Answers
sqrt (7x)(sqrt (x) - 7sqrt (7)) =
sqrt (7x) * sqrt (x) - sqrt (7x) * 7sqrt (7)
now if you have two things multiplied by each other and they are both under the sqrt sign then we can multiply them by each other But we have to leave them under the sqrt sign. so this becomes:
sqrt (7x * x) - 7sqrt (7x *7) =
sqrt (7x^2) - 7sqrt (7^2 *x)
in the first sqrt we have x^2 And in the second we have 7^2. The sqrt of anything squared is the same number without the square. So sqrt (x^2) becomes x and sqrt(7^2) becomes 7. So now we have:
x * sqrt (7) - 7 * 7sqrt (x) =
xsqrt (7) - 49sqrt (x)
Answer:
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
Step-by-step explanation:
Given: [tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Simplify the expression.
[tex]\Rightarrow \sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]
Distribute [tex]\sqrt{7x}[/tex] over parentheses
[tex]\Rightarrow \sqrt{7x}\cdot\sqrt{x}-\sqrt{7x}\cdot7\sqrt{7}[/tex]
[tex]\Rightarrow \sqrt{7x^2}-7\sqrt{7^2x}[/tex]
square term take out from square root
[tex]\Rightarrow x\sqrt{7}-7\cdot 7\sqrt{x}[/tex]
[tex]\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]
Related Questions
Let f(x)=√7x and g(x)=x+8, whats the smallest number that is the domain of f^o g?
Answers
(f○g)(x)=√(7x+56)
Since there is no real square root of a negative value, the smallest value in the domain would make the radicand equal to zero. x=-8 is the smallest number in the domain of (f○g)(x)
Final answer:
The smallest number in the domain of the composite function f^o g, is -8.
Explanation:
To find the smallest number that is in the domain of the composite function fo g, we need to consider the domains of the individual functions f(x) and g(x). First, since f(x) = √7x, f is only defined for x ≥ 0, as the square root function requires non-negative input. Secondly, g(x) = x+8 is defined for all real numbers, as it's a linear function.
However, the composite function f(g(x)) will also require that the output of g(x) be non-negative, because this output becomes the input for f(x). Thus, we need to find the smallest x such that g(x) is non-negative, which occurs when x+8 ≥ 0. Solving for x gives us x ≥ -8.
Hence, the smallest x in the domain of fo g is -8.
The probability of winning on a split bet in a specific game of roulette is 1 19. Find the actual odds in favor of winning on the bet.
Answers
With that being said, I think the probability given in your problem is 1/19. This means that in every 19 bets, you have a chance to win once. If the probability of winning the roulette is 1/19, that means that you have a 1/19 or 5.3% chance of winning. Therefore, the actual odds of winning the roulette is also 1/19.
The answer is 1:18. I just took the statistics quiz and got it wrong due to the other person.
Compare and contrast the perpendicular bisectors, medians, and altitudes of a triangle. How are they alike? How are they different?
Answers
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.
An altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base.
At the beginning of every year molly deposits 200 in a savings account thst offers 20% interest annually. The total amount molly woukd have in her account after 3 years is? I got 345.60 but wrong?
Answers
200 * (1.2)^3 = 345.60
2 years
200 * (1.2)^2 = 288.00
1 years
200 * 1.2^1 = 240.00
It seems you calculated 200.00 for 3 years.
You need the total which equals:
345.60 + 288.00 + 240.00
= 873.60
There is a formula for this:
Total = Amount * ([(1+rate)^(years+1) -1] / rate) - amount
Total = 200 * ([(1.20^4) -1] / .20) - 200
Total = 200 * [( 2.0736 -1) / .20] -200
Total = 200 * ( 1.0736 / .20) - 200
Total = 200 * 5.368 -200
Total = 1073.6 -200
Total = 873.60
In a 36 minute gym period, 24 boys want to play basketball. if only 10 can play at the same time, and each boy plays the same amount of time, how many minutes does each boy play
Answers
15 minutes
Final answer:
To determine how many minutes each boy plays in a 36-minute gym period with 24 boys wanting to play basketball, with only 10 able to play at a time, each boy would play for 15 minutes.
Explanation:
To find out how many minutes each boy plays in a 36-minute gym period with 24 boys and 10 playing at a time:
Calculate the total time for 24 boys: 24 boys / 10 boys playing at a time = 2.4 sets.
Divide the gym period by the number of sets: 36 minutes / 2.4 sets = 15 minutes per set.
A bridge is 28 meters long. Find the length of a scale model if the scale is 1 cm = 5.5 meters. Round to the nearest tenth.
a.
5.1 cm
c.
4.7 cm
b.
5.5 cm
d.
6.4 cm
Answers
≈5.1 cm (to nearest tenth of a centimeter, or to nearest millimeter)
Based on the length of the bridge and the scale used, the length of the scale model is a. 5.1 cm.
What is the length of the scale model?This can be found as:
= Length of Bridge / Number of meters per centimeters
Solving gives:
= 28 / 5.5
= 5.09
= 5.1 cm
In conclusion, option A is correct.
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Evaluate the factorial expression. (N+4)! N+4
Answers
Answer:
The simplified form of given factorial expression is (N+3)!.
Step-by-step explanation:
The given expression is
[tex]\frac{(N+4)!}{N+4}[/tex]
The n! is defined as
[tex]n!=n(n-1)(n-2)...3(2)(1)[/tex]
[tex]n!=n(n-1)![/tex]
The given expression can be written as
[tex]\frac{(N+4)!}{N+4}=\frac{(N+4)(N+4-1)!}{N+4}[/tex]
[tex]\frac{(N+4)!}{N+4}=\frac{(N+4)(N+3)!}{N+4}[/tex]
Cancel out the common factors.
[tex]\frac{(N+4)!}{N+4}=(N+3)![/tex]
Therefore the simplified form of given factorial expression is (N+3)!.
Given f(x) = x2 + x − 2 and g(x) = 2x − 4, identify (f + g)(x).
Answers
x^2 + 3x - 6 <=
f(x)+g(x)=
(x²+x-2)+(2x-4)=
x²+x-2+2x-4=
x²+x+2x-2-4=
x²+3x-6
2nd option
What is the power of 10 when 0.000028 is written in scientific notation?
Answers
just count how many places you need to move the decimal to put it after the 2
Answer:
The power of 10 would be -5
Step-by-step explanation:
In scientific notation we write a very small or very large number as the product of a number from 0 to 9 and the exponent of 10,
For getting a number between 0 to 9 if the decimal shifted right side then the exponent of 10 is negative power of total shifting while if the decimal shifted left side then the exponent of 10 is positive power of total shifting.
Here, the number is,
0.000028
By the above explanation, we need to shift the decimal five time to the right so the exponent of 10 would be 5.
[tex]\implies 0.000028=2.8\times 10^{-5}[/tex]
A certain isotope decays so that the amount A remaining after t years is given by: A = A0 · e -0.03t where A0 is the original amount of the isotope. To the nearest year, the half-life of the isotope (the amount of time it takes to decay to half the original amount) is a0years.
Answers
0.5=e^(-0.03t) take the natural log of both sides
ln(0.5)=-0.03t
t=ln(0.5)/(-0.03)
t≈23 years (to the nearest whole year)
Jameel has a college degree, lives in a nice neighborhood, and earns more than $50,000 a year. this information defines his _____.
Answers
brainliest g:))))))))))))))))))
Answer:
This information defines his socioeconomic status.
Step-by-step explanation:
Jameel has a college degree, lives in a nice neighborhood, and earns more than $50,000 a year.
This information defines his socioeconomic status.
Socioeconomic status tells the social class of a person.It is measured in terms of education, income and occupation.
We can say that with high socioeconomic comes some privilege, power and control.
Lisa and Kate are playing a card game, and a total of 900 points has been scored. Lisa scored 250 more points than Kate. If you let l=l=the number of points that Lisa scored, and k=k= the number of points that Kate scored, then the problem can be represented by the system:
l+k=900l+k=900 and l=k+250l=k+250
Graph the system. How many points did each of them score?
Select one:
a. Kate = 575 and Lisa = 325
b. Kate = 250 and Lisa = 650
c. Kate = 450 and Lisa = 450
d. Kate = 325 and Lisa = 575
Answers
because it says that LIsa has scored 250 points more.
Answer:
Lisa score 575 points and Kate scored 325 points.
Step-by-step explanation:
We are given the following information:
Total score for Lisa and Kate is 900 and Lisa scored 250 more points than Kate.
Scores for Lisa and Kate can be expressed with the help of two equations:
[tex]L + K = 900\\L = K + 250 \Rightarrow L-K = 250[/tex]
Solving these equations we have:
[tex]L + K + L - K = 900 + 250\\2L = 1150\\L = 575\\K = 575 - 250 = 325[/tex]
Hence, Lisa score 575 points and Kate scored 325 points.
The graph of the equations is attached.
A bridge builder wants to know the width of a river. He stands at point A along the river. He picks a point C directly across the river. He then walks downstream 90 feet from point A to point B. From point B, he sites C and determines the angle between the bank and point C (θ), to be 43º. What is the width of the river?
Answers
The bridge builder used the tangent function to calculate the width of the river. The equation tan(43) = width/90 was set up, and solving for width gives an answer of approximately 91.6 feet.
Explanation:The question gives us a right triangle set up, where point A is where the builder starts, point B is where he walks to, and point C is directly across the river. We can use trigonometry, specifically the tangent function, to find the unknown side. In a right triangle, the tangent of an angle is equal to the ratio of the opposite side (the side across from the angle) to the adjacent side (the side next to the angle).
The angle (θ) in this case is 43 degrees, the side adjacent to the angle is the walk of 90 feet, and the side opposite the angle is the width of the river, which we'll call 'w'. So we get the equation: tan(43) = w/90. Solving for 'w' gives us the width of the river.
Therefore, w = 90 * tan(43), which calculates to approximately 91.6 feet. So the width of the river is approximately 91.6 feet.
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Corinne has a job selling magazines. She earns $7.50 per hour plus 20% of the total amount of her sales. She also gets an allowance of $40 per week for gas. She knows her weekly earnings can be shown using the following expression: 7.50h + 0.20s + 40 Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points) Part B: If Corinne works for 25 hours and sells $300 in magazines, how much does she earn for the week? Show your work to receive full credit. (4 points) Part C: If Corinne gets a raise and begins earning $9 per hour, would the coefficient, variable, or constant in the equation change? Why? (3 points) (10 points)
Answers
242.5 dollars
For C, since she gets 7.5 dollars per hour, we simply change the 7.5 to 9. Since 7.5 is a number multiplied by a variable, it is a coefficient.
When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm divided by min0.02 cm/min. at what rate is the plate's area increasing when the radius is 4040 cm?
Answers
Since the plate is circular, therefore the area of the plate is jut equal to the area of a circle, so:
Area of plate = πr² = A
Taking the derivative:
dA / dr = 2πr --->
1
By
the idea of partial differentiation, the equation can also take in the form of:
dA/dt = dA/dr x dr/dt ---> 2
Where
we are given that:
change in radius over time = dr/dt = 0.02 cm/min
change in area with changing radius = dA/dr = 2πr ---> from equation 1
at r = 40
dA/dr = 2π(40) = 80π
Substituting
all the known values into equation 2:
dA/dt = (80π)(0.02)
dA/dt = 1.6π cm^2 /s = 5.03 cm^2/s
If pentagon OPQRS is dilated by a scale factor of seven over four from the origin, to create O'P'Q'R'S', what is the ordered pair of point P'?
Answers
128 is the product of Julie's savings and 8
Use the variable j to represent Julie's savings.
Answers
128=8j; divide both sides by 8
j=16
A company plans to sell a new type of vacuum cleaner for $280 each. The company’s financial planner estimates that the cost, y, of manufacturing the vacuum cleaners is a quadratic function with a y-intercept of 11,000 and a vertex of (500, 24,000). Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit?
Answers
y = a(x - 500)² + 24000
Because the y-intercept is 11000, therefore
a(0 - 500)² + 24000 = 11000
a = (11000 - 24000)/500² = -0.052
The cost function is
y = -0.052*(x - 500)² + 24000
If x vacuums are sold at $280 per vacuum, then to make a profit requires that
280x ≥ y
or
280x ≥ -0.052(x-500)² + 24000
0.052(x - 500)² + 280x - 24000 ≥ 0
Answer:
The cost function is
y = -0.052(x - 500)² + 24000
To make a profit,
0.052(x - 500)² + 280x - 24000 ≥ 0
Answer:
A) on Edge
Step-by-step explanation:
Took the test
what is the coefficient of x^2y^3 in the expansion of (2x+y)^5
Answers
Answer:
The coefficient of x²y³ is 40.
Step-by-step explanation:
The binomial expansion is defined as
[tex](a+b)^n=^nC_0a^n+^nC_1a^{n-1}b+...+^nC_ra^rb^{n-r}+....+^nC_nb^n[/tex]
The expression is
[tex](2x+y)^5[/tex]
Expand the binomial expansion.
[tex](2x+y)^5=^5C_0(2x)^5+^5C_1(2x)^{4}(y)+^5C_2(2x)^{3}(y)^2+^5C_3(2x)^{2}(y)^3+^5C_4(2x)^{1}(y)^4+^5C_5(y)^5[/tex]
Combination formula:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
[tex](2x+y)^5=32 x^5 + 80 x^4 y + 80 x^3 y^2 + 40 x^2 y^3 + 10 x y^4 + y^5[/tex]
Therefore the coefficient of x²y³ is 40.
Answer:40
Step-by-step explanation:
algebra 2 test
When is buying a house and renting it out a profitable venture?
Answers
Answer:
When what you enter for rent is greater than the mortgage, taxes, maintenance and rent.
Step-by-step explanation:
Buying the house is an investment if we do it to generate income. Otherwise, it is simply the place where we live, spend time and enjoy with our family
The purchase for investment purposes is when we buy apartments for rent or for the purpose of renovating and selling them quickly for a higher price.
The length of a screw produced by a machine is normally distributed with a mean of 0.65 inches and a standard deviation of 0.01 inches. What percent of screws are between 0.61 and 0.69 inches?
HELP
A. 65%
B. 68%
C. 99.7%
D. 99.9936%
Answers
That's almost everything. So (D) is the answer.
99.993666%
Answer:
D. 99.9936%.
Step-by-step explanation:
We have been given that the length of a screw produced by a machine is normally distributed with a mean of 0.65 inches and a standard deviation of 0.01 inches.
To find the percent of screws that are between 0.61 and 0.69 inches, first of we will find z-score for our given raw scores using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{z-score}[/tex],
[tex]x=\text{Raw-score}[/tex],
[tex]\mu=\text{Mean}[/tex],
[tex]\sigma=\text{Standard deviation}[/tex].
Now let us find z-score corresponding to our given raw scores.
[tex]z=\frac{0.61-0.65}{0.01}[/tex]
[tex]z=\frac{-0.04}{0.01}[/tex]
[tex]z=-4[/tex]
Now let us find z-score for raw score 0.69.
[tex]z=\frac{0.69-0.65}{0.01}[/tex]
[tex]z=\frac{0.04}{0.01}[/tex]
[tex]z=4[/tex]
Now we will use formula to find the probability between two z-score as:
[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]
Upon substituting our given values in above formula we will get,
[tex]P(-4<z<4)=P(z<4)-P(z<-4)[/tex]
Using normal distribution table we will get,
[tex]P(-4<z<4)=0.99997-0.00003[/tex]
[tex]P(-4<z<4)=0.99994[/tex]
Now let us convert our answer into percent by multiplying 0.99994 by 100.
[tex]0.99994\times 100=99.994\%[/tex]
Therefore, 99.994% of screws are between 0.61 and 0.69 inches and option D is the correct choice.
Find all solutions to the equation. (sin x)(cos x) = 0
Answers
(sin x)(cos x) = 0
sinx = 0 or cosx= 0
all solutions in : R
1) sinx= 0 : x = kπ...... k∈ Z
2) cosx= 0 : x= π/2 + kπ ....k∈ Z
To solve the equation (sin x)(cos x) = 0, we find that sin x equals zero when x is an integral multiple of π , while cos x equals zero at odd multiples of π/2 . Therefore, our solutions are x = nπ and x = (2n + 1)π/2 for any integer n.
To find all solutions to the equation (sin x)(cos x) = 0, we need to identify the values of x at which either sin x = 0 or cos x = 0, because if either factor on the left-hand side is zero, the product will be zero.
For sin x = 0, the solutions are where x is an integral multiple of π . This can be written as x = nπ, where n is any integer (..., -3, -2, -1, 0, 1, 2, 3, ...).
For cos x = 0, the solutions occur at odd multiples of π/2. Therefore, the solutions can be represented as x = (2n + 1)π/2, where n is any integer.
Combining both sets of solutions, we have x = nπ and x = (2n + 1)π/2, for n being any integer.
Sadie the dog is sitting on the roof of his doghouse, 4.5 ft off the ground. He is watching a cat that is 16 ft away from the base of the doghouse. What is the angle of depression from the roof of the doghouse to the cat? Round to the nearest hundredth. I watched the lesson but it all just went over my head, can someone simplify the explanation of how these problems work?
Answers
Suppose the dog is on the top vertex of the triangle while the cat is the rightmost corner of the triangle. The angle denoted as x° is the angle of depression. To determine this, we use the tangent function. The tangent of an angle is the ratio of its opposite side to its adjacent side.
tanx° = 16/4.5
x = 74.29°
which decimal is closest in value to the fraction below 1/9 ?
a) 0.111
b) .33333
c) 0.7
Answers
so the correct option is (a).
[tex]1.9 = 0.111...[/tex]
It is a repeating decimal. Thus, your answer is A) 0.111
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If a binomial event has a probability of success of 0.2, how many successes would you expect out of 6000 trials?
Answers
Answer:
The success would expect are 1200.
Step-by-step explanation:
Given : If a binomial event has a probability of success of 0.2.
To find : How many successes would you expect out of 6000 trials?
Solution :
The probability of success p=0.2.
The number of trials is n=6000
The formula to find number of successes is
The mean (expected value) of number of successes is the multiple of success and number of trials,
[tex]M=np[/tex]
[tex]M=6000\times 0.2[/tex]
[tex]M=1200[/tex]
Therefore, The success would expect are 1200.
Hey 5ever can u solve dis please.
Factor:
(3x+5xy)^2
Answers
(3x+5xy)(3x+5xy)
If you were to work this out, you would get:
25 x^2 y^2 + 30 x^2 y + 9 x^2
Choose the correct simplification of (2xy^7)^2(y^4)^3.
2x^2y^26
2x^2y^2
4x^2y^2
4x^2y^26
Answers
=(2^2)(x^2)(y^7*2+4*3)
=(4)(x^2)(y^14+12)
=4x^2y^26
Need help. Have photo
Answers
Square root 96
= square root (6×16)
= 4square root 6
=4 square root 2×square root 3
Square root 8
= square root (2×4)
=2 square root 2
4square root 2× square root 3÷ 2 square root 2
=2 square root 3
In your lease agreement you are allowed 25000 km per year for free. After that you are charged $0.08 per km. After yoir 5 year term, you drove a total of 140000 km. How much do you owe?
Answers
After 5 year term, the distance covered is 140000 km, the charge paid is, $1200
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
Given that,
In lease agreement, the distance allowed 25000 km per year for free
After that the charge will be $0.08 per km
After 5 year term, you drove a total of 140000 km
The owed amount = ?
So, in 5 year term the distance which is free according to agreement,
⇒ 5 × 25000
⇒ 125000
Now, the distance for which charge has given
⇒ 140000 - 125000
⇒ 15000
Charged amount = $0.08 per km
The owed amount = 0.08 × 15000
= $1200
Hence, the amount owed is $1200
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The sum of two numbers is 64 . the smaller number is 14 less than the larger number. what are the numbers?
Answers
x=25
...x+y=64
25+y=64
y=39
x is the smallest,y is the largest
The value of a larger number is 39 and the smaller number is 25.
Given that,
The sum of the two numbers is 64.
And, the smaller number is 14 less than the larger number.
Let us assume that,
The larger number is = x
Then, the value of smaller numbers = x - 14
Since the sum of the two numbers is 64.
Hence we get;
x + (x - 14) = 64
2x - 14 = 64
2x = 64 + 14
2x = 78
x = 78/2
x = 39
Thus, The larger number is = 39
Then, the smaller number = 39 - 14
= 25
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