The product of three successive integers is represented by the symbol n3 n=(n1)(n)(n+1).
n3 n can be divided by 6.
What is consecutive integers ?Consecutive integers are the numbers that follow one another. They go either alphabetically or sequentially. For instance, a series of integers is a group of natural numbers. The term "consecutive" in mathematics refers to an unbroken flow or succession of numbers; hence, a sequence of consecutive integers is one where each following number is one more than the one before it. An array of consecutive integers (or numbers) has an identical mean and median. If x is a positive integer, then x + 1 and x + 2 are likewise positive integers. We shall learn in-depth details regarding formulas, characteristics, illustrations, and the significance.
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Given: triangle ABC,
Angle B=120°,
AB= 6, BC = 10
Find: The area of triangle ABC
The area of triangle ABC when Angle B=120°, AB= 6, BC = 10 is 25.980 square unit.
As per the question statement, we are supposed to find out the area of triangle ABC in which angle B=120°, AB= 6, BC = 10.
Lets find out AC for which we should know about Cosine formula
i.e., [tex]AC^{2} =AB^{2} +BC^{2} -2(AB)(BC)cos(B)\\AC^{2} =6^{2} +10^{2} -2*6*10cos120\\AC^{2}= 36+100-120*(-0.5)\\AC^{2}=196\\AC=\sqrt{196} =14[/tex]
Hence We have measures of all three sides of the triangle ABC.
Now we use the Heron's formula for calculating the area of triangle ABC.
We need semi perimeter i.e., [tex]s=\frac{AB+BC+AC}{2}[/tex]
[tex]s=\frac{30}{2} =15[/tex]
Now Area is given by,
[tex]area=\sqrt{s(s-AB)(s-BC)(s-AC)} \\area=\sqrt{15(15-6)(15-10)(15-14)} \\area=\sqrt{15*9*5*1} \\area=\sqrt{675} \\area = 25.980 unit^{2}[/tex]
Area: The space occupied by an object or a shape in square units.Cosine Formula: Uses the cosine of an angle to determine the remaining sides of the triangle.Heron's Formula: Uses the measure of the all sides of triangle to calculate the area of the triangle.To learn more about Heron's questions, click on the link given below:
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how to solve? …………….
Answer:
6x + 9
3(2x + 3)
please correct me if I'm wrong
The number of apples in a fruit basket is
directly proportional to the number of
oranges. If there are 2 apples and 5 oranges
in Mary's basket, how many more apples are
there in a basket that contains 35 oranges?
(01.02 mc) solve for x: two thirds(x − 2) = 4x. a x = negative two fifths b x = negative five halves c x = two fifths d x = −2
The correct option is a) x = negative two fifths. The value of x is obtained by solving it with rules of linear equation in two variable as x = -2/5.
What is linear equation in one variable?A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable.
Now, as per the given expression;
2/3(x -2) = 4x
Multiply both sides of equation by 3.
2(x - 2) = 12x
Simplifying;
2x - 4 = 12x
Subtract 2x on both sides of the equations.
-4 = 12x - 2x
Again Simplifying;
-4 = 10x
Divided by 10 on both sides
x = -4 / 10
x = -2/5
Therefore, the value of x is obtained as x = -2/5.
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If angle 5 is 120 degrees, find the value of <8
Answer:Answer:
The measurement of the angle is 60
Step-by-step explanation:
The two blue lines are straight and parallel lines. The sum of the angles on a straight line is 180 degrees. Angle 5 and angle 6 are on a straight line. Therefore
Angle 5 + angle 6 = 180
If angle 5 is 120 degrees, then
Angle 6 = 180 - 120 = 60 degrees.
biker bikes 2 1/4 miles in 15 min or 1/4 of an hour
Answer:
Should be 9 mph
Step-by-step explanation:
2.25 miles divided by .25 hours will give you a speed measured in miles per hour.
Write a difference quotient that best approximates the instantaneous rate of change of g at x=2.5.
A difference quotient that best approximates the instantaneous rate of change of g at x=2.5 is; -3
What is the Difference Quotient?We can define the average rate of change of a function g(x) in an interval [a, b] as:
r = [g(b) - g(a)]/(b - a)
Particularly, if we want to find an approximation of the rate of change for a particular value x', we can choose:
a < x' < b
Such that a and b are really close to x'.
Then if we want to find the instantaneous rate of change of g at x = 2.5, we need to find values of a and b really close to 2.5.
Looking at the graph, we can choose:
a = 2
b = 3
(are the two closer ones to 2.5)
Then the rate of change can be written as:
f'(x) = g(3) - g(2)]/(3 - 2)
f'(x) = (1 - 4)/1
f'(x) = -3
Thus, we can conclude that a good approximation of the instantaneous rate of change is -3.
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3/5(1/2p + 2r) + 2p
please simplify!!!
The simplified form of the algebraic expression is [tex]\frac{23}{10} p+\frac{6}{5} r[/tex] .
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).
A good example of an algebraic expression is 3x² + 2xy + c.Any expression that can be converted into a rational fraction using the properties of the arithmetic operations is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions). In other terms, a rational expression is one that can be created using only the four arithmetic operations and the variables and constants.Given expression is of the form:
[tex]\frac{3}{5} (\frac{1}{2}p+2r )+2p[/tex]
Now we will use the distributive property to expand the algebraic expression:
[tex]or, (\frac{3}{5} \times\frac{1}{2}p+\frac{3}{5} \times2r) +2p\\\\or,\frac{3}{10}p+\frac{6}{5} r+2p\\ \\or,\frac{3+20}{10} p+\frac{6}{5} r\\\\or,\frac{23}{10} p+\frac{6}{5} r[/tex]
Hence the simplified algebraic expression is [tex]\frac{23}{10} p+\frac{6}{5} r[/tex] .
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What ordered pair is a solution of the equation y = 4x?
A. (1, 3)
B. (-1, -4)
C. (-4, -1)
D. (1, -4)
To the nearest mile, what is the total distance that he ran?
6 miles
8 miles
11 miles
25 miles
-1/2=y-1 solve for y and I need to know how you solved it
Solution:
[tex]y = \frac{1}{2}[/tex]
Process of Solution:
1. Switch sides.
[tex]y-1=-\frac{1}{2}[/tex]
2. Add 1 to both sides.
[tex]y-1+1=-\frac{1}{2} +1[/tex]
3. Simplify.
[tex]y = \frac{1}{2}[/tex]
Hope this helps!
5. Which equation in point-slope form contains the points (6, 2) and (2, 4)?
O,
O
O
O
y-2=-2(x-6)
y-4=--(x-6)
y-4--2(x-2)
y-2---(x-6)
A number 1-10 is selected at random. What is the probability of selecting an odd or a number greater than 8?
Answer:
0.6
Step-by-step explanation:
Answer: 20%
Step-by-step explanation: If you look at it like 100 then think of 20% of 100.
20% or 2.
Lucinda has three packages of baseball cards. the first package has thirteen cards. the second package has twenty-six cards, and the third package has twenty-two cards. using front end estimation, what is the best estimate for the total number of baseball cards she has? a. 30 b. 40 c. 50 d. 60
which expression is equivalent to squareroot 4j^4/9k^8
Answer:
It's the third choice:
2/3 j^2/k^4
Step-by-step explanation:
√ [4j^4/9k^8)]
= √(4j^4) / √9k^8
= 2j^2 / 3k^4
= 2/3 j^2/k^4
The amount of money raised at a fundraiser is directly proportional to the number of attendees. The amount of money raised for 12 attendees is $300. How much money is raised for 75 attendees? $300 $1,875 $900 $2,775
The amount of money raised for 75 attendees will be $1875. The correct option is B.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that the money raised for 12 attendees is $300. The money raised for 75 attendees will be calculated as below:-
12 attendees = $300
1 attendees = $300 / 12
75 attendees = $300 x 75 / 12
75 attendees = $1875
Therefore, the amount of money raised for 75 attendees will be $1875. The correct option is B.
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David has 11 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating and 2F. Then grab your equation using the axes below
The linear equation from the given statement is the N + F+11 = 2F.
According to the statement
We have to write the linear equation.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
David has 11 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating and 2F.
Then
The number of shirts left = N
The number of the shirts which are folded = F+11
The total number of shirts = 2F
And then
The linear equation becomes :
N + F+11 = 2F
This the linear equation for the given statement.
So, The linear equation from the given statement is the N + F+11 = 2F.
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The triangle O'P'Q' is a dilation of the triangle OPQ. What is the scale factor of the dilation?
104
-10 -8 -6
Pr
-4
-2
do
P
6
4
2
O
o
-2
-4
-6
8
6
00
10
10
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole
number.
Answer: the scale factor is 5
Step-by-step explanation:
5 squares on the dilated shape and for the original shape it’s only 1 and the original shape is always going to be the denominator while the numerator is going to be the shape after it’s dilated so it’s 5/1 which equals 5
So THE ANSWER IS 5
PLEASE HELP WITH THID QUESTIONS ASAPPP
Answer:
12
Step-by-step explanation:
16/4=4
4*3=12
Hope this helps!
Write an equation in slope-intercept form for the perpendicular bisector of the segment with the given endpoints. Justify your answer. (Lesson 5-1)
D(-2,4) and E(3,5)
The equation of the perpendicular bisector of the segment with the endpoints located at D(-2 , 4) and E(3 , 5) is y = -5x + 7
A perpendicular bisector of a segment is a line that divides the segment into two equal parts forming right angles at the point of intersection.
To get the perpendicular bisector of a segment, get the point of intersection of the two lines which is the midpoint of the segment.
midpoint (x , y) = [(x1 + x2)/2 , (y1 + y2)/2]
midpoint (x , y) = [(-2 + 3)/2 , (4 + 5)/2]
midpoint (x , y) = (1/2 , 9/2)
Get the slope of the perpendicular bisector of a segment by taking the negative reciprocal of the slope of the segment.
slope of segment = (y2 - y1)/(x2 - x1)
slope of segment = (5 - 4)/(3 - -2)
slope of segment = 1/5
slope of the perpendicular bisector = -5
Solving for the y-intercept, b, plug in the point (1/2 , 9/2) and the slope -5 to the slope-intercept form of the equation, y = mx + b.
y = mx + b
9/2 = -5(1/2) + b
b = 7
Setting up the equation in slope-intercept form, where m = -5 and b = 7.
y = mx + b
y = -5x + 7
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What is the equation of the line that passes through the point (−4,5) and has a slope of 0?
Answer:
y = 5
Step-by-step explanation:
A line with a slope of 0 is a horizontal line parallel to the x- axis with equation
y = c ( c is the value of the y- coordinates the line passes through )
the line passes through (- 4, 5 ) with y- coordinate 5 , then
y = 5 ← equation of line
(a) The area of a rectangular field is 7546 m².
If the length of the field is 98 m, what is its width?
Width of the field: m
Answer:
77m
Step-by-step explanation:
Area of rectangle = L x W
7536m² = 98 x W
(Divide both sides by 98 to get W)
W = 7536m ÷ 98m
W = 77m
Pls solve part e for me thanks
Using it's concept, the probability of at least 1 red face upper most is 17/18 = 0.9444 = 94.44%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For each cube, the probability of no red faces is:
Cube A: 1/6.Cube B: 3/6 = 1/2.Cube C: 4/6 = 2/3.Hence the probability of no red faces in anu cube is:
1/6 x 1/2 x 2/3 = 1/18.
Which means that the probability of at least 1 red face is given by:
1 - 1/18 = 17/18 = 0.9444 = 94.44%.
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for a randomly selected worker, what is the approximate probability the bolt will be inserted in 19 minutes or less? round to the nearest whole percent.
The probability that the bolt will be inserted in 19 minutes or less is 0.8413.
How to calculate the probability?It should be noted that the probability will be illustrated as:
P(X < x) = P[z < (x - u/sd)]
where
x = number
u = mean
SD = standard deviation
Therefore given the numbers, this will be:
P(x < 19) = P(z < (19 - 15)/4)
= P(z < 4/4) = P(z < 1)
= 0.8413
Therefore, the probability that the bolt will be inserted in 19 minutes or less is 0.8413.
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The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately Normally distributed. For a randomly selected worker, what is the approximate probability the bolt will be inserted in 19 minutes or less?
Simplify this expression and show ALL steps ( PLEASE HELPP )
-5(4) + (-40) divided by (-10)
Answer:
-16
Step-by-step explanation:
Use pemdas:
1. -5 times 4 is -20
2. -40 divided by -10 is 4
3. -20 plus 4 is -16
Add signs to make true:
3 3 3 3 3=6
suppose you want to estimate the proportion of students at a large university that approve of the new health care bill. you take an srs of 200 of the 25,000 undergraduate students and an srs of 100 of the 5,000 graduate students.
According to the question, srs is a simple random sample whose size consists of individuals from the population and chosen in such a way that every set of individuals has an equal chance to be sampled.
What is Stratified random samples?
For stratified random samples, initially classify the population into the groups of similar individuals which is called as “strata”. Later choose simple random samples and combine them to form a full sample.
As per question, srs of [tex]200[/tex] of the [tex]25000[/tex] undergraduate students and the srs of [tex]100[/tex] of the [tex]500[/tex] graduate students. This overall sample is a stratified sample.
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(-7/2z+4)Z+(1/5z-15)
Answer:
I D K if this even helps at all T B H
Find an equivalent ratio to 8:7. O a. 40:35 O b. 40:30 O c. 20:19 O d. none of the above
Answer
a. 40:35
Step-by-step explanation:
8 * 5 is 40 and 7 * 5 is
PLEASE HELP 15 points
Step-by-step explanation:
(4h⁴)⁴ / (4h^-8)
remember, multiplying exponents means adding them. exponents of exponents means multiplying them.
and dividing exponents means subtracting them.
also, n^-a = 1/(n^a).
let's look at the numerator (top part) first :
(4h⁴)⁴ = 4^1×4 × h^4×4 = 4⁴×h¹⁶
now, for the denominator, the exponent -8 applies only to h. not to 4.
so,
1/(4h^-8) = h⁸/4
and so, the whole expression is then simplified
4⁴×h¹⁶ × h⁸/4 = 4³ × h²⁴