Solve -3x^2-4x-4=0. Use the quadratic formula.
Answer:
[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]
[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]
Step-by-step explanation:
we have
[tex]-3x^{2} -4x-4=0[/tex]
Rewrite (Multiply by [tex]-1[/tex] both sides)
[tex]3x^{2}+4x+4=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]3x^{2}+4x+4=0[/tex]
so
[tex]a=3\\b=4\\c=4[/tex]
substitute
[tex]x=\frac{-4(+/-)\sqrt{4^{2}-4(3)(4)}} {2(3)}[/tex]
[tex]x=\frac{-4(+/-)\sqrt{-32}} {6}[/tex]
remember that
[tex]i=\sqrt{-1}[/tex]
[tex]x=\frac{-4(+/-)4i\sqrt{2}} {6}[/tex]
Simplify
[tex]x=\frac{-2(+/-)2i\sqrt{2}} {3}[/tex]
[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]
[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]
find m<p the diagram is not to scale
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. Which property justifies this statement?
If x = −2, then 5x = −10.
A. Symmetric Property of Equality
B. Multiplication Property of Equality
C. Subtraction Property of Equality
D. Transitive Property of Equality
2. Drag a statement or reason to each box to complete the proof.
If 3(x−4)=x+4, then x=8.
Statement: Reason:
1. 3(x−4)=x+4 ----> Given
2. 3x−12=x+4 ----> ________
3. 3x−12+12=x+4+12 ----> ________
4. 3x=x+16 ----> Simplifying
5. 3x−x=x+16−x ----> ________
6. 2x=16 ----> Simplifying
7. 2x2=162 ----> ________
8. x=8 ----> Simplifying
A. Subtraction Property of Equality
B. Distributive Property
C. Addition Property of Equality
D. Division Property of Equality
This is irrelevant, but was THAT many exclamation points necessary?
Anyway, these aren't that hard, you gotta just use your brain a bit. These problems use a bit of simple common sense if you put 2-and-2 together and look into it. Look for signs and just use your head, it's hard to explain but just try. ^^
Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options: Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months. Option B: Increase the amount of money they save each month by $80 from what they've been saving. Which of the following is a true statement? a. Only option A will allow them to meet their goal. b. Only option B will allow them to meet their goal. c. Both options A and B will allow them to meet their goal. d. Neither option A nor option B will allow them to meet their goal.
Solve for t. −5t≥65
a. t≥13
b. t≤13
c. t≤−13
d. t≥−13
PLEASE HELP ME WITH THIS! WILL MARK BRILLIANT!!! ✨✨
Answer:
b. linear; y +2 = -5/4(x +9)
Step-by-step explanation:
From the first line of the table to the second, we have ...
slope = (change in y)/(change in x) = (-7-(-2))/(-5-(-9)) = -5/4
Only one equation shows a slope of -5/4: the second one.
__
We know the relation is linear because the same slope can be computed from any pair of lines of the table. In particular, from one row to the next, x changes by the constant value +4 and y changes by the constant value -5.
Find the dimensions of a right circular cylindrical can with both a top and a bottom that holds 5832 cubic cm and is constructed with the least amount of material possible.
The dimensions of a right circular cylindrical can that holds 5832 cubic cm and uses the least amount of material are a radius of approximately 10.614 cm and a height of approximately 16.526 cm.
Explanation:The question asks for the dimensions of a right circular cylindrical can that holds 5832 cubic cm of liquid and is designed to use the least amount of material. This scenario fits into the realm of mathematical optimization. Here, we’re being asked to identify dimensions that minimize the surface area of the cylinder while holding a fixed volume. This kind of problem is typically addressed using calculus.
The volume V of a cylinder is given by the formula V = πr²h where r is the cylinder radius and h is the cylinder height. The surface area A of a cylinder closed at both ends is given by A = 2πrh + 2πr².
From the volume equation, we can express h in terms of V and r, h = V/πr². Substituting this into the surface area equation yields: A = 2πr(V/πr²) + 2πr² = 2V/r + 2πr².
To find the radius that minimizes the surface area, we would set the derivative of the surface area with respect to r equal to zero and solve for r. After these calculations, we find that r = (V/(2π))^(1/3). For V = 5832 cubic cm, this yields r ≈ 10.614 cm.
Substitute r ≈ 10.614 cm back into the equation h = V/πr² to find h ≈ 16.526 cm. So, the dimensions of the can that minimizes the material used are radius 10.614 cm and height 16.526 cm.
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To find the dimensions of the cylindrical can that holds a specific volume and is made from the least material, utilize the volume and surface area formulas for a cylinder. Using calculus, find the radius that minimizes the surface area, then find the corresponding height.
Explanation:This problem is a classic calculus optimization problem. The volume of the cylindrical can is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder. To minimize the amount of material used in constructing the can, we need to minimize the surface area, given by the formula [tex]A = 2\pi rh + 2\pi r^2[/tex] (which includes both top and bottom of the can).
From the volume formula, we can express h as h = V/πr² = 5832/πr². Substituting this value into the surface area equation, we get A = [tex]2\pi r(5832/\pi r^2) + 2\pi r^2 = 11664/r + 2\pi r^2.[/tex] Differentiating this equation with respect to r and setting the derivative equal to zero, will provide the radius that minimizes the material used. The height can be obtained by substituting this radius value back into the equation h = 5832/πr².
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what is the estimate 5% of 59
I if 700 tickets were sold for a concert and only 587 people attended, how many people bought a ticket but Did not attend
Final answer:
There were 113 people who bought a ticket but did not show up to the concert, calculated by subtracting the number of attendees (587) from the total tickets sold (700).
Explanation:
To determine how many people bought a ticket but did not attend the concert, you would subtract the number of people who attended from the total number of tickets sold. In this case, 700 tickets were sold and only 587 people attended. So, the calculation would be:
700 tickets sold - 587 attendees = 113 people who did not attend
Thus, 113 people bought a ticket but did not show up to the concert.
Determine the vertex point, domain, and range of the following function
y = -|x| + 2
Which equation represents a line which is parallel to the line y=4x-8y=4x−8?
BRAINLIEST!!!
Gary earns $12 an hour plus $16 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week.
Part A: Create an equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime. (3 points)
Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 30 hours. (3 points)
Part C: Gary earned $408 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)
The solutions to the inequality y<-x+1 are shaded on the graph. Which point is a solution?
Answer:
the answer is B
Step-by-step explanation:
Determine algebraically whether the function is even, odd, or neither even nor odd.
f(x) = -4x3 + 4x
Select one:
a. Neither
b. Even
c. Odd
The sum of two numbers is 50 . the smaller number is 12 less than the larger number. what are the numbers?
The two numbers are 31 and 19, where 31 is the larger number and 19 is the smaller number which is 12 less than the larger number.
The sum of two numbers is given to be 50, and the question states that the smaller number is 12 less than the larger number. To find these numbers, let's denote the larger number as x and the smaller number as x - 12. According to the problem, the sum of these two numbers is 50, so we can write the equation:
x + (x - 12) = 50
Simplifying the equation gives us:
2x - 12 = 50
Adding 12 to both sides gives us:
2x = 62
Dividing both sides by 2 gives us:
x = 31
Now that we know the larger number is 31, we can find the smaller number by subtracting 12:
x - 12 = 31 - 12
x - 12 = 19
Therefore, the two numbers are 31 and 19.
Regina took out a 30-year loan for $190,000 at 4.5% interest, compounded monthly. If her monthly payment on the loan is $962.70, and if $712.50 of her first payment went toward interest, how much of her second payment went toward interest?
A.$962.70
B.$712.50
C.Less than $712.50
D.More than $712.50 but less than $962.70
please please please help
Answer:
C.Less than $712.50
Step-by-step explanation:
Given details are :
Loan amount = $190,000
Rate = 4.5% or 0.045 compounded monthly.
Time = [tex]30\times12=360[/tex] months
Monthly payments are = $962.70
First month interest = $712.50
I have calculated this using excel sheet and the answer is - C.Less than $712.50 .
Please find attached the excel sheet to see the working. You can see the highlighted interest that is less than first month interest.
Answer:Less than $712.50
Step-by-step explanation:
Why does the square root of 64 have a positive and negative value?
What is the standard form of y=3/8x-4
Final answer:
The standard form of the equation y = (3/8)x - 4 is 8y - 3x = -32.
Explanation:
The standard form of the equation y = (3/8)x - 4 is written as 8y - 3x = -32.
To convert a linear equation from slope-intercept form (y = mx + b) to standard form (Ax + By = C), you need to multiply the entire equation by the common denominator of the coefficients.
In this case, the common denominator is 8, so multiplying both sides of the equation by 8 gives us 8y = 3x - 32. Moving all the terms to one side, we have 8y - 3x = -32, which is the standard form of the equation.
To transform the equation y = 3/8x - 4 into standard form, subtract 3/8x from both sides and then multiply through by 8 to eliminate the fraction, resulting in -3x + 8y = -32.
Explanation:The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are integers and A should not be negative. To convert the equation y = 3/8x - 4 to standard form, you need to manipulate the equation so that it fits the standard form criteria.
Step-by-step, we start by moving the x-term to the left side of the equation:
Subtract 3/8x from both sides: -3/8x + y = -4.Multiply through by 8 to eliminate the fraction: -3x + 8y = -32.Normally, we would want A to be positive, but since 3 is already negative, we can leave the equation as is.Therefore, the standard form of the given equation is -3x + 8y = -32.
Select the correct product.
(2x + 9)(x + 1)
2x^2 + 11x + 9
3x^2 + 11x + 9
2x^2 - 7x + 9
2x^2 + 11x + 10
A segment with endpoints X Left parenthesis negative 6 comma 2 right parenthesis and Y Left parenthesis negative 1 comma negative 3 right parenthesis is rotated 90º about the origin. What are the coordinates of X Prime and Y Prime?
A. X prime Left parenthesis negative 1 comma negative 3 right parenthesis and Y prime Left parenthesis negative 6 comma 2 right parenthesis.
B. X prime Left parenthesis 2 comma 6 right parenthesis and Y prime Left parenthesis negative 3 comma 1 right parenthesis.
C. X prime Left parenthesis negative 2 comma negative 6 right parenthesis and Y prime Left parenthesis 3 comma negative 1 right parenthesis
D. X prime Left parenthesis 6 comma negative 2 right parenthesis and Y prime Left parenthesis 1 comma 3 right parenthesis
Answer:
The correct answer is C.
Step-by-step explanation:
This can be done using complex numbers and its relations with plane geometry. The endpoints of the segment are X(-6,2) and Y(-1,-3). These points can be seen as complex numbers, just recall the geometric interpretation of complex numbers.
So, the complex counterpart of [tex]X(-6,2) is x=-6+2i[/tex], and the complex counterpart of [tex]Y(-1,-3) = -1-3i[/tex]. Moreover, a rotation about the origin has an interpretation as multiplication by a complex number of modulus 1. In this particular case, a rotation of 90 degrees is equivalent to multiply by the complex unit: [tex]i=\sqrt{-1}[/tex].
Then,
[tex] x' = (-6+2i)\times i = -2-6i[/tex] which gives the point [tex]X'(-2,-6)[/tex]
[tex] x' = (-1-3i)\times i = 3-1i[/tex] which gives the point [tex]Y'(2,-1)[/tex].
The other option is to use a software to make geometrical constructions as Geogebra. Bellow there is an image attached made with Geogebra with the solution of the exercise.
Compare rational numbers what is bigger 4.9 vs 4.6
wilson jarred 45 liters of jam after 5 days. how much jam did wilson jar if he spent 7 days making jam? solve using unit rates.
Find the median of the data: 206, 194, 198, 172, 190
belinda has twice as many nickels as dimes. how many of each does she have if they total
A) 80 cents
B) $1.20
Show all work using an equation
Angles of the elevation and depression: Find the value of x. Round to the nearest tenth.
Rounded to the nearest thousandth, what is the decimal equivalent of 6 7/9%?
Final answer:
To convert 6 7/9% to a decimal, we change the mixed number to an improper fraction, divide by 100 and round to the nearest thousandth, resulting in approximately 0.068.
Explanation:
To find the decimal equivalent of 6 7/9%, we must first convert the mixed number to an improper fraction and then to a decimal. To convert 6 7/9% to an improper fraction, we multiply the whole number 6 by the denominator 9 and add the numerator 7 to get 7 + (6 × 9) = 7 + 54 = 61. Then we place 61 over the original denominator to obtain 61/9. The percentage sign indicates that we are dealing with a part out of 100, so we must divide 61/9 by 100 or, equivalently, multiply by 1/100.
Therefore, the calculation to convert the percentage to a decimal is: (61/9) × (1/100) = 61/900. Using a calculator, or performing the division manually, gives us approximately 0.0677777....
Finally, to round this to the nearest thousandth, we would look at the fourth decimal place (which is 7 in this case). Since 7 is greater than 5, we round up the third decimal place, resulting in 0.068.
The vertex form of the equation of a parabola is x=8(y-1)^2-15. What is the standard form of the equation?
The standard form of the equation is:
[tex]x=8y^2-16y-7[/tex]
Step-by-step explanation:We know that the standard form of a quadratic equation is given by the expression:
[tex]x=ay^2+by+c[/tex]
where a,b and c are real numbers.
and a≠0
Here we are given the vertex form of the equation of a parabola by:
[tex]x=8(y-1)^2-15[/tex]
Now, on expanding the parentheses term by using the formula:
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Here a=y and b= 1
Hence, we have:
[tex]x=8(y^2+1-2y)-15\\\\i.e.\\\\x=8\times y^2+8\times 1-2y\times 8-15\\\\i.e.\\\\x=8y^2+8-16y-15\\\\i.e.\\\\x=8y^2-16y+8-15[/tex]
( Since, in the last step we combined the constant term i.e. 8 and -15 )
Hence, we get the standard form of the equation as:
[tex]x=8y^2-16y-7[/tex]
The ideal circumference of a woman's basketball is 28.75 in. The actual circumference may vary from the ideal by at most 0.25 in. What are the acceptable circumferences for a woman's basketball? Let the variable c represent circumference.
The acceptable circumferences for a woman's basketball range from 28.5 inches to 29 inches.
Explanation:To find the acceptable circumferences for a woman's basketball, we need to consider the ideal circumference and the allowable variation. The ideal circumference is 28.75 inches and the actual circumference can vary by at most 0.25 inches. So, the acceptable circumferences can be found by adding and subtracting the maximum allowable variation from the ideal circumference:
Acceptable circumference = 28.75 ± 0.25 inches
This means the acceptable circumferences for a woman's basketball range from 28.5 inches to 29 inches.
Calculate δe, if q= 0.764 kj and w= -830 j . express your answer using two significant figures.
When calculating the change in internal energy (δe) using the First Law of Thermodynamics, first convert all units to the same kind, then apply the formula δe = q + w. In this case, the answer is -0.07 kJ or -70 J.
Explanation:This is a Chemistry question involving the calculation of change in internal energy (δe) using the First Law of Thermodynamics, which states that the change in internal energy is equal to heat (q) added to the system plus the work (w) done on the system. Specifically, the formula is: δe = q + w.
In this case, you have a value for heat (q) of 0.764 kJ and a value for work (w) of -830 J, but these values are not in the same units. In order to add them, you need to convert work (w) to kJ:-830 J * (1 kJ / 1000 J) = -0.83 kJ.
Now you can put these values into the formula: δe = 0.764 kJ + (-0.83 kJ) = -0.07 kJ, which may also be written as -70 J.Therefore, using two significant figures, the answer is -0.07 kJ or -70 J.
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The change in internal energy (ΔE) is -0.07 kJ. Since ΔE is negative, this indicates that the system has lost internal energy.
Given:
q = 0.764 kJ
w = -830 J
We can calculate the change in internal energy (ΔE) using the following equation:
ΔE = q + w
where:
ΔE is the change in internal energy (kJ)
q is the heat absorbed by the system (kJ)
w is the work done by the system (kJ)
First, convert the work from joules to kilojoules:
w = -830 J * (1 kJ/1000 J) = -0.830 kJ
Now, plug in the values for q and w to calculate ΔE:
ΔE = 0.764 kJ + (-0.830 kJ) = -0.066 kJ
Round the answer to two significant figures:
ΔE ≈ -0.07 kJ
Therefore, the change in internal energy (ΔE) is -0.07 kJ. Since ΔE is negative, this indicates that the system has lost internal energy.
For what values of x and y must each figure be a parallelogram?
The required values are x = 60 and y = 30 for the given parallelogram.
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal. A parallelogram is a square and a rhombus is a square.
The parallelogram is represented in the given figure
A parallelogram has two pairs of adjacent sides that are congruent.
As per the given figure, we have
x + 5x - 180 = 180
6x = 360
x = 360/6
Apply the division operation, and we get
x = 60
2y + 4y = 180
Apply the addition operation, and we get
6y = 180
y = 180/6
y = 30
Thus, the required values are x = 60 and y = 30
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