Problem 1
Answer: Yes a triangle can be formed with side lengths 5,5,3
--------------------
Explanation:
Take any two sides and add them up. If we get a sum larger than the third side, then a triangle is possible. This is the triangle inequality theorem.
5+5 = 10 is larger than 3
5+3 = 8 is larger than 5
This shows a triangle is possible. The triangle is isosceles because two sides are the same length.
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Problem 2
Answer: Yes a triangle can be formed with side lengths 8,8,8
--------------------
Explanation:
This triangle is equilateral because all sides are the same length.
Take any two sides, add them up, and you'll find the sum is larger than the third side.
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Problem 3
Answer: No a triangle cannot be formed with sides 7,8,15
--------------------
Explanation:
Yes it is true that
8+15 = 23 is larger than 7
7+15 = 22 is larger than 8
but
7+8 = 15 is not larger than 15
So this means a triangle is not possible.
Imagine you had 3 strips of paper that were 7 inches, 8 inches and 15 inches long. The 7 and 8 inch strips add to 15 inches, but those two smaller strips only form a straight line. We cannot pull them so a triangle forms. If we did, then the third side would be smaller than 15 inches. This is one way to get hands on to see why the triangle inequality theorem works.
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Problem 4
Answer: Yes a triangle is possible with side lengths 5,6,10
--------------------
Explanation:
Same idea as before. We can take any two sides, add them, and get a sum larger than the third side. A triangle is possible.
5+6 = 11 is larger than 106+10 = 16 is larger than 55+10 = 15 is larger than 6How do you do this question?
Answer:
18π
Step-by-step explanation:
Arc length for a parametric equation is:
s = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt
dx/dt = -9 sin(9t)
dy/dt = 9 cos(9t)
s = ∫₀²ᵖⁱ √((-9 sin(9t))² + (9 cos(9t))²) dt
s = ∫₀²ᵖⁱ √(81 sin²(9t) + 81 cos²(9t)) dt
s = ∫₀²ᵖⁱ 9 dt
s = 9t |₀²ᵖⁱ
s = 18π
You can check your answer with geometry. The curve is a circle centered at the origin with radius 1. From 0 to 2π, the particle makes 9 revolutions, or travels 18π radians. So the arc length is 1 × 18π = 18π.
Answer:
18π
Step-by-step explanation:
what equation represents the road that passes through the point shown and is perpendicular to the road represented by the red line
Answer: The equation that represents the road is y= - 1/3x +1/3
Step-by-step explanation:
The perpendicular equation that represents the road that passes through the point is [tex]\mathbf{y = -\frac 13x + \frac 13 }[/tex]
The points of the red line (see attachment) are given as:
[tex]\mathbf{(x,y) = (0,2), (2,8)}[/tex]
Start by calculating the slope (m) of the line using:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{8 - 2}{2 -0}}[/tex]
[tex]\mathbf{m = \frac{6}{2}}[/tex]
[tex]\mathbf{m = 3}[/tex]
Next, calculate the slope (m2) of the perpendicular line using:
[tex]\mathbf{m_2 = -\frac 1m}[/tex]
So, we have:
[tex]\mathbf{m_2 = -\frac 13}[/tex]
The perpendicular line passes through point (1,0).
So, the line equation is calculated using:
[tex]\mathbf{y = m_2(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y = -\frac 13(x - 1) + 0}[/tex]
[tex]\mathbf{y = -\frac 13(x - 1) }[/tex]
Open bracket
[tex]\mathbf{y = -\frac 13x + \frac 13 }[/tex]
Hence, the line equation is [tex]\mathbf{y = -\frac 13x + \frac 13 }[/tex]
Read more about perpendicular equations at:
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f(x) = 15% for x = 3
Jackson has 2,000 baseball cards Gabe has 1/10 as many as Gabe how many baseball cards does Gabe have in his collection
Answer:
200 baseball cards
Step-by-step explanation:
We write the expression:
2000 x 1/10 =
200
If Amy bought $113 worth of
groceries and paid $7.91 in taxes,
what was the percent tax?
Answer:
stupid noob
Step-by-step explanation:
solve x^2-12x+36=44 by factoring!!
please help asap with work shown :)
x^2 - 12x + 36 is a perfect square trinomial and can be written as (x-6)(x-6).
(x - 6)^2 = 44.
Take the square root of both sides to get...
x - 6 = ±√44 (Always make the square root + or - when you square root)
Add 6 to both sides...
x = √44 + 6
x = -√44 + 6
These are the 2 values of x.
You can also write it to be -0.633 and 12.633. (Once you round.)
The point P(-2, - 5) is rotated 90° about the origin, and then the image is reflected across the line
x= 3. What are the coordinates of the final image p’’?
Given:
The point P(-2, - 5) is rotated 90° about the origin, and then the image is reflected across the line x= 3.
To find:
The the coordinates of the final image P’’.
Solution:
The point P(-2, - 5) is rotated 90° about the origin. It means the point is rotated 90° counter clockwise about the origin
[tex](x,y)\to (-y,x)[/tex]
[tex]P(-2,-5)\to P'(-(-5),(-2))[/tex]
[tex]P(-2,-5)\to P'(5,-2)[/tex]
Then the image is reflected across the line x= 3.
[tex](x,y)\to (-x+6,y)[/tex]
[tex]P'(5,-2)\to P''(-5+6,-2)[/tex]
[tex]P'(5,-2)\to P''(1,-2)[/tex]
Therefore, the \coordinates of the final image P'' are (1,-2).
Use the given information to find the measure.
Answer:
From the image, we can see that ∠AOC = ∠AOB + ∠BOC
We are given the following values:
∠AOC = 104
∠AOB = 7x + 30
∠BOC = 9x + 42
Plugging these values in the equation above:
∠AOC = ∠AOB + ∠BOC
104 = 7x + 30 + 9x + 42
104 = 16x + 72
16x = 32
x = 2
Now that we have the value of x, we can easily find the value of ∠BOC
We are given that:
∠BOC = 9x + 42
∠BOC = 9(2) + 42 (since x = 2)
∠BOC = 18 + 42
∠BOC = 60°
Therefore, ∠BOC is 60 degrees
Which descriptions of a histogram are true? Check all that apply..
A peak is a bar that is lower than the other bars around it.
A peak is where the frequency is lowest.
A peak is where the frequency is the highest.
A cluster is a group of bars, meaning the frequency is higher in these intervals.
A peak is a bar that is higher than the other bars around it.
Intervals on a histogram where there are no bars mean the frequency is 0.
If the graph is symmetrical, the data is clustered toward the right side.
If the graph is symmetrical, the data is evenly distributed.
Answer:
A peak is where the frequency is the highest.
A cluster is a group of bars, meaning the frequency is higher in these intervals.
A peak is a bar that is higher than the other bars around it.
Intervals on a histogram where there are no bars mean the frequency is 0.
If the graph is symmetrical, the data is evenly distributed.
Step-by-step explanation:
The correct statement about histogram is as follows;
A peak is where the frequency is the highest.
A cluster is a group of bars, meaning the frequency is higher in these intervals.
A peak is a bar that is higher than the other bars around it.
Intervals on a histogram where there are no bars mean the frequency is 0.
If the graph is symmetrical, the data is evenly distributed.
We have to determine, which descriptions of a histogram are true?
According to the question,
A histogram meaning can be stated as a graphical representation that condenses a data series into an easy interpretation of numerical data by grouping them into logical ranges of different heights which are also known as bins.
Characteristics of a Histogram are as follows;
A histogram is used to display continuous data in a categorical form.
In a histogram, there are no gaps between the bars, unlike a bar graph.
The width of the bins is equal.
A histogram is a type of representation of a data set where bars are used to represent the frequencies.
The area of these bars is said to be proportional to the frequency of the variable.
The peak of a histogram represents the highest value of frequency. Also, the peak is a bar that is higher than the other bars around it.
In a histogram intervals wherein bars cannot be seen would represent the frequency of that would zero.
Also, if the histogram is said to be symmetrical, then the data should be distributed evenly.
A peak is where the frequency is the highest.
A cluster is a group of bars, meaning the frequency is higher in these intervals.
For more details refer to the link given below.
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Need Help ASAP please‼️
Answer:
i cant see
Step-by-step explanation:
make a more clear pic
Suppose a, b, and c are all negative numbers. How do you find the distance between the points (a,b) and (a,c)?
if f(x)=x²+3x+5 what is f(a+h)
A) a²+2ah+h²+3a+3h+5
B) h²+3a+3h+5
C) (a+h)²+3(a+h)+5(a+h)
D) (x²+3ax+5)(a+h)
99 points and votes the brainiest
A candy company used 18 pints of chocolate to make 3 boxes of candy. What is the rate of chocolate per box?
Answer:
6 chocolates per box.
Step-by-step explanation:
Need help ASAP!If you don’t mind
Answer:
each green line is 45 degrees
Step-by-step explanation:
Answer:
first box should be EAF then next FAL and the last would be ray AL and its a ray because it has one endpoint which is A.
Step-by-step explanation:
What is the value of x in the equation 2x – 3 = 9- 4x?
0 -6
O-3
O 1
o 2
Answer:
x = 2
Step-by-step explanation:
2x - 3 = 9 - 4x
6x - 3 = 9 (added 4x to both sides)
6x = 12 (added 3 to both sides)
x = 2 (divided 12 by 6)
hope this helps :)
If CD = 8 and BD = 11, what is BC?
Find the LCM of the set of numbers 4 5 6
Answer:
C dont trust me wait for someone else to anser
Step-by-step explanation:
the ratio of girls to boys in a bicycling club was 3:6. There were 18 girls. How many boys were in the club?
Answer:
36 boys
Step-by-step explanation:
Evaluate
3x (x + 2) – 3x? for x = 19
Answer:
1140
Step-by-step explanation:
3x(x + 2) - 3x
x = 19
3 * 19( 19 + 2) - 3 * 19
3 * 19(21) - 3 * 19
3 * 19 = 57
57(21) - 3 * 19
57 * 21 = 1197
1197 - 57
1140
Hope this helped!
4= Sx+10/2
that’s a fraction btw
Answer:
4= Sx+10/2 simplifies to -s*x-1=0
Step-by-step explanation:
65 is 13% of what number?
The graph below represents the volume of water in Susan's watering can while
she waters her plants.
Water in Watering Can (liters)
2.
X
0
1 2. 3 4
Minutes Spent Watering Plants
How much water is in Susan's watering can when she starts watering her plants?
A.1.8
B.3.0
C.3.7
D.5.5
is this angilic from vista hills and dessert view if so this is josh a
Answer:
5.5 liters hope this works for u
Step-by-step explanation:
Please help me please
Answer:
Alternate Interior Angles Theory
Step-by-step explanation:
Any number inside the angle is known as an Alternate Interior Angle.
Find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon. Round to the nearest tenth, if necessary. 24 b 15, 345 24, 156 7.5, 172.5 15, 165
Answer: Find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon. Round to the nearest tenth, if necessary. 24 b 15, 345 24, 156 7.5, 172.5 15, 165
Step-by-step explanation: sum, S, of the measure of the interior angles of a polygon with n sides is: ... The sum of the interior angles of a 24 -gon is 3960. ... angles of a polygon is (n−2)⋅180 , where n is the number of sides. ... Each exterior angle measures 36024=15 . ... The sum of the 24 interior angles is then 24⋅165=3960 .
Which of these graphs below represents a function?
Answer:
the one you've selected pink, (the one that looks like a U)
Step-by-step explanation:
if you can pass a vertical line through a supposed function and have it only cross once, it's a function.
If the length of AC equals 18, what is the length of the midsection DE
Answer:
The length of the midsegment is 9 ⇒ (B)
Step-by-step explanation:
In a triangle,
The midsegment is the segment which joining the midpoints of two opposite sides of itThe length of the midsegment is half the length of the third side in the triangle which opposite to itLet us use this rule to solve our question
In Δ AC
∵ DE is the midsegment of it
∵ DE is opposite to the side AC
∴ The length of DE = 1/2 the length of AC
∵ The length of AC = 18
∴ The length of DE = 1/2 × 18
∴ The length of DE = 9
∴ The length of the midsegment is 9
The correct answer is B
1. Jack and Jill both begin working new jobs for the summer. Jack is offered $18 per hour and will also be given $699 up front for accepting the job. Jill is offered $20 per hour for her work, with no up front bonus. After how many hours of work will Jack and Jill have earned the same (or equal) amount of money?
Answer:
BRuh
Step-by-step explanation:
Girl my math skills are no where near subpar to that. Good luck!
Answer:
I think the answer is 35 hours to get the same amount of money
-2 (3a – 2) = 1/3(7 – 3a)
Answer:
i have no idea. But i will answer because i'm still learning.
Step-by-step explanation:
-2 (3a – 2) = 1/3(7 – 3a)
is whats the question
ok its i'm guessing -2 (3a – 2) = 1/3(7 – 3a)
-2.15384615385
Hope this helps ;)
If the radius of a melting snowball decreases at a rate of 5 ins/min, find the rate at which the volume is decreasing when the snowball has diameter 4 inches
Answer:
The rate at which the volume is decreasing when the snowball has a diameter of 4 inches is approximately 251.327 cubic inches per minute.
Step-by-step explanation:
Let suppose that snowball geometry correspond to a sphere. In this case, the volume of the sphere is:
[tex]V = \frac{4\pi}{3}\cdot R^{3}[/tex] (Eq. 1)
Where:
[tex]R[/tex] - Radius of the sphere, measured in inches.
[tex]V[/tex] - Volume of the sphere, measured in cubic inches.
We know that volume decreases due to melting, so we need an expression of the rate of change of volume in time. By differentiating (Eq. 1) we get:
[tex]\frac{dV}{dt} = 4\pi\cdot R^{2}\cdot \frac{dr}{dt}[/tex] (Eq. 2)
Where:
[tex]\frac{dV}{dt}[/tex] - Rate of change of the volume of the snowball in time, measured in cubic inches per minute.
[tex]\frac{dr}{dt}[/tex] - Rate of change of radius of the snowball in time, measured in inches per minute.
If we know that [tex]R = 2\,in[/tex] and [tex]\frac{dr}{dt} = -5\,\frac{in}{min}[/tex], the rate at which the volume of the snowball is decreasing is:
[tex]\frac{dV}{dt} = 4\pi\cdot (2\,in)^{2}\cdot \left(-5\,\frac{in}{min} \right)[/tex]
[tex]\frac{dV}{dt}\approx -251.327\,\frac{in^{3}}{min}[/tex]
The rate at which the volume is decreasing when the snowball has a diameter of 4 inches is approximately 251.327 cubic inches per minute.
The table below shows the typical hours worked by employees at a company. A new employee is offered an annual salary of $37,000. Hourly employees get paid $14 per hour, but get $21 per hour for each hour over 40 hours. Should the new employee choose the salaried or hourly pay? Explain your reasoning.
Sun.
Mon.
Tues.
Wed.
Thurs.
Fri.
Sat.
0
8.5
9.5
7.5
8
8.5
4
The new employee should select the salary pay because a $37,000 yearly income is more than a $35,672 hourly wage.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
The table below shows the typical hours worked by employees at a company.
Based on the data given:
Total number of hours = 0+ 8.5 + 9.5 + 7.5 + 8 + 8.5 + 4
Total number of hours = 46
Hourly pay = (40×$14) + (6×$21)
Hourly pay = $686 per week
Annual earnings = 52×686
Annual earnings = $35,672
The new employee should select the salary pay based on the calculations above since a $37,000 yearly income is more than a $35,672 hourly wage.
Thus, the new employee should select the salary pay because a $37,000 yearly income is more than a $35,672 hourly wage.
Learn more about the arithmetic operation here:
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