The following set of numbers, 20, 21 and 31, can be the measures of the sides of an obtuse triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 20, b = 21, and c = 31
a + b > c 20 + 21 > 31 41 > 31 True
a + c > b 20 + 31 > 21 51 > 21 True
b + c > a 21 + 31 > 21 52 > 20 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
20^2 + 21^2 = 841
2. Compare it to the square of the largest side.
31^2 = 961
961 > 841
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 20, 21 and 31 can be the measure of the sides of an obtuse triangle.
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What is the mean of 3, -10, -2, 13, 11
Answer:
= (3 + -10 + -2 + 13 + 11) / 5
= 15/5
Step-by-step explanation:
3
Hey there!
Your mean simply means, your average….
To find it you have to ADD all of your numbers and DIVIDE it by the total number you have in your data plot.
3 + -10 + -2 + 13 + 11 / 5
= 3 - 10 - 2 + 13 + 11 / 5
= -7 - 2 + 13 + 11 / 5
= -9 + 13 + 11 / 5
= 4 + 11 / 5
= 15 / 5
= 3
Therefore, your answer should be: 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
In this problem, you will investigate the relationship between same-side exterior angles.
e. Write a proof of your conjecture.
Eight angles are formed when two parallel lines are intersected by a third line that intersects them at an acute angle, known as a transversal line. These angles interact in a number of ways, one of which is the same-side exterior. Both angles are on the same side of the transversal line, as indicated by the word "same-side," and both are "external," or "outside," of the parallel lines, as represented by the term "outside."
When a transversal crosses two parallel lines, it creates an angle between the lines and outside the lines on the same side. Because the alternate interior and alternate exterior angles are the same, and because linear pairs of angles are supplementary, the identical side angles are also supplementary.
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Solve 5x - 2.5 = 17.5
X =
Write an equation for each line in point-slope form and then convert it to standard form.
through (2,3) and (3,5)
The point-slope form is y - 3 = 2(x - 2) and 2x - y = 1 be the standard form.
How to find the equation in point-slope form?Given: (x1, y1) = (2, 3) and (x2, y2) = (3, 5)
The point-slope form is given by,
y - y1 = m(x - x1)
m = (y2 - y1)/(x2 - x1)
substitute the values in the above equation, we get
m = (5 - 3)/(3 - 2)
The value of m = 2.
Point-slope form is y - 3 = 2(x - 2)
Therefore, the point-slope form is y - 3 = 2(x - 2).
How to rewrite the equation in standard form?
The standard form is Ax + By = C
Since, slope-intercept form is y = 2x - 1
⇒ 2x - y = 1
Therefore, 2x - y = 1 is the standard form.
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Use the Distributive Property to rewrite and evaluate 8.598 by filling in the blanks below.
8-598 = 8(600- __)
=
8 (600) - 8(__)
= 4800 - __
= __
Answer:
4784.
Step-by-step explanation:
8 * 598 = 8(600- _2_)
=
8 (600) - 8(_2_)
= 4800 - _16_
= 4784__
please help with this question and determine a,b,c,d and e
Answer:
a=7
b=8
c=12
d=33
find e by adding up all numbers in the Venn diagram then subtract the total amount of people by total from the Venn diagram to find e
What is the answer to this problem?
Answer:
b = 8
........................
need help w this please
what si the answer for 2+2
Answer:
4
Step-by-step explanation:
2+2=4
Solve each system.
(1/2)x + (2/3)y= 1 , (3/4)x - (1/3)y = 2
The solution of the given system of equations is (3//2, -3/8)
We can solve a system of equations using:
- graphical method
- elimination method
- substitution method
The given system of equations:
(1/2)x + (2/3)y= 1 ......... (1)
(3/4)x - (1/3)y = 2 ..........(2)
Multiply equation (1) by 6
3x + 4y = 6 ..... (3)
Multiply equation (2) by 12
9x - 4y = 24 ...... (4)
Add equation (3) and (4)
3x + 4y = 6
9x - 4y = 24 +
12x = 30
x = 30/12 = 5/2
Substitute x = 5/2 into equation (3)
3x + 4y = 6
3. (5/2) + 4y = 6
15/2 +4y = 6
4y = (12 - 15)/2 = -3/2
y = -3/8
The solution is (3/2, -3/8)
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Evaluate the expression for the given values of the variables.
9t+6(2v-t)-7v;t=1 and v=5
The expression will give value 28
To evaluate the expression for the given value of variables, we will keep the value of each variable in the equation. The expression will be solved based on the arithmetic operators given in expression.
Rewriting the expression -
Value = 9t + 6 (2v - t) - 7v
Now keeping the value of v and t in expression to find the value.
Value = 9×1 + 6 (2×5 - 1) - 7×5
Firstly solving the bracket and performing multiplication of extreme left and right values of expression
Value = 9 + 6 (10 - 1) - 35
Value = 9 + 6 (9) - 35
Value = 9 + 54 - 35
Performing addition before subtracting the values
Value = 63 - 35
Performing subtraction
Value = 28
Hence, the expression according to given variables is equal to 28.
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please help me with this geometry question
Answer:
-t*(t -16) ≥ 39
-t*(t -16) = 39
t = 3 or 13 hours
Step-by-step explanation:
When number of people is at 39 or more means the number of people of greater than or equal to 39.
So, the inequality is,
-t*(t -16) ≥ 39
When the number of people is 39, the equation is,
-t*(t - 16) = 39
-t²+ 16t = 39
0 = 39 + t² - 16t
t² - 16t + 39 = 0
Sum = -16
Product = 39
Factors = -3 , -13 [ (-3) * (-13) = 39 & (-3) +(-13) = -16 ]
Rewrite the middle term using the factors.
t² - 3t - 13t + 39 = 0
t(t -3) - 13(t - 3) = 0
(t -3)( t - 13) = 0
t -3 = 0 ; t- 13 = 0
t = 3 or t = 13
t = 3 hours or 13 hours.
HELP I WILL MAKE BRANLIEST CHECK SCREENSHOT FOR QUESTION
The following angles of the given triangles arranged from the smallest to the largest:
In triangle ΔXYZ: ∠X, ∠Z, and ∠Y
In triangle ΔXYW: ∠X, ∠Y, and ∠W
What is the Relationship between Angles and Sides of a Triangle?The size of the angles of a triangle are relative to the side lengths of each side opposite each of the angles in a tringle.
This implies that, a larger angle will face the longest side of the triangle, the mid-sized angle faces the mid-sized side, while the smallest angle is opposite to the shortest side of the triangle.
Based on the relationship between angles and sides of a triangle, we have the following angles of the given triangles arranged from the smallest to the largest:
In triangle ΔXYZ: ∠X, ∠Z, and ∠Y
In triangle ΔXYW: ∠X, ∠Y, and ∠W
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Write an explicit formula for each sequence. Then generate the first five terms. a₁ = 1, r=0.5
The explicit formula for the given sequence is a(n) = 2 . (0.5)ⁿ and the first five terms are: 1, 0.5, 0.25, 0.125, 0.0625
Given the parameters:
First term, a(1) = 1, and
common ratio, r = 0.5
We are ask to find the explicit formula for the geometric sequence and generate the first five terms.
Recall that in a geometric sequence:
a(n) = a(1) . rⁿ⁻¹
Where a(n) is the nth term.
Substituting a(1) = 1 and r = 0.5:
a(n) = 1 . (0.5)ⁿ⁻¹
= (0.5)⁻¹. (0.5)ⁿ
= 2 . (0.5)ⁿ
To generate the first five terms, we can use the above explicit formula for n = 1, 2, ..., 5 or we can use a recursive procedure. Remember that in a geometric sequence:
a(n) = a(n-1) . r
Therefore,
a(1) = 1 (given)
a(2) = 1 . (0.5) = 0.5
a(3) = 0.5 . (0.5) = 0.25
a(4) = 0.25 . (0.5) = 0.125
a(5) = 0.125 . (0.5) = 0.0625
Thus, the first five terms are: 1, 0.5, 0.25, 0.125, 0.0625
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A spinner contains the numbers 1 through 80. what is the probability that the spinner will land on a number that is not a multiple of 11?
The probability that the spinner will land on a number that is not a multiple of 11 is 73/80.
What is probability ?Multiples of 11 are 11,22,33,44,55,66,77.
That means there are 7 multiples of 11
80 -7 = 73
There are 73 non multiples of 11
P( non multiples of 8) = non multiples of 11 / total
= 73/80
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
The likelihood that an event will occur is measured by probability. It is difficult to provide a complete prediction for many events. By employing it, we are only able to forecast the likelihood of an event, or how likely it is, to occur.
According to the probability formula, the likelihood of an event occurring, or P(E), is determined by the proportion of positive outcomes to all other outcomes.
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Is it possible to find a value of $x$ so that the value of the surface area (in square inches) is equal to the value of the volume (in cubic inches)? a rectangular prism with length labeled 9 inches, width labeled 4 inches, and height labeled x inches.
A rectangular prism can have a surface area equal to its volume given the dimensions are 9 inches long, 4 inches wide and x inches high, where x is equal to 7.2 inches.
A rectangular prism is a three-dimensional figure with 8 vertices, 12 edges, and 6 rectangular faces.
If the dimensions of a rectangular prism is:
L = 9 inches
W = 4 inches
H = x inches
then the value of its surface area is equal to the value of its volume.
SA = V
2(lw + wh + lh) = lwh
Substitute the values and solve for x.
2(lw + wh + lh) = lwh
2[(9)(4) + 4x + 9x] = (9)(4)x
2(36 + 13x) = 36x
72 + 26x = 36x
10x = 72
x = 7.2 inches
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Hannah is baking two cakes.
One cake needs 1 1/3 cup of milk han had 1 1/4 cup of milk how much does she need
Answer: 2 2/3
Step-by-step explanation:
A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
c. What is the probability that the first chip is green and the second is brown?
The probability that the first chip is green and the second is brown is 1/20,
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.
P(E) = Number of favorable outcomes / total number of outcomes
Given that A bag contains 3 red chips, 5 green chips, 2 yellow chips, 4 brown chips, and 6 purple chips. One chip is chosen at random, the color noted, and the chip returned to the bag.
The probability of selecting the chip is green;
= 5/20
= 1/4
The probability of selecting the chip is brown;
= 4/20
= 1/5
Then the probability that the first chip is green and the second is brown
= 1/4 x 1/5
= 1/20
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Find the slope of the line through each pair of points. (1,3) and (4,9)
The slope of the line passing through the pair of points, (1 , 3) and (4 , 9), is 2.
The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:
m = (y2 - y1)/(x2 - x1)
where m is the slope
x1 and y1 are the coordinates of one point
x2 and y2 are the coordinates of the 2nd point
Given two points in the line, (1 , 3) and (4 , 9), plug in the values to the formula for the slope.
m = (y2 - y1)/(x2 - x1)
m = (9 - 3)/(4 - 1)
m = 6/3
m = 2
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help please with all answers !☹️
Answer:
Here are the answers!
Step-by-step explanation:
When there are two angles on a line that are touching you can subtract what you know from 180° (Ex: 138° and angle 4)
The angles across from each other are the same.
The total of all three angles in a triangle should be 180°
you earn $10 per hour babysitting and you babysit 25 hours each week. You also help your neighbor with household chores and are paid $8 per hour. If you spend 12 hours helping your neighbor, how much will you earn in one week?
Answer:
$346
Step-by-step explanation:
Babysitting = $250
($10 × 25 hrs)
Neighbour's Chores = $96
($8 x 12 hrs)
Total Earning = $346
($250 + $96)
Which function is the inverse of f (x) = 2 - 6?
O f¹(z) = +6
Of¹ (2)=+9
Of-¹ (z)=-6
Of¹ (2)=4-9
Betsy has a bag with three mint sticks eight jelly treats and nine fruit tart chews if she eats one piece every three minutes what is the probability her first two pieces will be a fruit tart chew and a jelly treat
If Betsy has a bag with three mint sticks, eight jelly treats, and nine fruit tart chews and she eats one piece every three minutes, the probability her first two pieces will be a fruit tart chew and a jelly treat is 18.9%.
The probability of her first two pieces being a fruit tart chew and a jelly treat can be calculated as follows,
First, we divide the expected outcomes by the total possible outcomes.
Total possible outcomes = 3(mint sticks) + 8(jelly treats) + 9(fruit tart chews) = 20
Hence,
Probability for fruit tart chew: 9 ÷ 20
Probability for jelly treat: 8 ÷ 19 (as one possibility is considered to be fruit tart chew)
The probability of her first two pieces to be fruit tart chew and jelly treat can be determined by multiplying the probability for fruit tart chew with the probability for jelly treat,
Probability = (9/20)(8/19)
Probability = 72/380 = 0.189
Converting into percentage,
Probability = 0.189 × 100 = 18.9%
Hence, the probability that her first two pieces will be a fruit tart chew and a jelly treat is equal to 18.9%.
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How many books does Jeff own if he has more than 14 books? Describe the number of books that Jeff owns if you add the constraint that he owns fewer than his sister, who owns 19 books.
Jeff can own 15,16,17 or 18 books as per the given question
The following question is based on inequality. Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. In this type of question, we will get a range of answers and not a specific answer.
No. of books owned by Jeff > 14
No. of books owned by his sister = 19 books
As per the question "He owns books fewer than his sister"
So, he owns >14 and <19 books
Therefore, he can own 15, 16, 17 or 18 books as per the given inequality.
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A student incorrectly claims that 2/3 divided by 5/9 = 5/6 find the correct quotation.What was the students error
Answer:
See explanation
Step-by-step explanation:
2/3 / 5/9=
2/3 * 9/5= ==> Dividing by a number is basically multiplying by its reciprocal.
(2*9)/(3*5)=
18/15=6/5 ==> The student just switched the numerator and denominator.
Answer:
6/5
Step-by-step explanation:
2/3÷5/9=2/3x9/5=2/1x3/5=6/5
Name the geometric term modeled by a bridge support beam
Answer:
Line
Step-by-step explanation:
Extends in two directions
The geometric term modeled by a bridge support beam is "cylinder."
Given data:
A bridge support beam often takes the form of a cylindrical shape to provide structural integrity and distribute the weight of the bridge and its load evenly. Cylinders have circular cross-sections.
A bridge support beam is often modeled as a "cylindrical" structure in geometry. Cylinders are three-dimensional geometric shapes characterized by their curved lateral surface and two circular bases of the same size and shape. When designing bridge support systems, engineers often opt for cylindrical beams due to their inherent strength and ability to distribute weight efficiently.
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Inverses from Algorithms
Suppose you were given the following algorithm:
Start with a number "n"
• Add 2
• Multiply the result by 3
• Subtract 10 from that result
• Square the final number
Use this algorithm to respond to the questions.
What is the correct order?
The steps to get the inverse of the given function are;
Take the square rootAdd 2Divide by 3Subtract 2How to find the inverse of a function?We are given the function;
Start with a number "n"
• Add 2
• Multiply the result by 3
• Subtract 10 from that result
• Square the final number
An inverse function is a function that undoes the action of the another function
Thus, the steps to get the inverse of the above function is as follows;
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The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 2,100 people entered the park, and the admission fees that were collected totaled $4,900. How many children and how many adults were admitted?
From the calculation carried out below, the number of children admitted was 1,400 and the number of adults admitted was 700.
How do we calculate the different numbers of people admitted?
This question can be solved using the substitution method as follows:
x = Number of children admitted
y = Number of adults admitted
x + y = 2,100 ............................................. (1)
1.50x + 4y = 4,900 ................................ (2)
From equation (1), we have:
x = 2,100 - y ................................................. (3)
Substituting x = 2,100 - y into equation (2) and solving for y, we have:
1.50(2,100 - y) + 4y = 4,900
3,150 - 1.50y + 4y = 4,900
2.50y = 4,900 - 3,150
2.50y = 1,750
y = 1,750 / 2.50
y = 700
Substituting y = 700 into equation (3), we have:
x = 2,100 - 700
x = 1,400
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im stuck on this problem and i need help. oh also make sure that your answer is completely right
Click the pair of numbers that are relatively prime.
11 and 121
35 and 125
39 and 75
34 and 49
34 and 49 is pair of numbers that are relatively prime.
What is relatively prime example?
If there isn't an integer bigger than one that divides two integers, then those two numbers are substantially prime (or coprime) (that is, their greatest common divisor is one). For instance, 12 and 13 are not very prime numbers, whereas 12 and 14.What do you mean by relatively prime?
If there are no other positive factors (divisors) between two integers other than 1, they are considered to be relatively prime. Two integers and are said to be relatively prime if using the notation to represent the greatest common divisor.34 and 49 is the pair of numbers that are relatively prime.
The numbers have no common prime factors.
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Answer:
D
Step-by-step explanation:
Just did it on T4L
