Answers
Solutions are given below:
1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14
2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]
3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)
4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2
What is a solution?
A designation of values to that same unknown variables that establishes the equality inside this equation is referred to as a solution.To put it another way, a solution is a figure or set of values one for every unknown) that, when used to replace the unknowns, cause the equation to equal itself.Equations or networks of equations can have just one unique solution when they are solved mathematically.Solutions are given below:
1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14
2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]
3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)
4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2
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Related Questions
Find the sum of two hundred even numbers from 0 to 398
Answers
The sum of two hundred even numbers in the sequence from 0 to 398 is 39800
Sum of an APTo find the sum of two hundred even numbers from 0 to 398, we can use the formula of sum of an arithmetic progression.
[tex]S_n = \frac{n}{2}[2a(n-1)]d[/tex]
n = number of termsa = first termd = common differenceThe number of terms given here is 200, the first term is 0 and the common difference is 2
Substituting the values into the equation
[tex]S_n = \frac{n}{2}[2a+(n-1)]d\\S_n = \frac{200}{2}[2*0+(200-1)*2\\S_n = 100(0+199)*2\\S_n = 39800[/tex]
The sum of two hundred even numbers from 0 to 398 is 39800
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2u - 17 = 11 solve for u simplify your answer as much as possible
Answers
Answer:
u = 14
Step-by-step explanation:
2u - 17 = 11
add 17 to both sides:
2u - 17 + 17 = 11 + 17
2u = 28
divide both sides by 2:
2u/2 = 28/2
u = 14
Solve for f(-2).
f(x) = 2x - 4
f(-2) = [?]
Answers
Answer:
f(-2) = -8
Step-by-step explanation:
GivensWe are given a function:
[tex]f(x)=2x-4[/tex]
We are told to find f(-2).
SolveFirst, substitute -2 as x in f(x):
[tex]f(x) = 2x-4\\\\f(-2) = 2x-4[/tex]
Then, substitute -2 as x in the equation itself:
[tex]f(-2) = 2(-2) - 4[/tex]
Then, simplify by multiplying 2(-2):
[tex]f(-2) = 2(-2) - 4\\\\f(-2) = -4 - 4[/tex]
Finally, simplify by performing the final arithmetic:
[tex]f(-2) = -4 - 4\\\\f(-2) = -8[/tex]
Final AnswerTherefore, f(-2) = -8.
What is the area of the square aboye?
156 square units
52 square units
65 square units
169 square units
OA.
OB.
OC.
OD.
13 units
Will mark brainiest
Answers
The area of the square with a side length of 13 units is 169 square units.
What is the area of the given square?A square is simply a regular quadrilateral having all four sides and angles equal.
The area of a square is expressed as;
A = a²
Where a is the side length.
Given the data in the question;
Side length of the square a = 13 unitsArea A = ?To determine the area of the square, plug the given value into the area of square formula and solve for A.
A = a²
A = ( 13 )²
Area A = 169 square units.
Therefore, the area of the square is 169 square units.
Option D) is the correct answer.
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If m/3 = 4x + 10 and m/4 = 5x
find m/4.
Answers
Answer:
m/4 = 3x - 30
Step-by-step explanation:
Hello!
Let's subtract the second equation from the first equation:
[tex]\frac m3 = 4x + 10\\\frac m4 = 5x[/tex][tex]\frac m3 - \frac m4 = 4x + 10 - 5x[/tex]Now, solve for m.
Solve for m[tex]\frac m3 - \frac m4 = 4x + 10 - 5x[/tex]Multiply both sides by 12 to get rid of the denominators
[tex]4m - 3m = 48x + 120 - 60x[/tex][tex]-m = 120 - 12x[/tex][tex]m = 12x - 120[/tex]Plug in 12x - 120 for m in m/4
Find m/4[tex]\frac m4; m = 12x - 120[/tex][tex]\frac{12x - 120}{4}[/tex][tex]\frac{4(3x - 30)}{4}[/tex][tex]3x - 30[/tex]The value of m/4 is 3x - 30.
Find the length of x and y
Answers
Answer:
y = 15/4 mm
x = 36/5 mm
Step-by-step explanation:
In similarity triangles, the corresponding sides are in same ratio.
[tex]\sf \dfrac{3}{y}=\dfrac{4}{5}\\\\\bf Cross \ multiply,\\\\ y*4 = 3*5\\\\ y =\dfrac{15}{4}\\\\\boxed{y = \dfrac{15}{4}}[/tex]
[tex]\sf \dfrac{x}{9}=\dfrac{4}{5}\\\\x = \dfrac{4}{5}*9\\\\x = \dfrac{36}{5}\\\\\boxed{x = \dfrac{36}{5} \ mm}[/tex]
What is the answerrrrrrr
Answers
Answer:
c
Step-by-step explanation:
c
g(a)=a²+2a-63 find g(8)
Answers
Answer:
g(8)=17
Step-by-step explanation:
Given :
g(a)=a²+2a-63
Substitute a = 8 :
g(8)=8^2+2(8)-63
= 64+16-63
=17
shirt sold at buyer for $7.00 each.
buyer sells shirt for $10.50, what is
his gain?
Answers
Answer:
His gain is 3.50$ which is also 50% of 7
Step-by-step explanation:
for next time so you dont gotta waste points all you have to do is go 10.50 -7.00 =3.50 and then just ask go ogle if you are able what percentage is 3.50 of 7.00 because 7.00$ is what he had to pay for so he is making a 50% gain
Deion's cab company charges a one-time pickup fee of $2 for every ride, as well as a $1.10 charge for each mile traveled. Find the rate of change.
Answers
Answer:
p=2+1.1m
Step-by-step explanation:
p=price, m=miles
Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $225. Now the cost is $310. What is the percent increase? Responses 38% 38% 27% 27% 73% 73%
Answers
The percentage increase in the cost of the airline tickets is 38%.
What is the percentage increase?Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency. In order to convert a value to a percentage, multiply the value by 100.
in order to determine the percentage increase, multiply the fraction of the change in price and the initial price by 100.
Percentage increase = (change in price / initial price) 100
Change in price = new price - initial price = $310 - $225 = $85
Initial price = $225
($85 / $225) x 100 = 38%
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8 circles and 20 squares what is the simplest ratio of total shapes
Answers
Answer
8:28 Hope this helps.
A Student recorded a temperature of 75 degrees Fahrhet at
hour 9 and 95 degrees fahreneit at hour 13.
- which caculation could be used to determine the avenge
rate of change between this two temperatures?
Answers
At hour 9, the temperature recorded was = 75 degrees
At hour 13, the temperature recorded was = 95 degrees
The rate of change = Change in the temperature / Change in the time
⇒ The rate of change = 95 - 75 degrees / 13 - 9 hour
⇒ The rate of change = 20 degrees / 4 hours
⇒ The rate of change = 5 degrees per hour
What is meant by the Rate of change?The rate of change (ROC) measures how quickly a variable varies over a predetermined amount of time. When discussing momentum, the term ROC is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another.The momentum of a variable is represented by the rate of change, which is a mathematical term that describes the percent change in value over a specified period of time. Because it enables investors to identify trending securities and other trends, rate of change is a crucial financial term.Acceleration and deceleration are examples of rates of change with regard to speed or velocity. The slope of the line of best fit is used in statistics and regression modeling to determine the rate of change. It is the growth rate of the population. Momentum is a term frequently used in financial markets to describe rate of change.To learn more about the Rate of change, refer to:
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if the divided is 782 and the divisor is 1523 what is the quotient
Answers
If the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.
What is dividend, divisor and quotient?
The dividend in this case refers to the number that is being divided. The divisor is the integer that divides a given number. The quotient is the sum that we arrive at as a result. The residual is the number that the divisor leaves after partially dividing the original integer.
Let x be the quotient after dividing 782 by 1523.
[tex]\frac{782}{1523} = x\\0.5134 = x\\x = 0.51[/tex]
Therefore, if the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.
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Write an equation of a line that is parallel to 6x-2y=4 and goes through (-5,2)
Answers
Answer:
y = -1/3 x + 1/3
Step-by-step explanation:
In the picture.
Please help me. I fell asleep during class on accident and I missed steps on how to do this.
Answers
Reason:
The equation is in y = mx+b form where
m = 20 = slope
b = 0 = y intercept
The slope is the rate of change. It tells us how fast y increases.
slope = rise/run = 20 = 20/1
rise = 20 = increase the earnings by 20 dollars
run = 1 = each time the number of hours go up by 1
Find the area of this parallelogram. Be sure to include the correct unit in your answer.
Answers
Answer:13x9x6=702
Step-by-step explanation:
Which of the given number sequences represents an arithmetic sequence?
A) 32, 16, 8, 4, 2,...
B 5, 10, 20, 40, 80,...
C)-4, -1/2, 3, 13/2, 10,…
D) 4, 8/3, 16/9, 32/27, 64/81,…
Answers
-4, -1/2, 3, 13/2, 10,… represents an arithmetic sequence.
An arithmetic sequence progresses with a common difference which is the difference of consecutive terms.
So for each of the number sequences, we will try to check if the consecutive terms has a common difference.
A) 32, 16, 8, 4, 2,...
16-32 = -16
8-16 = -8
4-8 = -4
2-4 = -2
As the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.
B)5, 10, 20, 40, 80,...
10-5 = 5
20-10 = 10
40-20 = 20
80-40 = 40
Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.
C) -4, -1/2, 3, 13/2, 10,…
-1/2- -4 = 7/2
3- -1/2 = 7/2
13/2-3 = 7/2
10-13/2 = 7/2
This sequence has a common difference and hence is an arithmetic sequence.
D) 4, 8/3, 16/9, 32/27, 64/81,…
8/3-4 = -4/3
16/9-8/3 = -8/9
32/27-16/9 = -16/27
64/81-32/27 = -32/81
Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.
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suppose that y is independent of explanatory variables and it takes on the values -2, -1, 0, 1, 1 with equal probability. does this violate the gauss- markov assumption
Answers
the parameters we are estimating using the OLS method must be themselves linear
What are the Gauss Markov assumptions?
Gauss Markov Assumptions
Linearity: the parameters we are estimating using the OLS method must be themselves linear. Random: our data must have been randomly sampled from the population. Non-Collinearity: the regressors being calculated aren't perfectly correlated with each other.
What are the properties of Gauss Markov Theorem?
The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.
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Problem 2 Charlie estimates the height of a building to be 924 feet. Charlie's father tells him that his estimate has a 20% error. Explain why this is not enough information for Charlie to find the actual height of the building. Based on this information, what are the two possible values for the actual height of this building?
Answers
The actual height of the building is 739.2 feet.
Given the height of a building estimated by Charlie is 924 feet.
His father said that there is 20% error in the estimation.
we should determine 20% of the estimated height.
⇒ height = 924 feet
⇒ error = 20%
⇒ 924 × 20/100
⇒ 924/5
= 184.8 feet
Subtract the error in height with the height given.
⇒ estimated height - error in height
⇒ 924 - 184.8
= 739.2 feet.
hence the actual height is 739.2 feet.
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if test scores for an exam were normally distributed with a mean of 75 and a standard deviation of 5, find the probability that a randomly selected student scored less than 82
Answers
The probability that a randomly selected student in the class test scored marks which is less than 82 is 0.9192
It is given that in a test, the scores for an exam normally distributed has a mean of 75 and a standard deviation of 5. We have been asked to find the probability that a randomly selected student scored less than 82.
From the question we have,
Mean = 75
Standard deviation (SD) = 5
Therefore, the probability that a randomly chosen student has a score of less than 82 is represented as:
(P) Probability ( X < 82) = P { Z < [tex]\frac{82-75}{5}[/tex] }
= P {Z < 7/5}
= P {Z <1.4}
= Area from - ∞ to 1.4
= 0.9192
From the z table the area under the normal curve that corresponds to 1.4 is 0.9192
Hence the required probability of that a randomly selected student scored less than 82 is 0.9192
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Carlita had -$15 in her checking account. She earned $87.99 from her job and decided to pay her phone bill for $47.82. After paying her phone bill, how much money is left in her account? Responses
Answers
Carlita has $25.17 in her checking account.
A deposit account held at a bank or other financial institution is known as a transaction account.
It is also referred to at credit unions as a share draught account, checking account, chequing account, current account, and demand deposit account. It is accessible frequently and instantly to both the account holder and any other users they may name. The account owner can access it "on demand." It is possible to gain access using a variety of techniques, including cash withdrawals, debit card use, cheques, and electronic transfers. Economically speaking, the funds in a transaction account are regarded as liquid funds. They are treated as currency in the context of accounting.The amount of money in her checking account = -$ 15
She earned $87.99
Now money in her checking account = -15+87.99 = $ 72.99
She paid her phone bill worth $47.82
money in her checking account = $ ( 72.99 - 47.82 ) = $25.17
Therefore she has $25.17 in her checking account.
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− is 55 units to the right of 0
use the drop down menus to complete the statement about x
x is ------- units to the -------- 0
Answers
The value illustrated shows that x is -55 units to the left of 0.
How to illustrate the information?From the given statement we have the value of x is negative. Therefore, we need the complete statement about x being positive.
Therefore we have to put an alternate sign to the given statement we get -x is 55 units to the right of 0.
Negation to the given statement about x is -(-x) is -(55) units to the left of 0. The statement will be that x is -55 units to the left of 0.
By using the drop-down menus to complete the given statement about x is -55 units to the left of 0.
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Which answer choice is not a correct method to illustratethe answer to this problem?876 ÷ 43 = ?A) 876 ÷ 43 ≈ 20 B) 876 ÷ 43 = 20 16/43C) 876 ÷ 43 = 20.16D) 876 ÷ 43 = 20r16 note: the r stands for reminder
Answers
The answer to this question represents the possible choices that we have when solving a division.
When solving this division operation, and we use technology, we get the following result:
[tex]\frac{876}{43}=20.3720930233[/tex]Then, we can conclude that:
First CaseWe can conclude that the answer to this division is, approximately, 20. This could be an answer to this operation.
Second CaseIn this case, we can see the integer part of the answer, 20, and a fraction:
[tex]20\frac{16}{43}=20+\frac{16}{43}[/tex]And we know that:
[tex]undefined[/tex]What is the slope of 7x + 2y = -10
Answers
y=-7/2x-10/7 in slope intercept form (y=mx+b) slope is m In this case it is -7/2
What is 6 2/3 divided 1/5
Answers
Hello!
Let's solve:
[tex]\text{Write down the equation}\\\dfrac{6\dfrac{2}{3} }{\dfrac{1}{5} } \\\\\\\text{Convert the nominator, a mixed partial fraction to an improper fraction}\\\dfrac{\dfrac{20}{3} }{\dfrac{1}{5} } \\\\\\\text{When dividing by a fraction, flip the fraction over and multiply its reciprocal}\\\dfrac{20}{3} *\dfrac{5}{1} = \dfrac{100}{3} \\\\\\\text{Convert the improper fraction back mixed partial fraction}\\\dfrac{100}{3} =33\dfrac{1}{3}[/tex]
Answer: [tex]\dfrac{100}{3} \text{ or }33\dfrac{1}{3}[/tex]
Hope that helps!
write an equation of the line in slope intercept format (-3,3) (0,-1)
Answers
write an equation of the line in slope intercept format (-3,3) (0,-1)
the equation of the line is
y=mx+b
so
step 1
Find the slope
m=(-1-3)/(0+3)
m=-4/3
step 2
Find the equation
we have
m=-4/3
b=-1 ----> is given
substitute
y=-(4/3)x-1A delivery truck drives three routes in one day. The first route is 123 miles long, the second
route is 10 miles long, and the third route is 15 miles long.
What is the total number of miles the delivery truck drives?
Answers
To calculate the total number of miles the delivery truck drove, we add the lengths of the three routes together.
-> It drove 123 + 10 + 15 = 148 (miles).
Diane wants to measure the height of a tree. She sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 35 ft from the tree, and
Diane is standing 7.9 ft from the mirror, as shown in the figure. Her eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot.
Answers
The tree is approximately 27 ft tall if the answer is rounded off to the nearest foot when the similar triangle formula is applied.
What are properties of similar triangles?Two triangles can be said to be similar if their corresponding angles are seen as congruent and thereafter their corresponding sides are in proportion.
What are the 3 similar triangles?Similar Triangles Definition
Angle - Angle (AA)
Side - Angle - Side (SAS)
Side - Side - Side (SSS)Similar triangles are triangles that have the same shape, but their sizes may vary.
If Diane, mirror, and the exact bottom of the tree are placed as points on the ground all lying on one line, then the two right triangles can be stated as:
LEFT: y and 35 as the legs and unknown hypotenuse.
RIGHT: 6 and 7.9 as the legs and unknown hypotenuse.
The two angles pointed at the mirror are seen as of same measure that means that 35 and the hypotenuse of LEFT triangle makes same angle measure as the 7.9 and the hypotenuse of that of the RIGHT triangle.
Since these two are seen as similar triangles,
y/35 = 6/7.9
⇒y = 26.58
⇒ y ≈ 27 ft
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The product of -3 and x is 18
Answers
Answer:
-6
Step-by-step explanation:
-3x = 18
divide both sides by -3
18 ÷ -3 = -6