The solution to the radical equation is 2/5
How to determine the solutionFrom the question, we have the following radical equation
6y2−22y+16⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√+4=4y
Complete the equation
So, we have the following representation
6√y² − 22y + √16 + 4 = 4y
Evaluate the radicals
The equation becomes
6y - 22y + 4 + 4 = 4y
So, we have
6y - 22y + 8 = 4y
Evaluate the like terms
So, we have the following
20y = 8
Divide both sides by 20
y = 2/5
Hence, the solution is 2/5
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∫[tex]\frac{xdx}{(x^{2}+4)^{3} }[/tex]
Substitute [tex]u=x^2+4[/tex] and [tex]du=2x\,dx[/tex]. Then the integral transforms to
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}[/tex]
Apply the power rule.
[tex]\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C[/tex]
Now put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}[/tex]
What is the current yield on a 3 year bond with 10% annual coupons, a par value of 100, and a current price of 107.87?
The current yield of the bond is 9.27%.
What is current yield?
Current yield is the bond rate of return computed as the annual coupon divided by the current price of the bond
The annual coupon is the coupon rate of 10% multiplied by the bond's par value of 100
annual coupon=10%*100
annual coupon=10
current bond price=107.87
current yield=annual coupon/current bond price
current yield=10/107.87
current yield=9.27%
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A concert manager counted 525 ticket receipts the day after a concert. The price for a student ticket was $10.50, and the price for an adult ticket was $18.00. The register confirms that $8,325.00 was taken in. How many student tickets and adult tickets were sold?
Answer:
150 student tickets and 375 adult tickets
Step-by-step explanation:
Let x = # of student tickets sold, and y = # of adult tickets sold.
Total of 525 tickets were sold, so the first equation is x + y = 525. The register gained $8325, so 10.50x + 18y = 8235 is the second equation.
x + y = 525
10.50x + 18y = 8325
18x + 18y = 9450
10.50x + 18y = 8325
7.5x = 1125
x = 150
150 + y = 525
y = 375
Select all the terms that are like terms
Answer:
-8 x^2
1.25 x^2
1/2 x^2
Step-by-step explanation:
They are like terms because they have the same variable x^2, yx^2 is not the same because it has the variable y
Answer:
the 2nd, 3rd and 4th options (all with x²)
Step-by-step explanation:
"like terms" means the exactly same variable(s) with exactly the same exponents of these variables.
constants in the terms can be different and even have different signs.
5yx² is not "like", because of the additional y variable.
what is the measure of the reference angle for a 102 degree angle? A. 78 degrees B. 68 degrees C. 57 degrees D. 12 degrees
Answer:
A. The reference angle measures 78 degrees
: A native wolf species has been reintroduced into a national forest. Originally 210 wolves were transplanted. After 10 years, the population had grown to 410 wolves. If the population grows exponentially, write an explicit formula for the number of wolves, where w is the number of wolves and t is the number of years.
The explicit formula that can be used to determine the number of wolves is w = 210 (1.0692^t) .
What is the explicit formula?The first step is to determine the growth rate of the wolf species.
Growth rate = [(future population / present population)^(1/number of years)] - 1
[(410 / 210)^(1/10)] - 1 = 6.92
The exponential function would have the form:
FV = P (1 + r)^t
FV = Future population P = Present populationR = rate of growtht = number of yearsw = 210 (1.0692^t)
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Find the zeros of polynomial function
X³-4x²-7x+5
The zeros of the polynomial function are -1.728, 0.56 and 5.167
How to solve the zeros?The polynomial function is given as:
x^3 - 4x^2 - 7x + 5
Next, we plot the graph of the polynomial
From the graph, the polynomial cross the x-axis when
x = -1.728, 0.56 and 5.167
Hence, the zeros of the polynomial function are -1.728, 0.56 and 5.167
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The equations of four lines are given. Identify which lines are parallel.
Line 1: y=−5x−5
Line 2: x+12y=−4
Line 3: y=−2x+4
Line 4: y+8=−15(x−9)
None of the equation of the line is parallel because there slope are not equal.
How to find lines that are parallel?Parallel line have the same slope.
Therefore, using slope intercept equation,
y = mx + b
where
m = slopeb = y-interceptHence,
y = −5x − 5 , slope = -5
x + 12y = −4; y = -1 / 3 - 1 / 12 x, slope = 1 / 12
y = −2x + 4: slope = -2
y + 8 = -15x + 135; y = -15x + 127, slope = -15
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AB = 6cm, AC = 12cm
Calculate the length of CD.
Give your answer to 3 significant figures.
In the given diagram, the length of CD is 12.7 cm
TrigonometryFrom the question, we are to determine the length of CD
First, we will calculate the length of CB
From the Pythagorean theorem,
|CA|² = |CB|² + |BA|²
12² = |CB|² + 6²
144 = |CB|² + 36
|CB|² = 144 - 36
|CB|² = 108
|CB| = √108
|CB| = 6√3 cm
Now, to find CD
Using SOH CAH TOA
sin55° = |CB| / |CD|
sin55° = 6√3 / |CD|
|CD| = 6√3 / sin55°
|CD| = 12.7 cm
Hence, the length of CD is 12.7 cm
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Find the equation of a line with a slope of 13/2
that passes through the point (−2, — 10).
Answer: [tex]y=\frac{13}{2} x+3[/tex]
Step-by-step explanation:
Remember the point-slope equation which is [tex]y-y_{1} = m(x-x_{1} )[/tex] where[tex](x_{1} , y_{1} )[/tex] is your point and [tex]m[/tex] is your slope.
Given that we substitute what you have:
[tex]y-(-10) =\frac{13}{2} (x - (-2))[/tex]
Minus and minus give us positive:
[tex]y+10 =\frac{13}{2} (x +2)[/tex]
Multiply slope into the parenthesis:
[tex]y+10= \frac{13}{2}x + \frac{13}{2}*2\\[/tex]
Calculate it:
[tex]y+10= \frac{13}{2}x +13[/tex]
Isolate the [tex]y[/tex] by subtracting 10 from both sides:
[tex]y=\frac{13}{2} x + 13 -10[/tex]
Your final equation is:
[tex]y=\frac{13}{2} x +3[/tex]
Hope this makes sense!
And here's the graph to prove that the line actually goes through the point [tex](-2,-10)[/tex]:
what is the lower quartile in the following distribution 82, 90, 66, 78, 88, 72, 60, 80 A)69 B)78 C)79 D) 85
Answer:
A) 69
Step-by-step explanation:
• First , we put the numbers of the distribution in order:
60 , 66 , 72 , 78 , 80 , 82 , 88 , 90
• Notice that the set has 8 numbers which is an even number.
Then
→ the lower quartile is the mean of the set :
60 , 66 , 72 , 78
Which is the average of the two middle numbers 66 and 72.
Then
[tex]\text{the lower quartile}=\frac{66+72}{2} = 69[/tex]
Two friends board an airliner just before departure time. There are only 11 seats left, 4 of which are aisle seats. How many ways can the 2 people arrange themselves in available seats so that at least one of them sits on the aisle?
The 2 people can arrange themselves in blank ways?
Using the Fundamental Counting Theorem, it is found that:
The 2 people can arrange themselves in 40 ways.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
With one people in the aisle and one in the normal seats, the parameters are:
n1 = 4, n2 = 7
With both in the aisle, the parameters is:
n1 = 4, n2 = 3
Hence the number of ways is:
N = 4 x 7 + 4 x 3 = 28 + 12 = 40.
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A scientist wants an 81milliliter of saline solution with a concentration of 5% she has concentrations of 3% and 9%. How much of each solution must she use to get the desired concentration
The quantity of each concentrations of 3% and 9% needed to get the desired concentration is 54 milliliters and 27 milliliters respectively
Simultaneous equationLet
Quantity of 3% needed = xQuantity of 9% needed = yx + y = 81
0.03x + 0.09y = 81 × 5%
0.03x + 0.09y = 4.05
x + y = 81
0.03x + 0.09y = 4.05
From (1)
x = 81 - y
Substitute into0.03x + 0.09y = 4.05
0.03(81 - y) + 0.09y = 4.05
2.43 - 0.03y + 0.09y = 4.05
- 0.03y + 0.09y = 4.05 - 2.43
0.06y = 1.62
y = 1.62/0.06
y = 27
substitute y = 27 intox = 81 - y
x = 81 - 27
x = 54
Simultaneous equation:
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Handre runs a paragliding and adventure touring company. For each paragliding trip (p) he takes he makes $55 and for each adventure tour (a) he makes $75. Last week, he made $2725. Write the equation to represent the relationship between the number of paragliding trips, adventure tours, and his total pay
The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let a represent the number of adventure tours and p represent the number of paragliding trip, hence:
55a + 75p = 2725
The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725
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Landscape artists frequently hand-draw their landscape layouts (blueprints) because this allows them more creativity and precision over their plans. Although done by hand, the layouts must be extremely accurate in terms of angles and distances.
a. A landscape artist has drawn the outline of a house. Describe three different ways to make sure the corners of the house are right angles.
b. A bench needs to be placed in the exact middle of two trees. Describe three different methods the designer can use to find out where to place the bench.
c. The landscape designer has drawn an angle on one side of the yard and wants to draw the same angle on the other side. Describe three different ways he can do this.
The information given about the landscape is illustrated below:
How to explain the landscape?a. You'll need a measuring tape, two range poles, pegs, and three people.
The first person holds the zero mark between their thumbs and fingers, the second person holds the 3m mark on the tape between their thumbs and fingers, and the third person holds the 8m. When all sides of the rope are stretched, a triangle is created, and an angle near one is a right angle.
Wrap one loop of the rope around peg A with a peg through the other loop, draw a circle on the ground, place pegs B and C where the circle crosses the base line, and place peg D half way between pegs B and C, allowing pegs D and A to form lines perpendicular to the base line, forming a right angle.
B. Method 1; Take a measurement of the distance between both trees and divide by 2 to get the midpoint.
Method 2; By use of a compass to bisect the distance between both points.
Method 3; By using a protractor to mark the 90° vertical point when placed between the two endpoints.
C The three different ways he can do this.
1) by using a protractor
2) by finding a point
3) by extending the line of the angle until it reaches the other side of the field.
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Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take to ensure that the margin of error is below 29?
Using the z-distribution, it is found that she should take a sample of 46 students.
What is a z-distribution confidence interval?
The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence, by the Empirical Rule the standard deviation is found as follows:
[tex]6\sigma = 800 - 200[/tex]
[tex]6\sigma = 600[/tex]
[tex]\sigma = 100[/tex]
The sample size is n when M = 29, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]29 = 1.96\frac{100}{\sqrt{n}}[/tex]
[tex]29\sqrt{n} = 196[/tex]
[tex]\sqrt{n} = \frac{196}{29}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{196}{29}\right)^2[/tex]
n = 45.67.
Rounding up, a sample of 46 students should be taken.
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Cuál es el número que no pertenece a esta sucesión 99 koma 105 koma 111 koma 117 koma 123 koma 129 koma 135 koma 141 koma 147 koma 153 Cuál es el número que no pertenece esta sucesión 99coma 105 koma 111 koma 117 koma 123 koma 129 koma 135 koma 141 koma 147 koma 153
Based on the calculations, all of the numbers belong to this arithmetic sequence.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
[tex]a_n = a_1 +(n-1)d[/tex]
Where:
d is the common difference.a₁ is the first term of an arithmetic sequence.n is the total number of terms.Next, we would determine the common difference as follows:
d = a₂ - a₁
d = 105 - 99 = 6.
d = a₃ - a₂
d = 111 - 105 = 6.
d = a₄ - a₃
d = 117 - 111 = 6.
Based on the calculations, all of the numbers belong to this arithmetic sequence.
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Complete Question:
What is the number that does not belong to this sequence 99, 105, 111, 117, 123, 129, 135, 141, 147, 153
3
3
4
Possible inputs for the quadratic when the
output is 3 are
(Note: Fill in the least input first)
or
[tex]x {}^{(1)} = - 3 \: \: \: \: \: \: x {}^{(2)} = - 1[/tex]
Type 4 points found on the circumference of the following equation. Exact points only, no approximations.
(x-3)^2 +(y+2)^2+49
The points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24))
How to determine the points on the circumference of the circle?The circle equation is given as:
(x-3)^2 +(y+2)^2= 49
Rewrite as:
(y+2)^2= 49 -(x-3)^2
Take the square root of both sides
y+2= ±√[49 -(x-3)^2]
Subtract 2 from both sides
y = -2 ± √[49 -(x-3)^2]
Next, we determine the points
Set x = 3
y = -2 ± √[49 -(3-3)^2]
Evaluate
y = -2 ± 7
Solve
y = 5 and y = -9
So, we have
(x, y) = (3, 5) and (3, -9)
Set x = 8
y = -2 ± √[49 -(8-3)^2]
Evaluate
y = -2 ± √24
Solve
y = -2 - √24 and y = -2 + √24
So, we have
(x, y) = (8, -2 + √24) and (8, -2 - √24)
Hence, the points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24)
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The graph of a quartic function crosses the x-axis at -4 and -2 and touches it at 3. State the equation for the family.
The equation of the quartic function is f(x) = x⁴ - 18 · x² + 6 · x + 72.
How to find the possible equations for a quartic polynomial that passes through the x-axis at three points
Herein we must construct at least a polynomial that satisfies all conditions described in the statement. According to the fundamental theorem of algebra, quartic functions may have no real roots, two real roots or four real roots, which means that one of the roots must have a multiplicity of 2.
The root with a multiplicity of 2 is x = 3 and both x = - 4 and x = - 2 have only a multiplicity of 1, then we have the following expression by using the factor form of the definition of polynomials:
f(x) = (x - 3)² · (x + 4) · (x + 2)
Now we expand the expression to get the standard form:
f(x) = (x² - 6 · x + 9) · (x² + 6 · x + 8)
f(x) = x⁴ - 6 · x³ + 9 · x² + 6 · x³ - 36 · x² + 54 · x + 8 · x² - 48 · x + 72
f(x) = x⁴ - 18 · x² + 6 · x + 72
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Which point lies on the circle represented by the equation x² + (y-12)² = 25²?
A. (20.-3)
B. (-7,24)
c. (0.13)
D. (-25,-13)
Answer: B
Step-by-step explanation: Trust me bro
Question 2(Multiple Choice Worth 2 points)
(03.01 LC)
Assume you are working with a standard deck of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace) in each of four suits
and spades).
What is P(Jack Heart) if you draw one card?
O
-
52
13
52
Question 3(Multiple Choice Worth 2 points)
(03.02 MC)
Answer:
Assume you are working with a standard deck of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace) in each of four suits
and spades).
What is P(Jack Heart) if you draw one card? 13
Calculate the price elasticity of supply for Bobbie's Bakery's banana bread. When the price changes by 29% the quantity supplied changes by 55%. Round your answer to two decimal places.
The price elasticity of demand is 1.90.
What is the price elasticity of demand?Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good. It is expected that quantity supplied would be positively related to the price of the good.
Price elasticity of supply = percentage change in quantity supplied / percentage change in price
55% / 29% = 1.90
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Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
y > 2x + 4
x + y ≤ 6
The solution to the system of inequalities is (0.667, 5.333)
How to graph the inequalities?The system of inequalities is given as:
y > 2x + 4
x + y ≤ 6
Next, we plot the graph of the system using a graphing tool
From the graph, both inequalities intersect at
(0.667, 5.333)
Hence, the solution to the system of inequalities is (0.667, 5.333)
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In the geometric pattern below, n represents the number of blocks in the bottom row of each figure.
n = 1
n=2
Write a function that models the total number of blocks in terms of n.
OA f(1) = 2; f(n) = f(n-1) + 2n; for n ≥ 2
OB. f(1) = 1; f(n) = f(n-1) + 2n; for n ≥ 2
Oc f(1) = 1; f(n) = f(n-1) + n; for n ≥ 2
OD. f(1) = 2; f(n) = f(n-1) + 4n; for n ≥ 2
n=3
You deposit $4000 each year into an account earning 2% interest compounded annually. How much will you have in the account in 30 years?
The amount that will be in the account after 30 years is $162,272.32.
How much would be in the account after 30 years?When an amount is compounded annually, it means that once a year, the amount deposited and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.
The formula that can be used to determine the future value of the yearly deposit of $4,000 in 30 years is : annuity factor x yearly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest raten = number of years$4000 x [{(1.02^30) - 1} / 0.02] = $162,272.32
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The Rangers won five of the first six games. how many of the next 30 games must the rangers wins have twice as many wins as losses?
Using proportions, it is found that they must win 19 of their next 30 games.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
We want a win-to-loss proportion of 2:1, which is equivalent to a win-to-total proportion of 2:3. We have that:
The team will have won 5 + x games.The team will have played 36 games.Hence:
[tex]\frac{5 + x}{36} = \frac{2}{3}[/tex]
3(5 + x) = 72
15 + 3x = 72
3x = 57
x = 19.
The Rangers must win 19 of their next 30 games.
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The inverse of G(x) is a function.
• A. True
• B. False
Answer: False
Step-by-step explanation:
G(x) is not a one-to-one function (since it fails the horizontal line test). Therefore, it doesn't have an inverse.
A dry Waller wants to order core board for a 15-story elevator shaft. Each floor uses 18.5 sheets.Calculate the number of boards needed. Add 10%of the total for waste.
Answer:
305.25
Step-by-step explanation:
18.5 for one floor, multiply by 15 to get the amount for 15 floors: 18.5*15 = 277.5 sheets
We need to add 10% for waste, meaning 277.5 plus the waste: 1.1*277.5 = 305.25
The drywaller needs to order 306 core boards for the 15-story elevator shaft, considering the 10% waste.
How to determine the number of boards needed. Add 10%of the total for wastecalculate the number of core boards needed for the 15-story elevator shaft, we can follow these
Calculate the total number of sheets for all floors:
Total sheets = Number of floors × Sheets per floor
Total sheets = 15 floors × 18.5 sheets per floor
Total sheets = 277.5 sheets
Add 10% of the total for waste:
Waste percentage = 10% = 0.10 (in decimal form)
Waste sheets = Total sheets × Waste percentage
Waste sheets = 277.5 sheets × 0.10
Waste sheets = 27.75 sheets
Calculate the final number of boards needed (including waste):
Number of boards = Total sheets + Waste sheets
Number of boards = 277.5 sheets + 27.75 sheets
Number of boards = 305.25 sheets
Since you can't have a fraction of a sheet, we need to round up to the nearest whole number.
Therefore, the drywaller needs to order 306 core boards for the 15-story elevator shaft, considering the 10% waste.
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Select the story problem that this division problem represent 1/2 2/5 (Repost)
The story problem that aligns with the division problem is A. A whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
How to illustrate the division problem?From the information given, it can be seen that 1/2 is divided by 2/5.
In this case, the story that aligns with it is that a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
In this case, the length is multiplied by width to get the area.
Therefore, the correct option is A.
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