The value of c=12 will makes the equation true. for the given expression.
what is the value?Here in the question we have expression:
[tex]\dfrac{3\sqrt{x^3}}{cy^4}}=\dfrac{x}{4y^3\sqrt{y}}[/tex]
By solving the above equation we will get:
[tex]12\sqrt{x}=c\sqrt{y}[/tex]
So value of c=12 will makes the equation true. for the given expression.
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The correct value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].
To find the value of [tex]\( c \)[/tex], we start by simplifying the given equation:
[tex]\[ 3\sqrt{\frac{x^3}{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]
First, we simplify the left side of the equation by applying the cube root to both the numerator and the denominator:
[tex]\[ \frac{3\sqrt{x^3}}{3\sqrt{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]
The cube root of [tex]\( x^3 \)[/tex] is [tex]\( x \)[/tex] , and the cube root of [tex]\( y^4 \)[/tex] is [tex]\( y \)[/tex] times the cube root of [tex]\( y \)[/tex], which is [tex]\( y \cdot y^{1/3} \)[/tex]. Simplifying further, we get:
[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x}{4y}(3\sqrt{y}) \][/tex]
Now, we simplify the right side of the equation:
[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x \cdot 3\sqrt{y}}{4y} \][/tex]
Since [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are positive, we can multiply both sides by [tex]\( 4y \)[/tex] to eliminate the denominators:
[tex]\[ \frac{4yx}{3\sqrt{c} \cdot y} = x \cdot 3\sqrt{y} \][/tex]
Simplifying, we get:
[tex]\[ \frac{4x}{3\sqrt{c}} = 3x\sqrt{y} \][/tex]
Now, we can divide both sides by [tex]\( x \)[/tex] since [tex]\( x > 0 \)[/tex]:
[tex]\[ \frac{4}{3\sqrt{c}} = 3\sqrt{y} \][/tex]
Next, we square both sides to eliminate the square root:
[tex]\[ \left(\frac{4}{3\sqrt{c}}\right)^2 = (3\sqrt{y})^2 \][/tex]
[tex]\[ \frac{16}{9c} = 9y \][/tex]
Since [tex]\( y > 0 \)[/tex], we can multiply both sides by [tex]\( 9c \)[/tex] to get rid of the denominator:
[tex]\[ 16 = 81cy \][/tex]
Now, we divide both sides by [tex]\( y \)[/tex]:
[tex]\[ \frac{16}{y} = 81c \][/tex]
Finally, we multiply both sides by [tex]\( y \)[/tex] to solve for [tex]\( c \)[/tex]:
[tex]\[ 16 = 81c \][/tex]
[tex]\[ c = \frac{16}{81} \][/tex]
[tex]\[ c = \left(\frac{2^4}{3^4}\right) \][/tex]
[tex]\[ c = \left(\frac{2}{3}\right)^4 \][/tex]
[tex]\[ c = \left(\frac{3}{2}\right)^{-4} \][/tex]
[tex]\[ c = 64 \][/tex]
Therefore, the value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].
Solve for :
(x+3)/2=6
Answer:
x=9
Step-by-step explanation:
(x+3)/2=6
Multiply each side by 2
2*(x+3)/2=6*2
x+3 = 12
Subtract 3 from each side
x+3-3 = 12-3
x = 9
Find the value of x in the solution to the system of equations shown.
Answer:
x=3
Step-by-step explanation:
i just did it on ttm
the y=14x-6
y=-4x=48
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
Using four different numerators, write an equation in which four fractions, when added, have a sum of 1.
Answer:
1/2 + 1/4 + 1/12 + 8333/10000
A group of men and women were given a maze puzzle
Sooo whats the question
A cylinder has a circular base with a radius that measures 9 inches. Determine the diameter of the base of the cylinder.
3 inches
4.5 inches
18 inches
81 inches
The answer is 18 inches.
Let r=radius and d=diameter
2r=d
2(9)=d
18=d
Hope this helps!
Answer:
18 inches
Step-by-step explanation:
If f(x)= x^2-2x and g(x)= 6x+4 for which value of x does (f+g)(x)=0
Answer:
x = - 2
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x) = x² - 2x + 6x + 4 = x² + 4x + 4 ← equating to 0
x² + 4x + 4 = 0 ← in standard form
(x + 2)² = 0 ← in factored form, thus
x + 2 = 0 ⇒ x = - 2
City planners anticipate an 8.2% population growth per year, including new residents and births. The population, in millions of people, based on this increase can be modeled by the function p(x) = 2.5(1.082), where x is the number of years of tracked growth. The planners also estimate a 3% population loss over the same time period that can be modeled by the function L(p) = p(0.97).
Answer:
D) L(p(x)) = 2.5(1.04954)x
Step-by-step explanation:
what is 30% of 70. show your work
Answer: 21
Step-by-step explanation:
we have two simple equations:
1) 70=100%
2) x=30%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
70/x=100%/30%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 30% of 70
70/x=100/30
(70/x)*x=(100/30)*x - we multiply both sides of the equation by
70=3.33333333333*x - we divide both sides of the equation by (3.33333333333) to get x
70/3.33333333333=x
The fore, the answer is 21
Answer:
21
Step-by-step explanation:
30% of some quantity is equivalent to 0.30 times that quantity.
In this case, 30% of 70 is 0.30(70) = 21.
If a function f(x) is defined as (4x)/(1-x), what is the expression for f(x + h)
ANSWER
[tex]f(x + h) = \frac{4x + 4h}{1 - x - h}[/tex]
EXPLANATION
The given expression is
[tex]f(x) = \frac{4x}{1 - x} [/tex]
To find an expression for f(x+h), we substitute x+h, wherever we see x in the given expression.
This implies that,
[tex]f(x + h) = \frac{4(x + h)}{1 - (x + h)} [/tex]
We simplify to obtain;
[tex]f(x + h) = \frac{4x + 4h}{1 - x - h} [/tex]
Answer:
A
Step-by-step explanation:
(4x+4h)/(1-x-h)
need help asap choose all answers that apply
Hello There!
None of them would be the correct answer
Have a great day!
Find the interest earned and the future value of an annuity with weekly payments of $400 for three years into an account that pays 7% interest per year compounded semiannually.
Answer:
the interest earned= 93.401
and the future value of an annuity= 493.401
Step-by-step explanation:
Given Data:
Interest rate= 7%
time,t = 3 years
weekly payment, P= 400
At the end of 3 years, final investment A= ?
n= 52 as it is weekly
As per the interest formula
A= P(1+r/n)^nt
Putting value in above equation
= [tex]400\left(1+\frac{0.07}{52}\right)^{156}[/tex]
= 493.401
Interest earned = A-P
= 493.401-400
= 93.401 !
A group of 5 men and 5 women are applying for a job at a local company. Each of the 10 job candidates has the same chance of receiving a job offer. Using the diagram, what is the probability that the company will hire two women for two positions?
A:3/4
B:1/4
C:1
D:1/2
Answer: 1/4
Explanation: Because there is a 1/2 chance that a female will get the first job, and a half chance that a lady will get a second job. So (1/2)*(1/2)=(1/4)
HELP!!!! Which of the following is a counterexample that proves the conditional statement false?
If a number is divisible by four, then it is divisible by eight.
12
16
24
48
Answer:
12 I think........?....
Answer:
The answer is 12
Step-by-step explanation:
In this case, we just have to try with all of them:
12/4=312/8=1,5Then it is not divisible (it is not integer). This proves the statement false.
Let's try with the others as well, just to check:
16/4=416/8=224/4=624/8=348/4=1248/8=6All the others don't prove false that statement.
What is the solution to the inequality |x-4|<3?
|x-4| <3
=>. x-4<3 or -(x-4)<3
=>. x-4<3 or x+4>3
=>. x<7 or x>1
So solution is x>1 & x<7. =x€(1,7)
Hope it helps...
Regards,
Leukonov/Olegion.
The solution to the given inequality is:
[tex]1<x<7[/tex] i.e. in the interval form it is given by: (1,7)
Step-by-step explanation:We are given a inequality in term of variable x as follows:
[tex]|x-4|<3[/tex]
Now, we know that any inequality with modulus function is opened as follows:
If
[tex]|x-a|<b[/tex]
Then we have:
[tex]-b<x-a<b[/tex]
i.e. we may write it as:
[tex]a-b<x<a+b[/tex]
Here in the given expression we have:
a=4 and b=3
Hence, the solution is given by:
[tex]4-3<x<4+3\\\\i.e.\\\\1<x<7[/tex]
Which of the following digits could replace the □ in the thousands place to make this statement true?39□,077 rounds to 394,000 if we round to the nearest thousand.
Choose all answers that apply:
:3
:4
:5
Answer:
the answer would be 4
Step-by-step explanation:
The number 39□,077 to the nearest thousand and get 394,000, the thousands place digit must be 5 since that's the digit which would lead to rounding up. Hence, the correct digit to replace the □ would be 5.
Digits in the thousands place of the number 39□,077 would make it round to 394,000 when rounded to the nearest thousand. When rounding to the nearest thousand, we look at the hundreds place to decide whether to round up or down. The rules for rounding are if the hundreds place digit is 5 or higher, we round up, and if it is 4 or lower, we do not round up.
Therefore, to round up to 394,000, the digit in the hundreds place should be 5 or higher. This means that the options provided as possible answers:
3
4
5
Can be evaluated based on this rule. The digit 3 or 4 in the thousands place would not cause the number to round up, but the digit 5 would result in the number being rounded up to 394,000. Thus, the correct answer is 5.
If the dot product of two nonzero vectors v1 and v2 is nonzero, what does this tell us?
A) v1 is not perpendicular to v2
B) v1 is a scalar
C) v1 is parallel to v2
D) v1 is perpendicular to v2
ANSWER
A) v1 is not perpendicular to v2
EXPLANATION
Two non-zero vectors are orthogonal or perpendicular if their dot product is zero.
In other words,if two non-zero vectors are not orthogonal or perpendicular then their dot product is not equal to zero.
From the question v1 and v2 are non-zero vectors and their dot product is not equal to zero.
This tells us that, the two vectors are not perpendicular.
The correct choice is A.
Answer:
A) v1 is not perpendicular to v2
Step-by-step explanation:
This proves that the test for orthogonality fails (doesn’t equal zero) meaning that V1 is not perpendicular to V2.
leon is installing a fence around a rectangular vegetable garden with a perimeter of 60 feet. the garden is 12 feet wide. how long is the garden?
The wide side of the garden is 12 feet, so the other side would be 12 feet aswell.
12+12=24
To find the length of each long side, you subtract 60-12, then divide by 2.
60-12=48/2=24
show me how to do this
Answer:
x = 7 cmStep-by-step explanation:
The perimeter of the given triangle:
P = (2x + 1) + (x + 2) + (3x - 9) and P = 36 cm.
Therefore we have the equation:
2x + 1 + x + 2 + 3x - 9 = 36 combine like terms
(2x + x + 3x) + (1 + 2 - 9) = 36
6x - 6 = 36 add 6 to both sides
6x = 42 divide both sides by 6
x = 7
Someone help PLEASE
Answer:
Q4. (-7)Q5. (-8)Step-by-step explanation:
The perfect square:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Q4
We have
[tex]y^2+14y+49=0\\\\y^2+2(y)(7)+7^2=0\\\\(y+7)^2=0\iff y+7=0\qquad\text{subtract 7 from both sides}\\\\\boxed{y=-7}[/tex]
Q5
We have
[tex]y^2+16y+64=0\\\\y^2+2(y)(8)+8^2=0\\\\(y+8)^2=0\iff y+8=0\qquad\text{subtract 8 from both sides}\\\\\boxed{y=-8}[/tex]
Simplify the following expression (3i+4-i+4(6+2i)
Answer:28 + 10i
Step-by-step explanation: You first distribute.
(3i+4-i+4(6+2i)
3i +4-i+24+8i (Distribute)
3i - i = 2i + 8i= 10i and 4 + 24= 28 (Combine like terms)
10i + 28 or 28 + 10i
Answer:
Answer: 28 + 10i
Step-by-step explanation:
A P E X
state the degree 5r^2s^3t^4
Answer:
Degree 9.
Step-by-step explanation:
The degree is the sum of all the exponents.
So it is 2 + 3 + 4 = 9.
The degree is the sum of all the exponents 5r^2s^3t^4, So it is 2 + 3 + 4 = 9.
What is the degree of the sum?The degree sum formula says that if you add up the degree of all the vertices in a (finite) graph, the result is twice the number of the edges in the graph. There's a neat way of proving this result, which involves double counting: you count the same quantity in two different ways that give you two different formulae.
The degree is the sum of all the exponents 5r^2s^3t^4
So it is 2 + 3 + 4 = 9.
What is the sum of the exponents called?Degree of the Term is the sum of the exponents of the variables. Example. 2x 4y 3 4 + 3 = 7 7 is the degree of the term. 5x-2y 5 NOT A TERM because it has a negative exponent.
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(HELP ASAP PLEASE)
Zoe often orders party trays from her favorite Mexican food restaurant for company events. For a recent company party, she spent $239 on 4 burrito platters and 5 taco platters. For a company meeting, she spent $208 on 3 burrito platters and 5 taco platters. How much does each type of platter cost?
Each burrito platter costs $___ and each taco platter costs $___ .
Answer:
Each burrito platter costs $_31__ and each taco platter costs $_23__ .
Step-by-step explanation:
Let the cost of a burrito platter be x and the cost of a taco platter be y;
4 burrito platters and 5 taco platters would cost;
4x + 5y = 239
3 burrito platters and 5 taco platters would cost;
3x + 5y = 208
We can solve the two equations simultaneously via elimination method. We subtract the two equations in order to eliminate y and solve for x;
4x - 3x = 239 - 208
x = 31
Using the first equation, substitute x = 31 and solve for y;
4(31) + 5y = 239
124 + 5y = 239
5y = 115
y = 23
If f(x) = x+7 and g(x) = x=13, what is the domain of (fºg)(x)?
Answer:
The domain is {x I x ≠ 13} ⇒ the last answer
Step-by-step explanation:
* Lets talk about the composite function
- It is a function is found from two given functions by applying one
function into the second function.
- The applying function is the domain of the second function
- (f °g)(x) means g(x) is applying into f(x)
* Lets solve the problem
∵ f(x) = x + 7
∵ g(x) = 1/(x -13)
- To apply g(x) into f(x) replace x in f(x) by g(x)
∴ f(g(x)) = f(1/(x - 13)) = 1/(x - 13) + 7
- The domain of the function is all values of x which make the function
defined
- The domain is all real numbers except the value which makes
the denominator = 0
- To find this value put the denominator = 0
∵ The nominator of (f ° g)(x) is x - 13
∴ Put x - 13 = 0
∴ x - 13 = 0 ⇒ add 13 to both sides
∴ x = 13
∴ The domain of (f ° g)(x) is all real numbers except x = 13
* The domain is {x I x ≠ 13}
Find the Slope of a line That contains the points (5, 6), (1,4).
Answer:
1/2
Step-by-step explanation:
Use the slope formula:
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] slope = m = \dfrac{6 - 4}{5 - 1} [/tex]
[tex] slope = m = \dfrac{2}{4} [/tex]
[tex] slope = m = \dfrac{1}{2} [/tex]
[tex] \frac{y2 - y1}{x2 - x1} = \frac{4 - 6}{1 - 5} = - 2 \div - 4 = 1/2
Solve for x. show your work
6/9 = x+2/24
Simplify 6/9 to 2/3
2/3 = x + 2/24
Simplify 2/24 to 1/12
2/3 = x + 1/12
Subtract 1/12 from both sides
2/3 - 1/12 = x
Simplify 2/3 - 1/12 to 7/12
7/12 = x
Switch sides
x = 7/12
When given a function and the point at which it is discontinuous, how do you classify the discontinuity as jump, removable, or asymptotic?
Answer:
Jump discontinuities - No defined limit; the left-handed and right-handed limits will be different, converging at two different finite values
Removable - The limit at this point is defined; the left and right-hand limits both converge on the same value
Asymptotic - The left-and-right-handed limits at this point will either tend to ∞ or -∞
what is 10 radical 12 times 6 radical 6
Answer:
360 radical 2 or 509.11688
Step-by-step explanation:
simplify the radicals
12 =2 radical 3
calculate the products
10* 2 radical 3 * 6 radical 6
= 120 radical 18
again simplify
360 radical 2
Answer:
360 radical 2
Step-by-step explanation:
What is the value of X in the equation 2x+3y=36, when y=6?
Answer:
x = 9
Step-by-step explanation:
Substitute y=6 into 2x+3y=36
2x+3(6) =36
2x + 18 = 36
2x = 18
x = 9
Answer:
x = 9
Step-by-step explanation:
Substitute y=6 into 2x+3y=36
2x+3(6) =36
2x + 18 = 36
2x = 18
x = 9
Sheila bought a new computer for $2000 and has agreed to finance it at 12% interest, with $100 payments each month. When she makes her first payment next month, how much will she pay for interest alone?
Answer:
rate per month = .01 agreed = r
Luckily they only ask for the first month so it is 0.01 * 20 .
Later months get more complicated and it is like paying off a mortgage with the term unknown but the rate and payment known.
Payment = principal value [ r / {1-(1+r)^-n } ]
100 = 2000 [ .01 / {1 - (1.01)^-n } ]
5 = 1/ {1 - (1.01)^-n }
.2 = 1 - (1.01)^-n
.8 = 1.01^-n
log .8 = -n log 1.01
n = 22.4 months :)
so over the almost two years pay 2240 total :)
* Hopefully this helps:) Mark me the brainliest:)!!!
Final answer:
For Sheila's first payment on her new computer financed at 12% annual interest with $100 monthly payments, she will pay $20 towards interest and the remaining $80 will go towards the principal.
Explanation:
Sheila bought a new computer for $2000 and agreed to finance it at 12% annual interest, with $100 monthly payments. To calculate the interest she will pay with the first payment, we need to find 1% of $2000 (since 12% per year is equivalent to 1% per month).
(1% of $2000) = 0.01 * $2000 = $20
Therefore, when Sheila makes her first monthly payment of $100, $20 will go towards interest, and the remaining $80 will reduce the principal on her loan.
What’s the perpendicular slope of 4/3
Answer:
-3/4
Step-by-step explanation:
Perpendicular slopes are reciprocal opposites of the original slope. This means that the reciprocal of 4/3 is 3/4, and the opposite of 3/4 is -3/4.
To find the perpendicular slope you must take the given slope take the opposite reciprocal (aka switch the sign and flip the fraction)
so...
[tex]\frac{-3}{4}[/tex]
^^^slope perpendicular to 4/3
Hope this helped!
~Just a girl in love with Shawn Mendes