Answers
The sides of triangle WXY can be listed from smallest to largest as YW, WX, XY, by matching the side lengths to a set of Pythagorean triplets (5, 12, and 13 cm). This corresponds to option A of the provided choices.
To list the sides of triangle WXY in order from smallest to largest, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
According to the given information, we have two right triangles with sides 5 cm, 12 cm, and 13 cm.
Recognizing these are Pythagorean triplets, where 5 and 12 are the legs and 13 is the hypotenuse, it indicates that the side measures 13 cm is the longest side, followed by the 12 cm side, and then the 5 cm side is the shortest.
Therefore, if we match these lengths to the sides of triangle WXY, we can list the sides from smallest to largest based on their corresponding lengths, with the assumption XY matches the 13 cm side (as it is not specified and must be inferred).
The correct listing of triangle sides from smallest to largest would be: YW, WX, XY. This correlates to option A in your list.
The probable question may be:
list the sides of triangle WXY in order from smallest to largest
A. YW, WX, XY
B. XY, YW,WX
C. WX,XY,YW
D. XY, WX,YW
Related Questions
Factor the following.
Answers
(x-10)^2
Answer: B
Hope this helps :)
Please give brainliest
Once again, I'll just go through all of the answer choices :)
a) (x - 5)(x - 4)
Simplify.
x² - 4x - 5x + 20
Add like terms.
x² - 9x + 20
So, A is incorrect.
b) (x - 10)(x - 10)
Simplify.
x² - 10x - 10x + 100
Add like terms.
x² - 20x + 100
So, B is correct.
c) (x + 10)²
(x + 10)(x + 10)
Simplify.
x² + 10x + 10x + 100
Add like terms.
x² + 20x + 100
So, C is incorrect.
d) (x + 10)(x - 10)
Simplify.
x² - 10x + 10x - 100
Add like terms.
x² - 100
So, D is incorrect.
Therefore, B is correct.
~Hope I helped!~
Determine whether the sequence converges or diverges. If it converges, give the limit.
11, 44, 176, 704, ...
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This sequence, therefore, diverges to infinity
if <6 = <10 and <5 = <7, which describes all the lines that must be parallel?
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A ball is thrown from an initial height of 1 meter with an initial upward velocity of 13 m/s. The ball's height h (in meters) after t seconds is given by the following.
h=1+13t-5t^2
Find all values of t for which the ball's height is 8 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
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I hope I don't have to explain it again.
For t=1.84 and t=0.76 the ball's height is 8 meters in equation h=1+13t-[tex]5t^{2}[/tex].
What is equation?An equation is a relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+ by=c. It is solved in order to find the values of variables.
How to solve equation?We have been given an equation h=1+13t-[tex]5t^{2}[/tex] and we have to find the values of t for which h=8.
So,
1+13t-[tex]5t^{2}[/tex]=8
[tex]-5t^{2}[/tex]+13t+1-8=0
[tex]-5t^{2}[/tex]+13t-7=0
Removing negative signs.
[tex]5t^{2}[/tex]-13t+7=0
We cannot solve through factorization so e use the following formula:
x=-b+-[tex]\sqrt{b^{2} -4ac}/2a[/tex]
t=(13+-[tex]\sqrt{-13^{2} -4*5*7}[/tex])/2*5
t=(13+-[tex]\sqrt{169-140}[/tex])/10
t=(13+5.38)/10, (13-5.38)/10
t=1.838, 0.762
By rounding off to nearest hundred t=1.84, 0.76.
Hence value of t for which h=8 meters are 1.84 and 0.76.
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PLEASE HELP ME!!!!
Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.
Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours.
Part B: Write the equation obtained in Part A using function notation.
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
Answers
The equation in standard form is given Ax+By+C = 0
where x is the gradient of a straight line (or the rate of change)
The rate of change = (113-43) / (8-3) = 70/5 = 14
This value means there's an increase of $14 for every hour rented.
We also need to work out the value of C, which is the fixed value (happen at x=0)
We know that Amir paid $43 for 3 hours.
Amir would have paid $29 for 2 hours
Amir would have paid $15 for 1 hour
Since the hourly rate is $14, the fixed fee is 15 - 14 = $1
The equation that represents the total cost of renting a scooter is
y = 14x + 1
Rearranging this equation to get the standard form
14x - y + 1 = 0
Part B:
Writing the equation as function ⇒ f(x) = 14x + 1
Part C:
To graph the equation, we can start by choosing the x-intervals, say we have the value of x between 0 and 10
x 0 1 2 3 4 5 6 7 8 9 10
y 1 15 29 43 57 71 85 99 113 127 141
Each pair of x-value and y-value is then plotted on a graph then each plot is joined to draw a straight line.
Answer:
Step-by-step explanation:
Part A: The two points that represent this situation are (3,43) and (8,113). To put this in standard form, I will first find the slope-intercept form. I did this in the image below.
Now, to find the standard form I will rearrange, 14x -y +1 = 0.
Part B: To put this in function notation I simply take my slope-intercept equation of y=14x+1, and replace y with f(x) so, f(x)=14x+1
Part C: To graph this, put the y, intercept at 1, and give the line a slope of 14/1. Label the x-axis with hours, from 0 - 8, and the y-axis with dollars, from 0-150.
decimal fundamentals
add 729.3 + 3.4006
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If 3a2 – 5ab – 2b2 is factored, one of the factors might be:
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Note that
(3a)*(-2b) + a*b = -6ab + ab = -5ab
(3a)*a = 3a²
b*(-2b) = -2b²
Therefore
3a² - 5ab - 2b² = (3a + b)(a - 2b)
The factors are (3a + b) and (a - 2b).
Answer:
One of the factors is (3a + b).
Another factor is (a - 2b).
Help!!!!! Identify KPN
Answers
answer D. 70 (last choice)
Answer:
it is 70
Step-by-step explanation:
I guessed and got it right, lol
how to solve 46.2 x 10 with a negative 2 exponent
Answers
hope this helps:)
Tobius is going to climb a ladder to reach and fix a piece of siding located 30 feet above the ground on the building. If he places the ladder at a 60° angle with the ground, about how long is the ladder?
Answers
Let BC represent the wall, AC the ladder and AB the distance of the feet of the ladder to the wall.
ABC form a right triangle, with m(B)=90°, m(A)=60° and m(C)=30°.
AB is the side opposite the angle 30°, so the length of AB is half of the length of the hypotenuse AC.
Thus, let |AC|=2x, and |AB|=x.
By the Pythagorean theorem:
[tex] (2x)^{2}= x^{2} +30^{2} [/tex]
[tex] 4x^{2}= x^{2} +30^{2} [/tex]
[tex] 3x^{2}=30^{2}=900 [/tex]
[tex] x^{2}=300 [/tex]
thus [tex]x= 10\sqrt{3} [/tex]
the length of the ladder is [tex]2x= 20\sqrt{3}=34.64 [/tex] feet
Answer: [tex]20\sqrt{3}=34.64 [/tex] feet
The height of the ladder will be;
⇒ 20√3 feet
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Tobius is going to climb a ladder to reach and fix a piece of siding located 30 feet above the ground on the building.
And, He places the ladder at a 60° angle with the ground.
Now,
Let the height of the ladder = h
So, We can formulate;
⇒ sin 60° = 30/h
⇒ √3/2 = 30/h
⇒ h = 30 × 2/√3
⇒ h = 20√3
Thus, The height of the ladder = 20√3 feet
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Find two consecutive positive integers such that thw sqaure of the first decreased by 25 equa;s three times the second
Answers
so
square of the first decreased by 25 equals 3 time the 2nd
the 2 integers are x and x+1
x²-25=3(x+1)
distribute
x²-25=3x+3
minus (3x+3) from both sides
x²-3x-28=0
factor
what 2 numbers muliply to get -28 and add to get -3
-7 and 4
(x-7)(x+4)=0
set to zero
x-7=0
x=7
x+4=0
x=-4
false, we want positive integers
x=7
x+1=8
the inegers are 7 and 8
for which of the following numbers does 5 appear in the tens place ?
*check all that applies*
a. 125.634
b. 56.89
c. 1250
d. 3.5
e. 92.57
Answers
answer:
b. 56.89
c. 1250
Rewrite the rational exponent as a radical.
5 to the 3 over 4 power, to the 2 over 3 power
A.the cube root of 5 squared
B. the twelfth root of 5
C. the square root of 5
D.the cube root of 5 the fourth power
Answers
C. the square root of 5
P(A)=25,P(B|A)=920,P(A∩B)=?
Answers
We use the product rule in probability to find P(A∩B) = P(B|A) * P(A). Substituting given values, P(A∩B) = (9/20) * 25, which equals 11.25.
Explanation:The subject area of this question is probability, a topic within mathematics. Here, we are asked to find the intersection of Events A and B given the probabilities of A and the conditional probability of B given A. The rule of product in probability states that P(A∩B) = P(B|A) * P(A).
Let's calculate: P(B|A) is given as 9/20 while P(A) is 25. Thus,
P(A∩B) = P(B|A) * P(A) = (9/20) * 25 = 11.25
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Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.
Answers
so, the left-part of the picture is the focus point and the directrix... .so.. notice, the focus is above the directrix, meaning is a vertical parabola and is opening upwards.
now, looking at the right-part of the picture, bear in mind that, the vertex is "p" units away from the directrix and the focus, so, the vertex is half-way between those fellows, notice in the picture what "p" is, keep in mind that, because the parabola is opening upwards, "p" is a positive unit, thus is 3.
[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}}) }\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \begin{cases} h=-5\\ k=2\\ p=3 \end{cases}\implies [x-(-5)]^2=4(3)(y-2) \\\\\\ (x+5)^2=12(y-2)\implies \cfrac{(x+5)^2}{12}=y-2\implies \cfrac{(x+5)^2}{12}+2=y \\\\\\ \cfrac{1}{12}(x+5)^2+2=y[/tex]
Answer: D
Step-by-step explanation: took the test
D: y> -1/3 x+1 helpppp
Answers
Celia is staring at the clock waiting for school to end so that she can go to track practice. She notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:25 to 1:50? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time?
Answers
there are 60 minutes marks on a clock
360/60 = 6
6 degree between every minute
From 1:25 to 1:50 there are 25 minutes
25 x 6 = for a total of 150 degrees
150*pi/180 = 5pi/6 radians. ( 2.61799 radians)
Total distance the tip of minute hand has traveled in this time = 2pi*(4 in) * (5pi/6)/(2pi) = 10pi/3 inches (10.47 inches)
The question is "Find the number of elements in the following sets"
I sort of get it but it docks me points every time I get it wrong so I don't want to risk it
Answers
U=66+17+53+82=218
A' = 53+82=135
A'∩B=53
(A∩B)'=66+53+82=201
(A∪B)'=82
A' ∩ B' = 82
20 POINTS PLUS BRAINLIEST!!!
Which function is represented in the table of values?
x 0 -1 -2 -3
y 2 4 8 16
A.
y=2^x
B.
y=2(1/2)
C.
y=-2^x
D.
y=(1/2)^x
Answers
y = (1/2)^x
y = (1/2)^-1 = 2
y = (1/2)^-2 = 4
y = (1/2)^-3 = 8
Hope it helped!
what is the least common multiple of X and Y? X=2*2*2*2 Y=2*2*2*3
Answers
2*2*2*2*3=48
Help please..........,.,,,
Answers
The lengths of three sides of a quadrilateral are shown below: Side 1: 1y2 + 3y − 6 Side 2: 4y − 7 + 2y2 Side 3: 3y2 − 8 + 5y The perimeter of the quadrilateral is 8y3 − 2y2 + 4y − 26. Part A: What is the total length of sides 1, 2, and 3 of the quadrilateral? (4 points) Part B: What is the length of the fourth side of the quadrilateral? (4 points) Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.
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B. 8y^3 - 2y^2 + 4y - 26 - (6y^2 + 12y - 21) =
8y^3 - 2y^2 + 4y - 26 - 6y^2 - 12y + 21 =
8y^3 - 8y^2 - 8y + - 5 <==
C. (part A) this is closed under addition
(part B) this is closed under subtraction
Polynomials will be closed under an operation if the operation produces another polynomial
Answer:
Part A: 12y^2+9y-21
Part B: 4y^2+6y^2+7y-5
Part C: A set of numbers is closed, or has closure, under a given operation if the result of the operation on any two numbers in the set is also in the set. For example, the set of real numbers is closed under addition, because adding any two real numbers results in another real number. Likewise, the real numbers are closed under subtraction, multiplication and division (by a nonzero real number), because performing these operations on two real numbers always yields another real number. Polynomials are closed under the same operations as integers.
Step-by-step explanation:
Hope this helps!!
The scale of a map is 1 1/4 inches = 100 miles. On that map, 2 cities are 4 1/8 inches short. What is the actual distance between the cities?
Answers
need to divide 4 1/8 by 1 1/4
4 1/8 = 33/8
1 1/4 = 5/4
33/8 / 5/4 = 33/8 * 4/5 = 132/40 reduces to 33/10 = 3 3/10
100* 3 3/10 = 330 miles
Final answer:
Using the map scale of 1 1/4 inches equals 100 miles, and the measured map distance of 4 1/8 inches, the actual distance between the two cities is calculated to be 330 miles.
Explanation:
To find the actual distance between two cities on a map, we can set up a proportion based on the scale of the map. In this case, the scale is 1 1/4 inches = 100 miles. The measured distance on the map between the two cities is 4 1/8 inches.
We'll convert these measurements to an easier-to-calculate form by changing the mixed numbers to improper fractions.
First, we convert 1 1/4 inches to an improper fraction: 1 1/4 = 5/4 inches. Likewise, we convert 4 1/8 inches to an improper fraction: 4 1/8 = 33/8 inches. Now we set up the proportion using the scale.
(5/4 inches) / (100 miles) = (33/8 inches) / (x miles)
To solve for x, cross-multiply and divide:
(5/4) * x = (33/8) * 100
x = (33/8 * 100) / (5/4)
x = (33 * 100 * 4) / (8 * 5)
x = (33 * 4) / (2)
x = 66 miles
Therefore, the actual distance between the two cities is 330 miles.
PLZ HEEEEEEEELPPPPPPPP!!!!!!!!!
Answers
for x = -8 → y = ∛-(-8) - 3 ↔ y = 2-3 ↔y = -1
for x= 8 → y= ∛(-8) - 3 ↔ y = -2 -3 ↔ y = -5
Then - 5≤ y≤ - 1
hence the range of y is {y|-5≤y≤-1}
Someone please help me out!
Answers
try it with a couple different numbers
try 4: 1^2 +2^2 +3^2 +4^2 = 1 +4 +9 +16 =30
formula: 4(4+1)(2*4+1)/6 = 4*5*9 = 180/6=30
this one works
now try 5
1^2 + 2^2+3^2+4^2+5^2 = 55
formula: 5(5+1)(2*5+1)/6 = 5*6*11 = 330/6=55
I tried a larger number ( 14) as well and it worked
so you can say that this is true
Please check my work!
Answers
Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80°. Approximately how tall is the tree?
Answers
tan theta=[opposite]/[adjacent]
theta=80
height=h
adjacent=5 m
hence;
tan80=h/5
hence;
h=5tan80
h=28.36 m
A "Local" train leaves a station and runs at an average rate of 35 mph. An hour and a half later an "Express" train leaves the station and travels at an average rate of 56 mph on a parallel track. How many hours after the Express train starts will the it overtake the Local?
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so...Local say "L" is going at a speed of 35mph...ok... and Express or "X" is going at 56mph.
by the time the two trains meet, and X is ready to overtake L, the distance that both have travelled, since is a parallel road, is the same, say "d". So if L has travelled "d" miles, then X had travelled "d" miles too, over the same road, maybe different lane.
now, because X left 1 1/2 hour later, by the time they meet, say X has been running for "t" hours, but because it left 1 1/2 hour later, L has been running for " t + 1 1/2 " hours, or " t + 3/2 " hours.
[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ Local&d&35&t+\frac{3}{2}\\ Express&d&56&t \end{array} \\\\\\ \begin{cases} \boxed{d}=35\left( t+\frac{3}{2} \right)\\ d=56t\\ ----------\\ \boxed{35\left( t+\frac{3}{2} \right)}=56t \end{cases} \\\\\\ 35t+\cfrac{105}{2}=56t\implies \cfrac{105}{2}=21t\implies \cfrac{105}{42}=t \\\\\\ \cfrac{5}{2}=t\implies 2\frac{1}{2}=t[/tex]
so, they met 2 and a half hours later after X left, and a milllisecond later X overtook L.
Answer:
2.5 hrs.
Hope this helps <3
10 POINTS!!! TO ANSWER CORRECTLY AND BRAINLIEST!!!!
Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum.
Answers
2/3 = 10/15
3/15 + 10/15 = 13/15
this leaves us with 10/15. Now, if we add 3/15 and 10/15, we get 13/15. This cannot be simplified because 13 is a prime number, thus it is only divisible by itself and 1.
If the perimeter of the adult pinball machine is 172 inches, what is the length, in inches of ? Type the numeric answer only in the box below.
Answers
2L = 172 - 2W
L = 86 - W