
2
:
((3x2 + 2x2) + 4) - -6x = 0
STEP
3
:
Trying to factor by splitting the middle term
3.1 Factoring 5x2+6x+4
The first term is, 5x2 its coefficient is 5 .
The middle term is, +6x its coefficient is 6 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 5 • 4 = 20
Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is 6 .
-20 + -1 = -21
-10 + -2 = -12
-5 + -4 = -9
-4 + -5 = -9
-2 + -10 = -12
-1 + -20 = -21
1 + 20 = 21
2 + 10 = 12
4 + 5 = 9
5 + 4 = 9
10 + 2 = 12
20 + 1 = 21
Equation at the end of step
3
:
5x2 + 6x + 4 = 0
STEP
4
:
Parabola, Finding the Vertex:
4.1 Find the Vertex of y = 5x2+6x+4
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 5 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -0.6000
Plugging into the parabola formula -0.6000 for x we can calculate the y -coordinate :
y = 5.0 * -0.60 * -0.60 + 6.0 * -0.60 + 4.0
or y = 2.200
Solve Quadratic Equation by Completing The Square
4.2 Solving 5x2+6x+4 = 0 by Completing The Square .
Divide both sides of the equation by 5 to have 1 as the coefficient of the first term :
x2+(6/5)x+(4/5) = 0
Subtract 4/5 from both side of the equation :
x2+(6/5)x = -4/5
Now the clever bit: Take the coefficient of x , which is 6/5 , divide by two, giving 3/5 , and finally square it giving 9/25
Add 9/25 to both sides of the equation :
On the right hand side we have :
-4/5 + 9/25 The common denominator of the two fractions is 25 Adding (-20/25)+(9/25) gives -11/25
So adding to both sides we finally get :
x2+(6/5)x+(9/25) = -11/25
Adding 9/25 has completed the left hand side into a perfect square :
x2+(6/5)x+(9/25) =
(x+(3/5)) • (x+(3/5)) =
(x+(3/5))2
Things which are equal to the same thing are also equal to one another. Since
x2+(6/5)x+(9/25) = -11/25 and
x2+(6/5)x+(9/25) = (x+(3/5))2
then, according to the law of transitivity,
(x+(3/5))2 = -11/25
We'll refer to this Equation as Eq. #4.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x+(3/5))2 is
(x+(3/5))2/2 =
(x+(3/5))1 =
x+(3/5)
Now, applying the Square Root Principle to Eq. #4.2.1 we get:
x+(3/5) = √ -11/25
Subtract 3/5 from both sides to obtain:
x = -3/5 + √ -11/25
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Since a square root has two values, one positive and the other negative
x2 + (6/5)x + (4/5) = 0
has two solutions:
x = -3/5 + √ 11/25 • i
or
x = -3/5 - √ 11/25 • i
Note that √ 11/25 can be written as
√ 11 / √ 25 which is √ 11 / 5
100 pts and brainiest for the right answer
A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?
(0, 20); y equals one over eighty times x squared plus 20
(0, 20); y equals one over eighty times x squared minus 20
(0, 10); y equals one over forty times x squared plus 10
(0, 10); y equals one over forty times x squared minus 10
Answer:
Option A , (0, 20); y equals one over eighty times x squared plus 20
Step-by-step explanation:
The equation of parabola is given by
(X-h)^2 = 4p(Y-k)^2
In this case h = 0
So we get
Y = X^2/4P +k
Focus point is (h, p+k) , p+k = 40
Hence h, k = (0,20)
P = 40-k = 20
Equation Y = X^2/80 +20
Hence, option A is correct
plz mark brainliest
Answer: A
Step-by-step explanation:
Mama kupiła szampon do włosów, mydło i krem do rąk. Za te zakupy zapłaciła 19 zł. Szampon kosztował o 7 zł więcej niż mydło, a krem do rąk był cztery razy droższy niż mydło.
Ile kosztowała każda z rzeczy zakupionych przez mamę? Ułóż odpowiednie równanie i je
rozwiąż.
Answer:
you language is i don't know
Step-by-step explanation:
for now I did
Right Triangles
Solve the right triangle shown in the figure
∠C = 90°, BC = 7.50mi, AC = 11.43mi
a. AB = 19.5mi, ∠A = 31.2°, ∠B = 58.8°
b. AB = 16.mi, ∠A = 35.2°, ∠B = 54.8°
c. AB = 13.7mi, ∠A = 33.3°, ∠B = 56.7°
d. No triangle satisfies the given conditions.
Please select the best answer from the choices provided
Answer:
C. AB = 13.7mi, ∠A = 33.3°, ∠B = 56.7°
Step-by-step explanation:
I calculated it logically
the width of a rectangular yard is 3 yards more than twice its length. the perimeter of the garden is 192 yards
Answer:
Step-by-step explanation:
W = 2L + 3, and:
P = 2W + 2L = 192
Substituting 2L + 3 for W, we get:
P = 2(2L + 3) + 2L = 192, or
4L + 6 + 2L = 192, or:
6L = 186
L = 186/6 = 31
The length is 31, the width is 62 + 3, or 65
Therefore, the perimeter P is P = 2(31) + 2(65) = 130 + 62 = 192 (OK!)
im trying to test u to see if u know it. :D
28 ÷ 13
Answer:
[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]
[tex] \frac{28}{13} \\ = 2.15[/tex]
Answer:
28/13 or 2.15384615
Step-by-step explanation:
28/13 is the most simplified form of the fraction. If you were to calculate it out it would be 2.15384615.
3X + 2 = 17 how do i show my work for this help
pls help quick it is in the picture
Answer:
90 degrees it looks like
Step-by-step explanation:
Suppose that there is a school bond referendum in Greensboro, and 73% of voters support it. You randomly ask 20 Greensboro voters whether they support the bond referendum. The standard error of the sample proportion is _____. The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is _____. Group of answer choices 0.0993; 0.6000 0.0993; 0.0951 0.1095; 0.1170 0.1095; 0.8830
Answer:
The standard error of the sample proportion is 0.0993.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
73% of voters support it.
This means that [tex]p = 0.73[/tex]
Sample of 20 voters
This means that [tex]n = 20[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.73[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.73*0.27}{20}} = 0.0993[/tex]
The standard error of the sample proportion is 0.0993.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is
12/20 = 0.6, so this is the p-value of Z when X = 0.6.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.6 - 0.73}{0.0993}[/tex]
[tex]Z = -1.31[/tex]
[tex]Z = -1.31[/tex] has a p-value of 0.0951.
So
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.
The standard error of the sample proportion is 0.0098.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951
Given that,
Suppose that there is a school bond referendum in Greensboro, and 73% of voters support it.
You randomly ask 20 Greensboro voters whether they support the bond referendum.
We have to determine,
The standard error of the sample proportion is.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is .
According to the question,
There is a school bond referendum in Greensboro, and 73% of voters support it.
20 Greensboro voters whether they support the bond referendum.
To find standard deviation of sample proportion.
[tex]standard \ deviation = \sqrt{\dfrac{p(1-p)}{n}}[/tex]
Where, p = 73% = 0.73
And n = 20
Therefore,
[tex]Standard \ deviation = \sqrt{\dfrac{p(1-p)}{n}}\\\\ Standard \ deviation = \sqrt{\dfrac{0.73(1-0.73)}{20}}\\\\Standard \ deviation = \sqrt{\dfrac{0.73\times 0.27}{20}}\\\\Standard \ deviation = \sqrt{\dfrac{0.19}{20}}\\\\Standard \ deviation = 0.0098[/tex]
The standard error of the sample proportion is 0.0098.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is,[tex]\dfrac{12}{20 }= 0.6[/tex]
This is the p-value of Z when X = 0.6.
Therefore,
[tex]Z = \dfrac{X-\mu}{\sigma}\\\\Z = \dfrac{0.6-0.73}{0.993}\\\\Z = -1.31\\\\[/tex]
Z = -1.31 has a p-value of 0.0951.
Hence, The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.
To know more about Probability click the link given below.
https://brainly.com/question/24248147
Can someone help me find the measure of each angle indicated please
Answer:
Option B, 105 would be correct
Step-by-step explanation:
The Vertical Angles Theorem states that angles that are opposite diagonally are congruent, therefore; ? = 105°
Hope this helps!
Pls help me with math
Answer:
true
Step-by-step explanation:
They are dependent because the outcome of the event affects them
Pls help I’ll brainlest hurry due in 3 minutes
Answer:
B
Step-by-step explanation:
MOVE TO THE RIGHT 9 TIMES!!
How many outcomes are possible if you chose one letter from the word FUN and another letter from the word NOT.
Answer:
9
Step-by-step explanation:
The first question is how many ways can I get one letter from the word FUN?
That is 3.
Similarly, how many ways can I get one letter from the word NOT?
That is also 3.
Then one letter from FUN and one letter from NOT gives= 3 * 3 = 9
What is the measure of X , in degrees? HELPP!
Answer:
86°
Step-by-step explanation:
What are the coordinates of the image of ABC after a dilation with center (0, 0) and a scale factor of 1/2 ? Drag numbers to complete the coordinates. Numbers may be used once, more than once, or not at all.
Use numbers 1,2,3,4,5,6
Please help I will give 100 points.
Answer:
A(2,2) _scale factor ½--(1,1)
B(4,6)_scale factor ½--(2,3)
C(6,2)_scale factor ½--(3,1)
is a required coordinate
Scale factor=1/2
Apply and get new coordinates
A'=(1,1)B'=(2,3)C'=(3,1)Each day 1/2 of the money that is in a bank is removed .no money is added to the vault .which of the following models the situation
The total number of running yards in a football game was less than 100. The inequality x <100 represents the
situation. Which graph represents the inequality?
95 96 97 98 99 100101102103104105
95 96 97 98 99 100 101 102103104105
95 96 97 98 99 100 101 102103104105
95 96 97 98 99 100101102103104105
Answer:
answer is B
Step-by-step explanation:
got it right on edge :)
The knockoff Jersey store sold 6 more Leafs jerseys than Senators. Four times the number of Senators Jersey sold plus three times the number of Leafs jerseys sold is 102. How many Leaf Jerseys were sold?
Answer:
72
Step-by-step explanation:
6x4=24x3=72
Which of the following is NOT a way to write a probability?
O Decimal
O Percent
O Fraction
O Mr. Eisenberg
A flashlight flashes every 45 seconds. After 10 ½ minutes, how many times does the light flash?
Answer:
14
Step-by-step explanation:
Answer:
14 flashes.
Step-by-step explanation:
1 minute = 60 seconds
x minutes = 45 seconds.
1/x = 60/45 Cross multiply
60x = 45 Divide by 60
x = 45/60
x = .75
10 1/2 minutes = 10.5 minutes.
x flashes / 10.5 minutes = 1 flash / 0.75 minutes Multiply by 10.5
x = 10.5/0.75
x = 14
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Aaron sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
41 visitors purchased no costume.
78 visitors purchased exactly one costume.
10 visitors purchased more than one costume.
If next week, he is expecting 2000 visitors, about how many would you expect to buy more than one costume? Round your answer to the nearest whole number.
Answer:
115
Step-by-step explanation:
41 no costume, 78 exactly one costume, 10 more than one costume.
41+78+\color{steelblue}{10}=
41+78+10=
\,\,\color{indianred}{129}
129
There were a toal of 129 visitors. 10 purchased more than one costume.
Probability the next customer will purchase more than one costume:
\frac{\color{steelblue}{10}}{\color{indianred}{129}}\phantom{=}
129
10
=
\,\,
Out of 2000 new trials, we would expect more than one costume to be selected:
\color{purple}{2000}\times\frac{\color{steelblue}{\color{steelblue}{10}}}{\color{indianred}{\color{indianred}{129}}}=
2000×
129
10
=
\,\,155.038759...
155.038759...
\approx
≈
\,\,155
155
The number of visitors that expect to buy more than one costume will be 155.
What is the expected value?The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
Aaron creates a website where players may trade and purchase these costumes. The numbers below show how many people visited the website and how many costumes were bought in a single day.
The probability of visitors purchasing more than one costume is calculated as,
p = 10 / (41 + 78 + 10)
p = 10 / 129
If next week, he is expecting 2000 visitors. Then the expected value is given as,
E = 2000 x (10 / 129)
E = 155.038
E ≈ 155
The number of visitors that expect to buy more than one costume will be 155.
More about the expected value link is given below.
https://brainly.com/question/13945225
#SPJ2
What is the area of the isosceles triangle shown?
Answer:
672 meters squared
Step-by-step explanation:
Area of Triangle: b*h*1/2
The isosceles triangle's height, splits the base in half.
Answer:
672
Step-by-step explanation:
Area of a triangle = [tex]\frac{bh}{2}[/tex]
where b = base length and h = height
In the triangle shown, we are only given the base length
This means that we must find the height in order to find the area.
We can do this by using the Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]
where a and b = legs and c = hypotenuse
Two right triangles are formed within the isosceles triangle.
Each has a hypotenuse of 50 m, a base length of 28/2=14m ( because they are sharing the base length ) and they are both sharing the height.
So we are given the hypotenuse and a leg and we need to find the other leg
So we plug in what we are given and solve for the missing side length
[tex]50^2=a^2+14^2\\50^2=2500\\14^2=196\\2500=a^2+196[/tex]
step 1 subtract 196 from each side
2500 - 196 = 2304
196 - 196 cancels out
we now have 2304 = a²
step 2 take the square root of each side
[tex]\sqrt{a^2} =a\\\sqrt{2304} =48[/tex]
we're left with a = 48
This means that the height of the isosceles triangle is 48m
Now we can find the area.
Using the formula stated previous....
[tex]A=\frac{28*48}{2} \\28*48=1344\\\frac{1344}{2} =672[/tex]
Hence, the area is 672m²
If you invest $2500 at a rate of 3.5%, how much money will be in the
account after 10 years if it is compounded yearly?
Answer:
A = $3,526.50
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = [tex]\frac{R}{100}[/tex]
r = [tex]\frac{3.5}{100}[/tex]
r = 0.035 rate per year,
Then solve the equation for A
A = P(1 + [tex]\frac{r}{n}[/tex])nt
A = 2,500.00(1 + [tex]\frac{0.035}{1}[/tex])(1)(10)
A = 2,500.00(1 + 0.035)(10)
A = $3,526.50
Hence:
The total amount of over 10 years is $3,526.50.
The following is a geometric series.
6+8+11+15+20+26+...
O True
False
EXPLAIN ANSWER FOR BRAINLIEST
9514 1404 393
Answer:
False
Step-by-step explanation:
The terms of a geometric series would have a common ratio. The terms of this series do not. (The differences increase by 1 each time, so it is a quadratic series.)
False, the series is not geometric.
Answer:
Solution :-We are given with the series
6 + 8 + 11 + 15 + 20 + 26
Since
the series is increasing by +1. So, it will be not a geometric series
[tex] \\ [/tex]
will give 50 point privetely if correct and show work
Ms. White invests $ 2000 in a savings plan. The savings account pays an annual interest rate of 5.75 % on the amount she puts in at the end of each year. How much will be in her savings plan at the end of 10 years?
Answer:
The solution is 2000 + 0.0575*2000*10 = 3150 dollars at the end of 10 years.
Step-by-step explanation:
What is the volume, in cubic meters, of a cylinder with a height of 3 meters and a base
radius of 4 meters, to the nearest tenths place?
Answer:
answer is 150
Step-by-step explanation:
hope it helps
Can someone help me with this?
Answer:
I can help you via Watsapp
Find the area of the parallelogram shown below 5 3
Answer:
15 square units
Step-by-step explanation:
If you were to cut off the bottom triangle (separated by the dotted line), and put it on top of the other triangle, you would get a rectangle.
All you have to do is length x height
5 x 3 = 15
Find the measure of the angle(s)
Help
Answer:
759
Step-by-step explanation:
solve for x 9.2, 16.5, x
Answer:
152
Step-by-step explanation:
Solve for x.
Your answer must be simplified.
х
--30 <
-4.
First to answer correctly is Brainlyest
Answer:
x < 26
Step-by-step explanation:
Given the following algebraic expression;
x - 30 < -4
To find the value of x in its simplest form;
First of all, we would have to rearrange the algebraic expression to make the variable on one side and the integer on the other side;
Simplifying an expression simply means to collect like terms that are having the same variables or constants and combining them, so as to reduce the expression to the lowest possible value.
x < -4 + 30
x < 26