Solve this quadratic equation using the quadratic formula.
x2 - 6x + 6 = 0
The solutions of the quadratic equation are 3 ± √3.
What are Quadratic Equations?Quadratic equations are defined as the polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given quadratic equation is x² - 6x + 6 = 0.
The solutions of a quadratic equation ax² + bx + c = 0 can be found using the quadratic formula,
x = [-b ± [tex]\sqrt{b^2-4ac}[/tex] ] / 2a
From the given equation,
a = 1, b = -6 and c = 6
Substituting in the quadratic formula,
x = [-(-6) ± [tex]\sqrt{(-6)^2-(4*1*6)}[/tex] ] / [2 × 1]
= [6 ± [tex]\sqrt{36-24}[/tex]] / 2
= [6 ± [tex]\sqrt{12}[/tex]] / 2
= [6 ± 2√3] / 2
= 3 ± √3
Hence the solutions of the given quadratic equation are 3 + √3 and 3 - √3.
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Question help the critical value of a twominus−sided tminus−test computed from a large sample
a. is 1.64 if the significance level of the test is 5%.
b. cannot be calculated unless you know the degrees of freedom.
c. is the same as the pminus−value.
d. is 1.96 if the significance level of the test is 5%.
A car recently sold for $32,345. If there's a 6% sales tax on automobile sales, how much tax will be added to the price of the car
Answer:
1940.70
Step-by-step explanation:
geometry help will give brainliest
How do you do 6p-(5p+5)=-8-2(p+12)
Consider the following expression.
9v+2u+1
select all the true statements below.
*9v is a coefficient
*v+2u+1 is is written as a sum of three terms
*9v and 1 are like terms
*9v is a factor
*1 is a constant
*None of these are true
The statements that are true are: v+2u+1 is written as a sum of three terms, and 1 is a constant.
Explanation:Let's analyze each statement one by one:
9v is a coefficient: False. Coefficients are the numbers that multiply the variables. In this case, 9v is a term where 9 is the coefficient and v is the variable. v+2u+1 is written as a sum of three terms: True. The expression v+2u+1 can be separated into three terms - v, 2u, and 1. 9v and 1 are like terms: False. Like terms have the same variables raised to the same power. In this case, 9v and 1 are not like terms. 9v is a factor: False. Factors are multiplied together to get a product. In this case, 9v is not being multiplied by anything. 1 is a constant: True. Constants are terms that do not contain variables. In this case, 1 is a constant term. None of these are true: False. As we have identified, statement 2 and 5 are true. Learn more about Algebra here:
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What is the slope of a line parallel to the line 4x - 7y = -14?
Final answer:
The slope of a line parallel to the line 4x - 7y = -14 is determined by converting the equation to slope-intercept form, revealing that the slope is 4/7. Thus, any line parallel to it will have the same slope of 4/7.
Explanation:
The slope of a line parallel to the line 4x - 7y = -14 is first determined by rewriting the given line in slope-intercept form (y = mx + b), where m represents the slope. For the line 4x - 7y = -14, we can solve for y to find the slope:
Add 7y to both sides: 4x = 7y - 14.
Then add 14 to both sides: 4x + 14 = 7y.
Finally, divide every term by 7 to solve for y: (4/7)x + 2 = y.
The slope of the line is 4/7. Since parallel lines have equal slopes, any line parallel to the given line will also have a slope of 4/7.
a rectangular flower bed is five feet longer than it is wide. its area is eighty-four square feet.
What are its dimensions?
Show all work using an equation
by graphing the system of constraints find the values of x and y that maximize the object function.
Answer with Step-by-step explanation:
The solution of system of equations is all those values of x and y which satisfy both the inequalities or the points which lie in the region common between both the inequalities.
N=100x+40y
The optimal solution will be find from the points which lie on the extreme end of the region common between the inequalities i.e. (2,6), (0,8) or (5,0)
(x,y)=(2,6)
N=100×2+40×6
N= 200+240
N=440
(x,y)=(0,8)
N=100×0+40×8
N= 0+320
N=320
(x,y)=(5,0)
N=100×5+40×0
N= 500+0
N=500
Hence, optimal solution is:
(5,0)
List all of the number sets that contain the number 15.
A.
rational numbers and integers
B.
rational numbers, integers, and natural numbers
C.
rational numbers, integers, and whole numbers
D.
rational numbers, integers, natural numbers, and whole numbers
Final answer:
The number 15 belongs to several sets of numbers: it is a rational number, an integer, a whole number, and a natural number. Therefore, the correct answer to which sets contain the number 15 is D. Rational numbers, integers, natural numbers, and whole numbers.
Explanation:
Number sets form a hierarchy where certain numbers fit into multiple categories based on their characteristics. Starting from the broadest categories, we have complex numbers, which include all numbers with a real and imaginary part. However, the number 15 does not have an imaginary part, so we look to smaller sets.
The real numbers include all the values that can be found on the number line, which includes rational numbers (like fractions), irrational numbers (like √2), integers, whole numbers, and natural numbers. The number 15 is a real number because it can be found on the number line, but it is also specifically a rational number, an integer, a whole number, and a natural number because:
As a rational number, it can be expressed as the ratio of two integers, specifically 15/1. As an integer, it is a whole number and does not have a fractional or decimal part. As a whole number, it is a non-negative integer, starting from 0 and moving upwards. As a natural number, it is a positive integer used for counting (1, 2, 3, ...).
Therefore, the correct answer to the question is D. Rational numbers, integers, natural numbers, and whole numbers all contain the number 15.
What time is 8 hours and 51 minutes before 11:13 P.M.?
8 hours and 51 minutes before 11:13 P.M. is 2:22 P.M.
To find what time it is 8 hours and 51 minutes before 11:13 P.M., we need to subtract 8 hours and 51 minutes from 11:13 P.M. Here's a step-by-step explanation:
Start with the minute subtraction. Since 13 minutes is less than 51 minutes, we need to borrow one hour from the 11 P.M. So, we change 11:13 P.M. to 10:73 P.M.Now, subtract the minutes: 73 - 51 = 22 minutes. So now we have 10:22 P.M.Next, subtract the hours: 10 P.M. - 8 hours = 2 P.M.Thus, 8 hours and 51 minutes before 11:13 P.M. is 2:22 P.M.
A travel bureau estimates that when 20 tourists go to a resort with ten hotels. find the probability that no hotel is left vacant when the first group of 20 tourists arrives.
The solution for this problem is:
One way to solve is to using the "stars and bars" approach, but this could be the other one:
x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = 20
then use (20+10-1) C(10-1), this will
result to 29C9.
Then find the way to distribute x
as a result, (20-10+10-1) C (10-1) = 19C9
Thus, the probability is 19C9/29C9 or 0.0093
Jennifer is planning a vacation. The hotel cost $60 per night and her flight costs $150 round-trip. she has a budget of $50 for the flight and hotel up to how many nights can she afford in hotel?
Well if the hotel costs 60 dollars per night and she is only willing to spend $50 she wouldn't be able to spend any nights in the hotel I believe.
Hope this helps!
Guys please help! In triangle CDE, the measure of angle C is 90 degrees, side CD is 15 and DE is 3 more than CE. Find the length of the longest side of CDE.
Final answer:
Using the Pythagorean theorem, the length of the longest side of right-angled triangle CDE, which is the hypotenuse DE, is found to be 39 units.
Explanation:
In triangle CDE, angle C is given as 90 degrees, making this a right-angled triangle. According to the information provided, side CD is 15 units long, and side DE is 3 units more than side CE. We are asked to find the length of the longest side, which would be the hypotenuse in a right-angled triangle. To find the hypotenuse, which we'll designate as side DE, we must first establish the relationship between the sides. Let's call CE 'x'; therefore, DE will be 'x + 3'. Since we've established that the triangle is right-angled at C, we can use the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
So, the equation becomes CD² + CE² = DE², or 15² + x² = (x + 3)². If we solve for 'x' we have:
225 + x² = x² + 6x + 9216 = 6xx = 36As a result, CE = 36 units and DE, the longest side, equals 36 + 3, which is 39 units.
By applying the Pythagorean theorem correctly, we've found that the length of the longest side of triangle CDE is 39 units.
Find the measure of angle Q
The value of ∠Q in the figure is 146⁰.
How to determine the value of The value of ∠Q in the figure.
From the figure
Given
∠P = 2x + 10
∠R = 6x - 4
In ∆PQR
∠P + ∠Q + ∠R = 180⁰(sum of angles in triangle)
Substitute
2x + 10 + ∠Q + 6x - 4 = 180
8x + 6 + ∠Q = 180
But m∠P = m ∠R(base angles of issoceles triangle)
2x + 10 = 6x -4
-4x = -14
x = 7/2
Substitute into 8x + 6 + ∠Q = 180
8(7/2) + 6 + ∠Q = 180
28 + 6 + ∠Q = 180
34 + ∠Q = 180
∠Q = 180 - 34
= 146⁰
The value of ∠Q is 146⁰
2x + 12 - 7x = -2 for x
leave your answer as an improper fraction or convert to a decimal
2x+12-7x=-2
-5x+12=-2
-5x=-14
x=14/5
The population in Utah was 2,763,888 in 2010. The number of people living in Utah in 2016 increased by 10.4% percent. What was Utah's approximate population in 2016?
Write the conversion factor for converting meters to centimeters.
Answer:
1 meter = 100 centimeter
Step-by-step explanation:
A conversion factor is a numerical value that we use to change one set of unit to another set by performing actions like multiplication or division. When we are converting something, we must use the appropriate conversion factor of an equal value. Few conversions are :
1 meter = 100 centimeter
1 kilometer = 1000 meter
1 foot = 12 inches
1 gallon = 4.54 liters
We want the conversion factor for converting meters to centimeters. this is 1 m = 100 cm.
Write the contrapositive of the statement below.
If a triangle is an obtuse triangle, then it has one angle with measure greater than 90°
A triangle has one angle greater than 90°.
A triangle is an obtuse triangle.
If a triangle is not an obtuse triangle, then it does not have one angle greater than 90°.
If a triangle does not have one angle greater than 90°, then it is not an obtuse triangle.
If a number is subtracted from its square, the result is 2. find the number.
Michael's score is 586. moises' score is 754. michael estimates he needs about 200 more points to reach moise' score. explain how michael came up up with his estimate what strategy did he use
Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.
The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.
Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?
Select each correct answer.
(0, 33)
(4, 36)
(4.8, 30.5)
(9, 26)
(2, 22)
a computer code is based on the prime factorization of 160. Find the prime factorization of 160
Answer:
[tex]2\times 2\times 2\times 2\times 2\times 5[/tex]
Step-by-step explanation:
We have been given that a computer code is based on the prime factorization of 160. We are asked to find prime factorization of 160.
We know that prime factorization of a number is writing the prime factors of a number such that their product gives the original number.
To find prime factors of 160, we will divide 160 by 2 for 5 times and then divide by 5.
Prime factorization of 160: [tex]2\times 2\times 2\times 2\times 2\times 5[/tex].
Therefore, the prime factorization of 160 is [tex]2\times 2\times 2\times 2\times 2\times 5[/tex].
The environmental club is selling indoor herb gardens for Earth Day. Each member is encouraged to sell at least 10 gardens. You sell 3 gardens on Monday and 4 gardens on Tuesday. Write and save an inequality to find the possible numbers of gardens you can sell to reach your goal.
If each member are encouraged to sell at least 10 gardens, and you have already sold 3 + 4 = 7 gardens, therefore you only lack 3.
Let us say that x = the number of gardens you can sell, therefore the inequality equation is:
x ≥ 3
or we can also say
x > 2
The line passes through the points ( 7, -7) and ( 6, -5) a. y = -2x + 7 c. y = -2x - 7 b. y = 2x - 21 d. y = 2x - 7
Final answer:
The equation of the line passing through the points (7, -7) and (6, -5) is determined by finding the slope, which is -2, and then using the point-slope formula. However, the correct equation y = -2x + 21 is not listed among the student's provided options.
Explanation:
The student's question asks for the equation of a line that passes through two given points: (7, -7) and (6, -5). To find the equation of the line, we first need to determine its slope.
We use the formula for slope which is (change in y) / (change in x), often written as (y2 - y1) / (x2 - x1)
Slope = (-5 - (-7)) / (6 - 7) = 2 / -1 = -2. Therefore, the slope (m) is -2.
With the slope known, the next step is to use the point-slope form of the line equation, which is y - y1 = m(x - x1). Substituting one of the points and the slope, we get y - (-7) = -2(x - 7). Simplifying this gives us y = -2x + 14 + 7, which simplifies further to y = -2x + 21.
Therefore, among the options provided by the student, none of the equations match precisely, which means either there is a mistake in the question's options or in the calculation. However, the closest match, by the slope, would be option y = -2x - 7, considering only the slope and not the intercept.
Simplify 8(xy + 8) + 1
Final answer:
The expression 8(xy + 8) + 1 simplifies to 8xy + 65 by applying the distributive property and combining like terms.
Explanation:
The question asks to simplify the expression 8(xy + 8) + 1.
To simplify this expression, we need to apply the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Hence, we distribute the 8 across the terms inside the parentheses:
8 × xy = 8xy8 × 8 = 64After distributing we combine the like terms:
8xy + 64 + 1
Then we combine the numerical terms:
8xy + 65
So, the expression simplifies to 8xy + 65. This is the final simplified form of the given expression.
The formula V = IR shows the relationship between voltage, current, and resistance. Solve this formula for R.
R = VI
R = V divided by I
R = V + I
R = V – I
The formulae for resistance R is R = V/I
What is Ohm's Law ?
Providing that all physical conditions and temperatures are constant, Ohm's law says that the voltage across a conductor is directly proportional to the current flowing through it.
Ohm's law is given as :
V = IR
Now to find the value of R we divide both side by current I :
[tex]\begin{aligned}V&=IR\\R&=\frac{V}{I}\end{aligned}[/tex]
Therefore, the formulae for resistance R is R = V/I
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How many solutions does the equation have?
2x + 3 = 4x + 2
A. No solutions
B. One solution
C. Many solutions
The equation will have only one root.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation.
Given equation:
2x + 3 = 4x + 2
On solving
2x - 4x = 2-3
-2x = -1
x= -1/(-2)
x= 1/2
Also, the equation as only one variable of degree one which implies that it will have only one solution.
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Describe two ways to solve the equation 2(4x-11)=10
The volume of a rectangular prism is measured in cubic iscubic inches. WhatWhat units will the length, width, and height of the prism be measured in?
A. Inches
B. square inches
C. cubic inches
D. feet