Answers
Answer:
The first one
Step-by-step explanation:
We want to find the roots of the equation -2x + 3 = -8x²
Step 1: Our first step is to get the equation in quadratic form so we can use the quadratic formula to find the roots
Quadratic form: ax² + bx + c = 0
We can easily get this equation in quadratic form by moving -8x² to the right side. We can do this using inverse operations. The inverse of subtraction is addition so to get rid of -8x² we add 8x² to both sides
After adding -8x² to both sides we acquire 8x² - 2x + 3 = 0
The equation is now in quadratic form meaning we can now use the quadratic formula to find the roots.
Quadratic Formula : \(\frac{-b+-\sqrt{b^2-4(a)(c)} }{2(a)}\)
where the values of a, b and c are derived from the equation
Remember that the equation is in quadratic form ax² + bx + c = 0
8x² - 2x + 3 = 0 so a = 8 , b = - 2 and c = 3
We then plug in these values into the quadratic formula ( note that the +- means plus or minus meaning that we have to evaluate this twice, once when the discriminant ( b² - 4(a)(c) is the discriminant ) is being add to -b and once when the discriminant is being subtracted from -b )
First lets evaluate when the discriminant is being added to -b
Recall the quadratic formula : \(\frac{-b+\sqrt{b^2-4(a)(c)} }{2(a)}\)
a = 8 , b = - 2 and c = 3
\(\frac{2+\sqrt{2^2-4(8)(3)} }{2(8)}\)
Work being done inside of the square root: 2² = 4 , -4 * 8 = -32 , -32 * 3 = -96
4 - 96 = - 92
Work being done at denominator : 2 * 8 = 16
\(\frac{2+\sqrt{-92} }{16}\)
The first root is \(\frac{2+\sqrt{-92} }{16}\)
We now do this same process but instead we subtract the discriminant.
We would be left with the same thing but it would be \(\frac{2-\sqrt{-92} }{16}\) instead of \(\frac{2+\sqrt{-92} }{16}\)
In some cases we would get a completely different answer, so evaluating it twice, once when the discriminant is being add to -b and once when the discriminant is being subtracted from -b may be important in some cases.
We then simplify the two roots. You may notice that there is a negative number under the radical and you might ask how can you square root a negative? well you can't which is when imaginary roots come in. Imaginary roots: i = -1 . We can take out an i from -92 making it 92 because i = -1 and -92/-1 = 92. We would be left with i√92
So we can conclude that the roots of the equation are \(\frac{2+i\sqrt{92} }{16} and \frac{2-i\sqrt{92} }{16}\)
Looking at the answer choices we notice that there are two very similar answers. The first and second one. The only difference between the two is that 2 is positive on the first one and 2 is negative on the second one. Looking at the roots we just found, the 2 should be positive therefore the answer is the first one.
Note that ± means plus or minus and it means that the expression can either be added or subtracted and it will be a root. This means that saying the roots are \(\frac{2+-i\sqrt{92} }{16}\) is the same as saying the roots are \(\frac{2+i\sqrt{92} }{16} and \frac{2-i\sqrt{92} }{16}\)
Related Questions
A cone has surface area 360π in2 and volume 800π in3. The cone is dilated, and the surface area of the dilated cone is 2,250π in2. What is the dilated cone's volume?
Answers
This means that the height, radius, and volume of the dilated cone are 2.5 times larger than the corresponding dimensions of the original cone.
What is the equation of the line that passes through the points (2, 4) and (-1, 6)?To find the volume of the dilated cone, we can use the concept of similarity.
The ratio of the surface areas of similar objects is equal to the square of the ratio of their corresponding dimensions.
In this case, the surface area of the dilated cone is 2,250π in², which is 6.25 times larger than the surface area of the original cone (360π in²).
Since the surface area is proportional to the square of the dimensions, the dimensions of the dilated cone are √6.25 times larger than the dimensions of the original cone. Let's calculate the scale factor for the dimensions:
√6.25 = 2.5The original cone has a volume of 800π in³. Multiplying it by the scale factor (2.5) cubed gives us the volume of the dilated cone:
Volume of dilated cone = (2.5)³ ˣ 800π in³
= 15.625 ˣ 800π in³= 12,500π in³Therefore, the dilated cone's volume is 12,500π in³.
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The graph of f(x)=3x^2+12 is vertically compressed by a factor of to get the graph of function g.What is the simplified function rule for function g?
Answers
Answer: The function g(x) will have a simplified rule of g(x) = 3/9 x^2 + 12.
The vertical compression by a factor of 1/3 means that the y-values of the graph of f(x) will be multiplied by 1/3 to get the corresponding y-values of the graph of g(x). So, the coefficient of x^2 in the rule for g(x) will be 3/9 or 1/3, and the constant term remains the same as 12.
Simplifying 3/9, we get 1/3, so the simplified function rule for g is g(x) = 1/3 x^2 + 12.
Step-by-step explanation:
I have 25 coins in my pocket all of which are 5 penny or 20 penny coins. if their total value is 2.90 pounds how many penny coins do I have?
Answers
Answer:
14 coins of 5p11 coins of 20pStep-by-step explanation:
Given
5p coins = x20p coins = yTotal = 2.90 = 290 pNumber of coins = 25Equations
x + y = 255x + 20y = 290 ⇒ x + 4y = 58Consider the first equation in the second one
x + y + 3y = 5825 + 3y = 583y = 33y = 11Then x is
x = 25 - 11 = 14Answer
14 off 5p coins and 11 off 20p coinsa man bought a set of furniture listed 2350. he received a discount of 5% and then paid 3 % sales tax on the selling price. the sales tax was
Answers
Answer:
Sales tax on selling price: $2232.50(0.03) = $66.98
Step-by-step explanation:
List price: $2350
5% discount: 0.05($2350) = $117.50
Sale (selling) price: List price less discount: $2350 - $117.50 = $2232.50
Sales tax on selling price: $2232.50(0.03) = $66.98
6
A bag of sweets contains jellies, mints and toffees.
The ratio of jellies to mints is n : 2.
The ratio of mints to toffees is 5 : 3n.
Work out the ratio of jellies to toffees.
Give your answer in its simplest form.
Answers
Answer:
jellies : toffees = 5 : 6
Step-by-step explanation:
expressing the ratios in fractional form
\(\frac{jellies}{toffees}\) = \(\frac{jellies}{mints}\) × \(\frac{mints}{toffees}\)
= \(\frac{n}{2}\) × \(\frac{5}{3n}\)
= \(\frac{5n}{6n}\) ( cancel n on numerator/ denominator )
= \(\frac{5}{6}\)
then jellies : toffees = 5 : 6
Substitute each variable to determine whether the inequality statement is true or false.
1/6 >3, if j = 24
Answers
Answer:
false
Step-by-step explanation:
95 divided by 2?? Please help!
Answers
Answer:
47.5
Step-by-step explanation:
95 divided by 2 is equal to 47 with a remainder of 1.
To divide 95 by 2, you need to perform long division.
Here's the step-by-step process:
Write the dividend (95) inside the division bracket, and the divisor (2) outside the bracket.
Place the quotient above the division bracket.
__
2 | 95
Start with the leftmost digit of the dividend (9) and divide it by the divisor (2). Since 9 is smaller than 2, we move to the next digit.
__
2 | 95
4
Bring down the next digit of the dividend (5) to the right of the remainder
(1) obtained from the previous step.
__
2 | 95
4 1
Divide 15 by 2. The quotient is 7, and the remainder is 1.
__
2 | 95
47 1
Since there are no more digits in the dividend, we have completed the division.
The quotient is 47, and the remainder is 1.
Therefore, 95 divided by 2 is equal to 47 with a remainder of 1.
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I need answers pretty quickly
Answers
Answer:
Step-by-step explanation:
Linear is C .
Quadratic is A
Exponential is B
Answer: c, a, b in that order top to bottom
Step-by-step explanation:
LINEar is a straight line, quadratic is a parabola and exponetial increases at an EXPONENTIALly fast rate
Add. Simplify the answer to lowest terms before entering the numerator and denominator in their boxes.
11/16 + 3/16 =
PS: 14/16 is wrong
Answers
Answer: 7/8
Step-by-step explanation:
You start at (7, 10). You move right 2 units and down 4 units. Where do you end?
Answers
Solve for a.
1. all real numbers
2. -1
3. 0
4. no solution
Answers
does a parallelogram have 2 pairs of parallel sides
Answers
Answer:
A parallelogram is a quadrilateral with 2 pairs of parallel sides
What is the diameter of a hemisphere with a volume of 2507 in³, to the
nearest tenth of an inch?
Answers
Answer:
The formula for the volume of a hemisphere is V = (2/3)πr³. Solving for r, we get r = (3V/4π)^(1/3). Substituting V = 2507 in³, we get r ≈ 7.5 in. The diameter of a hemisphere is twice its radius, so the diameter of this hemisphere is approximately 15 inches to the nearest tenth of an inch.
Step-by-step explanation:
V = (2/3)πr^3
where V is the volume and r is the radius.
We are given that the volume of the hemisphere is 2507 in^3, so we can set up the equation:
(2/3)πr^3 = 2507
Solving for r, we get:
r^3 = (2507 × 3) / (2π) = 3764.51
Taking the cube root of both sides, we get:
r = 15.67
The diameter of the hemisphere is twice the radius, so:
d = 2r = 31.34
Rounding to the nearest tenth of an inch, we get:
The volume of a hemisphere is given by the formula:
V = (2/3)πr^3
where V is the volume and r is the radius.
We are given that the volume of the hemisphere is 2507 in^3, so we can set up the equation:
(2/3)πr^3 = 2507
Solving for r, we get:
r^3 = (2507 × 3) / (2π) = 3764.51
Taking the cube root of both sides, we get:
r = 15.67
The diameter of the hemisphere is twice the radius, so:
d = 2r = 31.34
Rounding to the nearest tenth of an inch, we get:
Answer:
d ≈ 31.3 inches
Step-by-step Explanation:
Therefore, the diameter of the hemisphere with a volume of 2507 in^3 is approximately 31.3 inches.
Explain, with at least 2 complete sentences, how to find the slope from a table.
Answers
Answer:
Step-by-step explanation:
We know the slope is rise over run. You can also find slope by using the formula (y2-y1)/(x2-x1) where x1, x2, y1 and y2 are points from the table. These points also aren't random and must correspond with each other. Example x1 and y1.
Hello help please
4. While watching an American television station, Jordan hears an ad for a grocery store. The store sells a gallon of milk for $2.99. Without considering currency exchange, what is the milk’s approximate price per litre?
Answers
So it’s $2.99/3.785 litres
= $0.78996037/litre
Maybe round it to $0.79/litre?
What is 42.5 rounded to the nearest whole number?
Answers
Answer:
The answer is 43
Step-by-step explanation:
when you have a whole number and .5 you automatically round up to the next whole number
A notebook is $8 more expensive than a
pen.
four notebook and two pens cost $56.
How much does one notebook cost?
How much does one pen cost?
Answers
Answer:
n = 12, p = 4
Step-by-step explanation:
Hi there!
n = notebook
p = pen
If we know that one notebook costs 8 dollars more than a pen,
we can set the equation for the cost of the pen as n - 8 = p. Now, we have to create an equation for the total cost. This could be represented as 4n + 2p = 56.
Let’s plug in that equation for the pen into our total cost equation.
This would become \(4n + 2(n-8) = 56\)
Using distributive property, the equation becomes \(4n + 2n - 16 = 56\)
After we combine like terms and add 16 to both sides, we find out that \(6n = 72\) or n = 12
Now that we know the cost of the notebook, we can solve for the pen. Plug in 12 for the n values in the original equation \(4n + 2p = 56\)
This leaves us with 48 + 2p = 56. Subtract 48 from both sides and then divide that by two to find p.
p = 4
I hope this helped!
Answer:
Cost of one notebook = $12
Cost of one pen = $4
Step-by-step explanation:
Let,
Cost of one notebook = x
Cost of one pen = y
According to given statement;
x = y+8 Eqn 1
4x+2y=56 Eqn 2
Putting value of x from Eqn 1 in Eqn 2
4(y+8)+2y=56
4y+32+2y=56
6y=56-32
6y=24
Dividing both sides by 6
\(\frac{6y}{6}=\frac{24}{6}\)
y=4
Putting y=4 in Eqn 1
x = 4+8
x=12
Hence,
Cost of one notebook = $12
Cost of one pen = $4
28+12
—————
13-5
7th Grade Math Book (McGraw-Hill) page 9 exercise 26
Answers
Barton wants to know how much his packed suitcase weighs before he leaves to catch a flight. The airline will charge an extra fee if his suitcase weighs more than 50 pounds. Which method should Barton use to get the most accurate and appropriate measurement?
Answers
Barton should use a luggage scale to get the most accurate and appropriate measurement of his packed suitcase before he leaves to catch a flight. A luggage scale is a compact and portable device that is designed specifically to weigh luggage. Using a luggage scale is easy and convenient as it allows travelers to weigh their bags accurately, ensuring that they are within the airline's weight limit. To use a luggage scale, Barton should follow these simple steps:
Step 1: Attach the luggage strap Barton should attach the luggage strap to the handle of his suitcase.The strap should be attached in such a way that it can support the weight of the suitcase without slipping or coming off.
Step 2: Turn on the luggage scale Barton should turn on the luggage scale and wait for it to calibrate. This usually takes a few seconds. Once the scale is calibrated, it will display a zero reading.
Step 3: Lift the suitcase Barton should lift the suitcase by the luggage strap until it is off the ground. The luggage scale will display the weight of the suitcase on its digital display. This reading is the weight of the suitcase including all the contents inside.
Step 4: Check the weight If the weight of the suitcase is less than 50 pounds, Barton can go ahead and catch his flight without worrying about any extra charges. If the weight of the suitcase is more than 50 pounds, Barton will have to remove some items from the suitcase or pay the extra fee charged by the airline.
Therefore, using a luggage scale is the most accurate and appropriate method for travelers like Barton to measure their suitcase weight before boarding their flight.
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Answer:
use a standard digital bathroom scale.
Step-by-step explanation:
2. Solve for x given given the following
Answers
Answer:
Step-by-step explanation:
Since the triangles are equivalent,
3x - 2 = 5
Solve for x.
3x = 7
x = 7/3
Your aunt offers you a choice of $22,000 in 17 years or $950 today. At a discount rate of 20 percent, how much is your aunt's offer of $22,000 worth today? (Enter your answer as a positive number rounded to 2 decimal places.) If you invest $12,500 today, how much will you have in each of the following cases? Enter all answers as positive amounts. a. In 8 years at 7 percent? (Round your final answer to 2 decimal places.) b. In 17 years at 10 percent? (Round your final answer to 2 decimal places.) c. In 20 years at 12 percent (compounded semiannually)? (Round your final answer to 2 decimal places.)
Answers
At a discount rate of 20%, the present value of your aunt’s offer of $22,000 in 17 years is approximately $190.46.
To calculate the present value of your aunt’s offer, we use the discount rate of 20%. The formula for present value is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. Plugging in the values, we have PV = $22,000 / (1 + 0.20)^17, which gives us approximately $190.46.
For the investment scenarios, we use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial investment), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values for each case, we calculate the final amounts.
a. A = $12,500(1 + 0.07/1)^(1*8) ≈ $19,956.77.
b. A = $12,500(1 + 0.10/1)^(1*17) ≈ $46,426.32.
c. A = $12,500(1 + 0.12/2)^(2*20) ≈ $73,785.59.
Therefore, if you invest $12,500 today, you will have approximately $19,956.77 in 8 years at 7%, $46,426.32 in 17 years at 10%, and $73,785.59 in 20 years at 12% compounded semiannually.
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The figure below shows two pair of congruent triangles. ΔDEF ≅ ______. ΔWXY ΔWYX ΔYWX ΔYXW
Answers
Answer:
YXW
Step-by-step explanation:
Answer:
YXW
Step-by-step explanation:
A suit is being sold for 194.49, discount is 73% from the original price.
What’s the original price?
Answers
The original price is $720.33 .
What is original price ?
Convert the percent discount to a decimal by dividing by 100% . Step 2: Set up the equation P=(1−d)x P = ( 1 − d ) x to find the original price of the item where P is the sale price, d is the discount as a decimal, and x is the original price of the item.You need to be aware of the selling price as well as the discount % in order to determine the item's original cost. The calculations contain a straightforward method that divides the sale price by the percentage-based result of 1 minus the discount. To determine an item's original or list price, use this formula.
SInce $194.49, is what is owed after the discount you will want to subtract 73 from 100 to get the percent of what is owed. Then you will set it up like a percent equation. 27/100 = 194.49/X where X = the original price. You will then multiply 194.49 by 100 and divide that answer by 1.9449. This equals $720.33 as the original price.
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35 gallon to fl oz plz answer.
Answers
Answer: 4480 fluid ounces
Step-by-step explanation:
To solve the question, we should note that:
1 gallon = 128 fluid ounces
Therefore, 35 gallons converted to fluid ounces will be:
= 35 × 128 fluid ounces
= 4480 fluid ounces
jorje wants to estimate the percentage of people who play sports. he surveys 330 individuals and finds that 65 play sport. find the margin of error for the confidence interval for the population proportion with a 95% confidence level.
Answers
The margin of error for the confidence interval for the population proportion with a 95% confidence level is 0.000207
How to find the margin of errorfinding the percentage of 65 of 330 individuals
65 / 330 * 100 = 19.697% = 0.19697
number of samples, n = 330
standard deviation, σ is calculated from
= √{(p(1 - p)) / n}
= √{(0.197 * (1 - 19.7)) / 330}
= √{(0.197 * (0.803)) / 330}
= 0.022
Margin of error, E
= Z(0.95) * σ/√(n)
= 0.171 * 0.022/√(330)
= 0.171 * √(0.022²/330)
= 0.000207
= 0.021%
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Graph a line with a slope of -3,that contains the point (4, -2)
Answers
Answer:
Hi! The equation used to graph a line with a slope of -3 that contains the point (4,-2) is (-3x+10).
The graph would look like this (if it doesn't show up please let me know)
Two angles inside the triangle that do no share a vertex with the exterior.
Remote Interior Angles
Triangle Sum Theorem
Exterior Angle Theorem
Angle-Angle Criterion
Answers
Solve by separating variables. 3y^2 dy/dx=8x
Answers
The solution of the given differential equation 3y² dy/dx = 8x by separating the variables is given by y³ = 4x² + 8.
Given that
3y² dy/dx = 8x
We can solve this differential equation using the method of Separation of Variables.
For that, we can write it as,
3y² dy = 8x dx
Integrating both sides of the equation,
∫ 3y² dy = ∫ 8x dx
Using the integration formulae,
∫ y² dy = 8/3 ∫ x dx
[ ∵ ∫ x dx = x²/2 ]
y³/3 = 8/3 (x²/2) + C
where C is the constant of integration
So the general solution of the given differential equation is
y³ = 4x² + C .......(1)
Let's solve for constant C using the initial condition y(0) = 2Substituting x = 0 and y = 2 in equation (1)
2³ = 4(0)² + C
8 = C
Thus the required solution is
y³ = 4x² + 8
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there are 7 cows and 5 chicken in the farmer's filed
write the ratio of cows to all the animals in the filed
Answers
Answer:
7:12
Step-by-step explanation:
Total no of animals in the field = 7 + 5 = 12
Ratio of cows 2 all d animals in the field =
\( \frac{no \: of \: cows}{total \: no \: of \: animals \: on \: the \: field} \)
Ratio = 7/12 = 7:12
What is the diameter of a sphere with a volume of 170m3