In a class of 20 students, how many conversations must be had so that every student talks to every other students in the class?
Answer:
190
Step-by-step explanation:
Similar to the handshake problem, if every student must talk with another person, each student will talk to 19 other students. However, a conversation consists of two people, so we must divide the number of ways we can rearrange the two people. Therefore, our answer is 190
Factor the equation.
Answer: factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
Step-by-step explanation:
justin launches a rocket straight up into the air. The table below gives the height(t) of the rocket (in meters) at a few times t (in seconds) during its flight.
FIND THE AVERAGE RATE OF CHANGE!
Using it's formula, the average rates of change are given as follows:
a) 30 meters per second.
b) -10 meters per second.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the following equation:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For item a, taking the data from the table, we have that:
f(0) = 0.f(4.6) = 138.Hence the rate is given as follows:
r = (138 - 0)/(4.6 - 0) = 30 meters per second.
For item b, taking the data from the table, we have that:
f(9.2) = 23.f(11.5) = 0.Hence the rate is given as follows:
r = (0 - 23)/(11.5 - 9.2) = -10 meters per second.
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Which sequence could be partially defined by the recursive formula f (n 1) = f(n) 2.5 for n ≥ 1?
The sequence partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 is -10, -7.5, -5, -2.5, …
Given recursive formula is f(n+1) = f(n)+2.5, n ≥ 1.
So the first term of the sequence is f(1) since n ≥ 1.
Given options for the sequences are:
a. 2.5, 6.25, 15.625, 39.0625, …
b. 2.5, 5, 10, 20
c. -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
We compare the first term of each sequence with the given recursive formula.
a. 2.5, 6.25, 15.625, 39.0625, …
In this sequence, the first term, f(1) = 2.5
Using recursive formula, f(2) = f(1) + 2.5 = 2.5 +2.5 = 5.
But the second term in the given sequence is 6.25. So the recursive formula does not match with this sequence.
b.2.5, 5, 10, 20
Here, f(1) = 2.5
By the recursive formula, f(2) = f(1) + 2.5 = 5
f(3) = f(2) + 2.5 = 5 +2.5 = 7.5, which does not match with the third term of the given sequence. So this sequence is not defined by the recursive formula.
c. -10, -7.5, -5, -2.5, …
Here, f(1) = -10
Using recursive formula, f(2) = f(1) + 2.5 = -10 + 2.5 = -7.5
f(3) = f(2) + 2.5 = -7.5 +2.5 = -5
f(4) = f(3) +2.5 = -5 +2.5 = -2.5
So far the recursive formula matches with the given sequence. So the sequence defined partially by the recursive formula, f(n+1) = f(n)+2.5, n ≥ 1 is -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
Here the first term is, f(1) = -10.
But the sequence which matches with the recursive formula and starting with -10 is option c. So this sequence does not need to be verified.
The question is incomplete. Find out the complete question below:
Which sequence could be partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 ?
a. 2.5, 6.25, 15.625, 39.0625, …
b. 2.5, 5, 10, 20
c. -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
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An interior designer is creating a custom coffee table for a client. The top of the table is a glass triangle that needs to balance on a single support. If the coordinates of the vertices of the triangle are at (3,6),(5,2) , and (7,10) , at what point should the support be placed?
According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.
The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).
What is the rule of centroid?The centroid method is an agglomerative clustering method in which the similarities (or dissimilarities) between clusters are defined in terms of the centroids (i.e., the multidimensional means) of the clusters on the clustering variables.
According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.
The triangle has a balance point at the centroid.
Find the centroid of the triangular coffee table.
Use the centroid formula [tex](x_1+x_2+x_3/3, y_1+y_2+y_3/3)[/tex]
The centroid of the triangle is (3 + 5 + 7/3, 6 + 2 + 10/3) or(5, 6).
Let the points be A(3, 6), B(5, 2), and C(7, 10). The midpoint D of BC is (5 + 7/2, 2 +10/2) OR (6, 6).
Note that AD is a line that connects the vertex A and D, the midpoint of BC. The distance from D(6, 6) to A(3, 6) is 6 – 3 or 3 units.
If P is the centroid of the triangle ABC, then So, the centroid is 2/3(3) or 2 units to the right of A.
The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).
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Evaluate 6(x-5) at x=8
Answer:
18
Step-by-step explanation:
Substitute x with 8 :
6(8-5) =
8-5 = 3
6(3) = 6 × 3 = 18
Therefore 18 is our final answer
Hope this helped and have a good day
Hey there!
6(x - 5)
= 6(8 - 5)
= 6(8) + 6(-5)
= 48 - 30
= 18
OR EVEN:
6(x - 5)
= 6(8 - 5)
= 6(3)
= 18
18 = 18
Therefore, your answer should be:
18
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Help please need it for rn
Check the picture below.
i need help on this.
Answer:
what
Step-by-step explanation:
−4 5/9+8/9 pls help and hurry
exact form:
-11/3decimal form:
-3.6666mixed number form:
-3 2/3Answer:
-11/3
Step-by-step explanation:
Convert −4 5/9 to improper fraction -41/9 and do the math.
-41/9 + 8/9
-33/9
-11/3
Write an equation of a parabola with vertex at the origin and the given focus.
focus at (-1,0)
The equation of the parabola that has vertex at (0,0 ) and focus (-1, 0) is
x = -y²What is known as a parabola?A parabola is a quadratic function that can move on any axis, it is composed of:
vertexfocal axisdirectrixThe equation that defines a parabola can be given by:
(x - h)² = 4p(y - k)
(y - k)² = 4p(x - h)
This will depend on its aperture
Since the vertex and the focal axis are on the same axis, we analyze that:
v (0, 0)f (-1, 0) the focus is on the right so the parabola is of the form X = Y².(y - 0)² = 4p(x - 0)
f = (0 + p, 0)
0 + p = -1
p = 0 - 1
p= -1
(y - 0)² = 4*-1(x - 0)
(Y)² = -1(X)
x = -y²
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Lisa wants to buy some new shirts are her favorite store. Each shirt costs $15 and she wants to buy a pair of shoes that are $35. Lisa only has $137 to
spend
Let S represent the number of shirts that Lisa buys
Which inequality describes this scenario?
O 137 < 158 +35
O 137 > 158 +35
O 137 >_ 158 +35
O 137 <_158 +35
The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let s represent the number of shirts that Lisa buys. Lisa only has $137 to spend, therefore:
15x + 35 ≤ 137
The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137
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If mA = 29° and m/B= 29°, then mZA = m/B represents the property of what?
The statement, m∠A ≅ m∠B, represents the congruence property.
What is the Congruency Property of Equality?The congruency property of equality states that if two angles have measures that are equal to each other, then both angles are said to be congruent to each other.
Given that:
The measure of angle A = 29 degrees
The measure of angle B = 29 degrees.
Since both angles have the same measure, then both angles are congruent to each other.
Therefore, the statement, m∠A ≅ m∠B, represents the congruence property.
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Jim is running a race against his best friend ryan. jim runs at a rate of 18 miles in 3hours while ryan runs at a rate of 11miles in 2 hours. how much further can jim run in an hour compared to his friend ryan
If Jim is running a race against his best friend Ryan and Jim runs at a rate of 18 miles in 3 hours while Ryan runs at a rate of 11 miles in 2 hours, then Jim can run 0.5 miles further compared to his friend Ryan.
If Jim runs at a speed of 18 miles in 3 hours, it can be represented as,
Speed = distance / time = 18 miles / 3 hours = 6 miles per hour
As Ryan runs at a rate of 11 miles in 2 hours, it can be given as,
Speed = distance / time = 11 miles / 2 hours = 5.5 miles per hour
To determine how much further Jim can run in an hour compared to his friend Ryan,
Distance ( Jim ) = speed x time = 6 x 1 = 6 miles
Distance ( Ryan) = speed x time = 5.5 x 1 = 5.5 miles
The distance that Jim can run further in an hour can be calculated by subtraction.
Distance ( Jim ) - Distance ( Ryan) = 6 - 5.5 = 0.5 miles
Thus, Jim can run 0.5 miles further in an hour compared to his friend Ryan.
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Which square does not touch one of the perimeter
quares?
What is the combined area of rows 4 and 5?
5
4
3
2
1
ABCDE
a) The square that does not touch one of the perimeter squares is the square 3C.
b) The area is 10 units.
Which square does not touch one of the perimeter squares?
The perimeter squares are the outer squares of the image. So, the only square that does not touch one of the perimeter squares is the central one. To identify it, you need to first see in which row it is, and you can see that it is row 3.
Then you need to identify the column, the central square is in column C.
Then the square that does not touch one of the perimeter squares is the square 3C.
What is the combined area of rows 4 and 5?
Let's say that each square has an area of one unit. Now, we have 5 columns, then each row has 5 squares, then the area of each row is 5 units.
So, if we have two rows, the area will be: 2*5 units = 10 units.
The area is 10 units.
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Write the equation of each line in standard form.
slope =0 ;(0,2)
The standard equation for the given slope is y - 2 = 0
These are two methods for finding the equation of a line given a point and slope. Create the equation y = mx + b.
We just solved using the m given in the problem and the b. Point-slope form = y-y1 = m (x-x1), where (x1, y1) is the specified point and m is the specified slope. "x" and "y" remain as variables.
Putting (0,2) for (x1, y1) and m=0, we get
y-2=0(x-0)
(y-2) =
y-2=
+y-2=0
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Pls answer this by 11:00
Answer:
1.)
[tex]\frac{3a}{4} =\frac{1}{4} \\[/tex]
cross multiply
[tex]12a=4\\\frac{12a}{12} =\frac{4}{12} \\a=\frac{1}{3}[/tex]
2.)[tex]\frac{7}{2} =\frac{c}{\frac{8}{7} }[/tex]
cross multiply
[tex]c=\frac{7}{2} *\frac{8}{7} \\c=\frac{56}{14} \\c=4[/tex]
3.)[tex]\frac{6}{5} =\frac{h}{\frac{3}{8} } \\[/tex]
cross multiply
[tex]\frac{6}{5} *\frac{3}{8} =h\\h=\frac{18}{40} \\h=\frac{9}{20}[/tex]
4.)[tex]\frac{-2}{9} =\frac{-3m}{2} \\[/tex]
cross multiply
[tex]-2(2)=9(-3m)\\-4=-27m\\\frac{-4}{-27}=\frac{-27m}{-27} \\m=\frac{4}{27}[/tex]
5.)[tex]\frac{7}{6} =\frac{7p}{3} \\42p=21\\ \frac{42p}{42} =\frac{21}{42} \\p=\frac{1}{2}[/tex]
6.)[tex]\frac{x}{\frac{1}{7} } =-\frac{4}{7} \\x=\frac{1}{7} *\frac{-4}{7} \\x=\frac{-4}{49}[/tex]
7.)[tex]\frac{n}{\frac{4}{9} } =\frac{10}{9} \\n=\frac{10}{9} *\frac{4}{9} \\n=\frac{40}{81}[/tex]
8.)[tex]\frac{5}{3} g=-\frac{8}{3}\\ g=-\frac{8}{3} /\frac{5}{3} \\g=\frac{-8}{3}*\frac{3}{5} \\ g=\frac{-24}{15} \\g=\frac{-8}{5}[/tex]
The roof support on Lamar's house is in the shape of an isosceles triangle with base angles of 38°. Find x .
The value of top angle x will be 104° for the given isosceles triangle.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
Given the roof as an isosceles triangle with a base angle of 38°.
Since in an isosceles triangle two sides and two angles are equal.
Since the sum of all angles of a triangle is 180 degrees.
So,
x + 38 + 38 = 180
x + 76 = 180
x = 104°.
Hence "The value of top angle x will be 104° for the given isosceles triangle".
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Suppose B is the midpoint of -AC . Use the given information to find the missing measure. A B=6 y-14, B C=10-2 y, A C= ?
If AB = 6y - 14, BC = 10 - 2y then the value of AC = 8.
What is meant by midpoint?
In geometry, the midpoint is the point in the middle of a line segment. It is equidistant from both endpoints and serves as the segment and endpoint centroid. It cuts the segment in half.
Given: AB = 6y - 14, BC = 10 - 2y
Since B is the midpoint of AC, AB = BC then
6y - 14 = 10 - 2y
Add 14 on both sides of the equation, and we get
6y - 14 + 14 = 10 - 2y + 14
6y = - 2y + 24
Add 2y on both sides of the equation
6y + 2y = - 2y + 24 + 2y
simplifying the above equation, we get
8y = 24
y = 24/8
y = 3
Substitute the value of y in AC then we get
AC = 2(6(3) - 14)
= 2(4)
AC = 8
Therefore, the value of AC = 8.
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A cube is a solid figure with six square faces. If the edges of a cube have length 1.5 \mathrm{~cm} , what is the surface area of the cube?
a. What is the relationship between the length of the edges and the area of each face?
13.5 cm² is the surface area of the cube .
What is surface area of cuboid?
The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.If the edge of a cube have a length = a unit
then, the surface area of the cube = 6a² unit
here, the edge of a cube have length a = 1.5 cm
Therefore , the surface area of the cube 6a² = 6 × 1.5²
= 13.5 cm²
The area of each face = ( the length of the edges)²
The surface area of whole cube = 6 × the area of one face
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Show work will give 30 points NEED ASAP
2(5-10x)+8x=19x+52
Answer:
[tex]x=-\frac{42}{31}[/tex]
Step-by-step explanation:
2 ( 5 - 10x ) + 8x = 19x + 52
→ Expand brackets
10 - 20x + 8x = 19x + 52
→ Simplify
10 - 12x = 19x + 52
→ Minus 19x from both sides
10 - 31x = 52
→ Minus 10 from both sides
-31x = 42
→ Divide both sides by -31
[tex]x=-\frac{42}{31}[/tex]
The grades in period 3 algebra 2 have an average of 82 nd vary by 12 percentage points. formulate an absolute value equation that could be used to solve for the maximum and minimum grade.
The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.
What is an absolute value equation?A statement that contains an absolute value is known as an absolute value equation. The absolute value contains the variable of the equation.Now,
Given:
The average of grades = 82%Variation = 12%Let 'x' be the value that gives the value of grades.
The absolute value equation to find the grades will be given by: | x - 82 | = 12
=> x - 82 = ± 12
For maximum value of the grades, x - 82 = 12
=> x = 82 + 12
=> x = 94.
For minimum value of the grades, x - 82 = -12
=> x = 82 - 12
=> x = 70.
Hence, The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.
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A construction crew is building a straight ramp that rests on two beams. One
3.5 feet tall and the other is 10.5 feet tall. The beams are 40 feet apart. What is the
slope of the ramp?
According to the solving the slope of the ramp = 0.175.
What exactly is Slope?shows the steepness of an inclination The slope is just the ratio of the rise over the run, or the change there in vertical out over change in the horizontal, as seen below:
How do you calculate slope?find the coordinates of two points on the line. Calculate the difference in y-coordinates between these two places (rise). Determine the x-coordinate difference between these two places (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).
According to the given data:The given values are indeed the heights of a two beams and indeed the distance between them, which are:
Y₁ = 3.5ft
Y₂ = 10.5 ft
ΔX = 40 ft
To get the slope of both the ramp, enter the following values into the slope formula:
m = (Y₂ - Y₁)/ΔX
= (10.5 - 3.5)/40
= 7/40
= 0.175
According to the solving the slope of the ramp = 0.175
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Select the correct answer. Which equation has no solution? A. 24x + 32 − 2.1x = 20.9x + 30 + x + 2 B. 24x + 32 − 2.1x = 20.9x + 30 + x − 2 C. 24x + 32 − 2x = 20.9x + 30 + x − 2 D. 24x + 32 = 20.9x + 30
The equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2
Part A
24x+32-2.1x = 20.9x+30+x+2
Add like terms
24x-2.1x-20.9x-x = 30+2-32
0x = 0
Infinitely many solutions
Part B
24x+32-2.1x = 20.9x+30+x-2
Add like terms
24x-2.1x-20.9x-x = 30-2-32
0x = -4
There is no solution
Part C
24x+32-2x = 20.9x+30+x-2
Add like terms
24x-2x-20.9x-x = 30-2-32
0.1x = -4
x = (-4)/0.1
x = -40
It has only one solution
Part D
24x+32 = 20.9x+30
Add like terms
24x-20.9x = 30-32
3.1x = -2
x= (-2)/3.1
x = -0.64
It has only one solution
Hence, the equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2
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Before signing a contract, you must review the terms and conditions of the contract. How many terms are there in the surface area formula below?
2(lw + wh + hl)
How many terms are there in the surface area formula below?2(lw + wh + hl) 3 terms.
What are the three terms ?
The total surface area of a cuboid= 2(lw + wh + hl)
Here, w= width, h= height, l= length
Thus, there are 3 terms in the surface area formula.
What is a total surface area?
There may be numerous flat surfaces throughout an entire object (such as a cube), each of which needs to be measured independently. The total surface area of an object is the sum of all the faces that make up the object.Keep in mind that the total surface area only accounts for the flat exterior of an object, treating it though it were two-dimensional.Even if there are many of them, these many flat surfaces join together to form the three-dimensional entity.Surface area and total surface area do not always represent the amount of space that an object occupies.To learn more about total surface area, refer:
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if the lenght and breadth of the rectangular sheet of paper is 49 1/2 cm and 23 1/2 cm repsectivly . Find its perimeter
Answer: 146 cm
Step-by-step explanation:
A simple way to find the perimeter of a rectangle is to double both sides and add them.
(49.5 * 2) + (23.5)
= 99 + 47
= 146
598 rounded to the nearest 1000
Answer:
1000
Step-by-step explanation:
The closest 1000 to 598 is 1000.
What are the solutions of the quadratic equation x²-20=8 x ?
F. 2,10
G. 20,1
H. -1,20
J. -2,10
The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.
The given quadratic equation is [tex]x^{2}[/tex] - 20 = 8 x . To get the solutions of the given quadratic equation we need to simplify the quadratic equation. The step wise simplification of the given quadratic equation is,
[tex]x^{2}[/tex] - 20 = 8 x
[tex]x^{2}[/tex] - 8x -20 =0
on breaking -8x in two parts as -10x + 2x , we will get
[tex]x^{2}[/tex] -10x + 2x -20 = 0
x (x - 10) + 2 (x - 10) = 0
On taking (x-10) as common, we get
(x-10) (x+2) = 0
x = -2 , 10
The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.
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x=2
#4a&b
The perimeter of the rectangle below is 42 inches. Write an equation that could be used to
find the value of x. Then, find the dimensions of the rectangle.
5x
Equation:
Dimensions of Rectangle:
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
for our rectangle here that means
2×(5x) + 2×(x - 3) = 42
10x + 2x - 6 = 42
12x - 6 = 42
12x = 48
x = 4
length = 5x = 5×4 = 20 in.
width = x - 3 = 4 - 3 = 1 in.
8 x 10^-3 is how many times greater than 4 x 10^-6
Answer:
.002 or
2x10^-3
Step-by-step explanation:
make sure the exponents match
8 x 10^-3 =
.008 × 10^-3
(.008 × 10^-6) ÷ (4 x 10^-6)
10^-6 cancels out
.008 ÷ 4 = .002
or
2x10^-3
Define the variable?
Write the constraints ?
What is the Objective Equation?
Variable - These are the unknown quantities that expected to estimate it as an output.
Example:- In an optimization model for labor scheduling, the number of nurses to employ during the morning shift in an emergency room may be a Decision variable.
Constraints - the restrictions on the variable open linear programming problem are called constraints.
The conditions x ≥ 0, y ≥ 0 called non negative restrictions.
Objective equation - the objective equation should be specified in a quantitative way.
It is of the form Z = ax + by
where x and y are decision variable.
Z is to be maximized or minimized to find the solution.
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