which method would i use to solve ax^2+c=d? justify your answer.
Answers
9514 1404 393
Answer:
x = ±√((d -c)/a)
Step-by-step explanation:
The usual "solve for ..." approach works fine in this case.
ax^2 +c = d
ax^2 = d - c . . . . . subtract c
x^2 = (d -c)/a . . . . divide by a
x = ±√((d -c)/a) . . . take the square root
_____
When there are numbers, a graphical solution could work. It depends on whether an exact or approximate solution is required.
_____
Comment on "solve for ..."
When solving an equation for a specific variable, it is worthwhile to consider the Order of Operations. Look at what has been done to the variable, then undo those operations in reverse order. Here, the variable has been squared, the product multiplied by 'a', that product added to c. So, the "undo" consists of subtracting 'c', dividing by 'a', and taking the square root.
Related Questions
Multiply. Write the answer in simplest form.
Or look at screenshot answer correctly
**PLS HELP!**
Answers
3/5x2 5/6= 5/7
Step-by-step explanation:
i hope this helps
How do I do this ( answer please )
Answers
Answer:
I think see what circuit is connected to the light
Step-by-step explanation:
Slope intercept and all that stuff
Answers
Answer:
what?
Step-by-step explanation:
I need help thank you. here is the question...............................
Answers
If an object is dropped from a high cliff or a tall building, then the distance it has fallen after t seconds is given by the function f(t)=16t^(2)
Answers
When an object is dropped from a high cliff or a tall building, the distance it has fallen after t seconds is given by the function f(t)=16t².
This is because the force of gravity pulls objects towards the earth, and this force is a constant acceleration of 9.81 meters per second squared.To calculate the distance an object has fallen after t seconds, we use the equation d = ½at², where d is the distance, a is the acceleration due to gravity, and t is the time.
In this case, a = 9.81 m/s², but the equation you've been given uses a slightly different acceleration value, 16 feet per second squared (ft/s²). To convert this to meters per second squared, we can use the conversion factor 1 ft/s² = 0.3048 m/s².
Therefore,
a = 16 ft/s² × 0.3048 m/ft = 4.9 m/s².
So the distance an object has fallen after t seconds is given by
d = ½at² = ½ × 4.9 m/s² × t² = 4.9t² meters
This is the same equation as the one you were given: f(t) = 16t². However, it is important to note that the units of measurement are different, and you should use the appropriate units depending on the context of the problem.
In summary, if an object is dropped from a high cliff or a tall building, the distance it has fallen after t seconds is given by the function f(t) = 16t², which is derived from the equation d = ½at².
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WAGES Mark has already earned money for mowing lawns over the summer when he takes a job at the local grocery store, earning $9.50 per hour. After working 16 hours at the grocery store, Mark has earned a total of $292. Write a linear equation to represent the amount of money m that Mark has earned this summer after working h hours at the grocery store.
Answers
The linear equation m = 9.50h + 140 represents the amount of money m earned by Mark in h hours while working at the grocery store in summer.
Mark earns $9.50 per hour while working at local grocery store
Total money earned by Mark after working for 16 hours is $292
As per the given condition, the points are (16, 292)
The slope of the linear equation is represented by $9.50
Hence, M = 9.5(16, 292)
Standard linear equation is given by
m = Mx + b … (1)
Substitute the values in the equation to get the values of b
292 = 9.5(16) + b
⇒ b = 292 - 152
⇒ b = 140
Substitute the values in the equation (1) again to get linear equation
⇒ m = 9.50h + 140
Hence, the linear equation is m = 9.50h + 140
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Ali has hired mark and alexis to work for his shipping company. mark can load a truck with packages in 120 minutes. alexis can load the same number of packages in 240 minutes. if mark and alexis work together on a particular truck, they can load all of the packages in___minutes.
Answers
If mark and Alexis work together on a particular truck, they can load all of the packages in 90 minutes.
It will take 90 minutes for both Mark and Alexis to load all of the products.
Given,
that Mark can load a truck with items in 120 minutes and Alexis can do the same in 240 minutes, the average time for the two of them is as follows:
Average = (120 + 240) ÷ 2
= 360 ÷ 2
= 180
In this case, the term "Average" refers to the value that should be used to represent the sample. By dividing the total number of values in a particular set by the sum of all the values in that set, the average is determined. also known as the arithmetic mean.
Since there were two parties engaged, our calculation is 180 ÷ 2 = 90.
Hence, in this case, it is concluded that the correct answer is option B. 90 minutes.
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A bicycle that normally costs $450 is on sale for 20% off the original price, with an additional discount of $25.
What is the cost of the bicycle?
Answers
Answer: 335
Step-by-step explanation:
20% = 0.2
450 x .2 = 90
450 - 90 = 360
360 - 25 = 335
Which angle is formed by EA−→
and EG−→−?
Select all that apply.
Answers
Answer:
Step-by-step explanation:
\(\angle 2,\angle AEG, \angle GEB\)
Is 2.5 closer to 0 or 5
Answers
Answer:
2.5 is closer to 0
Step-by-step explanation:
when using 2.5 you have to round down and if you round down you get 0 not 5.
Well, think of it as going home. Say you are 2.5 miles away from your school, and you need to walk 2.5 more miles to your house, then say it's about to rain. Will you run back to school or to your home? The problem with this is it's close to each number because it's equal. If you add or subtract, you get both answers, so this is a trick question.
What can you see in this form of the linear equation? 6x+2y=13
Answers
The given equation 6x+2y=13 is a linear equation in two variables. In this equation, x and y are variables while 6 and 2 are their respective coefficients, and 13 is a constant term. The equation can be represented as a straight line on a graph. The slope of this line is -3, and it intersects the y-axis at the point (0, 13/2).
In this equation, if we substitute x=0, then y=13/2, and if we substitute y=0, then x=13/6. These are the two points that the line passes through the x and y-axis.
A linear equation is a polynomial equation that is of the first degree, meaning the variables in the equation are not raised to any powers other than one. This equation is in the standard form where the variables are in the first degree. 6x + 2y = 13 is the form of the given linear equation. x and y are the two variables, and 6 and 2 are their respective coefficients. The equation can be represented as a straight line on a graph. The slope-intercept form of this equation is y = -3x + 13/2. The equation is also in standard form.
When x = 0, the equation becomes 2y = 13. This means that the point of intersection is (0, 13/2) when y = 0, the equation becomes 6x = 13, and the point of intersection is (13/6, 0). The slope of the line is -3. When x increases by 1, y decreases by 3.
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In a circle with radius 2.1, an angle intercepts an arc of length 21.2. Find the angle in
radians to the nearest 10th.
Answers
Given:
Radius of a circle = 2.1 units
Arc length = 21.2 units
To find:
The central angle in radians to the nearest 10th.
Solution:
We know that the intercepted arc length is
\(s=r\theta\)
Where, s is the arc length, r is the radius and \(\theta\) is the central angle in radians.
Putting the given values, we get
\(21.2=2.1\theta\)
\(\dfrac{21.2}{2.1}=\theta\)
\(10.095238=\theta\)
\(\theta\approx 10.1\)
Therefore, the angle in radians is 10.1.
Find the radius of a circle if a 28 foot chord is 6 feet from the center of the circle. (Must be
perpendicular. ) Find the exact value and then round to the nearest hundredth.
Answers
Check the picture below.
PLEASE HELP FINAL QUESTION TO UNIT TEST
A company makes cars at two factories. Some of the cars need repairs in the first year and some do not. This two-way frequency table shows the proportion of cars at each factory that need repairs or do not need repairs in the first year.
Which conclusions can be made from this table?
Select each correct answer.
Responses
Compared to Factory A, Factory B has a larger percentage of cars that do not need repairs.
Compared to Factory A, Factory B has a larger percentage of cars that do not need repairs.
More cars from Factory B need repairs than do not need repairs in the first year.
More cars from Factory B need repairs than do not need repairs in the first year.
For both factories, more cars need repairs than do not need repairs in the first year.
For both factories, more cars need repairs than do not need repairs in the first year.
Among cars from Factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.
Among cars from Factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.
Need repairs in first year Do not need repairs in first year
Factory A 0.05 0.95
Factory B 0.02 0.98
Answers
The conclusions that can be made from this table include:
Compared to Factory A, B has a larger percentage of cars that do not need repairs.Among cars from factory A, a larger percentage of cars do not need repairs than do need repairs in the first yearHow to explain the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
From the information, factory A for those who need repairs is 0.05 in the first year. In this case, among cars from factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.
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The Bandwagon fallacy occurs when someone attacks an idea by using irrelevant information.
true or False?
Answers
False. The bandwagon fallacy is when someone believes that an argument is valid because most people believe it to be true.
The idea is that since everyone believes it, then it must be true. It is also called an argument from popularity, argumentum ad populum, appeal to the masses, appeal to belief, and consensus fallacy.The fallacy occurs when one claims that an idea is true or false because many other people believe it to be so.
The fallacy works because humans are social animals and they tend to believe things that others believe. Therefore, when people see that many others believe in an idea, they are more likely to accept it as true without giving much thought to whether it is actually true or not. The bandwagon fallacy is a logical error because the truth of an idea does not depend on how many people believe it.
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Liam watched a ladybug in the yard. It crawled 1/4 of an inch, then rested for a bit, and then crawled 1/6 of an inch more. How far did the ladybug crawl in all?
Answers
help me pls fast plsssssssss
Answers
Answer:
8
Step-by-step explanation:
120÷15=8
Answer:
s = 8
Step-by-step explanation:
15 x 8 = 120
Solve for x and y. show work
Answers
Answer:
Solution given:
y+135°=180°[sum of opposite angle of a cyclic quadrilateral is supplementary]
y=180°-135°
y=25°
again
2x-1+3x+1=180°[sum of opposite angle of a cyclic quadrilateral is supplementary]
5x=180
x=180/5.x=36
x=36°,y=25°
Marla noticed that her friend Ron had three times as many pieces of candy as she did. She told him, "If you give me seven pieces of your candy, we'll have exactly the same number of pieces." Ron responded, "I didn't know that until you mentioned it. But I'll make you a deal: If you can show me how to solve this puzzle using algebra, I'll give you the seven pieces. "One minute later, Ron was shocked to see that Marla had solved it perfectly. Can you do the same?
Answers
Answer:
This question seems to be asking for the work, so I put it below.
Anyhow, Marla had 3.5 candies, and Ron had 10.5.
Step-by-step explanation:
x = 3x - 7 (lets set this as "a") { a = 3x - 7}
x + 7 = 3x -7 + 7
x + 7 = 3x
( x + 7 ) / 3 = 3/3x
( x + 7 ) / 3 = x = *(same as "a") {a}
( x + 7 ) / 3 = 3x - 7
( x + 7 ) / 3 * 3 = ( 3x - 7 ) * 3
x + 7 = 9x - 21
x - x + 7 = 9x - x - 21
7 = 8x - 21
7 + 21 = 8x - 21 + 21
28 = 8x
28 / 8 = 8/8x
3.5 = x
We can plug this back into the original equation and find that it is correct because:
x = 3x - 7
x = 3.5 =====
3.5 = 3( 3.5 ) - 7
3.5 = 10.5 - 7
3.5 = 3.5
Answer:
Marla has 7 and Ron has 21
Step-by-step explanation:
lets take
no. of candies Marla has as "x"
and no. of candies Ron has will be "3x"
Marla says if Ron gives her seven candies, they will have the same no. of candies
so your equation will be -
x + 7 = 3x - 7 (as Marla gets the candy, Ron loses the candy)
3x - x = 7 + 7
2x = 14
∴x = 7
and 3x = 3 x 7 = 21
YOUR WELCOME
before taxes, the food for a party costs 386.54. of that cost, 64.83 is taxed at a rate of 8.65%. what is the total cost of the party after taxes?
Answers
Answer:
To calculate the total cost of the party after taxes, we need to determine the tax amount and add it to the pre-tax cost.
The amount taxed is given as $64.83, and the tax rate is 8.65%. To calculate the tax amount, we can multiply the taxed amount by the tax rate:
Tax amount = $64.83 * 8.65% = $5.61
Now, to find the total cost of the party after taxes, we can add the tax amount to the pre-tax cost:
Total cost = Pre-tax cost + Tax amount
Total cost = $386.54 + $5.61
Total cost = $392.15
Therefore, the total cost of the party after taxes is $392.15.
Sheldon wants to feed his strawberry plants 2 more times and his tomato plants two more times. He will use the same amounts of plant food as before . How much plant food will he need? Does he have enough left to do so/ explain your answer using words or numbers
Answers
Answer:
He doesn't have enough plant to feed strawberry 2 more times and tomato 1 more time
Step-by-step explanation:
On sunday , sheldon bought 4 1/2 kg of plant food. He uses 1 2/3 kg on his strawberry plants and used 1/4 kg for his tomato plants. b. Sheldon wants to feed his strawberry plants 2 more times and his tomato plants one more time. He will use the same amounts of plant food as before. How much plant food will be need? Does he have enough left to do so.
Total food bought = 4 1/2 kg
Strawberry feed = 1 2/3 kg
Tomato feed = 1/4 kg
Total food used on Sunday = Strawberry + tomato
= 1 2/3 + 1/4
= 5/3 + 1/4
= (20+3)/12
= 23/12 kg
Total food remaining after Sunday = Total food bought - used food
= 4 1/2kg - 23/12kg
= 9/2 - 23/12
= (54-23)/12
= 31/12 kg
= 2 7/12 kg
Sheldon wants to feed his strawberry plants 2 more times and his tomato plants one more time.
Strawberry = 2 × 1 2/3kg
= 2 × 5/3
= 10/3 kg
Tomato = 1 × 1/4kg
= 1/4 kg
Total food needed to feed strawberry two more times and tomato 1 more time
= 10/3 kg + 1/4 kg
= (40+3)/12
= 43/12 kg
= 3 7/12 kg
He will need 3 7/12 kg of food
He has 2 7/12 kg of food left
Therefore, he doesn't have enough plant to feed strawberry 2 more times and tomato 1 more time
A number ending in ___ is never a perfect square.
Answers
Answer:
2, 3, 7 or 8
Step-by-step explanation:
Jared bought 7 cans of paint. A can of red paint costs $3. 75. A can of red paint costs $2. 75. Jared spent $22 in all. How many cans of red and black paint did he buy?
Answers
Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.
He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.
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Brantley tosses a ball out of a window that is 75 feet in the air. Its initial velocity is 12 feet per second. The path of the ball is represented by h=-16t^2+12t+75. How long does it take for the ball to hit the ground to the nearest hundredth?
Answers
Answer:
\(t = 2.57\)
Step-by-step explanation:
Given
\(h=-16t^2+12t+75\)
Required
Determine the time to hit the ground
The ground is at point 0.
So, to solve this; we simply set \(h =0\), then calculate the value of t
\(0=-16t^2+12t+75\)
Multiply through by -1
\(0=16t^2-12t-75\)
Reorder
\(16t^2-12t-75 = 0\)
Solve using quadratic formula:
\(t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}\)
Where
\(a = 16; b = -12; c = -75\)
\(t = \frac{-(-12)\±\sqrt{(-12)^2 - 4*16*(-75)}}{2*16}\)
\(t = \frac{12\±\sqrt{144 +4800}}{32}\)
\(t = \frac{12\±\sqrt{4944}}{32}\)
\(t = \frac{12\±70.31}{32}\)
Split:
\(t = \frac{12+70.31}{32}\) or \(t = \frac{12-70.31}{32}\)
\(t = \frac{82.31}{32}\) or \(t = \frac{-58.31}{32}\)
But time (t) can't be negative;
So, we make use of only
\(t = \frac{82.31}{32}\)
\(t = 2.57\)
Hence, the time to hit the ground is 2.57 seconds
Constant or variable ?
Answers
Answer: It would be a constant.
Step-by-step explanation: Its constant because the feet are always 3x as much as the yards.
water leaks out of a tank at a rate of r(t)=13−t23 for t≥0, measured in gallons per minute. initially the tank has 60 gallons of water in the tank. how much water is left in the tank after 3 minutes?
Answers
The amount of water left in the tank after 3 minutes is:
60 - 19.25 = 40.75 gallons
What is integration?
Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function. An antiderivative of a function f(x) is another function F(x) such that the derivative of F(x) with respect to x is equal to f(x).
To solve the problem, we need to use integration to find the total amount of water that has leaked out of the tank in the first 3 minutes. Then we can subtract that amount from the initial amount of water in the tank to find the amount of water left in the tank after 3 minutes.
The rate of water leaking out of the tank at time t is given by:
r(t) = 13 - t/2 - 3
Integrating r(t) from 0 to 3 gives us the total amount of water that has leaked out in the first 3 minutes:
∫[0,3] r(t) dt = ∫[0,3] (13 - t/2 - 3) dt
= [13t - (t²/4) - 3t] evaluated from t=0 to t=3
= 13(3) - (3²/4) - 3(3) - [13(0) - (0²/4) - 3(0)]
= 19.25 gallons
Therefore, the amount of water left in the tank after 3 minutes is:
60 - 19.25 = 40.75 gallons
So there are 40.75 gallons of water left in the tank after 3 minutes.
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Evaluate: 128{1/7}
a:2
b:4
c:8
d:not a real number
Answers
None of the given answers are correct, The value of 128{1/7} will be a fraction number.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given a number 128{1/7}
Simplification of this number
=> 128(1/7)
=> 18.28
therefore, the Given number is a fraction number or a real number.
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A clerk earns $125 per day, plus a commission equal to
10% of her sales, s. The clerk earns less than $180 on
Monday
Enter an inequality that represents all possible values for
the clerk's sales, s, on Monday.
Answers
The inequality represents all possible values for the clerk's sales, s, on Monday is 0.1s + 125 < 180.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
A clerk earns $125 per day, plus a commission equal to 10% of her sales, s. The clerk earns less than $180 on Monday.
The total commission on her sales s = 10% x s
= 0.1s
The total money earn on monday = 0.1s + 125
The inequality represents all possible values for the clerk's sales, s, on Monday.
The clerk earns less than $180 on Monday.
0.1s + 125 < 180
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The length of the base of an isosceles triangle is x. The length of a leg is 3x-7. The perimeter of the triangle is 70. Find x.
Answers
The length of a leg is 2x-5. (other leg the same length)
Question states*** perimeter of the triangle is 20
x + (2x-5) + (2x-5) = 20
5x - 10 = 20
5x = 30
x = 6, the length of th ebase. The length of each leg is 7
Answer:
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Find The Translation Rule. POINTS UP FOR GRABS! IMAGE BELOW WITH ANSWERS AND FULL QUESTION. GEOMETRY MATHEMATICS. NEEDING ANSWER ASAP
Answers
For the above coordinate sets, the translation rule is (x,y)⇒(x+11,y-10).
What is translation?A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. A translation is a transformation that moves every point in a figure in the same direction by the same amount. For example, this transformation shifts the parallelogram 5 units to the right and 3 units up. Translation in geometry refers to shifting a form into a different place without affecting it in any manner. Shape translation is presented to Year 5 students by providing them shapes on squared paper that must be moved a specified number of squares up, down, left, or right.
Here,
(x,y)⇒(x+11,y-10)
The translation rule for the given sets of coordinates is (x,y)⇒(x+11,y-10).
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