Answers
13.
The radii are the lines that go from the exact center of the circle to anywhere on the circumference of the circle.
Here we can see that segments AB AD and AC go from the center to somewhere on the circumference, thus these segments are radii.
14.
Since the triangles are congruent, their corresponding angles are congruent. Given this, angle A is congruent to angle D and angle C is congruent to angle F.
A tip for future problems like this - you don't necessarily need to look at the diagram; the congruent statement gives you all the information you need about which angles correspond with each other and thus are congruent. Triangle ABC is congruent to triangle DEF: A corresponds to D, B corresponds to E, and C corresponds to F. This is useful because sometimes the triangles in the diagrams are not oriented the same way and its confusing to try to figure out which angles correspond.
15.
The diameter of a circle is the is a line that goes from a side through the center and to the other side of a circle.
The diameter is segment RS.
16.
Obtuse = greater than 90 degrees.
Acute = less than 90 degrees
Right = 90 degrees
Straight = 180 degrees (a straight line)
For this angle to be 90 degrees, it would have to be indicated by a little box in the corner; you must never assume an angle is 90 degrees, unless this information is explicitly stated in the question or shown in the diagram. This is not a right angle, nor is it a straight angle (it is not a straight line). That leaves obtuse and acute. Think: Is this greater than or less than 90 degrees? It is less than 90 degrees. The angle is acute.
Related Questions
A right triangle has legs that are 18 centimeters and 27 centimeters long. What is the length of the hypotenuse?
Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.
Answers
Answer:
the length of the hypotenuse = 32.45 centimeters
Step-by-step explanation:
A right triangle has legs that are 18 centimeters and 27 centimeters long
In a right angle triangle , to find hypotenuse we use Pythagorean theorem
[tex]c^2= a^2+b^2[/tex]
where a and b are the length of two legs
Given a= 18 and b = 27
Lets find out C , plug in all the value in the formula
[tex]c^2= 18^2+27^2[/tex]
[tex]c^2=324 +729= 1053[/tex]
c^2 = 1053
now take square root on both sides
c= 32.45
So the length of the hypotenuse = 32.45 centimeters
Length of a rectangle is 4 inches less than twice it’s width of the perimeter is 70 inches what’s the dimensions?
Answers
L= length= 2W-4
Perimeter= 70
FIND WIDTH:
P= 2(L + W)
P= 2L + 2W
substitute 2W-4 for L
70= 2(2W-4) + 2W
multiply 2 by all in parentheses
70= (2*2W) + (2*-4) + 2W
70= 4W - 8 + 2W
combine like terms
70= 6W - 8
add 8 to both sides
78= 6W
divide both sides by 6
13= W
FIND LENGTH:
substitute w=13 to find width
L= 2W-4
L= 2(13)-4
L= 26-4
L= 22
CHECK:
P= 2(L + W)
70= 2(22 + 13)
70= (2*22) + 2(13)
70= 44 + 26
70= 70
ANSWER:
length= 22 inches
width= 13 inches
Hope this helps! :)
What is the number of possible outcomes if two quarters are tossed and the total numbers of heads and tails are counted?
A) 2
B) 3
C) 4
D) 6
Answers
Answer:
B
Step-by-step explanation:
TT two tails/no heads
TH one tail/one head
HT
HH two heads/no tails
The number of possible outcomes if two quarters are tossed and the total numbers of heads and tails are counted is 8.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Since there are number of possibility as;
TT two tails/no heads
TH one tail/one head
HTand HH two heads/no tails
Each quarter will come up heads or tails which is 2 possibilities.
Thus for three tosses the number of outcomes is 2 x 2 x 2 = 8.
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In the triangle below, what is the length of the side opposite the 60 angle?
Answers
Answer with explanation:
In the given right triangle
[tex]\sin 60^{\circ}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\ \frac{\sqrt{3}}{2}=\frac{\text{Perpendicular}}{2\sqrt{3}}\\\\ \text{Perpendicular}}=2\sqrt{3} \times\frac{\sqrt{3}}{2}\\\\\text{Perpendicular}}=\sqrt{3} \times\sqrt{3} \\\\\text{Perpendicular}}=3[/tex]
→Side opposite to 60° angle = 3 units
Option C : 3 Units
Some steps to rewrite the expression x3 − x + 2x2 − 2 as a product of three factors are shown below:
Step 1: x3 − x + 2x2 − 2
Step 2: x3 + 2x2 − x − 2
Step 3: x2(x + 2) − 1(x + 2)
Which of the following best shows the next two steps to rewrite the expression? Step 4: (x2 + 1)(x + 2); Step 5: (x + 1)(x + 1)(x + 2)
Step 4: (x2 − 1)(x + 2); Step 5: (x − 1)(x + 1)(x + 2)
Step 4: (x2 − 1)(x + 2); Step 5: (x + 1)(x + 1)(x + 2)
Step 4: (x2 + 1)(x + 2); Step 5: (x − 1)(x + 1)(x + 1)
Answers
Once you have the step 3 x2(x+2)-1(x+2)
You can combine the two (x+2)s and connect the x2 with the -1 as so:
(x2-1)(x+2)
Now, (x2-1) can be rewritten as:
(x-1)(x+1)
So total, for step 5:
(x-1)(x+1)(x+2)
I hope this Helps!
Which point slope equation represents a line that passes through (3, -2) with a slope of - 4/5
• y - 3 = -4/5 (x + 2)
• y - 2 = 4/5 (x - 3)
• y + 2 = -4/5 (x - 3)
• y + 3 = 4/5 (x + 2)
Answers
the equation of a line in the point slope form is
y-y1=m*(x-x1)
if m=-4/5 and the point is (3,-2)
the equation is
y-y1=m*(x-x1)------> y-(-2)=(-4/5)*(x-3)----> y+2=(-4/5)*(x-3)
the answer is
y + 2 = -4/5 (x - 3)
You have less than 120 minutes to spend in the gym and in the pool. You want to spend less than 45 minutes in the gym and more than 30 minutes in the pool. Which system represents the situation?
Answers
The situation can be represented as three inequalities: g + p < 120, g < 45, p > 30, where g is the time spent in the gym and p is the time spent in the pool.
Explanation:The situation you described can be represented as a system of inequalities. Let's denote gym time as g and pool time as p. Then, the system of inequalities would be the following:
g + p < 120 (you want to spend less than 120 minutes in the gym and in the pool total)g < 45 (you want to spend less than 45 minutes in the gym)p > 30 (you want to spend more than 30 minutes in the poolThese inequalities represent the constraints on how you can divide your time between the gym and the pool. Any solution to this system would be a pair of numbers (g, p) that satisfy all three inequalities, meaning it's a valid way for you to divide your time.
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The correct system of inequalities is Option 1: x + y < 120 (representing the total time constraint), x < 45 (reflecting the condition of spending less time in the gym), and y > 30 (representing the condition of spending more time in the pool). This corresponds to Option 1 in the given systems of inequalities.
Explanation:The correct system of inequalities that represents your time allocation between the gym and the pool is Option 1. Let's define x as the time you spend in the gym and y as the time you spend in the pool. According to the given conditions and constraints, the total time, which is the sum of x and y, should be less than 120 minutes (x + y < 120). Furthermore, you want to spend less than 45 minutes in the gym (x < 45) and more than 30 minutes in the pool (y > 30). These three inequalities jointly form a system that accurately represents your situation at the gym and pool.
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The complete question is given below:
You have less than 120 minutes to spend in the gym and in the pool. You want to spend less than 45 minutes in the gym and more than 30 minutes in the pool. Which system represents the situation?
Option 1:
x + y < 120
x < 45
y > 30
Option 2:
x + y = 120
x = 45
y = 30
Option 3:
x + y <= 120
x < 45
y > 30
Option 4:
x + y < 120
x <= 45
y >= 30
robert leaves his home to go to his office . he drives 6km due north and then 4 km due east. approximatel what is the shortest distance from roberts home to his office , in kms?
Answers
To find the shortest distance from Robert's home to his office, we use the Pythagorean theorem with the distances traveled north and east to calculate the length of the hypotenuse, which is approximately 7.2 kilometers.
Robert leaves his home and drives 6 km due north and then 4 km due east. To determine the shortest distance from Robert's home to his office, we can use the Pythagorean theorem. This scenario forms a right-angled triangle where the two sides are the north-bound and east-bound legs of his journey, and the hypotenuse is the shortest distance.
Step 1: Label the lengths of the two sides adjacent to the right angle as 'a' and 'b', where 'a' is the 6 km north-bound leg and 'b' is the 4 km east-bound leg.
Step 2: Apply the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides:
c² = a² + b²
Step 3: Substitute the known values into the theorem:
c² = 6² + 4²
Step 4: Calculate the squares of the sides and sum them:
c² = 36 + 16
Step 5: Sum the squares gives us:
c² = 52
Step 6: Take the square root of both sides to find 'c':
c = √52
Step 7: Calculate the square root which approximately equals:
c = 7.2 km
Therefore, the shortest distance from Robert's home to his office is approximately 7.2 kilometers.
Please help!!
If a 6-sided die is rolled 5 times and rolling a 2 is considered to be a success, what are the chances of rolling exactly three successes?
show work
A.) 0.32% B.) 16.67% C.) 32.15% D.) 33.33% E) none of these
Answers
The probability of rolling exactly three 2s in five rolls of a six-sided die is 32.15%, calculated using the binomial probability formula. The correct answer from the provided options is C) 32.15%.
Explanation:The student is asking about the probability of achieving a specific number of successes in a series of independent events, which is a problem that can be solved using the binomial probability formula. In this case, a success is defined as rolling a 2 on a six-sided die. The probability of rolling a 2 (success) on a single roll is \(\frac{1}{6}\), and the probability of not rolling a 2 (failure) is \(\frac{5}{6}\).
Therefore, the probability of rolling exactly three 2s in five rolls can be calculated by the formula:
\(P(X=k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}\)
where \(n\) is the number of trials, \(k\) is the number of desired successes, and \(p\) is the probability of a single success.
Substituting the values:
\(P(X=3) = \binom{5}{3} \cdot \left(\frac{1}{6}\right)^3 \cdot \left(\frac{5}{6}\right)^{5-3}\)
\(P(X=3) = 10 \cdot \left(\frac{1}{6}\right)^3 \cdot \left(\frac{5}{6}\right)^2\)
\(P(X=3) = 10 \cdot \frac{1}{216} \cdot \frac{25}{36}\)
\(P(X=3) = \frac{250}{7776}\)
\(P(X=3) \approx 0.03215 \text{ or } 3.215\%\)
So the correct answer from the provided options is C) 32.15%.
The chances of rolling exactly three successes when rolling a 6-sided die 5 times, where rolling a 2 is considered a success, is approximately 2.143%.
Explanation:To find the chances of rolling exactly three successes, we need to use the concept of binomial probability. In this case, the probability of rolling a 2 (success) is 1/6, and the probability of not rolling a 2 (failure) is 5/6. We can use the formula for binomial probability: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success in one trial.
For this problem, n=5 (since the die is rolled 5 times), k=3 (we want exactly three successes), and p=1/6 (probability of rolling a 2). Plugging these values into the formula:
P(X=3) = (5 choose 3) * (1/6)^3 * (5/6)^(5-3)
Simplifying, we get:
P(X=3) = 10 * (1/6)^3 * (5/6)^2 = 10 * (1/216) * (25/36) = 250/11664 ≈ 0.02143 ≈ 2.143%
An expression is shown below:
3x3y + 15xy − 9x2y − 45y
Part A: Rewrite the expression so that the GCF is factored completely. Show the steps of your work.
Part B: Rewrite the expression completely factored. Show the steps of your work.
Answers
I imagine that the expression you are asked to work with is:
[tex]3 x^{3}y+15xy-9 x^{2} y-45y [/tex]
When you use a keyboard it is customary to use "^" to denote an exponent is coming so you could have written: 3x^3y+15xy-9x^2y-45y just to be clear.
PART A
To factor out the GCF we are looking for the greatest factor among the terms. Looking at the coefficients (the numbers) the largest number they can all be divided by is 3 so we will pull out a 3. Notice also that each term has a y in it so we can pull out that.
This gives us: [tex] 3 x^{3}y+15xy-9 x^{2} y-45y=3y( x^{3}+5x-3 x^{2} -15)[/tex]
To factor is to write as a product (something times something else). It undoes multiplication so in this case if you take what we got and multiplied it back you should get the expression we started with.
PART B
Start with the answer in part A. Namely, [tex]3y( x^{3}+5x-3 x^{2} -15)[/tex]. For now let's focus only on what is in the parenthesis. We have four terms so let's take them two at a time. I am separating the expression in two using square brackets. [tex][( x^{3}+5x)]-[3 x^{2} -15][/tex]
Let's next factor what is in each bracket:
[tex][( x^{3}+5x)]-[3 x^{2} -15] = [x( x^{2} +5)]-[3( x^{2} +5)][/tex]
Notice that both brackets have the same expression in them so now we factor that out: [tex] [x( x^{2} +5)]-[3( x^{2} +5)] = (x-3)( x^{2} +5)[/tex]
Our original expression (the one we started the problem with) had a 3y we already pulled out. We need to include that in the completely factored expression. Doing so we get: [tex]3 x^{3}y+15xy-9 x^{2} y-45y =(3y) (x-3)( x^{2} +5)[/tex]
Any one know the next number
Answers
0.20+0.38+0.24+a+2a = 1
3a+0.82 = 1
3a = 1-0.82
3a = 0.18
a = 0.18/3
a = 0.06
A rental agency charges 6% of a month's rent for finding an apartment. Nikolai is looking at apartments with monthly rents of $880, $960, nad $1050. What is the lowest fee he might pay?
Answers
%6 of $960 is:57.6
%6 of $1050 is:64.8
You must use the substitution method. 3x+2y=11
y=5x-1
Answers
3x+2(5x-1)=11
3x+10x-2=11
13x=13
x=1
plug x=1 to y=5x-1 to find y
y=5(1)-1
y=5-1
y=4
ANSWER: x=1 and y=4 which is (1,4) as an ordered pair
Given that f(x) = 5x2 − 100, find x.
Answers
To find x, we need to solve the quadratic equation 5x^2 - 100 = 0 using the quadratic formula.
Explanation:To find x, we need to solve the quadratic equation 5x^2 - 100 = 0 using the quadratic formula. The formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 5, b = 0, and c = -100. Plugging these values into the quadratic formula, we get:
x = (-0 ± √(0^2 - 4 * 5 * -100)) / (2 * 5)
Simplifying further, we have:
x = (√2000) / 10
Therefore, x equals approximately ±14.14.
help needed
An unlabeled hierarchical diagram of various astronomical bodies is shown. The labels A, B, C and D can be used to represent the galaxy, Mars, universe, moon, and solar system.
Part 1: Which four astronomical bodies would you choose to represent the four labels in the diagram?
Part 2: Explain why the hierarchical level D is different from the rest.
Answers
Cant help you for number 2 though. Hope this helps :)
The midpoint of a segment is (6,−6) and one endpoint is (13,−1). Find the coordinates of the other endpoint.
Answers
13 is 7 away from 6, and -1 is 5 away from 6. Subtract 7 away from 6, and 5 away from -6.
Answer: The other endpoint of the segment is (-1, -11).
Step-by-step explanation: Given that the midpoint of a line segment is (6, -6) and one endpoint is (13, -1).
We are to find the co-ordinates of the other endpoint.
Let (a, b) be the co-ordinates of the other end-point.
Then, according to the given information, we have
[tex]\left(\dfrac{a+13}{2},\dfrac{b+(-1)}{2}\right)=(6,-6)\\\\\\\Rightarrow \left(\dfrac{a+13}{2},\dfrac{b-1}{2}\right)=(6,-6).[/tex]
Equating the x and y co-ordinates on both sides of the above, we get
[tex]\dfrac{a+13}{2}=6\\\\\\\Rightarrow a+13=12\\\\\Rightarrow a=12-13\\\\\Rightarrow a=-1[/tex]
and
[tex]\dfrac{b-1}{2}=-6\\\\\\\Rightarrow b-1=-12\\\\\Rightarrow b=-12+1\\\\\Righatrrow b=-11.[/tex]
Thus, the other endpoint of the segment is (-1, -11).
Part 1.] Which of the following is the inverse of the given function?
[tex]y= 3 x^{5}-4[/tex]
A.] [tex]y= \sqrt[5]{ \frac{x+3}{4}} [/tex]
B.] [tex]y= \sqrt[5]{ \frac{x-4}{3}} [/tex]
C.] [tex]y= \sqrt[3]{ \frac{x+4}{5}} [/tex]
D.] [tex]y= \sqrt[5]{ \frac{x+4}{3}} [/tex]
Part 2.] What is the inverse of the function [tex]y=3 e^{-4+1} [/tex]?
A.] [tex]y= \frac{1-log(x-3)}{4} [/tex]
B.] [tex]y= \frac{1-log( \frac{x}{3})}{4} [/tex]
C.] [tex]y= \frac{1-ln(x-3)}{4} [/tex]
D.] [tex]y= \frac{1-ln( \frac{x}{3})}{4} [/tex]
Answers
y = 3x⁵ - 4
Interchanging x and y
x = 3y⁵ - 4
solving for y in the equation; x=3y⁵-4
y = ((x+4)/3)^1/5
= ((x+4)/3)^1/5
2. inverse of the equation y = 3e^-4x+1
I think the answer is D;
Interchanging the variables x and y
x= 3e^-4y-1
Solving for y in x = 3e^-4y +1
y= -(In(x/3)-1)/4
= (1-In(x/3))/4
To the nearest tenth, what is the area of a circle whose diameter is 9 feet? Use 3.14 for π . Enter your answer in the box. ft2
Answers
Area of a circle = 3.14 * r^2
D = 2r
D = 9
r = 4.5
Area = 3.14 * (4.5)^2
Area = 63.6 ft^2
Trevor is analyzing a circle, y2 + x2 = 49, and a linear function g(x). Will they intersect?
Answers
[tex]x^{2}+y^{2}=49[/tex]
We can write this equation in its standard form as follows:
[tex]x^{2}+y^{2}=7^{2} \\ where \ the \ radius \ r=7[/tex]
On the other hand, the linear function is given as the following table:
[tex]x \ \ \ \ \ \ \ \ g(x) \\ -1 \ \ -9.2 \\ 0 \ \ \ \ \ -9 \\ 1 \ \ \ \ \ -8.8[/tex]
To check if the circle and the line intersects, let's substitute the equation of the line into the equation of the circle to see if there is a real solution, so:
[tex]x^{2}+(0.2x-9)^{2}=49 \\ \\ \therefore x^{2}+0.04x^{2}-3.6x+81=49 \\ \\ \therefore 1.04x^{2}-36x+32=0 \\ \\ Solving \ for \ x: \\ x_{1}=33.70 \\ x_{2}=0.91 \\ \\ Solving \ for \ y: \\ y_{1}=0.2(33.70)-9=-2.26 \\ y_{2}=0.2(0.91)-9=-8.18[/tex]
Finally the intersects are:
[tex]P_{1}(33.70, -2.26) \ and \ P_{2}(0.91, -8.18)[/tex]
The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measures 120 ft by 80 ft, and the expansion will increase its area by 4,400 ft2. By how many feet should the length of the parking lot be increased? A = lw 1.2 f
Answers
Answer: The length of the parking lot should be increased 20 ft.
Please, see the attached files.
Thanks.
Answer:
b on edge
Step-by-step explanation:
Jack unfolded a cardboard box. The figure of the unfolded box is shown below:
Which expression can be used to calculate the area of cardboard, in square inches, that was used to make the box?
A.8 x 6 x 6
B.6 x 4 x 4
C.4 x 6 x 6
D.6 x 8 x 8
Answers
Answer:
8*6*6
Step-by-step explanation:
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Naoya read a book cover to cover in a single session, at a rate of 555555 pages per hour. After 444 hours, he had 350350350 pages left to read.
Answers
The question involves a mathematical reading rate scenario where Naoya calculates how much of a book he has left to read. Since the numbers provided are unrealistic, an example with plausible figures is used to illustrate the process of determining total reading time and daily reading goals.
The question deals with a reading rate calculation problem involving Naoya, who has read part of a book and wants to figure out how much more he needs to read. We can figure out the total number of pages in the book by considering the pages he has read at the rate of 555,555 pages per hour over 444 hours, and adding the remaining 350,350,350 pages he has left to read. However, it appears there are typographical errors in the question with the repetition of numbers, which should likely be simplified to realistic figures before we can calculate the total number of pages in the book.To apply the concept efficiently, let's take an example with realistic numbers similar to the approach mentioned for Marta. Suppose Marta reads at a rate of 48 pages per hour and she needs to finish a 497-page novel. We divide the total page count (497) by her hourly rate (48 pages/hour) to find the total hours needed, which is approximately 10.35 hours or roughly 10 to 11 hours.
If Marta wishes to finish the novel over two weeks, she would divide her total reading time by the number of days she plans to read, ensuring she allocates enough time each day to reach her goal. Similar reading strategies can be applied whether balancing act, early bird, or taking the approach of reading a certain number of pages each day to make a larger task more doable.
Find the exact values of the remaining trigonometric functions of θ satisfying the given conditions. (if an answer is undefined, enter undefined.) csc θ = 14, cot θ < 0
Answers
Given that csc θ = 14 and cot θ < 0, we find that sin θ = 1/14 and cos θ must be negative. We use the identity sin² θ + cos² θ = 1 to solve for the exact value of cos θ, selecting the negative solution. The remaining trigonometric functions are then found using these values.
Explanation:Given that the cosecant of theta (csc θ) is 14 and cotangent of theta (cot θ) is less than zero, we can find the other trigonometric values. We begin by recalling that cosecant is the reciprocal of the sine function, so sin θ = 1/14. Subsequently, we are told cot θ < 0, which means either the cosine or the sine (or both) must be negative.
Since cot θ is negative and we know sin θ is positive (since csc θ is positive), then we can conclude that cos θ must be negative. However, the exact value of cos θ is not readily identifiable from these properties alone.
To find the trigonometric value of cos θ, we can utilize the identity sin² θ + cos² θ = 1. Substituting our known sin θ value, we solve for cos θ. This gives us two possible solutions for cos θ, either positive or negative. As previously deduced, we select the negative solution for cos θ. The remaining trigonometric functions can then be found given these values:
tan θ = sin θ / cos θ,sec θ = 1 / cos θ, andcot θ = 1 / tan θ, or alternatively, cos θ / sin θ.Learn more about Trigonometry here:https://brainly.com/question/11016599
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Which of these choices is considered an environmental cost?
A. Net profit
B. Processing expenses
C. Resource depletion
D. Product price
Answers
By definition we have to:
Natural resources are all the material goods and services provided by nature without alteration by human beings; and that they are valuable for human societies because they contribute directly to their well-being and development (raw materials, minerals, food) or indirectly (essential ecological services for the continuity of life on the planet).
Therefore, the depletion of natural resources is considered an environmental cost because without these resources, life on planet Earth is difficult as we know it today.
Answer:
C. Resource depletion
What is the simplified form of i13?
A. -i
B. 1
C. -1
D. i
Answers
i = root (-1)
We note that in this case the exponent is odd.
So we can rewrite the expression as:
i ^ 13 = (i ^ 2) * (i ^ 2) * (i ^ 2) * (i ^ 2) * (i ^ 2) * (i ^ 2) * i
i ^ 13 = (- 1) * (- 1) * (- 1) * (- 1) * (- 1) * (- 1) * i
i ^ 13 = (1) * i
i ^ 13 = i
Answer:
the simplified form of i ^ 13 is:
D. i
The simplified form of i^13 is -i.
The simplified form of i^13 is -i.
To find the simplified form, remember that i^4 = 1, so i^13 = i^(4*3+1) = i^(4*3) * i = (i^4)^3 * i = 1^3 * i = i.
Therefore, the simplified form of i^13 is -i.
Please please help asap!
What is the volume of this oblique cone?
Answers
Which system of equations can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x?
A). Y=-4x^5+12x^4-6x and y=5x^3-2x
B). Y=4x^5-12x^4+5x^3+4x and y=0
C). Y=4x^5-12x^4+6x and y= -5x^3+2x
D). Y=4x^5-12x^4+6x and y=5x^3-2x
Answers
Answer:
D). Y'= [tex]4x^{5}-12x^{4}+6x[/tex] and y'= [tex]5x^{3}-2x[/tex]
Step-by-step explanation:
We are given the equation [tex]4x^{5}-12x^{4}+6x=5x^{3}-2x[/tex].
On simplifying this equation, we get [tex]4x^{5}-12x^{4}-5x^{3}+8x=0[/tex]
i.e. Let, Y'= [tex]4x^{5}-12x^{4}+6x[/tex] and y'= [tex]5x^{3}-2x[/tex]
Now, according to the options,
A) Y = [tex]-4x^{5}+12x^{4}-6x[/tex] = -Y' , that means the graph will be inverse of the required graph.
B) As the coefficient of 'x' in our given equation and the equation of option B are different, both will have different graphs.
C) As y = [tex]-5x^{3}+2x[/tex] = -y', this means that the graph will be inverse of the required graph.
Hence, all above options are discarded and so option D is correct.
4. The distance covered by the cook in Triangle A equals _______________ eighteen-inch steps.
6,480
540
360
347
5. The distance covered by the cook in Triangle B equals _______________ eighteen-inch steps.
480
500
5,760
320
6. The distance covered by the cook in Triangle C equals__________eighteen-inch steps.
347
520
6,240
9,360
Answers
to convert feet to inches we must multiply by 12
4. The distance covered by the cook in Triangle A equals
a) fridge and stove-----------> 5*16*12=960 in
b) fridge and sink-------------> 10*22*12=2640 in
c) sink and stove--------------> 15*16*12=2880 in
then add, 960 + 2640 + 2880 = 6480 in
the answer asks for the distance in 18 in lengths
so divide 6480 by 18 -------------> 6480/18=360
the answer part N 4) is 360 eighteen-inch steps
5. The distance covered by the cook in Triangle B equals
a) fridge and stove-----------> 5*16*12=960 in
b) fridge and sink-------------> 10*16*12=1920 in
c) sink and stove--------------> 15*16*12=2880 in
then add, 960 + 1920 + 2880 = 5760 in
the answer asks for the distance in 18 in lengths
so divide 5760 by 18 -------------> 5760/18=320
the answer part N 5) is 320 eighteen-inch steps
6. The distance covered by the cook in Triangle A equals
a) fridge and stove-----------> 5*15*12=900 in
b) fridge and sink-------------> 10*22*12=2640 in
c) sink and stove--------------> 15*15*12=2700 in
then add, 900 + 2640 + 2700 = 6240 in
the answer asks for the distance in 18 in lengths
so divide 6240 by 18 -------------> 6240/18=346.67------> 347
the answer part N 6) is 347 eighteen-inch steps
Find the lateral area for the cylinder with the given measurement. r = 4, h = 5
Answers
Explanation:
1) The formula for the lateral area of a cylinder is:
Lateral area = 2 π * radius * height
That formula is developed from the fact that when you "open" the cylinder through a line on the lateral area and perpedicular to the bases of the cylinder, the resultant figure is a rectangle with length 2π * radius and width equal to the height of the cylinder.
2) Calculations:
Lateral area = 2 π * 4 * 5 = 40π ≈ 40 (3.14) = 125.6 units^2
which number is prime
A.) 49
B.) 27
C.) 14
D.) 97
Answers
Final answer:
Among the options provided, only D.) 97 is a prime number because it only has two divisors: 1 and itself. All other options have more than two divisors and thus are not prime.
Explanation:
To determine which number is prime, we must recall that a prime number is a number that has only two distinct positive divisors: 1 and itself. Now, let's evaluate the options given:
A.) 49 is 7 times 7, so this is not a prime number.
B.) 27 is 3 times 9, hence this is not a prime number either.
C.) 14 is 2 times 7, which means it is not a prime number.
D.) 97 does not have any divisors other than 1 and itself, so it is a prime number.
So, the correct answer is D.) 97, since it fulfills the conditions for being a prime number.