The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.
According to the statement
We have given that one evaluating expression which is √6 +√6+√27-√12
And we have to simplify this expression by evaluating it.
So, Given expression is:
√6 +√6+√27-√12
√6 +√6+√(9*3)-√(4*3)
√6 +√6+3√(3)-2√(3)
√6 +√6+√3( 3-2)
After evaluating the expression it become
√6 +√6+√3(1)
√(3*2) +√(3*2) +(1)√3
Take common from above expression then
√3(√2 +√2 ) +√3
√3(2√2) +√3
√3(2√2+ 1)
Now the expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.
So, The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Which choice is equivalent to the expression below?
√6 +√6+√27-√12
A. √3(2√2+ 1)
B. 2√3-√21
C. 3√3+√6
D. 5√3
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Use the Divergence Theorem to evaluate the surface integral
Compute the divergence of [tex]\vec F[/tex].
[tex]\mathrm{div}(\vec F) = \dfrac{\partial(2x^3+y^3)}{\partial x} + \dfrac{\partial (y^3+z^3)}{\partial y} + \dfrac{\partial(3y^2z)}{\partial z} = 6x^2 + 3y^2 + 3y^2 = 6(x^2+y^2)[/tex]
By the divergence theorem, the integral of [tex]\vec F[/tex] across [tex]S[/tex] is equivalent to the integral of [tex]\mathrm{div}(\vec F)[/tex] over the interior of [tex]S[/tex], so that
[tex]\displaystyle \iint_S \vec F\cdot d\vec S = \iiint_{\mathrm{int}(S)} \mathrm{div}(\vec F)\,dV[/tex]
The paraboloid meets the [tex]x,y[/tex]-plane in a circle with radius 3, so we have
[tex]\mathrm{int}(S) = \left\{(x,y,z) \mid x^2+y^2\le3 \text{ and } 0 \le z \le 9-x^2-y^2\right\}[/tex]
and
[tex]\displaystyle \iiint_{\mathrm{int}(S)} \mathrm{div}(\vec F) \,dV = \int_{-3}^3 \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int_0^{9-x^2-y^2} 6(x^2+y^2)\,dz\,dy\,dx[/tex]
Convert to cylindrical coordinates, with
[tex]\begin{cases}x = r\cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = r\,dr\,d\theta\,d\zeta\end{cases}[/tex]
so that [tex]x^2+y^2=r^2[/tex], and the domain of integration is the set
[tex]\left\{(r,\theta,\zeta) \mid 0 \le r \le 3\text{ and } 0 \le \theta\le2\pi \text{ and } 0 \le \zeta \le 9-r^2\right\}[/tex]
Now compute the integral.
[tex]\displaystyle \int_0^3 \int_0^{2\pi} \int_0^{9-r^2} 6r^2\cdot r\,d\zeta\,d\theta\,dr = 12\pi \int_0^3 \int_0^{9-r^2} r^3\, d\zeta \, dr \\\\ ~~~~~~~~~~~~ = 12\pi \int_0^3 r^3 (9 - r^2) \, dr \\\\ ~~~~~~~~~~~~ = 12\pi \int_0^3 (9r^3 - r^5) \, dr \\\\ ~~~~~~~~~~~~ = 12\pi \left(\frac94 r^4 - \frac16 r^6\right)\bigg|_0^3 = 12\pi \left(\frac94\cdot3^4-\frac16\cdot3^6\right) = \boxed{729\pi}[/tex]
A satellite orbits the Earth at a height of 343 kilometers. If the satellite makes 8 revolutions around the Earth, how many kilometers does it travel? (Earth's diameter is 6371 kilometers.) Use 3.14 as the approximate value of pi .
The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.
What is the distance in kilometres covered by the satellite after 8 revolutions?Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;
D = 6371 + (343)×2
Hence, we have; diameter, D = 7057 km.
Hence, the distance travelled after 8 revolutions is;
C = 8 × πd
C = 8 × 3.14 × 7057
C = 177,271.8 km.
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45.7 kilometers =
meters
Answer:
45.7 kilometers = 45,700 meters
Explanation:
Hi!
Okay, so basically, in one kilometer, there are 1000 meters.
Using this problem, all you have to do is multiply 45.7 by 1000, which is 45,700.
Whatever value is used for kilometers (ex. 2), just multiply by 1000, and you’ll get the value as meters (ex. 2 x 1000 = 2000 meters).
Hope this helps!
To convert kilometers to meters, multiply the kilometer value by 1000 meters which is equal to 1 km.
Convert 45.7 kilometers to meters:
Knowing that 1000 m = 1 km.[tex]\boldsymbol{\sf{Therefore \ \ \longmapsto \ \ 45.7\not{km}*\left(\dfrac{1000 \ m}{1\not{km}}\right)=45700 \ m }}[/tex]
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The spread of a disease can be modeled as N = 250√ where N is
the number of infected people, and t is time (in days).
How long will it take until the number of infected people reaches
2,500?
The spread of the disease will take a time 100 days to reach 2,500 infected people.
How to find the number of infected people at a certain time
In this problem we have a radical equation that represents the number of infected people as a function of time, we are suppose to find the time when that number will be 2,500 by algebra properties: (N = 2,500)
2,500 = 250 · √t
√t = 2,500 / 250
√t = 10
t = 10²
t = 100
The spread of the disease will take a time 100 days to reach 2,500 infected people.
Remark
The statement is poorly formatted and presents typing mistakes, correct form is shown below:
The spread of a disease can be modeled as N(t) = 250 · √t, where N is the number of infected people, and t is time (in days). How long will it take until the number of infected people reaches 2,500?
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6. A cube of side 10 cm is melted down
and made into ten identical spheres.
Calculate the surface area of one of the
spheres.
The surface area of the Spheres is 104.19 cm².
According to the statement
we have given that the
there is a cube with side 10 cm and convert into ten spheres and we have to find the surface area of a sphere.
So,
we know that the cube has a 6 sides, each one 10 x 10 cm
So,
A cube with sides of 10 cm will have a surface area of 600 cm².
And The volume of the cube will be 1,000 cm³ ( = 10 x 10 x 10).
If you melt it down to form ten identical spheres, each of them will have a volume of:
1,000 cm³ / 10 = 100 cm³
And the volume of a sphere is:
[tex]V = 4/3 (pi)r ^{2}[/tex]
So you can calculate the radius of the spheres:
r³ = 3V / 4pi = (300) / (12.5664) = 23.8732 cm³
r = 2.8794 cm
Now, you can use the radius to find the surface area of the spheres:
As = 4pi*r² = (12.5664)(2.8794)^2 = 104.19 cm²
So, The surface area of the Spheres is 104.19 cm².
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A two digit number has 6 more ones than tens. Twice the sum of the number and its reverse is 6 more than ten times the number. Find the number.
The number with the given properties is 17
How to determine the numbers?Let the tens be x and the units be y.
So, the number is 10x + y
The relationship between the digits is
[tex]y = x + 6[/tex]
The relationship between the number and the reverse is
[tex]2(10x + y + 10y + x) = 6 + 10 * (10x + y)[/tex]
Simplify the second equation
[tex]2(11x + 11y) = 6 + 100x + 10y[/tex]
Open the brackets
[tex]22x + 22y = 6 + 100x + 10y[/tex]
Substitute y = x + 6
[tex]22x + 22(x + 6) = 6 + 100x + 10(x + 6)[/tex]
Expand
[tex]22x + 22x + 132 = 6 + 100x + 10x + 60[/tex]
Collect like terms
[tex]22x + 22x - 100x - 10x = 6 + 60 - 132[/tex]
Evaluate the like terms
[tex]-66x = -66[/tex]
Divide by -66
x = 1
Substitute x = 1 in y = x + 6
[tex]y = 1 + 6[/tex]
y = 7
Recall that the number is 10x + y
So, we have
Number = 10 * 1 + 7
Evaluate
Number = 17
Hence, the number is 17
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Choose the equation that
matches the graph.
a. (1/2)x-4
b. y = 4x-1
C.
y = (1/1)
(¹²) ² − 4
-
d.
e.
x-4
y = (1/1)
y = 4x + 1
y = 4x+1
Answer: d
Step-by-step explanation:
The graph is increasing, so the base must be more than 1.
Eliminate a and c.Also, the y-intercept is 2.
Eliminate b and e.This leaves d.
ZAP is a right triangle, with right angle A and sin P = 3/5 What is cos Z?
The ratio of cos Z is cos Z = 3 / 5
How to find the trigonometric ratios of a right triangle?A right triangle has one angle of the triangle as 90 degrees.
The sides of the right triangle can be found using trigonometric ratios.
Therefore,
sin ∅ = opposite / hypotenuse
sin Z = 3 / 5
Using Pythagoras theorem,
c² = a² + b²
5² - 3² = b²
b² = 25 - 9
b² = 16
b = √16
b = 4
Hence,
P + A = 90 degrees (complementary angles)
Therefore,
sin P = cos Z
cos Z = 3 / 5
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In a student club, the probability that a randomly selected member volunteered for a recent activity was 24/43. What is the probability that a randomly selected member did not volunteer for the recent activity?
The probability that a randomly selected member did not volunteer for the recent activity is 19/43.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability that a randomly selected member did not volunteer for the recent activity = 1 - ratio of randomly selected members that volunteered
1 - 24/43
(43/43) - (24/43) = 19/43
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se the FOIL method to evaluate the expression: (5+2)(4-5)
The FOIL method is a method of expanding two given brackets by following the required steps. Thus using the FOIL method, the required answer is: -7
Expansion of brackets may be done using different methods, but these methods would give the same answer. Some methods that can be used are the binomial expansion method, FOIL method, etc.
The FOIL method is a shortened form of the steps required for the process. These required steps are First, Outside, Inside, and last.
Thus to expand the given brackets in the question, we have;
(5+2)(4-5) = 5(4 - 5) + 2(4 - 5)
= 20 - 25 + 8 - 10
= 28 - 35
(5+2)(4-5) = -7
Thus using the FOIL method, the answer to the question is -7.
Quick check: (5+2)(4-5) = (7)(-1)
= -7
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Rabbits are known for being extremely prolific—having a high reproductive rate. The average gestation period for rabbits is about 28 days and they have an unusual reproductive system that permits a female rabbit to be pregnant with two litters at once. This is an adaptation that allows rabbits to survive in the wild where they have a high mortality rate—they’re a source of food for many species of predators! In situations where there are no natural predators, two adult rabbits could easily become 1000 in one year’s time. i. Using this information, construct an exponential model to predict the number of rabbits after “x” years if there are no natural predators. ii. If the rabbit population were left unchecked (no predators and an abundance of food), how many rabbits would there be at the end of 3 years?
(i) The exponential growth model to predict the number of rabbits after 'x' years is [tex]A = 2e^{6.21460809842x}[/tex].
(ii) The number of rabbits at the end of 3 years will be 250000000.
A continuous exponential growth function is of the form [tex]A = Pe^{rt}[/tex], where A is the final amount, which was initially P, growing continuously at the rate of r, after a time of t years.
In the question, we are asked to construct an exponential model to predict the number of rabbits after 'x' years.
We assume the exponential growth model to be a continuous model, of the form [tex]A = Pe^{rt}[/tex], where A is the final amount of rabbits, which was initially P, growing continuously at the rate of r, after a time of t years.
The initial quantity of rabbits, P = 2.
Time, t = x years.
Substituting the values, we get:
[tex]A = 2e^{rx}[/tex] ... (i)
We have been told that after 1 year, the number of rabbits was 1000.
Thus, substituting A = 1000, and x = 1, we get:
[tex]1000 = 2e^{r*1}\\\Rightarrow 1000 = 2e^r\\\Rightarrow e^r = 1000/2 = 500[/tex]
Taking log on both sides, we get:
[tex]log_ee^r = log_e500\\\Rightarrow rlog_ee = log_e500\\\Rightarrow r = 6.21460809842[/tex]
Thus, the rate of growth, r = 6.21460809842.
Substituting r = 6.21460809842 in (i), we get:
[tex]A = 2e^{6.21460809842x}[/tex], which is the required model.
To find the number of rabbits at the end of 3 years, we put x = 3, in the above equation to get:
[tex]A = 2e^{6.21460809842*3}\\\Rightarrow A = 2e^{18.6438242953}\\\Rightarrow A = 2*125000000\\\Rightarrow A =250000000[/tex]
Thus, there would be 250000000 rabbits at the end of 3 years.
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A vector v has an initial (2,-3) point and terminal point (3,-4)
Write in component form.
The vector in component form is given by:
V = i - j.
How to find a vector?A vector is given by the terminal point subtracted by the initial point, hence:
(3,-4) - (2, -3) = (3 - 2, -4 - (-3)) = (1, -1)
How a vector is written in component form?A vector (a,b) in component form is:
V = a i + bj.
Hence, for vector (1,-1), we have that:
V = i - j.
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J(1)²,
x ≤ 0
x > 0
2²,
Complete the table of values for function f, and then plot the ordered pairs on the graph.
-2
-1
0
1
2
f(x)
=
X
f(x)
Drawing Tools
Select
Point
Open Point
>
O
Click on a tool to begin drawing.
-10
-8
-6
-4
-2
10
8
6
4-
2-
-2
पं
CC
f(x)
Delete
2
4
Undo
6
3
+00
8
Answer:
1/4 ,- 4, 1/2 2 1/2 4 1/4
Step-by-step explanation:
1/4, 4 1/2, 2,1/2,4, 1/4,
Q.2. Solve the following. a) How many triangles can you find in the figures below? b) How many different edges are used in these triangles? c) If the area of each of the 4 smallest triangles is the same and thi area is 1 square unit, what is the area of each triangle in the figure?
Total 8 triangles are formed in figure and 4 edges used to make triangles and The area of all triangle is 1 square unit.
According to the statement
we have given that a figure and we have to the number of triangle present in it and the area of each square and the number of edges used in all triangles.
So, For this purpose, we know that the
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
So,
A. The number of triangles present in figure:
There is a rectangle provided with two diagonals and due to this structure
Firstly 4 triangles are formed with 2 diagonals (big size).
And 4 triangles are formed in diagonals because diagonals cut each other (small size).
So, Total 8 triangles are formed in figure.
B. Edges used to form triangle :
there are 4 edges used to form triangles because of presence of overall shape of rectangle because triangles are formed in a rectangle shape.
So, 4 edges used to make triangles.
C. Area of the triangle:
If the area is 1 square unit and area of all triangles are same
So, The area of all triangle is 1 square unit.
So, Total 8 triangles are formed in figure and 4 edges used to make triangles and The area of all triangle is 1 square unit.
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A TV has a listed price of $540.99 before tax. If the sales tax rate is 9.75% , find the total cost of the TV with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
■ Sales tax: $52.75
■ Cost/Price before ST: $540.99
■ Total Cost/Price including ST: $593.74
Step-by-step explanation:
540.99 x 0.0975
= 52.75
Total
= 540.99+52.75
=593.74
urgently needing help
Answer:
the answer is 86,016
Step-by-step explanation:
i took the test
Answer:
The answer is 4.
Step-by-step explanation:
8(-1)^4 - 3(-1) - 7
8 + 3 - 7
11 - 7
4
Sketch the region enclosed by the given curves and find its area.
The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.
How to determine the area of a region enclosed by four functions
In this question we must determine the area generated by four functions: three linear functions and a radical function. First, we plot the four functions to determine the required combinations of definite integrals need for calculation:
[tex]A = \int\limits^{0.382}_0 {[f(x) - g(x)]} \, dx + \int\limits^2_{0.382} {[h(x) - g(x)]} \, dx[/tex], where f(x) = √x, g(x) = x - 3 and h(x) = - x + 1.
[tex]A = \int\limits^{0.382}_{0} {[\sqrt{x} - x + 3]} \, dx + \int\limits^{2}_{0.382} {[- 2 \cdot x + 4]} \, dx[/tex]
[tex]A = \int\limits^{0.382}_{0} {\sqrt{x}} \, dx - \int\limits^{0.382}_{0} {x} \, dx + 3 \int\limits^{0.382}_{0}\, dx - 2 \int\limits^{2}_{0.382} {x} \, dx + 4 \int\limits^{2}_{0.382}\, dx[/tex]
[tex]A= 2 \cdot x^{\frac{3}{2} }|_{0}^{0.382} - \frac{x^{2}}{2}|_{0}^{0.382} + 3\cdot x |_{0.382}^{2} - x^{2} |_{0.382}^{2}+4\cdot x |_{0.382}^{2}[/tex]
[tex]A = 2 \cdot (0.382^{\frac{3}{2} }-0^{\frac{3}{2} })-\left(\frac{1}{2} \right)\cdot (0.382^{2}-0^{2}) + 3 \cdot (2 - 0.382) - (2^{2}-0.382^{2})+4\cdot (2^{2}-0.382^{2})[/tex]
A = 16.815
The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.
Remark
The statement reports an inconsistency with at least one function and needs to be modified in order to apply definite integrals in a consistent manner. New form is shown below:
Sketch the region enclosed by the given curves and find its area: (i) x + y = 1, (ii) x - 3 = y, (iii) y = √x, (iv) x = 0.
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19. What is the probability that the student only plays football?
(a) 35 /66 (b) 20 /33 (c) 13 /33 (d) 5 /33
20. What is the probability that the student plays baseball, but not football?
(a) 3 22 (b) 7 22 (c) 411 (d) 8 33
Using the probability concept, we have that:
The probability that the student only plays football is: (c) 13 /33.The probability that the student plays baseball, but not football is: (d) 8/33.What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The total number of students is given by:
26 + 3 + 9 + 10 + 6 + 5 + 7 = 66
Of those, 26 play only football, hence the probability is:
p = 26/66 = 13/33
Which means that option c is correct for question 19.
Of those same 66 students, 9 + 7 = 16 play baseball but not football, hence the probability is:
p = 16/66 = 8/33
Which means that option d is correct for question 20.
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Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 18 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 150 and 156 miles in a day. Round your answer to four decimal places.
The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.
How to calculate the probability distribution?The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,
Z = (X - μ)/σ
Where X - random variable; μ - mean; σ - standard deviation;
Then the probability is calculated by P(Z < x), using the values from the distribution table.
Calculation:The given data has the mean μ = 120 and the standard deviation σ = 18
Z- score for X =150:
Z = (150 - 120)/18
= 1.67
Z - score for X = 156:
Z = (156 - 120)/18
= 2
So, the probability distribution over these scores is
P(150 < X < 156) = P(1.67 < Z < 2)
⇒ P(Z < 2) - P(Z < 1.67)
From the standard distribution table,
P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254
On substituting,
P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471
Rounding off to four decimal places,
P(150 < X < 156) = 0.0247
Thus, the required probability is 0.0247.
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In a mathematics class, half of the students scored 87 on an achievement test.
With the exception of a few students who scored 52, the remaining students
scored 71. Which of the following
statements is true about the distribution of
scores?
Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.
Therefore, the correct answer is option A. The mean is less than the median.
What are statistics?Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.
Half the students scored 87.
The next highest score exists at 71.
Then the median will be (71+ 87) / 2 = 79
A few students scored 52, so the mean exists a little lower than the mean of 71 and 87.
Therefore, the correct answer is option A. The mean is less than the median.
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The complete question is:
In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?
A. The mean is less than the median.
B. The mean and the median is the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
Show all work to write the expression in simplified radical form:
[tex]\sqrt[4]{3^{7}}[/tex]
(Fourth root of three to the seventh power)
Answer:
1.873
Step-by-step explanation:
Use the exponent rule for roots
[tex]\sqrt[4]{3^{7} } = 3^{\frac{4}{7} }=3^{0.5714} = 1.873[/tex]
Good luck!
Find the rational roots f(x) =3x3+ 2x2 + 3x + 6
The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)
How to determine the rational root of the function f(x)?The function is given as:
f(x) = 3x^3 + 2x^2 + 3x + 6
For a function P(x) such that
P(x) = ax^n +...... + b
The rational roots of the function p(x) are
Rational roots = ± Possible factors of b/Possible factors of a
In the function f(x), we have:
a = 3
b = 6
The factors of 3 and 6 are
a = 1 and 3
b = 1, 2, 3 and 6
So, we have:
Rational roots = ±(1, 2, 3, 6)/(1, 3)
Split the expression
Rational roots = ±(1, 2, 3, 6)/1 and ±(1, 2, 3, 6)/3
Evaluate the quotient
Rational roots = ±(1, 2, 3, 6, 1/3, 2/3, 1, 2)
Remove the repetition
Rational roots = ±(1, 2, 3, 6, 1/3, 2/3)
Hence, the rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)
The complete parameters are:
The function is given as:
f(x) = 3x^3 + 2x^2 + 3x + 6
The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)
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Is TriangleMNL ≅ TriangleQNL? Why or why not?
Yes, they are congruent by either ASA or AAS.
Yes, they are both right triangles.
No, AngleM is not congruent to AngleNLQ.
No, there are no congruent sides.
Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.
What are congruent triangles?A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angle triangle. Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other.
From triangle MNL and triangle QNL, in triangle MNL:
∠M + ∠N + ∠L = 180° (sum of angles in a triangle)
90 + 58 + ∠L = 180
∠L = 32°
Hence Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.
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Taylor is building doghouses to sell. Each doghouse requires 4 full sheets of plywood which Taylor cuts into new shapes. The plywood is shipped in bundles of 12 sheets.
How many doghouses can Taylor make from 16 bundles of plywood?
Answer: 48 doghouses
Step-by-step explanation:
We will look at the details given, then we will perform the necessary operations to solve the problem.
16 bundles of plywood * 12 sheets in a bundle = 192 sheets
192 total sheets / 4 sheets to build a dog house = 48 doghouses
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Factor problems 9 - 12 by using the difference of squares method.
9. x2 – 4
A. This polynomial cannot be factored by using the difference of squares method.
B. (x – 2)(x – 2)
C. (x – 2)(x – 1)
D. (x – 2)(x + 2)
E. (x – 1)(x – 4)
F. (x + 2)(x + 2)
10. x2 – 25
A. (-x – 5)(x - 5)
B. This polynomial cannot be factored by using the difference of squares method.
C. (-x + 5)(x + 5)
D. (x – 5)(x + 5)
E. (x + 5)(-x - 5)
F. (x – 5)(x - 5)
11. 36x4 – 4x2
A. (6x2 – 2x)(6x2 - 2x) = 4x2(3x - 1)(3x - 1)
B. (6x2 + 2x)(6x2 + 2x) = 2x2(3x + 1)(2x + 1)
C. This polynomial cannot be factored by using the difference of squares method.
D. (-6x2 – 2x)(-6x2 - 2x) = 4x2(-3x - 1)(-3x - 1)
E. (6x2 – 2x)(6x2 + 2x) = 4x2(3x - 1)(3x + 1)
F. (-6x2 + 2x)(6x2 - 2x) = 2x2(-3x + 1)(3x - 1)
12. x2 + 100
A. (x + 10)(x – 10)
B. (-x + 10)(x – 10)
C. (x + 10)(x + 10)
D. This polynomial cannot be factored by using the difference of squares method.
E. (x - 10)(x – 10)
F. (-x + 10)(-x – 10)
Answer:
Step-by-step explanation:
9. D
10.D
11.E
12.D
Answer:
9.
[tex]x^2-4\\(x-2)(x+2)[/tex]
10.
[tex]x^2-25\\(x-5)(x+5)[/tex]
11.
[tex]36x^4-4x^2\\4x^2(9x^2-1)\\4x^2(3x+1)(3x-1)[/tex]
12.
[tex]x^2+100\\[/tex]
This polynomial cannot be factored by using the difference of squares method
On a baseball
field, the
pitcher's
mound is 60.5
feet from home
plate. During
practice, a
batter hits a ball
226 feet at an
angle of 39° to
the right of the
pitcher's
mound. An
outfielder
catches the ball
and throws it to
the pitcher.
Approximately
how far does
the outfielder
throw the ball?
outfielder
batter
A. 147.2 ft
B. 172.1 ft
C. 183.0 ft
D. 162.8 ft
Based on the distance of the pitcher's mound from the home plate, the path of the ball, and the height the ball was hit, the distance the outfielder threw the ball is C. 183.0 ft.
How far did the outfielder throw the ball?Based on the shape of a mound, the law of cosines can be used.
The distance the ball was thrown by the outfielder can therefore be d.
Distance is:
d² = 60.5² + 226² - (2 x 60.5 x 226 x Cos(39))
d ²= 33,484.42ft
Then find the square root:
d = √33,484.42
= 182.9874
= 183 ft
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Gia is participating in a jump-a-thon to raise money for her school. After completing
20 jumps, she raised $50. Gia wants to know how much money she raises per jump.
Which rate shows how much money Gia raises per jump?
50
20
20
50
jumps per dollar
dollars per jump
20
50
50
20
jumps per dollar
dollars per jump
Answer:
50/20
Step-by-step explanation:
Rate of money raised raises per jump is
money raised / jumps
$50/ 20 jumps
We can think that if we divide the $50 into 20 equal parts,
each part will represent 1 jump and will have 50/20 = $2.5 per 1 jump.
Find the changes in each four month period
Month and Year Prices in Dollars per Gallon Absolute Change Relative Change
Apr-20 1.841 n/a n/a
Aug-20 2.183
Dec-20 2.195
Apr-21 2.858
Aug-21 3.158
Dec-21 3.307
Apr-22 4.109
b. How would you describe the change in the gas prices? Explain your answer.
c. Use the inflation calculator to find the costs of gas in April 2020 in 2022 dollars. Here is the
link to the calculator from the U.S. Bureau of Labor Statistics:
https://www.bls.gov/data/inflation_calculator.htm
d. How does the inflation-adjusted cost of gas in April 2020 compare to the April 2022 as an
absolute and relative change?
e. What can be attributed to the two most drastic rises in gasoline prices? Explain in a sentence
or two.
a. The changes in each four-month period are as follows:
Month and Prices Absolute Relative
Year in Dollars Change Change
Apr-20 1.841 n/a n/a
Aug-20 2.183 $0.342 18.58%
Dec-20 2.195 0.012 0.55%
Apr-21 2.858 0.663 30.21%
Aug-21 3.158 0.300 10.50%
Dec-21 3.307 0.149 4.72%
Apr-22 4.109 0.802 24.25%
b. The change in gas prices has been relatively unstable.
c. Using the inflation calculator, the costs of gas in April 2020 in 2022 dollars terms should be $2.08.
d. The inflation-adjusted cost of gas in April 2020 when compared to April 2022 as absolute and relative changes are as follows:
Absolute change = $2.268 ($4.109 - $1.841)
Relative change = 123.2% ($2.268/$1.841 x 100)
e. The two most drastic rises in gasoline prices in April 2021 and April 2022 can be attributed to spikes in demand relative to supply.
What causes gasoline prices to rise?Gasoline prices rise when there is an increased demand relative to supply.
Increasing prices in gasoline prices can also be attributed to cuts in production and supply by the oil cartel.
What is the difference between Absolute and Relative Changes?An absolute change is a dollar change from one period to another.
A relative change is an absolute change expressed in percentages.
The calculations of absolute change and relative change are demonstrated below.
Data and Calculations:Month and Prices Absolute Relative
Year in Dollars Change Change
Apr-20 1.841 n/a n/a
Aug-20 2.183 $0.342 18.58% ($0.342/$1.841 x 100)
Dec-20 2.195 0.012 0.55% ($0.12/$2.183 x 100)
Apr-21 2.858 0.663 30.21% ($0.663/$2.195 x 100)
Aug-21 3.158 0.300 10.50% ($0.3/$2.858 x 100)
Dec-21 3.307 0.149 4.72% ($0.149/$3.158 x 100)
Apr-22 4.109 0.802 24.25% ($0.802/$3.307 x 100)
Absolute Change for Aug-20 = $0.342 ($2.183 - $1.841)
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Patrick is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. He uses the following formula to calculate voltage: voltage=(current) × (resistance) The circuit he tests had a current of 4+j2 amps and a resistance of 2-j3 ohms. What is the voltage of the current?
Based on the given current and the given resistance, the voltage of the current is 14 + j8
How to determine the voltage of the current?From the question, we have the following parameters
current of 4+j2 amps and a resistance of 2-j3 ohms.
This can be rewritten as:
Current (I) = 4+j2 amps
Resistance (R) = 2-j3 ohms.
The formula to calculate voltage is given as
Voltage=(current) × (resistance)
Rewrite as:
V = I * R
Substitute the known values in the above equation
V = (4 + j2) * (2 - j3)
Expand the brackets
V = 8 - j4 + j12 + 6
Collect the like ters
V = 8 + 6 - j4 + j12
Evaluate the like term
V = 14 + j8
Based on the given current and the given resistance, the voltage of the current is 14 + j8
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I NEED HELP ASAP PLS!!!
Answer:
C looks most correct
Step-by-step explanation: