Answers
Correct option is A, The equation y = -5(x+4)² - 4 best describe the given graph. It is a Parabola.
Where Can You Use the Parabola Formula?Parabolas are used in physics and engineering for a variety of purposes, including the design of ballistic missile flight paths and car headlight reflectors.
How Do I Find the Equation for a Parabola?From the parabola's fundamental definition, one can obtain the equation for it. A parabola is the location of a point that is evenly distanced from a fixed point, known as the focus (F), and the directrix is the fixed line (x + a = 0). Consider the point P of the parabola (x, y). We can figure out the equation of the parabola using the formula PF = PM.
In this situation, the foot of the perpendicular from point P serves as point "M" on the directrix.
In the given parabola,
having equation y = -5(x+4)² - 4
The standard equation of parabola is [tex]y = a(x + h)^{2} + k[/tex] or[tex]x = a(y - k)^{2} +h[/tex]
As the parabola is downwards, so equation will be [tex]y = a(x + h)^{2} + k[/tex]
the vertex of parabola is (h,k) i.e. ( -4, -4),
which is correct in option A.
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Related Questions
the scale factor of two similar solids is 2:5. the volume of the smaller solid a is 200. which equation could you use to find the volume of the larger solid b
Answers
The volume of larger solid represented by b is 3125.
The scale factor of two solids will be equal to the following formula -
volume of solid a/volume of solid b = solid a³/solid b³
Keep the values in formula to find the volume of solid b
200/ volume of solid b = 2³/5³
Rewriting the equation according to volume of solid b
Volume of solid b = 5³ × 200/2³
Performing multiplication with cube of 5
Volume of solid b = 125 × 200/8
Volume of solid b = 25000/8
Performing division on Right Hand Side of the equation
Volume of solid b = 3125
Hence, the volume of solid b is 3125.
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4 (9) If p, b and h are the sides of a angled triangle then write right angled h in terms of p and b.
Answers
Step-by-step explanation:
Пісяжлшорркгашанргчгаппаппвмсап
confused about this
Answers
Answer:
d
Step-by-step explanation:
d
Whotube, the who’s who of online video sites, has offered to pay for a free trip to its headquarters for anyone who has posted an original viral video. To qualify as viral, a video must be viewed by at least one million people within two hours of being posted, not including the initial post.
Taylor, a self-proclaimed mathemagician, posts a video of a dancing log (one with rhythm) to Whotube at 10 p.m. Three arborists, devoted to their profession, immediately watch the video. Enamored with such a cutting edge clip, they each share it with three other tree trimming friends every five minutes, each of whom views and shares the video with three more friends every five minutes, and so on. They continue sharing the video this way until 10:20, at which point they all get distracted by a video of a campfire and immediately stop viewing and sharing.
Over the next four minutes, thirty fellow mathemagicians discover and view the video. This incredible phenomenon continues at a constant rate of thirty views by mathemagicians every four minutes until 11:32 p.m. at which point almost all of the mathemagicians in the world have viewed the video.
Then, the real magic happens when Kimmy Schmallon mentions it on the Late Night Show. Once it is mentioned on the Late Night Show at 11:32 p.m., the current number of views doubles every three minutes. This continues until the end of the show at 1 a.m.
Will Taylor get invited to Whotube headquarters? Use multiple representations to justify your conclusion.
Answers
Answer:
yes
Step-by-step explanation:
Taylor will get an offer for a free trip as within two hours (10 - 12) even before the end of the midnight show, he got the required views.
from 10: to 10:20
1 : 3
3: 3 in every five minutes i.e. 10:25, 10:30, 10:35 n so on
1: 30 in every four minutes
till 11:32
from 11:32 till 12:00
the views recorded till now doubles every three minutes!!
NEED HELP ASAP WILL GIVE BRAINIEST TO THE CORRECT ANSWER DUE IN 20 MIN
Answers
Answer:
They are not equal
one is -1 times the other answer C
Step-by-step explanation:
for t =2 15.8t - 3.8t = 24
3.8t - 15.8t = - 24
Answer:
C, 24, and -24
Step-by-step explanation:
Step 1a) No, so C
Step 1b) 15.8(2)- 3.8(2)
Step 2b) 31.6 -7.6
Step 3b) 24
Step 1c) 3.8(2)- 15.8(2)
Step 2c) 7.6 -31.6
Step 3c) -24
Which is the better buy?
2-cup bottle of mouthwash for $7.38
2-pint bottle of mouthwash for $8.04
Answers
Answer:Second option ( $8.04)
Step-by-step explanation:
Answer:
A cup
Step-by-step explanation:
Because a pint is smaller than a cup look it up it's true
help i will give alot of points
Answers
Answer:east
Step-by-step explanation:
north: LOW:-8F HIGH:10F this have the most change
+18F
south: LOW:-3F HIGH:2F this have the third most change
+5F
east: LOW:-2F HIGH:0F this have the least change
+2F
west: LOW:-4F HIGH:3F this have the second most change
+7F
the east only have +2F so it have the least change
Calculate P(3, 2) Help
12
8
7
6
Answers
6
Hope This Helps!
P2 = 90; 10P2 = 90. Combinations. There are also two types of combinations
Answer:
P(3, 2) = 6
Step-by-step explanation:
A permutation is an ordered combination, i.e. an arrangement in a definite order of a number of objects taken some or all at a time.
Permutation formula[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]
where:
n is the number of objects to choose from.r is the chosen number of objects.0 ≤ r ≤ nGiven P(3, 2):
n = 3r = 2So we need to calculate the permutations of two numbers taken from three numbers.
The numbers are 1, 2 and 3. As order matters, the number of ways two numbers from this set can be arranged is:
1 and 21 and 32 and 12 and 33 and 13 and 2Therefore, there are 6 ways two numbers from the set of three numbers can be arranged.
To prove this, substitute n = 3 and r = 2 into the permutation formula:
[tex]\begin{aligned}\implies P(3,2)&=\dfrac{3!}{(3-2)!}\\\\&=\dfrac{3!}{1!}\\\\&=\dfrac{3 \times 2 \times 1}{1}\\\\&=\dfrac{6}{1}\\\\&=6 \end{aligned}[/tex]
Therefore, P(3, 2) = 6.
Mindy and Daisy are making necklaces using beads. Mindy uses 4 red beads for every 5 white beads. Daisy uses 6 red beads for every 7 white beads. Use tables of equivalent ratios to determine who will use more white beads when Mindy and Daisy each use 12 red beads.
A.
Mindy will use 15 white beads and Daisy will only use 14 white beads, so Mindy will use more white beads.
B.
Daisy will use 42 white beads and Mindy will only use 20 white beads, so Daisy will use more white beads.
C.
Daisy will use 13 white beads and Mindy will only use 9 white beads, so Daisy will use more white beads.
D.
Mindy will use 20 white beads and Daisy will only use 13 white beads, so Mindy will use more white beads.
Answers
Beatriz Cruz purchased a home for $98,500. She made a $28,500
down payment and mortgaged the rest. Her annual expenses
for mortgage interest, taxes, repairs, insurance, and depreciation
totaled $6,890. She rented the house for $750 a month.
a. What is the annual net income?
b. What is the annual yield?
e. What monthly rent would she have to charge to get
a yield of 90%?
Answers
Answer:
a. To find the annual net income, subtract the annual expenses from the annual rental income.
The annual rental income = $750 * 12 months = $9,000
So, the annual net income = $9,000 - $6,890 = $2,110
b. To find the annual yield, divide the annual net income by the investment cost (the down payment) and multiply by 100 to get the answer as a percentage.
The annual yield = ($2,110 / $28,500) * 100 = 7.41%
c. To find the monthly rent required to get a yield of 90%, divide the investment cost by the desired yield and divide by 12 to get the monthly rent.
The investment cost = $28,500
The desired yield = 0.90
So, the monthly rent = ($28,500 / 0.90) / 12 = $2,306.25
Step-by-step explanation:
in ∆XYZ, the measures of angles X, Y, and Z, respectively, are in the ratio 1:10:25. Find the measure of each angle.
m
m
m
Answers
The measures of the angles X, Y, and Z are 5, 50, and 125 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that in ∆XYZ, the measures of angles X, Y, and Z, respectively, are in the ratio 1:10:25.
We have to find the measure of each angle.
Let the measures can be expressed as 1x, 10x, and 25x, respectively, where x is an arbitrary value.
We know that the sum of the angles of a triangle is always 180 degrees, so:
1x + 10x + 25x = 180
36x = 180
Divide both sides by 36
x = 5
Therefore, the measures of the angles X, Y, and Z are 5, 50, and 125 degrees.
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Suppose that Antonia rolls a pair of fair six-sided dice. Let A be the event that the first die lands on 5 and B be the event that the sum of the two dice is 6. Using the sample space of possible outcomes below, answer each of the following questions.
What is P(A), left parenthesis, A, right parenthesis, the probability that the first die lands on 5?
What is P(B), left parenthesis, B, right parenthesis, the probability that the sum of the two dice is 6?
What is P(A\text{ and }B)P(A and B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the first die lands on 555 and the two dice add up to 6?
Are events A and B independent?
Answers
The answers for the asked probabilities are a) 1/6, b) 5/36, c) 1/36 and d) A and B events are not independent.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, Antonia rolls a pair of fair six-sided dice. A is the event that the first die lands on 5 and B is the event that the sum of the two dice is 6.
Probability = possible outcomes / favorable outcomes
Suppose that Antonia rolls a pair of fair six-sided dice.
All possible outcomes are:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
(36 outcomes in total)
a) A = the first die lands on 5
Favorable outcomes:
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6 outcomes)
Therefore, the probability that the first die lands on 5 = P(A) = 6/36 = 1/6
b) B = the sum of the two dice is 6
Favorable outcomes:
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = (5 outcomes)
Therefore, the probability that the sum of the two dice is P(B) = 6 = 5/36
c) A∩B = the first die lands on 5 and the two dice add up to 6
Favorable outcomes:
(5, 1) = 1 outcome
Therefore, the probability that the first die lands on 5 and the two dice add up to6 = P(A∩B) = 1/36
d) Two events are independent when;
P(A∩B) = P(A) · P(B)
Since,
1/36 ≠ 5/36 · 1/36
Therefore, A and B events are not independent.
Hence, the answers for the asked probabilities are a) 1/6, b) 5/36, c) 1/36 and d) A and B events are not independent.
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what is thhe sales tax on $58 at a rate of 5.5%
Answers
Answer:
3.19
Step-by-step explanation:
5.5% of 58 is 3.19
and is you need it,
58 - 3.19 = 54.81
I believe this is right
the sales tax on $58 at a rate of 5.5% is $3.19
How to find the tax on $58 at a rate of 5.5%?
Taxes are a mandatory contribution to the state. So sales must pay taxes, and it is stated that the rate of tax that must be paid is 5.5%
The way to calculate tax from sales is to multiply the tax rate by the income from sales.
the income = $58
the rate of tax = 5.5%
the tax to be paid by sales = the income x the tax
= $58 x 5.5%
= $3.19
so the answer to the question is $3.19
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y=4x^2-56x is the equation of a curve.
by completing the square, show that the co-ordinates of the turning point are (7,-196)
Answers
Answer:
[tex]y=4(x-7)^2-196[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]y=4x^2-56x[/tex]
Completing the squareFactor out the coefficient of the term x²:
[tex]y=4(x^2-14x)[/tex]
Add and subtract the square of half the coefficient of the term in x inside the brackets:
[tex]y=4\left(x^2-14x+\left(-\dfrac{14}{2}\right)^2-\left(-\dfrac{14}{2}\right)^2\right)[/tex]
Simplify:
[tex]y=4\left(x^2-14x+\left(-7\right)^2-\left(-7\right)^2\right)[/tex]
[tex]y=4\left(x^2-14x+49-49\right)[/tex]
Factor the perfect square trinomial created by the first three terms inside the brackets:
[tex]y=4\left((x-7)^2-49\right)[/tex]
Distribute:
[tex]y=4(x-7)^2-196[/tex]
Turning pointThe equation is now in vertex form y = a(x - h)² + k, where (h, k) is the vertex of the parabola (turning point).
Compare the equation with the vertex formula to identify the values of h and k:
h = 7k = -196Therefore, the coordinates of the turning point (vertex) are (7, -196).
Poseidon is in search for Zeus' lightning bolt after being accused of theft! Rumored to have
been among the luggage of a luxury cruiser that has disappeared, the god of the sea is
desperately searching the Bermuda Triangle: Given the approximate boundary of missing ships,
how much area is Poseidon searching?
GEORGIA
SOUTH
CAROLINA
FLORIDA
10-9-8-7-6-5-3-2
Cuba
9
946
S
43
2
0123
2 3 4 5 6 7 8 9 10
Dominican
Republi
Puerto Rico
Answers
The approximate area that Poseidon is searching is given as follows:
64.13 square units.
How to obtain the area of the triangle?The area of a triangle is given by half the multiplication of the base length by the height.
The coordinates of the vertices of the triangle in this problem are given as follows:
(-6,1), (4,-5) and (-1,9).
Any of the three sides can be chosen as the base, and we use the equation for the distance between two points to obtain it's length.
Choosing vertices (-6,1) and (4,-5) as the base, it's length is given as follows:
b = sqrt((4 - (-6))² + (-5 - 1)²)
b = 11.66.
The midpoint of the base has the coordinates given as follows:
x = (-6 + 4)/2 = -1.y = (1 - 5)/2 = -2.The height is the distance between the vertices (-1,-2) and (-1,9), hence, as they have the same x-coordinate, the height is given as follows:
h = 9 - (-2)
h = 11.
Then the area is given as follows:
A = 0.5 x 11.66 x 11
A = 64.13 square units.
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need help with this question
Answers
Answer:
I think it's c sorry if im wrong
Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf. She writes the expression (x−5)(50−2x) to represent her profit based on the price per scarf, x . Enter Sofie's average change in profit for two different sections of the graph.
Answers
Sofie will not make a profit if she sells her scarves for $5 or less.
The maximum profit Sofie can make is $200.
What is a Parabola?A parabola is a plane curve created when a point moves in such a way that the distance it travels from a fixed point to a fixed line.
According to the given problem,
y = (x - 5)(50 - 2x)
⇒ y + (-(x - 5)(50 - 2x) = (x - 5)(50 - 2x) + (-(x - 5)(50 - 2x)
⇒ y - (x - 5)(50 - 2x) = (x - 5)(50 - 2x) - (x - 5)(50 - 2x)
⇒ y - (x - 5)(-2x + 50) = 0
⇒ y - (-x *2x + x*50 + 5*2x -5*50) = 0
⇒ y - ( -2x² + 50x + 10x - 250) = 0
⇒ y - ( - 2x² + 60x - 250 ) = 0
⇒ y + 2x² - 60x + 250 = 0
⇒ 2x² -60x + y + 250 = 0
⇒ ( 2x² - 60x ) + y + 250 = 0
⇒ 2 ( x² - x) + y + 250 = 0
⇒ 2 ( x² - x) + y + 250 = 0
⇒ 2 ( x² - 30x ) + y + 250 = 0
⇒ 2( x² + 2(-15)x + 225 -225 +y + 250 = 0
⇒ 2( x - 15 )² + 2(-225) + y + 250 = 0
⇒ 2( x - 15 )² + y = -2(-225) - 250
⇒ 2( x - 15 )² + y = 450 - 250
⇒ 2( x - 15 )² + y = 200
⇒ y = -2( x - 15 )² + 200
This equation is in the form of y = a(x - h)² + k where the vertex of the parabola is (h , k).
Therefore the vertex of the parabola is at (15 , 200)
Hence, we can conclude that Sofie will maximum profit of $200 if she sells a scarf at 15$ and will make the least profit if she sells the scarf at $5 or less.
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Use the Distributive Property to find 1/3×6 1/2.
Answers
Answer: 1
Step-by-step explanation: The Distributive Property is nothing to get confused about. It is simply just a multiplication rule. Follow out the steps in this problem in order. 1/3 * 6 = 2. 2 * 1/2 = 1, and there you go! If this helped, please consider giving this a brainiest as I am one away from the next rank!
Answer: 2
Step-by-step explanation:
A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point
�
A, the boat’s crew measures the angle of elevation to the beacon, 12
∘
∘
, before they draw closer. They measure the angle of elevation a second time from point
�
B at some later time to be 20
∘
∘
. Find the distance from point
�
A to point
�
B. Round your answer to the nearest foot if necessary.
Answers
The distance between the points A and B is 209.4 feet
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.
A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 12°. Let a represent distance from point A to light house:
tan(12) = 107/a
a = 503.4 feet
They measure the angle of elevation a second time from point B at some later time to be 20°. Hence, if b represent distance from point A to light house:
tan(20) = 107/b
b = 294 feet
Distance from point A to B = 503.4 feet - 294 feet = 209.4
The distance between the points is 209.4 feet
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a six-sided number cube numbered 1 through 6 was tossed 150 times. the results are shown in the table. number cube results,. number,. frequency,. 1,. 16,. 2,. 28,. 3,. 24,. 4,. 15,. 5,. 37,. 6,. 30,. what is the experimental probability that the next toss will result in an odd number?
Answers
The experimental probability of getting an odd number on the next toss is 51.3%.
Probability is a measure of the likelihood of an event occurring. In the case of the six-sided number cube, the theoretical probability of getting an odd number on any one roll is 3 out of 6, or 1/2, or 50%. However, this is a theoretical value and may not match the actual results obtained from a set of experiments.
The experimental probability of an event is calculated by observing the actual results of a series of trials and comparing it to the number of possible outcomes. In this case, the number cube was tossed 150 times and the results were recorded in the table. The frequency of the odd numbers (1, 3, and 5) was found to be 77.
The experimental probability of getting an odd number on the next toss can be calculated by dividing the frequency of the odd numbers by the total number of tosses, which is 150. 77/150 = 0.513 or 51.3%.
Therefore, the experimental probability of getting an odd number on the next toss of the six-sided number cube is 51.3%.
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A pole 10 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Liam measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
Answers
42 feet is the length of the guy wire.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that a pole 10 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground.
After placing the pole, Liam measures the distance from the pole to the stake and from the pole to the tower.
We have to find the length of the guy wire
Let the required distance is x and the height of the tower is t.
Use similar triangle ratios to find the value of t:
t / 10 = (9 + 3) / 3
t / 10 = 4
t = 40 feet
Use Pythagorean to find the value of x:
x² = 40² + (9 + 3)²
x² = 1600 + 144
x² = 1744
x = √1744
x = 42 feet
Hence, 42 feet is the length of the guy wire.
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what is the graph for the problem y= 10 + 20x
Answers
This graph above portraiture the linear equation
2/3 * -4/5[tex]2/3* -4/5[/tex]
Answers
The value of the expression 2/3 x -4/5 is -8/15.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
An expression,
2/3 x -4/5.
Here, we have to multiply the fraction.
So,
2/3 x -4/5,
= -8/15
Therefore, -8/15 is the value.
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If tan theta equals 4/3 on the interval (pi, 3pi/2), find sin 2 theta, cos 2 theta, tan 2 theta
Answers
With the value tanθ = 4/3 on the interval (π, 3π/2), using trigonometric identities sin 2θ = 24/25 , cos 2θ = -7/25 , tan 2θ = -8/7.
First, we'll find sin 2θ:
sin 2θ = 2sinθcosθ
We can use the identity tanθ = sinθ/cosθ to find sinθ and cosθ:
sinθ = 4/5 and cosθ = 3/5
So,
sin 2θ = 2(4/5)(3/5) = 24/25
Next, we'll find cos 2θ:
cos 2θ = cos^2θ - sin^2θ = 1 - 2sin^2θ
Using the values of sinθ and cosθ that we found earlier:
cos 2θ = 1 - 2(4/5)^2 = 1 - 32/25 = -7/25
Finally, we'll find tan 2θ:
tan 2θ = (2tanθ)/(1 - tan^2θ)
Using the value of tanθ that we were given:
tan 2θ = (2(4/3))/(1 - (4/3)^2) = (8/3)/(-7/9) = -8/7
So, the values of sin 2θ, cos 2θ, and tan 2θ are:
sin 2θ = 24/25
cos 2θ = -7/25
tan 2θ = -8/7
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easyyyy but um.. please help QvQ
Answers
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
in our case
9.3 × 3.5 / 2 = 16.275 ft²
as you can see, yes, really easy.
what was the problem ? do you need any further explanation ?
help answer this equation in the image below 30 points
Answers
Answer:
x = -30
Step-by-step explanation:
25 = -7 (x+5) +5x expand brackets
25 = -7x -35 +5x simplify
25 = -2x -35 add 35 to both sides
60 = -2x multiply by sides by -1
-60 =2x divide by 2
x =-30
Answer:
-30
Step-by-step explanation:
25= -7x-35+5x
25+35= -2x
60= -2x both side by -2
-30=x
Please help me find the value of x and y
Answers
The side lengths x and y are √( 50² - y²) and √50² - x² respectively.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In a right angle triangle, the length of one side can be determined using the Pythagorean theorem:
x² + y² = hypotenuse²
In the given triangle the length of hypotenuse is 50 cm
x² = 50² - y²
x=√( 50² - y²)
y = √50² - x²
Hence, the side lengths x and y are √( 50² - y²) and √50² - x² respectively.
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To solve 3x = 9, we divide each side of the equation by
Answers
Answer: x=3
Step-by-step explanation:
divide by the common factor 3
3x ÷ 3 = x
9÷3 = 3
hence the reason we get x=3
Answer: 3
Step-by-step explanation:
To solve for x, you need to divide 9 by 3 which equals 3.
Since 3x = (3 ⋅ 3), x = 3.
ATTACHMENTTTTTTTTTTTTTTTTTTTT
Answers
a. The total of the two sides of the right triangle using Algebraic expression is 3x²+7x-4.
b. The length of the missing side of the triangle is 3x³-4x²-15x+5.
c. If the value of x=2, then the length of the three sides of the triangle is
a=11, b=11 and c= -17.
d. No, it is not possible to have these side lengths for a right triangle.
Define AlgebraAlgebra is a discipline of mathematics that studies symbols and the mathematical operations that can be applied to them. These symbols are referred to as variables because they don't have predetermined values. These values are usually represented in algebra by variables, which are symbols like x, y, z, p, or q. These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to ascertain the values.
a. Let the sides of the right triangle be a, b and c.
Given, one side of the triangle is 2x² + 2x - 1 and
another side is 5x + x² -3.
So, let a = 2x²+2x-1 and b = 5x+x²-3
Now, the total of the two sides= a+b
a+b
=2x²+2x-1 + 5x+x²-3
= 3x²+7x-4
Therefore, the total of the two sides of the right triangle = 3x²+7x-4.
b. Now the perimeter of the triangle is given= 3x³-x²-8x+1.
Given, a+b+c=3x³-x²-8x+1.
We already have a+b, so by simplifying the equation a+b+c=3x³-x²-8x+1
we can find the length of the third side, c.
a+b+c= 3x³-x²-8x+1
⇒3x²+7x-4 +c= 3x³-x²-8x+1
⇒c= 3x³-x²-3x²-8x-7x+1+4
⇒c= 3x³-4x²-15x+5.
Therefore, length of the missing side is 3x³-4x²-15x+5.
c. We have the three sides of the triangle with us which are:
a = 2x²+2x-1
b = 5x+x²-3
c = 3x³-4x²-15x+5
Now putting the value of x as 2 in the equations as follows:
a= 2(2²) +2(2)-1
= 8+4-1
=11
b=5(2) +2²-3
= 10+4-3
=11
c=3(2³)- 4(2²) -15(2) +5
=24-16-30+5
= -17
Therefore, the length of the three sides of the right triangle
are 11, 11 and -17.
d. The sides of the right triangle are.
a = 11
b = 11
c = -17
We know as per the Pythagorean theorem c² = a² + b².
Accordingly, c²= 289 & a² = 121 and b²= 121, a² + b²= 242
which shows that c² is not equal to a² + b².
As, the sides of the triangle does not follow the Pythagorean theorem, so these are not the sides of a right-angle triangle.
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Why is it important to use a device like a random number table in a simulation?
A. Chance plays a part in the process being simulated.
B. It helps to organize the data.
C. The calculations are difficult to complete by hand.
D. Random number tables include critical values
Answers
It is important to use a device like a random number table in a simulation because Option A Chance plays a part in the process being simulated.
In simulations, a random number table is used to incorporate the element of chance into the process being modeled. The reason this is important is that many real-world processes involve uncertainty and randomness, and to accurately simulate these processes, it is necessary to include these elements.
For example, in simulating the stock market, stock prices can be modeled as random variables, because they are influenced by a variety of unpredictable factors such as changes in interest rates, company earnings, geopolitical events, and investor sentiment. To simulate this process, a random number table can be used to generate random numbers that represent these unpredictable factors.
By using a random number table, the simulation can model the uncertainty and randomness inherent in the real-world process, which makes the simulation more accurate and realistic. This is why it is important to use a device like a random number table in a simulation when chance plays a part in the process being simulated.
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