Answer:
x = 6
Explanation:
completing square:
[tex]y=x^2-12x+7[/tex]
[tex]y=(x^2-12x)+7[/tex]
[tex]y=(x-6)^2+7-(-6)^2[/tex]
[tex]y=(x-6)^2+7-36[/tex]
[tex]y=(x-6)^2-29[/tex]
Comparing with quadratic equation [tex]y=ax^2 + bx+c[/tex], in vertex form where [tex]y = a(x-h)^2+k[/tex]. In this x - h = 0, x = h defines the symmetry of equation.
So here the symmetry for parabola:
x - 6 = 0
x = 6
Answer:
x = 6
Step-by-step explanation:
The axis of symmetry of a parabola is the x-value of its vertex.
For a quadratic function in the form [tex]y=ax^2+bx+c[/tex], the x-value of the vertex is:
[tex]x=-\dfrac{b}{2a}[/tex]
Given function:
[tex]y=x^2-12x+7[/tex]
Therefore:
[tex]a=1, \quad b=-12, \quad c=7[/tex]
So the axis of symmetry of the given quadratic function is:
[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-12}{2(1)}=\dfrac{12}{2}=6[/tex]
Two spheres (m = 3 g) on long threads repel each other after being equally charged. what is the charge q?
The charge q is ±7.46 × 10⁻⁷C.
Electrostatic Force, Coulomb's Law:The electrostatic force is a type of force that only charged objects experience. The term electrostatic is made up of two parts: 'electro,' which refers to electricity, and static,' which means stationary. As a result, an electrostatic force exists between any two fixed charges.The electrostatic force is attractive when the two charges have opposite charges and repulsive when they have the same charge.Coulomb's Law is used to calculate the strength of the electrostatic force between two points and stationary objects. The electrostatic force between two points and stationary charges is directly proportionate to the product of both charges and inversely proportional to the square of the distance between the charges, according to Coulomb's Law.
Give:
The mass of each charge, m = 3.0 g = 3 × 10⁻³ kgThe length of each thread, l = 1.0 mThe two charges are equal, q₁ = q₂ = qTake a look at the charge on the left. The following forces are at work in response to this charge:
The tension of the thread, TThe gravitational force, W = mg where m is the mass and g = 9.8 m/s² is the acceleration due to gravity.The electrostatic force, F due to the charge of the right.(Refer to the diagram below)
Because the charge is in equilibrium, the charge's vertical and horizontal forces must be zero.
We have the following in the vertical direction:
[tex]\begin{aligned}T \cos 20^{\circ} &=W \\\Rightarrow T &=\frac{m g}{\cos 20^{\circ}} \\&=\frac{3.0 \times 10^{-3} \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s}^2}{\cos 20^{\circ}} \\&=3.13 \times 10^{-2} \mathrm{~N}\end{aligned}[/tex]
Coulomb's Law states that the electrostatic force between two point charges, q₁, and q₂, separated by r is given by the equation:
[tex]\begin{aligned}F &=\frac{q_1 q_2}{4 \pi \epsilon_0 r^2} \\&=\frac{K q_1 q_2}{r^2}\end{aligned}[/tex]
Here,
The distance between the charges is r.The permittivity of free space is [tex]\epsilon_0[/tex].Coulomb's Constant is K = 9 × 10⁹ N.m²/C².Using trigonometric personalities, the distance between any two charges is:
[tex]\begin{aligned}r &=2 l \sin 20^{\circ} \\&=2 \times 1.0 \mathrm{~m} \times 0.342 \\&=0.684 \mathrm{~m}\end{aligned}[/tex]
We have the following in the vertical direction:
[tex]\begin{aligned}F_e &=T \sin 20^{\circ} \\\Rightarrow \frac{K q_1 q_2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow \frac{K q^2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow q^2 &=\frac{r^2 T \sin 20^{\circ}}{K} \\&=\frac{(0.684 \mathrm{~m})^2 \times 3.13 \times 10^{-2} \mathrm{~N} \times \sin 20^{\circ}}{9 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2} \\&=55.65 \times 10^{-14} \mathrm{C}^2 \\\Rightarrow q &=\pm 7.46 \times 10^{-7} \mathrm{C}\end{aligned}[/tex]
Therefore, the charge q is ±7.46 × 10⁻⁷C.
Know more about the charge here:
https://brainly.com/question/25922783
#SPJ4
The correct question is given below:
Two 3.0g point charges on 1.0m - long threads repel each other after being equally charged, as shown in the figure. What is the charge q?
On Elvis’s map, the area of a park is of thearea of the same park on Belinda’s map. Elvis’s map uses a 1/4 scale of 1 inch to 100 feet. What scale does Belinda’s map use?
Using proportions, it is found that Belinda's map uses a scale of 0.025 inches : 100 feet = 0.00025 inches : 1 feet.
What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
Scale problems are solved using proportions. Elvis’s map uses a 1/4 scale of 1 inch to 100 feet, hence:
1 inch represents 100 feet in the entire scale.1/4 of that is that 1/4 = 0.25 inches represent 100 feet.Belinda's map has the same area, hence they use the same scale, hence she uses a scale of 0.025 inches : 100 feet = 0.00025 inches : 1 feet.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Sergio and three friends went golfing two other friends rented clubs for six dollars each the total cost of the rented clubs in the green fees was $76 what was the cause of the green fees for each person
The cost of Green fees for each person is $16.
As per the question statement, Sergio went golfing with 3 other friends and two of them rented clubs for $6 each, the total cost of the rented clubs and the green fees being $76.
We are required to calculate the cost of Green fees for each person.
Let us assume that the cost of Green fees for each person is "x".
We will now form a linear equation of single variable "x" based on the conditions mentioned in the question statement, and solving for x, we will obtain our desired answer.
[tex][4x+(2*6)]=76\\or,4x+12=76\\or, 4x=76-12\\or, 4x=64\\or, x=\frac{64}{4}=16[/tex]
That is, the cost of Green fees for each person is $16.
Linear Equation: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line, as the name "Linear" itself suggests. Here, each term is of exponent 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept.To learn more about Linear Equations, click on the link below.
https://brainly.com/question/19549073
#SPJ9
Q.2 - What is the value of y in the equation 3(4y - 12) = 0 ? Show your work.
Hey there!
3(4y - 12) = 0
3(4y) + 3(-12) = 0
12y - 36 = 0
Add 36 to both sides
12y - 36 + 36 = 0 + 36
Cancel out: -36 + 36 because it give you 0
Keep: 0 + 36 because it help solve for the equation
New equation: 12y = 0 + 36
Simplify it
12y = 36
DIVIDE 12 to both sides
12y/12 = 36/12
Cancel out: 12/12 because that give you 1
Keep: 36/12 because it give you the y-value (also known as your overall result)
New equation: y = 36/12
Simplify it
y = 3
Therefore, your answer should be:
y = 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
the formula for the circumference of a circle is c equals 2 pi r. if the circumference is31.4 centimeters, what is the diameter of the circle? (let pi equals 3.14)
Answer: Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm. You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm². Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm.
Step-by-step explanation:
Lupita has five times as much money as David. Lupita also has $20 more than David. How much money does each person have?
The average price for regular gasoline in Toronto is $1.35 per liter, or L (in Canadian dollars, as of
April 2014).
Part A: The exchange rate between the US and Canada varies continuously. Assume that, in April
2014, the rate was US$ 0.92 for each Canadian dollar. Determine the cost in U.S. dollars (US$) for 1 L
of gasoline in Toronto. Round to the nearest cent.
Hint
$1.35 Canadian = US$
Part B: There are 3.78541 L in 1 gallon (gal). Determine the cost in U.S. dollars (US$) for 1 gal of
gasoline in Toronto. Round to the nearest cent.
Hint
1 gal costs US$
a. $1.35 Canadian dollar will be 124 cents.
b. cost in U.S. dollars (US$) for 1 gal of gasoline in Toronto will be $5.11.
How to calculate the value?A. It should be noted that the rate was US$ 0.92 for each Canadian dollar.
Therefore, $1.35 Canadian dollar will be:
= 1.35 × 0.92
= $1.24 = 124 cents.
B. The cost in U.S. dollars (US$) for 1 gal of gasoline in Toronto will be:
= 3.78541 × 1.35
= $5.11
Learn more about exchange rate on:
brainly.com/question/25970050
#SPJ1
Petrina had a piece of red ribbon that measured 2.4 m long. she also had a piece of blue ribbon which was 7 8 m long. what was the total length of both ribbons? round your answer to 2 decimal places.
The total length of red and blue ribbons is 10.2 m.
Given that, the length of the red ribbon =2.4 m and the length of the blue ribbon =7.8 m.
How to add two decimals?Adding decimals is similar to the usual addition of whole numbers. We know that a decimal number is a number with a whole number part and a fractional part which is separated by a decimal point.
Now, the length of the red ribbon + the length of the blue ribbon=2.4+7.8
=10.2 m
Therefore, the total length of red and blue ribbons is 10.2 m.
To learn more about the addition of decimals visit:
https://brainly.com/question/17612968.
#SPJ4
If the mean of a normal distribution is 20 and its standard deviation is 3, between which values would 99.5 percent of the data observations be expected to fall?
99.5% of the data observations should fall between 11.579 and 28.421 according to expectations for the given normal distribution.
What is a normal distribution?
A continuous probability distribution for just a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
According to the question, if the lower limit is a and the upper limit is b, then 99.5 percent of values fall between a and b.
part of values below a certain threshold, a= (1-0.995)/2 = 0.0025
Mean,m =20
Standard deviation,s = 3
Z = (X – m) / s
P(x<Z): 0.0025
P(x<Z) = 0.0025 can be determined for Z score.
according to the usual table, Z = -2.807
X = Zs+m
(-2.807 * 3) +20= 11.579
Lower limit = 11.579
Part of values that are less than b is equal to 0.995 + 0.0025 = 0.9975.
P(x<Z): 0.9975
Z score for which P(x<Z) = 0.9975 can be found
from the normal table as, Z = 2.807
X = Zs+m
(2.807 * 3) +20= 28.421
Upper limit = 28.421
99.5% of the data observations should fall between 11.579 and 28.421 according to expectations for the given normal distribution.
To learn more about normal distribution visit:
https://brainly.com/question/4079902
#SPJ1
Name the angle in as many different ways as possible.
Answer:
JGL, LGJ, 2
Step-by-step explanation:
Solve for a. Express your answer in simplest radical form if necessary.
Answer: =
√
شه دار
= 144
Answer:
12
Step-by-step explanation:
√144 = 12
Consider the polynomial function
p(x) = -9x⁹ + 6x6 - 3x³ +1.
End behavior of polynomials
What is the end behavior of the graph of p?
p has an odd degree and an odd leading coefficient.
So,
As x approaches infinity, p(x) approaches negative infinity.As x approaches negative infinity, p(x) approaches infinity.What is the force, in N, when a pressure of 18 N/m2 is exerted on an area of 500 cm2?
It's not 1.6
Please answer the question in the picture above.
explain why 8 < x < 2 has no solution? need the answer quick
Answer:
8 < x < 2 has no solution because there is no number greater than 8 (8 < x), yet less than 2 (x < 2). It's impossible, so there is no solution.
If the inequality was something like 8 < x < 10, then it will work because 8 can be less than x and x can be less than 10.
Hope this helps and have a great rest of your day! :)
Use the given information to find the unknown value. y varies inversely with the cube of x. when x=9, then y=1. find y when x=1. enter the exact answer.
When the value of x = 1, the value of y = 729.
What is inverse relation?An inverse relationship is one where the value of one parameter decreases as the value of the second parameter increases. It is frequently described as a bad relationship.
In other phrases, an inverse relationship, also recognized as a negative relationship, is a negative relationship between two variables that moves in the opposite direction. Like, we have two variables X and Y. As X increases, so does Y, and as Y increases, so does X.Now, as per the question.
y varies inversely with the cube of x.
y ∝ 1/x³
Removing inverse, a constant of proportionality will come (say k)
y = k/x³
k = x³y.
When x = 9 then y = 1. Substitute the values and find k.
k = 9³(1)
k = 729
Now, estimate the value of y when x = 1.
y = k/x³ ( put the value of k and x )
y = 729/1³
y = 729
Thus, the value of y when the value of x = 1 is 729.
To know more about the inverse relation, here
https://brainly.com/question/1266676
#SPJ4
which of the following conversion factors would be most useful in converting miles per gallon to kilometers per liter?
(C) 1 mile/0.62 km conversion factor would be most useful in converting miles per gallon to kilometers per liter.
What do we mean by conversion factor?A conversion factor is a ratio in dimensional analysis that converts one unit of measure into another without changing the quantity. A conversion factor is a number that is used to multiply or divide one set of units into another. When converting to an equal value, the acceptable conversion factor must be used. To convert inches to feet, for example, the suitable conversion value is 12 inches equal to 1 foot. Another example would be converting miles per gallon to kilometers per liter using a 1 mile/0.62 km conversion factor.Therefore, (C) 1 mile/0.62 km conversion factor would be most useful in converting miles per gallon to kilometers per liter.
Know more about conversion factors here:
https://brainly.com/question/97386
#SPJ4
The complete question is given below:
Which of the following conversion factors would be most useful in converting miles per gallon to kilometers per liter?
A) 1 gallon/4 quarts
B) 1 liter/1000 ml
C) 1 mile/0.62 km
D) 1 000 m/1 km
How to solve 1000/11 via long divison… pls help with full working out
What is the degree of x^2+3x+y?
Answer: 2
Step-by-step explanation:
as x is to a power of 2 so degree is 2
pls vote for brainliest
POWER TO A POWER
(ax) y =
When raising a base with an exponent to
another exponent, keep the
and
the exponents.
A number raised to a power represents a product where the same number is used as a repeated factor. The number is called the base and the power is given by the exponent. The base is the repeated factor and the exponent counts the number of factors. An exponent is that we are dealing with products and multiplication.
In the expression bn, b is the base and n is the exponent.
The Power Rule for Exponents: (am)n = am*n.
To raise a number with an exponent to a power, multiply the exponent times the power.
Negative Exponent Rule: x–n = 1/xn.
Invert the base to change a negative exponent into a positive.
Zero Exponent Rule: x0 = 1, for .
Any non-zero number raised to the zeroth power is 1.
For more information about Exponents
visit brainly.com/question/13669161
#SPJ9
simplify this expression
12g+9g
Answer:
21 g
Step-by-step explanation:
12g
+ 9g
_____
21g
======
I think this is the answer but i can't confirm because your theory and my theory can be different
!!ABSOLUTE VALUE!!
can anyone do this problem out for me and show the work and steps?
ILL GIVE BRAINLIEST!!!!!
An online store sells old video games and DVDs as a bundle. A bundle of two video games and three DVDs can be purchased for $90.00. A bundle of one video game and two DVDs can be purchased for $51.50. Find the cost of one video game and the cost of one DVD in the bundle.
Using system of equations, the cost of one video game is $25.5; the cost of one DVD is $13.
How to Apply System of Equations to Solve a Problem?Given the problem above, we would do the following:
Video games = vDVDs = dUsing the information given, we would form two equations for the system as shown below:
2v + 3d = 90 ---> equation 1
v + 2d = 51.5 ---> equation 2
Multiply equation 2 by 2 to get equation 3
2v + 4d = 103 ---> equation 3
Subtract equation 1 from equation 3
d = 13
The cost of one DVD = d = $13.00
Substitute d = 13 into equation 2
v + 2d = 51.5 ---> equation 2
v + 2(13) = 51.5
v + 26 = 51.5
v = 51.5 - 26
v = 25.5
The cost of one video game = v = $25.50.
Therefore, using system of equations, the cost of one video game is $25.5; the cost of one DVD is $13.
Learn more about the system of equations on:
https://brainly.com/question/13729904
#SPJ1
Find the equation of the line that passes through points A and B.
A(1,7)
B(-3,-1)
The equation for the line that connects the locations is y = 2x + 5.
What is the Slope of a Line?The slope of a line, commonly known as the gradient, is defined as the value of the steepness or direction of a line in a coordinate plane. Slope can be determined using many ways given the equation of either a line or the coordinates of points on the straight line. . The slope is defined mathematically as "climb overrun" (change in y divided by change in x).
According to the given data:x₁ = 1
y₁ = 7
x₂ = -3
y₂ = -1
To obtain the equation of a line, we must first determine its slope. This is computed as:
m = [y₂ - y₁ ]/[x₂ - x₁]
Substituting the value we get:
m = [(-1) - 7 )/((-3) - 1)]
= -8/-4
= 2
The slope of the line = 2.
The line's intercept is:
The slope is the next step toward solving for a such equation of the line.
A typical linear equation is presented as:
y = mx + c
Let us substitute the slope and intercept values.
y = 2x + 5
To know more about slope of the line visit:
https://brainly.com/question/15874858
#SPJ9
Lots took one hour to drive from his apartment to philips arena and back. the return drive took 8 minutes less than the trip to the arena. if x represents the time it took llya to drive from his apartment to the arena, which equation would you use to determine how long he drove each way
The equation would use to determine how long he drove each way is 2x - 8 = 60.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given that Lots took one hour to drive from his apartment to Philips arena and back. the return drive took 8 minutes less than the trip to the arena.
Since the return trip took 8 minutes less, the complete equation must be written in minutes.
Here x - 8 represents the time it took to return to Philips Arena.
The total travel time, including both directions, was 60 minutes;
thus, add x and x - 8 and set them both equal to 60.
So 2x - 8 = 60
Therefore, the equation would use to determine how long he drove each way is 2x - 8 = 60.
Learn more about the equation here:
brainly.com/question/10413253
#SPJ4
-2x(-3)=
(-3x4)÷(-8)=
(-2x(-3))x(-4)=
Answer:
61,5-24Step-by-step explanation:
[tex]1. \: \: - 2 \times - 3 = \\ = 6[/tex]
[tex]2. \: \: ( - 3 \times 4) \div ( - 8) = \\ = ( - 12) \div ( - 8)\\ = ( - 6 )\div ( - 4) \\ = ( - 3 )\div ( - 2 )\\ = 1.5[/tex]
[tex]3. \: \: ( - 2) \times ( - 3) \times ( - 4) = \\ = 6 \times ( - 4) \\ = - 24[/tex]
Add. 5/7 + 1/2 + 3/4
please help
Answer: 1²⁷/₂₈
Step-by-step explanation:
[tex]\displaystyle\\\frac{5}{7}+\frac{1}{2}+\frac{3}{4} =\\\\\frac{5*4+1*14+3*7}{28} =\\\\\frac{20+14+21}{28} =\\\\\frac{55}{28} =\\\\1\frac{27}{28}[/tex]
A plane is flying at a speed of 150 miles per hour. The pilot plans to fly at this speed for
the next 160 miles, plus or minus 25 miles. Write an absolute value equation to find the
minimum and maximum number of hours the plane will travel at that speed.
Maximum time = 0.914 hour , Minimum time = 1.28 hour
Speed is determined by dividing the distance traveled by the time taken to travel it. It gives the amount of time it took to travel a certain distance divided by the distance traveled.
Speed is inversely correlated with time and directly correlated with distance. Hence, Speed X time equals distance, and
Time is calculated as Distance / Speed; as speed increases, time decreases and vice versa.
Distance = speed x time
Maximum speed = 150 +25
= 175 miles/ hour
Minimum speed = 150 - 25
= 125
Distance = 160 miles
Maximum time = 160/175
= 0.914 hour
Minimum time = 160/125
= 1.28 hour
To learn more about speed distance and time, refer to https://brainly.com/question/4931057
#SPJ9
I NEEED HELPPP!!!! 17+18+19+ … +42+43
Let
S = 1 + 2 + 3 + … + (n - 2) + (n - 1) + n
Reversing the order of terms, we have
S = n + (n - 1) + (n - 2) + … + 3 + 2 + 1
and we observe that terms in the same position on the right side add up to n + 1.
2S = (1 + n) + (2 + (n - 1)) + (3 + (n - 2)) + … + (n + 1)
There are n terms in the sum, so each the right side is simply n copies of n + 1, and
2S = n (n + 1)
S = n (n + 1)/2
Now,
17 + 18 + 19 + … + 41 + 42 + 43
= (1 + 2 + 3 + … + 41 + 42 + 43) - (1 + 2 + 3 + … + 14 + 15 + 16)
= (S with 43 terms) - (S with 16 terms)
= 43 (43 + 1)/2 - 16 (16 + 1)/2
= 810
12. Feeling hot, hot, hot! Here is a stemplot using split stems for the daily high
temperature in Phoenix data from Exercise 8
From the given stem-and-leaf plot, we have that:
a) 80.65% of days in this month were hotter than 100 ºF.
b) The shape of the distribution is negatively skewed.
c) The value of 84, with key 8|4, appears to be an outlier in this data-set.
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
From the plot in this problem, the 31 observations are given as follows:
84, 93, 97, 99, 100, 101, 101, 102, 102, 103, 104, 104, 104, 105, 105, 106, 106, 106, 107, 107, 108, 108, 109, 109, 109, 110, 111, 111, 113, 115.
For item a, we have that of the 31 observations, 25 were hotter than 100 ºF, hence:
25/31 = 80.65%.
80.65% of days in this month were hotter than 100 ºF.
For item b, using a calculator, we have that:
The mean is of 104.6.The median is of 105.5.Since the mean is less than the median, the shape of the distribution is negatively skewed.
For item c, we have that:
The first quartile is of Q1 = 102.The third quartile is of Q3 = 109.The interquartile range is of IQR = Q3 - Q1 = 109 - 102 = 7.Outliers are values that are more than 1.5IQR from the quartiles, hence:
102 - 1.5 x 7 = 91.5.109 + 1.5 x 7 = 119.5.84 < 91.5, hence the value of 84, with key 8|4, appears to be an outlier in this data-set.
More can be learned about stem-and-leaf plots at https://brainly.com/question/28015028
#SPJ1