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]
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. ^^
how to solve a complex number
Complex numbers are "binomials" of a sort, and are added, subtracted, and multiplied in a similar way. (Division, which is further down the page, is a bit different.) First, though, you'll probably be asked to demonstrate that you understand the definition of complex numbers.
Solve 3 – 4i = x + yiFinding the answer to this involves nothing more than knowing that two complex numbers can be equal only if their real and imaginary parts are equal. In other words, 3 = x and –4 = y.To simplify complex-valued expressions, you combine "like" terms and apply the various other methods you learned for working with polynomials.
Simplify (2 + 3i) + (1 – 6i).(2 + 3i) + (1 – 6i) = (2 + 1) + (3i – 6i) = 3 + (–3i) = 3 – 3i
Simplify (5 – 2i) – (–4 – i).(5 – 2i) – (–4 – i)= (5 – 2i) – 1(–4 – i) = 5 – 2i – 1(–4) – 1(–i)= 5 – 2i + 4 + i= (5 + 4) + (–2i + i)= (9) + (–1i) = 9 – iYou may find it helpful to insert the "1" in front of the second set of parentheses (highlighted in red above) so you can better keep track of the "minus" being multiplied through the parentheses.
Simplify (2 – i)(3 + 4i).(2 – i)(3 + 4i) = (2)(3) + (2)(4i) + (–i)(3) + (–i)(4i)= 6 + 8i – 3i – 4i2 = 6 + 5i – 4(–1)= 6 + 5i + 4 = 10 + 5iFinal answer:
To solve a complex number, understand it as a sum of a real number and an imaginary number and use operations like conjugation. For division, multiply by the conjugate to simplify. Complex numbers ensure all polynomial equations have solutions.
Explanation:
To solve a complex number, one must understand that a complex number z is the sum of a real number and an imaginary number, which is written as z = a + ib. The terms a and b represent the real and imaginary parts respectively, often notated as Re(z) and Im(z).
To divide by a complex number, you multiply the numerator and the denominator by the conjugate of the denominator, simplifying to a form without imaginary numbers in the denominator. This can be expressed as z/z' = (aa' + bb')/(a'² +b'²) + i(ba' - ab')/(a'² + b'²). The conjugate of a complex number z is written as z* or z*.
Complex numbers are crucial in solving polynomial equations as they ensure that every polynomial equation has a solution. This is shown by the Fundamental Theorem of Algebra, which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. For instance, the equation x² - 2x + 5 = 0 has no real solutions but two complex solutions, x = 1±2i.
Solve for t. −5t≥65
a. t≥13
b. t≤13
c. t≤−13
d. t≥−13
Pablo's gas tank is 3/10 full. after he buys 10 gallons of gas, it is 4/5 full. how many gallons can pablo's tank hold?
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.
Learn more about First Law of Thermodynamics here:https://brainly.com/question/9614649
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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.
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.
You are on the way to the ski slopes to spend the week. the mountains are 678 miles from your home. if you drive 75 miles an hour and take six 15-minute rest breaks, how much time will you need to make the trip? round your answer to the nearest tenth.
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:
Why does the square root of 64 have a positive and negative value?
Compare rational numbers what is bigger 4.9 vs 4.6
Angles of the elevation and depression: Find the value of x. Round to the nearest tenth.
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 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.
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)
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.
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
What number is 8.2% of 50?
8.2% = 0.082
50 * 0.082 = 4.1
the answer is 4.1
I need help in math will give Brainliest
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]
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.
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:
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.
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.
Find the median of the data: 206, 194, 198, 172, 190
MATH HELP!!!!!!!!!!!!!
Select the correct product.
(2x + 9)(x + 1)
2x^2 + 11x + 9
3x^2 + 11x + 9
2x^2 - 7x + 9
2x^2 + 11x + 10
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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Which equation represents a line which is parallel to the line y=4x-8y=4x−8?