The area of the parallelogram with the given vertices is 30 units squared.
To calculate the area of the parallelogram, we need to find the base and height. Let's take (-1,-2) and (1,4) as the adjacent vertices of the parallelogram. The vector connecting these two points is (1-(-1), 4-(-2)) = (2,6). Now, let's find the height by projecting the vector connecting the adjacent vertices onto the perpendicular bisector of the base.
The perpendicular bisector of the base passes through the midpoint of the base, which is ((-1+1)/2, (-2+4)/2) = (0,1). The projection of the vector (2,6) onto the perpendicular bisector is (2,6) - ((20 + 61)/(0^2 + 1^2))*(0,1) = (2,4).
The length of the height is the magnitude of this vector, which is sqrt(2^2 + 4^2) = sqrt(20). Therefore, the area of the parallelogram is base * height = 2 * sqrt(20) = 30 units squared.
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On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3) crosses the x-axis at (negative 4, 0) and crosses the y-axis at (0, negative 3).
Which statement is true about the graphed function?
F(x) < 0 over the interval (–∞, –4)
F(x) < 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –3)
F(x) > 0 over the interval (–∞, –4)
The points on the graph of (-4, 0), (-2.5, -12), and (0, -3), gives;
F(x) > 0 over the interval (-∞, -4)Which method can be used to find the true statement?From the description of the graph, we have;
Furthest point left of the graph = (-4, 0)
The furthest point right on the graph = (0, -3) = The maximum point
The minimum point = (-2.5, -12)
F(x) < 0 at the minimum point
The minimum point is to the right of x = -4
The point the graph crosses the y-axis = (0, -3)
Therefore;
The interval of the graph where F(x) is larger than 0 is to the left of (-4, 0), is the interval (-∞, -4)
The true statement is therefore;
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Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate z dV E , where E lies above the paraboloid z
The resulted integral is [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].
What is integrals?In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or just an added to the initial, the derivative of which is initial function (indefinite integral).
Computation of the integrals:
Step 1: We employ the equations in cylindrical coordinates.
[tex]x=r \cos \theta, y=r \sin \theta, z=z[/tex]
Thus, in cylindrical coordinate system,
E lies above the paraboloid [tex]z=r^{2}[/tex] and below the plane [tex]z=2 r \sin \theta[/tex] .
Therefore, the top part E is [tex]z=2 r \sin \theta[/tex] is the cross-section between paraboloid and the plane.
Now, at the cross-section use, [tex]r^{2}=2 r \sin \theta[/tex] and [tex]z=2 r \sin \theta[/tex] .
Thus, the limits are given as ;
[tex]r^{2} \leq z \leq 2 r \sin \theta \quad 0 \leq r \leq 2 \sin \theta[/tex]
Apply the limits as compute the integration;
[tex]\begin{aligned}I=\iiint_{E} z d V &=\int_{0}^{\pi} \int_{0}^{2 \sin \theta} \int_{\tau^{2}}^{2 r \sin \theta} z r d r d z d \theta \\&=\int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[\frac{z^{2}}{2}\right]_{r^{2}}^{2 r \sin \theta} r d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{2} \sin ^{2} \theta-r^{4}\right] r d r d \theta\end{aligned}[/tex]
[tex]\begin{aligned}&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{3} \sin ^{2} \theta-r^{5}\right] d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi}\left[r^{4} \sin ^{2} \theta-\frac{r^{6}}{6}\right]_{0}^{2 \sin \theta} d \theta \\&=\frac{8}{3} \int_{0}^{\pi} \sin ^{6} \theta d \theta\end{aligned}[/tex]
Step 2: Now, calculate for the [tex]I_{1}=\int_{0}^{\pi} \sin ^{6} \theta d \theta[/tex].
[tex]\begin{aligned}\sin ^{6} \theta &=\left(\sin ^{2} \theta\right)^{2} \times \sin ^{2} \theta \\&=\left[\frac{1-\cos 2 \theta}{2}\right]^{2} \times\left[\frac{1-\cos 2 \theta}{2}\right] \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\cos ^{2} 2 \theta\right)(1-2 \cos 2 \theta) \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\frac{1+\cos 4 \theta}{2}\right)(1-2 \cos 2 \theta)\end{aligned}[/tex]
[tex]\begin{aligned}&=\frac{1}{16}(3-4 \cos 2 \theta+\cos 4 \theta)(1-2 \cos 2 \theta) \\&=\frac{1}{32}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta)\end{aligned}[/tex]
Further compute the value of
[tex]\begin{aligned}I_{1} &=\int_{0}^{\pi} \sin ^{6} \theta d \theta \\&=\frac{1}{32} \int_{0}^{\pi}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta) d \theta \\&=\frac{1}{32}\left[10 \theta-\frac{15 \sin 2 \theta}{2}+\frac{3 \sin 4 \theta}{2}-\frac{\sin 6 \theta}{6}\right]_{0}^{\pi} \\&=\frac{5 \pi}{16}\end{aligned}[/tex]
Therefore, the obtained integral is [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].
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The complete question is -
Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate ∫∫∫E z dV, where E lies above the paraboloid
z = x² + y²
and below the plane z = 2y. Use either the Table of Integrals or a computer algebra system to evaluate the integral.
A rectangular gate measures 1.2 m by 2.3 m with a 2.4 m diagonal. Is the gate
square? If not, should the diagonal be longer or shorter?
By use of technology, we investigated Mary’s investment and created the model, M(x) = 3.03(1.28)2x, in thousands of dollars. What was Mary’s initial investment? $4.96 $3,030 $4,960 $3.03
Using an exponential function, it is found that Mary's initial investment was of $3,030.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the rate of change.Her investment model, in thousands of dollars, is:
[tex]M(x) = 3.03(1.28)^{2x}[/tex]
Then a = 3.03, since we measure the amount in thousands of dollars, Mary's initial investment was of $3,030.
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Which of the following are identities? I. y=x II. 4=3x2+2 III. x=x−−√ A. II and III B. I and III C. all D. none
None of the expressions is an identity
How to determine the identities?The expressions are given as:
I. y=x
II. 4 = 3x^2 + 2
III. x=x
In algebra, there are three identities; and they are
(x+y)^2 = x^2 + y^2 + 2xy(x-y)^2 = x^2 + y^2 – 2xyx^2 – y^2 = (x+y) (x-y)None of the given expression take the above forms
Hence, none of the expressions is an identity
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please help me im stuck on this
Answer:
Step-by-step explanation:
dddfykb
Measure the angle shown below. a protractor showing an angle going through the tenth tick mark after ten degrees 15° 17° 20° 22°
The value of the angle will be C. 20°
How to calculate the angle?From the information given, it was stated that the protractor showed an angle going through the tenth tick mark after ten degrees.
This means the value of the angle will be:
= 10° + 10°
= 20°
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A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 6.5 inches and standard deviation of 0.5 inches. If a sample of 46 items are chosen at random, what is the probability the sample's mean length is greater than 6.3 inches? Round answer to four decimal places.
The probablity that the sample's mean length is greate than 6.3 inches is0.8446.
Given mean of 6.5 inches,standard deviation of 0.5 inches and sample size of 46.
We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.
Probability is the likeliness of happening an event. It lies between 0 and 1.
Probability is the number of items divided by the total number of items.
We have to use z statistic in this question because the sample size is greater than 30.
μ=6.5
σ=0.5
n=46
z=X-μ/σ
where μ is mean and
σ is standard deviation.
First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.
z=6.3-6.5/0.5
=-0.2/0.5
=-0.4
p value from z table is 0.3446
Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.
Hence the probability that the mean length is greater than 6.3 inches is 0.8446.
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A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible three-topping pizzas (3 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni.
The probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni is 1/560 given that there are 16 toppings to choose from. This can be obtained by finding the total number of all possible three-topping pizzas (3 distinct toppings) using combination formula and finding the probability.
What is the required probability?Given that there are 16 toppings,
the total number of all possible three-topping pizzas,
ⁿCₓ = [tex]\frac{n!}{x!(n-x)!}[/tex] = 16!/[3!(16-3)!] = 16!/[3!(13)!] = 14×15×16/3×2 =560
Probability of choosing pizza topped with ham, artichoke hearts, and pepperoni,
P(ham, artichoke hearts, pepperoni) = 1/560
Hence the probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni is 1/560 given that there are 16 toppings to choose from.
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which of the following statements would be most similar to an electiral current passing through a metal wire
The correct option is A. hot water moving through a pipe.
Electrical current passing through a metal wire is similar to hot water moving through a pipe.
What is Electrical current?Electrical charge carriers, often electrons or atoms deficient in electrons, travel as current. The capital letter I is a typical way to represent current. The ampere, denoted by the letter A, is the common unit.
The method of flowing of electrical current in metal wire is-
Faraday's Law established that when spinning magnets are close to a coil of wire, a voltage results. With the help of that voltage, you can force electrons through wires, and the moving electrons will travel to their intended locations and do useful tasks. In essence, that is how the electrical grid functions.Comparison of flow of electricity with flow of water in pipe-
Electrical charge (a current) flowing through a wire is comparable to water flowing through a conduit without any bubbles or leaks. The flow of charge is resisted by a resistor, just as the flow of water is resisted by a constriction in a pipe. A circuit's voltage can be compared to a pipe's pressure.To know more about Electric current, here
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The complete question is-
which of the following situations would be mist similar to an electrical current passing through a metal wire in a closed circuit?
A. hot water moving through a pipe
B. an automobile traveling through a tunnel
C. an airplane flying through clouds
D. a flying pan heating up on a hot plate
E. a bird building a nest
2. A high-speed train travels at a speed of 200 km/h. If the train sets off from Station A at 12 24 and reaches Station B at 14 12, find the distance between the two stations, giving your answer in metres.
The distance between the two stations is 360km.
What is speed?Speed is the rate of change of distance.
Rate is a measure of one quantity against another in this case distance and time.
Analysis:
time at station A = 12:24
time at station B = 14:12
time spent = 14:12 - 12:24 = 1 hour 48 minutes = convert 48 minutes to hour
we divide 48 by 60 = 0.8
Total time = 1.8 hours
Distance = speed x time = 200 x 1.8 = 360 km
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A house is octagon-shaped, and each side measures 22 feet long. How many lineal feet of exterior wall does this house have
Length of each side is 176 feet ² .
What is octagon ?A polygon of eight angles and eight sides.It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° ( radians). The central angle is 45° ( radians).each side of house = 22 feet long
Perimeter of octagon = 8 × sides
Length of each side of house = 8 × 22 ⇒ 176 feet²
Therefore, length of each side is 176 feet ² .
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The roots of the equation (p+2)x^2-2px=5-p are complex; find the range of values of p
Range of values of the variable p is [tex]0\leq p\leq \frac{10}{3}[/tex]
Step-by-step explanation:
From general quadratic equation [tex]ax^{2} +bx+c[/tex], for imaginary case-
[tex]D\leq 0\\b^2-4ac\leq 0[/tex]
In given question, [tex]a= p+2[/tex], [tex]b=2p[/tex], [tex]c= 5-p[/tex]
using above condition-
[tex]b^2-4ac = 4p^2-4(2p)(5-p)\leq 0\\4p^2 - 40p+8p^2\leq 0\\12p^2-40p\leq 0\\4p(3p-10)\leq 0[/tex]
Here, [tex]4p\leq 0, p\leq 0[/tex]
and
[tex]3p-10\leq 0\\p\leq \frac{10}{3}[/tex]
Therefore, range of values of the variable p is [tex]0\leq p\leq \frac{10}{3}[/tex].
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A sphere of radius 222 inches is cut by three planes passing through its center. This partitions the solid into 888 equal parts, one of which is shown above. The volume of each part is t\pitπt, pi cubic inches. What is the value of ttt?
The value of t based on the information about the sphere is 1.3π.
How to calculate the value?It should be noted that the volume of a sphere is 4/3πr³. In this case, it's divided into 8 equal parts.
Volume of each part = 1/8 × 4/3πr³
= 1/8 × 4/3 × π × 8
= 4/3π
= 1.3πin³
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Find the slope of the line that passes through the points (7 , 4) and (-9 , 4).
Answer:
0
Step-by-step explanation:
The y values are the same so this line is a straight line with a slop of 0
To check:
To find the slope we use y1-y2/x1-x2
Plug in the numbers: 4-4/-9-7 = 0/-16 = 0
Two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC, as shown:
Two right triangles ABC and EDC have a common vertex C. Angle ABC and EDC are right angles. AB is labeled 12 feet, AC is labeled 14 feet, EC is labeled 10 feet, and ED is labeled 7 feet.
What is the approximate distance, in feet, between the two poles?
7.14 feet
7.21 feet
14.35 feet
15.59 feet
Answer:
14.35 ft
Step-by-step explanation:
We can use the pythagorean theorem to find the distance between the poles since both triangles are right triangles.
a^2 + b^2 = c^2
a^2 + 12^2 = 14^2
a^2 + 144 = 196
a^2 = 52
a = 7.21 ft
a^2 + b^2 = c^2
a^2 + 7^2 = 10^2
a^2 + 49 = 100
a^2 = 51
a = 7.14 ft
7.21 + 7.14 = 14.35 ft
Brainliest, please :)
Answer: c; 14.35
Step-by-step explanation: I need help on this and i saw this guy asked for brainlist and i think two people need to anser so please give him brainlist.
PLEASE HELP ASAP
List these numbers from SMALLEST TO LARGEST
29.94
28.15
27.068
28.08
28.3
Answer:
Step-by-step explanation:
27.068
28.08
28.15
29.94
David invested $230 in a savings account that offers a 3% return on the investment. the value of david's investment will be at least $415 after a
period of years.
hint: use the formula a = a1 + ', where a is the amount after tyears, pis the amount invested, r is the rate of interest, and is the time period.
use a calculator to compute the answer, and round it off to the nearest year.
20 years is the answer.
A= R(1+r)^ t
A-415
R=230
r=3%
415=230 (1+3%)^ t
t=log1.03 315/230
t=19.89 (use calculator)
David will invest at least 20 years.
An investment is a dedication of an asset to achieve an increase in value over a period of time. Investing requires the sacrifice of current assets such as time, money and effort. In finance, the purpose of an investment is to generate a profit on the invested asset
The most common example of an investment type. Investment is generally what you want to use in the future with the aim of generating regular cash flow or increasing the value of something over time so that you can sell it at a higher price than you purchased.
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10 Points + BRANIEST
Answer:
Step-by-step explanation:
So, we’re probably looking at a n9-m0 cusp, since adding 0 to a number gives a sum lower than adding 9 to a slightly smaller number, something that isn’t true elsewhere in the cycle.
We need a n9 where the sum n+9 is divisible by 3. 9 is divisible by 3 already, so n must be divisible by 3 as well. So, it’s 0, 3, 6, or 9.
Taking as the most likely 3 (because a 39 year old is more likely than a 9 year old, 69 year old, or 99 year old to have a child who doesn’t already know their father’s age) we’ll try 39, 40. 3+9=12, 4+0=4, 12/3=4, this is a possible solution.
Do the others work?
0+9=9, 1+0=1, 9/4=/=1
6+9=15, 7+0=7, 15/4=/=7
9+9=18, 1+0+0=1, 18/4=/=1
1+2+9=12, 1+3+0=4, 12/3=4
there are at least two possibles. the father was correct, the father cannot determine his age from what she has been told, she must guess. From what she knows of him, is it more likely that he’s 39, or 129, or even older?
The width of a rectangle is 4 less than twice its length. if the area of the rectangle is 75 cm 2 , what is the length of the diagonal?
Answer:
Step-by-step explanation:
In the figure below, O is the center of the circle. Name a diameter of the circle.
The diameter of circle O in the image given is: AB.
What is the Diameter of a Circle?The diameter of a circle can be referred to as the largest chord in a circle which is the line segment that passes through the center of a circle with both ends on the circle.
In the image given, AB is the largest chord and also passes through the center of the circle, O.
Thus, the diameter is: AB.
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What is the circumference of a circle (to the nearest whole number) whose radius is 5?
Answer:
31
Step-by-step explanation:
C= 2πr We will used 3.14 for pi and the radius is 5
C = 2(3.14)(5)
C =31.4 Then round to the nearest whole number which would be 31. 31.4 is closer to 31 than 32
calculate the area of the shaded part to the nearest whole unit. (show your work)
The area of the shaded part in figure A and B are 2m² and 49 m² respectively.
Area of the shaded partTo determine the area, we must know the shape of the shaded part.
After identifying the shape, we move further to know the formula for such shape
From the figures given in A, we can see that the shaded region is in form of a triangle
a. The area of a right angle is given as;
The base multiplied by the half the height and vice versa
It is written mathematically as;
Area = 1/ 2 × base × height
Where
base = 2m
height = 2m
Substitute into the formula
Area = 1/ 2 × 2 × 2
Area = 2m²
For figure B, the shaded part is a rectangle
The formula for area of a rectangle is given as;
the width multiplied by the length
Area = width × length
Where width = 7m
length = 7m
Area = 7 × 7
Area = 49m ²
Thus, the area of the shaded part in figure A and B are 2m² and 49 m² respectively.
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On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3
The linear inequality of the given graph is: D. y < -2x + 3.
How to Determine the Linear Inequality of a Graph?First, using two points on the line, (0, 3) and (1.5, 0), find the slope (m).
Slope (m) = change in y / change in x = (3 - 0) / (0 - 1.5)
Slope (m) = 3/-1.5 = -2.
Next, substitute (x, y) = (0, 3) and m = -2 into y = mx + b to find the value of b.
3 = -2(0) + b
3 = 0 + b
b = 3
Substitute m = -2 and b = 3 into y < mx + b (the shaded part is at the left, so we use the "<" sign)
y < -2x + 3
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Which equation is equivalent to the given equation?
−4x = x² + 3
x² - 4x +3=0
x² - 4x - 3=0
x² + 4x - 3=0
x² + 4x +3=0
Answer: x² + 4x +3=0
Step-by-step explanation:
Add 4x to both sides.
Schwiesow corporation has provided the following information: cost per unit cost per period direct materials $ 7.40 direct labor $ 3.80 variable manufacturing overhead $ 1.80 fixed manufacturing overhead $ 16,000 sales commissions $ 1.00 variable administrative expense $ 0.50 fixed selling and administrative expense $ 5,600 if 7,500 units are produced, the total amount of manufacturing overhead cost is closest to:
The total amount of manufacturing overhead cost is closest to $ 29,500.
In business, overhead or overhead rate refers to an ongoing fee for working in a commercial enterprise. Overheads are the expenditure that can not be quite simply traced to or recognized with any unique revenue unit, not like running fees which include uncooked cloth and exertions.
Overhead fees, frequently referred to as overhead or working prices, confer with those expenses associated with running a commercial enterprise that cannot be connected to creating or producing a product or service. they're the prices the business incurs to live in the enterprise, irrespective of its success degree.
Examples of overhead encompass hire, administrative expenses, or worker salaries. Overhead fees may be observed on a business enterprise's income assertion, wherein they are subtracted from its profits to reach at the internet profits discern.
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PLEASE HELP I HAVE AN HOUR LEFT!!
Which statement correctly identifies an asymptote of g (x) = StartFraction 42 x cubed minus 15 Over 7 x cubed minus 4 x squared minus 3 EndFraction using limits?
Limit of g (x) as x approaches plus-or-minus infinity= 5, so g(x) has an asymptote at x = 5.
Limit of g (x) as x approaches plus-or-minus infinity= 6, so g(x) has an asymptote at x = 6.
Limit of g (x) as x approaches plus-or-minus infinity= 5, so g(x) has an asymptote at y = 5.
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
The statement that correctly describes the horizontal asymptote of g(x) is:
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the limit of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the function is:
[tex]g(x) = \frac{42x^3 - 15}{7x^3 - 4x^2 - 3}[/tex]
The horizontal asymptote is given as follows:
[tex]y = \lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{42x^3 - 15}{7x^3 - 4x^2 - 3} = \lim_{x \rightarrow \infty} \frac{42x^3}{7x^3} = \lim_{x \rightarrow \infty} 6 = 6[/tex]
Hence the correct statement is:
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
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Given: mAngleTRV = 60°
mAngleTRS = (4x)°
Prove: x = 30
3 lines are shown. A line with points T, R, W intersects with a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is 60 degrees and angle T, R, S is (4 x) degrees.
What is the missing reason in step 3?
A 2-column table with 6 rows is shown. Column 1 is labeled Statements with entries measure of angle T R V = 60 degrees and measure of angle T R X = (4 x) degrees, angle T R S and angle T R V are a linear pair, measure of angle T R S + measure of angle T R V = 180, 60 + 4 x + 180, 4 x =120, x = 30. Column 2 is labeled Reasons with entries given, definition of a linear pair, question mark, substitution property of equality, subtraction property of equality, division property of equality.
substitution property of equality
angle addition postulate
subtraction property of equality
addition property of equality
Mark this and return
https://brainly.com/question/68367When two lines intersect at a point, angles are formed. Some of these angles formed are vertically opposite and thus are equal.
Therefore, the required proof and answer to the question are stated below:
a) m< TRV = 60° (given)
m<TRS = 4x° (given)
Thus, it can be concluded from the diagram that:
<TRV ≅ m<BRW (vertically opposite angle property)
Also,
m<TRS ≅ m<VRW (vertically opposite angle property)
But,
m<VRW = m<VRZ + m<ZRW
Thus,
m<TRV ≅ m<BRW = 60°
m<TRV + m<BRW + m<TRS + m<VRW = [tex]360^{o}[/tex]
60° + 60° + m<TRS + m<VRW = [tex]360^{o}[/tex]
m<TRS + m<VRW = [tex]360^{o}[/tex] - [tex]120^{o}[/tex]
= [tex]240^{o}[/tex]
2m<TRS = [tex]240^{o}[/tex] (since m<TRB = m<VRW )
m<TRS = 120
4x = 120
x = [tex]\frac{120}{4}[/tex]
= [tex]30^{o}[/tex]
Thus, x = [tex]30^{o}[/tex]
b) The missing reason in step 3 is the angle addition postulate.
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The sum of two odd numbers is 80 and their difference is 6. work out these numbers.
The two odd numbers are 43 and 37.
What are whole numbers?Whole numbers are positive numbers belonging to the set W ∈ {1, 2,3, 4, ...}
The two odd numbers can be represented as (2m-1) and (2n-1) respectively sum=80 and difference = 6
Let m and n be two whole numbers
Therefore
,[tex]2m-1) + (2n-1)= 80\\(2m-1) - (2n-1)= 6\\\\2(m+n-1)=80\\2(m-n)=6\\\\m+n = 41\\m-n=3\\[/tex]
Adding the two equations
[tex](m+n)+(m-n)=2m=44\\m=22\\n=m-3=19\\[/tex]
so m=22 ad n=19. our two odd numbers are 2m-1 = 43 and 2n-1 = 37
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Which expression is equivalent to (q^6)^2