Answer:
x = -1 ± √109
Step-by-step explanation:
2x • 3x + (2 • 3)x + 6x = 648
According to PEMDAS (parentheses/exponents | multiplication/division | addition/subtraction), we should solve the parentheses first.
(2 • 3) = 6
Now we have:
2x • 3x + (6)x + 6x = 648
Now let's multiply.
2x • 3x = 6x²
6 • x = 6x
Now we have.
6x² + 6x + 6x = 648
Combine like terms.
6x² + 12x = 648
Let's factor out a 6.
6(x² + 2x) = 648
Divide both sides by 6.
x² + 2x = 108
Let's use completing the square.
Our equation is in a² + bx = c form.
Divide b by 2.
2/2 = 1
Then square it.
1² = 1
Add 1 to both sides.
x² + 2x + 1 = 108 + 1
Simplify.
x² + 2x + 1 = 109
Now we want to factor the left side. A shortcut is just to use b/2.
(x + 1)² = 109
Take the square root of both sides.
x + 1 = ±√109
The square root is as simplified as possible.
Subtract 1 from both sides.
x = -1 ± √109
Hope this helps!
What is the arithmetic mean of the following numbers?
1, 2, 4, 6, 4
Answer:
3.4
Step-by-step explanation:
7. Plumber A charges $60 an hour. Plumber B charges $40 to visit your home plus $55 for each
hour. For how many hours will the total cost for each plumber be the same? How much will that
cost be? If a customer thinks they will need a plumber for 5 hours, which plumber should the
customer hire? Explain.
The total cost will be $480.
What is an Equations?
Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) symbol. It demonstrates how the expressions written on the left and right sides are equivalent. Equations can be solved to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol in a sentence, it is not an equation. It will be viewed as a phrase.
There should be two equations
For Plumber A = 60x
For Plumber B = 40 + 55x
Now in order to consider the cost to be the same we equate these two equations
60x = 40 + 55x
5x = 40
x = 8 hours
And, the total cost for plumber B is
= 40 + 55(8)
= 480
Hence, The total cost will be $480.
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NEED HELP QUICKLY!
x=?
y=?
Four people each roll a fair die once. Quantity A: The probability that at least two people will roll the same number Quantity B: 70%
How likely something is to occur is known as its probability.Probability when die rolled 1st time is 6C1 i.e. (1,2,3,4,5,6).
Find the probability ?How likely something is to occur is known as its probability.We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.
Probability when die rolled 1st time=6C1 i.e. (1,2,3,4,5,6) suppose 1 comes, then 2nd time it should not be .as it is given that no 2 people will roll same number.
so 2nd time probability=5C1 i.e. (2,3,4,5,6). same way 3rd and 4th time probability=4C1 and 3C1 respectively.Probability that no one rolls the same no. = 6*5*4*3and total possibility =6^4
p(same number)= 6*5*4*3/ 6^4
= 5/18
p(no same number will roll)=1-5/18
=13/18
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For the coordinate (0,-3) the translation would be down 3.
A: True
B: False
What is the ratio of sin t?
Sine of an angle is defined as the ratio of the side opposite (perpendicular side) to that angle divided by hypotenuse of the triangle.
sin is a trigonometric ratio.
If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse.
sin Q = perpendicular / hypotenuse.
sin Q is the base of the trigonometry ratios and it is one of the ratio.
sine is an acute angle.
some formula of sine angle are ,
1- sine Q = 1/ cosec Q .
2- sin ^2 Q = 1- cos^2 Q .
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HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
Step-by-step explanation:
24=c
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Heeeeeeeyyyyyyyyyyyyy
(6b+ 2) - (4b + 3)
Help pls I don’t know how to do this
Answer:
2b - 1
Step-by-step explanation:
To solve this problem, we will need to open the parentheses. To do this, we will put an imaginary 1 in front of both sets of parentheses to open them using the distributive property, this gives us:
1(6b + 2) - 1(4b + 3)
We will open the first set of parentheses with no problem, but in the second set, we have -1, so we need to make every positive number negative and every negative number positive, giving us:
6b + 2 - 4b - 3
Then, we group our like terms:
6b - 4b + 2 - 3
Then, we subtract, giving us:
2b - 1
So the most simplified version is 2b - 1.
Hope this helped!
Answer:
Step-by-step explanation:
You begin by distributing the negative so -4b -3
then you will multiply (6b+2) by (-4b -3)
24b^2 - 18b - 8b - 6
answer = 24b^2 - 26b - 6
What is the solution to the system of equations on the graph below? - I WILL MARK BRAINLIEST
Answer:
(4,-1)
Step-by-step explanation:
y = -1/2x + 1
y = x - 5
(2)x - 5 = -1/2x + 1(2)
2x - 10 = -1x + 2
3x - 10 = 2
3x = 12
x = 4
y = x -5
y = 4 - 5
= -1
The UTM coordinates of Enchanted Rock State Natural Area in Fredericksburg, Texas, are 517266.07 E, 3374884.58 N, Zone 14R. How far is it from the zone's central meridian
Enchanted Rock State Natural Area is located at latitude 30.506130 and longitude -98.820064. The geographic coordinates of Enchanted Rock State Natural Area in Fredericksburg, United States, are 30° 30' 22.068" N and 98° 49' 12.2304" W. Enchanted Rock State Natural Area falls under the Mysterious Sites category.
Where can measurements be made using the WGS84 datum?The standard datum used by default for GPS devices used for commercial and recreational purposes is WGS84. GPS users are advised to always verify the datum of the maps they are utilising.
What datum does US Navstar GPS employ?WGS 84, also known as the datum, is now in use by US forces.
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morgan has a round garden. the diameter is 14ft. what is the area of her garden
Answer: I dont know
Explain Answer Step-By Step:Hey
if the length of a rectangle is (x+5) and the width is (x+2), what is the area of the rectangle?
Answer: x^2+7x+10
Step-by-step explanation:
You work at an oil refinery and are in charge of draining a tank until the
are 635 gallons left inside. The tank starts with 859 gallons, and you can
drain it at a rate of 56 gallons per minute. How many minutes do you
need to drain the tank to the right level?
You need
minutes.
Answer:
To drain the tank to the right level, you need to remove 859 - 635 = <<859-635=224>>224 gallons.
So you need to work for 224 / 56 = <<224/56=4>>4 minutes.
Step-by-step explanation:
The joint and marginal pdf's of x = amount of almonds and Y = amount of cashews are
F(x,y) = fx(x) =
with fy(y) obtained by replacing x by y in fx(x). It is easily verified that Mu x = Mu y = A, and E(XY) = 2/ 5 Compute the correlation coefficient p for X and Y. P=
The correlation coefficient ρ for X and Y is ρ = -0.6675 in the given function.
What is correlation coefficient?The correlation coefficient is a statistical concept that aids in establishing a relationship between expected and actual values obtained through statistical experimentation. The calculated correlation coefficient's value explains why the difference between the predicted and actual values is so exact.
Correlation Coefficient value is always in the range of -1 to +1. A similar and identical relationship exists between the two variables if the correlation coefficient value is positive. Otherwise, it reveals how differently the two variables behave.
Pearson's correlation coefficient is calculated by taking the covariance of two variables and dividing it by the sum of their standard deviations. is typically used to represent it (rho).
The correlation coefficient is computed as,
[tex]$ \rho & =\frac{{Cov}(X, Y)}{\sqrt{V(X)} \times \sqrt{V(Y)}}[/tex]
[tex]$=\frac{-0.0267}{\sqrt{0.04} \times \sqrt{0.04}}[/tex]
= -0.6675
Thus, the correlation coefficient ρ for X and Y is ρ = -0.6675.
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Find the point(s) on the surface at which the tangent plane is horizontal.
z = xy + 1 x + 1 y
The point(s) on the surface at which the tangent plane is horizontal are (0, 0, 1).
To find the point(s) on the surface at which the tangent plane is horizontal, we need to find the points at which the partial derivatives of z with respect to x and y are both equal to 0. This means we need to solve the system of equations:
∂z/∂x = 0 ∂z/∂y = 0Solving this system of equations yields x = 0, y = 0, and z = 1. Therefore, the point(s) on the surface at which the tangent plane is horizontal is (0, 0, 1).
To understand why solving the system of equations yields the points for which the tangent plane is horizontal, it is important to understand what the partial derivatives represent. The partial derivative of z with respect to x is the rate of change of z with respect to x, and similarly for y.
When the partial derivatives are both equal to 0, it means that the rate of change of z with respect to x and y is 0, which implies that the tangent plane is horizontal.
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If r is an odd integer and m=8r then m/2 will always be
a. odd
b. even
c. positive
d. negative
Answer:
b. even
Step-by-step explanation:
m is a multiple of 8, so it is also a multiple of 4. When a multiple of 4 is divided by 2, the result is a multiple of 2 (even).
The temperature of a heat-producing chemical reaction is directly proportional to the square of the time elapsed. The reaction started at 0 degrees
Gloria bought a coat through a payment plan. The coat was $75 and her payments were $15 each. What percent of the totalcost are the payments?
A. 15%
B. 20%
C. 25%
D.30%
What is 3 8 equivalent to as a fraction?
Answer:
6/16
Step-by-step explanation:
Answer:
Step-by-step explanation:
15/40 i think
Mrs. Porte wrote the equation below on the board.
ax+7=8x+b
Enter values of a and b for which x has infinitely many solutions in Mrs. Porte’s equation.
Answer:
a = 8
b = 7
Step-by-step explanation:
For us to have infinitely many solutions, then what we have on the right side must be equal to what is on the left
In this case, our a value will be equal to 8 whole out b value will be equal to 7
What is the surface area of a cylinder with base radius 4 and height 5?
Select the exact answer in terms of π.
Answer:
Solution given:
radius [r]=4
height [h]=5
we have
Surface area of cylinder=2πr(r+h)
=2π×4(4+5)
=72πunits³ is a required volume.
If the sum of n term of an ap is sn = 3n^2+5n writ its common difference
In the given arithmetic progression Common difference is 14.
what is an arithmetic progression?An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).
Given, the n term of ap is Sₙ = 3n² + 5n
Where n is the number of terms
S₁ = 3* 1 + 5*1
S₁ = 8
S₂ = 3 * 4 + 5*2
S₂ = 22
common difference = 22-8
Common difference = 14
therefore, the Common difference in the given AP is 14.
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heyy! i’ll give brainliest please help.
Answer: i'm pretty sure its c.
Step-by-step explanation:
On a coordinate plane, a line is drawn from point R to point Q. Point R is at (4, negative 1), and point Q is at (negative 5, 3). What are the coordinates of point P on the directed line segment from R to Q such that P is the length of the line segment from R to Q
The coordinate points of the point P is (-3.5, 2.3).
What is a coordinate plane?
Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line.
The ratio in which the point 'P' divides the line segment RQ is -
a:b = 5:1
The coordinates of the end-points of line segment RQ are -
R(4, -1) and Q(-5, 3).
The coordinates of the point H are obtained when a point H divides a line segment with end points (p, q) and (s, t) in the ratio a:b -
H = [(as + bp)/(a + b)], [(at + bq)/(a + b)]
H = [(5*-5 + 1*4)/(5 + 1)], [(5*3 + 1*-1)/(5 + 1)]
H = (-21/6, 14/6)
H = (-3.5, 2.3)
Therefore, the coordinate points are obtained as H = (-3.5, 2.3).
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Gcf of -28, 60, and 72
Answer:
4
Step-by-step explanation:
-28 = ±2^2 x ±7
60 = ±2^2 x ±3 x±5
72 = ±2^3 x ±3^2
=> Gcf of -28, 60, 72: 2^2 = 4
Answer: 12
Step-by-step explanation:
Therefore, the highest common factor of 60 and 72 is 12.
:) I know somebody already answered but like..im answering some stuff today, hope this helped by the way!
Solve the system. 3x+y = 10 y = 6x+1 Enter your answer by filling in the blanks. The solution is (/,/)
The estimated solution of the system 3x + y = 10 and y = 6x + 1 is (1, 7)
What is an equation?An equation is used to show the relationship between numbers and variables.
The standard form of a linear equation graph is:
y = mx + b
Where m is the slope of the line and b is the y intercept.
Given the linear equation:
3x + y = 10
y = -3x + 10 (1)
y = 6x + 1 (2)
Subtracting equation 2 from 1 to solve using elimination method gives:
0 = -9x + 9
9x = 9
x = 1
put x = 1 in eqn 2:
y = 6(1) + 1
y = 7
The solution is (1, 7)
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Make t the subject of n*2
After making the subject of [tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be [tex]$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$[/tex]
What is expression ?An expression is a combination of symbols, such as numbers and operators, that represent a computation or a value. Expressions can be used to perform calculations, assign values to variables, and control the flow of a program. They are a fundamental concept in computer programming.
What is simplification?Simplification is the process of making an expression or equation simpler, while still maintaining its meaning or function. This can be done by combining like terms, combining or removing unnecessary elements, or applying mathematical rules or identities.
For example, in algebra, simplifying an expression might involve combining the coefficients of similar terms (such as 2x + 3x = 5x), or factoring out a common factor from multiple terms (such as 2x^2 + 4x = 2x(x+2)).
Glven expression,
[tex]$$\begin{aligned}& n^2=4 \mathrm{~d}+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+1 \\& n^2-1=4 \mathrm{~d} / t^3 \\& t^3=4 \mathrm{~d} / n^2-1 \\& \mathbf{t}=\sqrt[3]{4 d / n 2-1}\end{aligned}$$[/tex]
Hence after making [tex]$\mathbf{t}$[/tex] the subject of[tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be
[tex]$$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$$[/tex]
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A submarine must descend at an average rate of at least 12 feet per minute for 5 minutes. The table shows how many feet the submarine descends
in the first 4 minutes. How many feet must the submarine descend in the fifth minute?
Answer:
Submarine must descend by 12 feet in the fifth minute.Average of the data:Average of a data set is calculated by dividing the sum of terms by the number of the terms of the set.From the table given in picture,Let the distance descended by submarine in 5th minute = x feetAverage distance descended by the submarine = = = feet per minuteStatement given in the question → "Submarine must descend at an average rate of at least 10 feet per minute"So the inequality for the statement will be,38 + x ≥ 50x ≥ 50 - 38x ≥ 12 Therefore, submarine must descend 12 feet in the 5th minute.
Step-by-step explanation:
What is the domain of the following function?
Therefore , the solution of the given problem of equation comes out to be each diagonal measures 8.4 units in length..
Define equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.
Here,
Given: 16x + 2 = 36x - 6
8 = 20x
x = 8/20,
simplifying to 2/5, or 0.4
You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.
Re-enter the value of x into a single of the equations.
=>16(0.4) + 2
=>6.4 + 2
=>8.4
To make sure, confirm with the other diagonal.
=>36(0.4) - 6
=>14.4 - 6
=>8.4
Each diagonal measures 8.4 units in length..
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The complete question is "To find the diagonal x value by the given equation 16x + 2 = 36x - 6 "