Answers
Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order.
What is meant by infinite series?Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order. In addition to being valuable in mathematics, infinite series are also useful in the sciences of physics, chemistry, biology, and engineering. Sigma notation can be used to depict an infinite series. An infinite series, for instance, is ∞∑n=110(12)n−1. The series is endless, as indicated by the infinity symbol above the sigma notation.Infinite series are useful for discovering approximations to complex problems and for highlighting minute details of mathematical precision. A finite series is the accumulation of all of its terms. An infinite series has an infinitely large term count and an infinitely high upper bound.We get,
a) [tex]$\sum_{n=0}^{\infty}$[/tex]
Infinity
b) [tex]$\sum_{n=1}^{\infty}\left(\frac{4}{2^n}\right)$[/tex]
[tex]\sum_{n=1}^{\infty} \frac{4}{2^n}[/tex]
[tex]& =4 \cdot \sum_{n=1}^{\infty} \frac{1}{2^n} \\[/tex]
[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]
[tex]& =4\left(\sum_{n=0}^{\infty} \frac{1}{2^n}-\frac{1}{2^0}\right)[/tex]
[tex]& \sum_{n=0}^{\infty} \frac{1}{2^n}=2 \\[/tex]
[tex]& =4\left(2-\frac{1}{2^0}\right)[/tex]
Then we get,
=4
c) [tex]$\sum_{n=1}^{\infty}\left(\frac{7}{10^n}\right)$[/tex]
[tex]$\sum_{n=1}^{\infty} \frac{7}{10^n}[/tex]
[tex]& =7 \cdot \sum_{n=1}^{\infty} \frac{1}{10^n} \\[/tex]
[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]
[tex]& =7\left(\sum_{n=0}^{\infty} \frac{1}{10^n}-\frac{1}{10^0}\right)[/tex]
[tex]& \sum_{n=0}^{\infty} \frac{1}{10^n}=\frac{10}{9} \\[/tex]
[tex]& =7\left(\frac{10}{9}-\frac{1}{10^0}\right)[/tex]
Simplify
[tex]$7\left(\frac{10}{9}-\frac{1}{10^0}\right): \quad \frac{7}{9}$[/tex]
= 7/9
Therefore,
a) infinity, b) =4, and c) = 7/9
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Related Questions
Instructions: Find the missing side. Round your answer to the nearest tenth.
X
-
16
65⁰
X
Answers
Answer:
Maybe the answer must be 90°
Which of the following describes the effect of the transformation given by (x, y) -› (-x, y) on points in the coordinate plane?
Answers
There are two numbers. One number is twice the other number. The difference of the smaller number and half the larger number is 20.
An equation created to find the smaller number will have_________
.
Answers
Step-by-step explanation:
x, y = 2 numbers
x = 2y
y - x/2 = 20
this is impossible to solve. there is no solution.
because the first equation tells us
y = x/2
and so the second equation is
x/2 - x/2 = 20
0 = 20
so, again, no solution.
Which equation can be simplified to find the inverse of y = 2x²?
0-2x²
O
y-1x²
O -y = 2x²
O x = 2y²
O
Answers
Answer:
D.) x = 2y²
Step-by-step explanation:
You can find the inverse of an equation by swapping the positions of the "x" and "y" variables. Then, you would need to rearrange the equation to re-isolate the "y" variable.
As such, D.) is the correct option because it is identical to the original equation except that the variables are swapped.
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]y = 2x^2\hspace{5em}\stackrel{\textit{quick switcheroo}}{\boxed{x = 2y^2}}\implies \cfrac{x}{2}=y^2\implies \sqrt{\cfrac{x}{2}}=\stackrel{f^{-1}(x)}{y}[/tex]
1. What is the value of the 4th iterate of
f(x) = 3x-1/x2 if x0 = -2? Round to three decimal places.
Answers
The value of the 4th iterate of the given function f(x) is -2.096
2nd option is correct.
A function's iterate is a function that is expressed as repetition of another (already iterated) function; this latter function may be referred to as the iterand.
Any function taken on its own is regarded as the first iteration.
A function is said to have an identity function at iteration zero.
According to the question,
f(x) = (3x-1)/[tex]x^{2}[/tex]
[tex]x_{o}[/tex] = -2
The first iterate is calculated by finding f(-2).
f(-2) = (3(-2)-1)/4
f(-2) = -1.75
Similarly, the next iterates are calculated as follows:
f(-1.75) = -2.048
f(-2.048) = -1.71
f(-1.71) = -2.096
Thus, the fourth iterate for the given function is [tex]x_{4}[/tex]= -2.096
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There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat.
Answers
Probability that a card selected at random is purple = 7/25
Probability of random selectionNumber of red cards, N(red) = 12
Number of blue cards, N(blue) = 17
Number of purple cards, N(purple) = 14
Number of yellow cards, N(yellow) = 7
Total number of cards, N(total) = 12 + 17 + 14 + 7
N(total) = 50
Probability that a card selected at random will be purple
P(purple) = N(purple) / N(total)
P(purple) = 14/50
Reduce to the lowest fraction
P(purple) = 7/25
Therefore, probability that a card selected at random is purple = 7/25
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Complete Question
There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat. If a card is selected at random, what is the probability that the card is purple
The graphs of f(x) = 5x and its translation, g(x), are
shown on the graph.
30 Iv
25-
20
15
10 1.5
g(x)
f(x)
65432 15.
10:
-15-
20
-25
-30
(0,
51
(2,25)
(2, 15)
2 3 4 5
(0, -9)
(1,-5)
X
What is the equation of g(x)?
g(x) = 5x-9
g(x) = 5x-10
g(x) = 5-9
Og(x) = 5* - 10
Answers
Answer: [tex]g(x)=5^x - 10[/tex]
Step-by-step explanation:
g(x) is the graph of f(x) translated 10 units down.
x+y=5:3 and x+y=56
Work out x-y
Answers
The value of x-y from the given condition is 14.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
The given ratio is x:y=5:3.
So, x/y =5/3
3x=5y
To the equation x+y=56, multiply 5 on both side, we get
5x+5y=280
5x+3x=280
8x=280
x=35
Substitute x=35 in equation x+y=56, we get
35+y=56
y=21
Now. x-y is
35-21=14
Therefore, the value of x-y from the given condition is 14.
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University Data
Receiving
Not Receiving
Total
Financial Aid
Financial Aid
Undergraduates
4222
3898
8120
Graduates
1879
731
2610
Total
6101
4629
10730
If a student is selected at random, what is the
probability that the student is a graduate
(rounded to the nearest percent)? [ ? ]%
Answers
Answer:
[tex] [/tex] [tex] [/tex] [tex] [/tex] [tex] [/tex]
Can someone help me please
Answers
Answer:
1/9, 3, 27
(A / the first option listed)
Step-by-step explanation:
Here, we are given an expression with an "x" in it, and we are to evaluate possible x values, which means we plug them in as the x in the expression
first,
x = -2
3ˣ → 3⁻²
when we raise something to a negative power, we simply find the positive version of that power, and put a 1 over it:
3² = 3 · 3 = 9
so, 3⁻² = [tex]\frac{1}{9}[/tex] (1/9)
next,
x = 1
3ˣ → 3¹
now, here we have something raised to the power of 1, which is always itself, so 3¹ = 3
(think of ^to the power of as how many times we multiply that number, so 3² = 3 · 3, 3¹ = 3)
and finally,
x = 3
3ˣ → 3³
here, we can multiply 3 by itself 3 times:
3 · 3 · 3 = 27
so, 3³ = 27
[important note: when we raise something to a power, we are not multiplying the base number by that number, but this is a common mistake. but the exponent is how many times we are multiplying that number, which is confusing at first}
So, our answers in order are:
1/9, 3, 27 (the first option listed)
hope this helps! let me know if I should clarify anything :)
Select the correct answer. What is the solution to the equation? -2√x+4=-12 A. 4 B. 8 C. 16 D. 64
Answers
Answer:
d. 64
Step-by-step explanation:
x^1/2 = 8
Square each side
(x^1/2 )^2=( 8)^2
x = 64
Please help I don’t know if I’m doing this correctly
Answers
Answers:
Exponential and increasingExponential and decreasingLinear and decreasingLinear and increasingExponential and increasing=========================================================
Explanation:
Problems 1, 2, and 5 are exponential functions of the form [tex]y = a(b)^x[/tex] where b is the base of the exponent and 'a' is the starting term (when x=0).
If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.
If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.
In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.
Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.
---------------------
Problems 3 and 4 are linear functions of the form y = mx+b
m = slope
b = y intercept
This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.
If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.
On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.
Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.
Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of cosines, what is the measure of angle A? Round your answer to the nearest whole number, if necessary.
a = 20 cm
b = 13 cm
C = 139°
Answers:
126°
16°
25°
38°
Answers
The measure of angle A rounded to the nearest whole number is 25°.
Hence, option C is the correct answer.
What is the measure of angle A?Given that?
side a = 20cmside b = 13cmAngle C = 139°side c = ?Angle A = ?First, we determine the length of side c using the law of cosines.
c = √( a² + b² - 2ab( cosC ) )
We substitute in our values
c = √( 20² + 13² - 2×20×13( cos 139° ) )
c = √( 400 + 169 - 520( cos 139° ) )
c = √( 569 + 392.44898 )
c = √961.44898
c = 31 cm
Next, we find Angle A, using the law of cosines.
A = cos⁻¹[ ( b² + c² - a² ) / 2cb ]
We substitute in our values
A = cos⁻¹[ ( 13² + 31² - 20² ) / ( 2 × 31 × 13 ) ]
A = cos⁻¹[ ( 169 + 961 - 400) / 806]
A = cos⁻¹[ 730 / 806]
A = cos⁻¹[ 0.9057 ]
A = 25°
The measure of angle A rounded to the nearest whole number is 25°.
Hence, option C is the correct answer.
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Given the function f(x) = -x - 3x², find the value of f(1/2) in simplest form.
Answers
Answer:
-5/4
Step-by-step explanation:
To evaluate the function, put the value of the argument where the variable is and do the arithmetic.
Function evaluationf(x) = -x -3x²
f(1/2) = -(1/2) -3(1/2)² = -1/2 -3(1/4) . . . . . use 1/2 in place of x
f(1/2) = -2/4 -3/4 = -5/4
The value in simplest form is ...
f(1/2) = -5/4
im new to algebra, so most of the stuff im writing here is basic stuff.
8x=24
4x=9
Answers
Answer:
x = 3, x = 9/4
Step-by-step explanation:
8x = 24
x = 3 Divide both sides by 8.
4x = 9
x = 9/4 Divide both sides by 4.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1.}[/tex]
[tex]\mathsf{8x = 24}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{8x = 24}[/tex]
[tex]\huge\textbf{Divide \boxed{8} to both sides:}[/tex]
[tex]\mathsf{\dfrac{8x}{8} = \dfrac{24}{8}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = \dfrac{24}{8}}[/tex]
[tex]\mathsf{x = 3}[/tex]
[tex]\huge\textbf{Therefore, the answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x =}\frak{\ 3}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{4x = 9}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{4x = 9}[/tex]
[tex]\huge\textbf{Divide \boxed{9} to both sides:}[/tex]
[tex]\mathsf{\dfrac{4x}{4} = \dfrac{9}{4}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = \dfrac{9}{4}}[/tex]
[tex]\mathsf{x = 2 \dfrac{1}{4}}[/tex]
[tex]\huge\textbf{Therefore, the answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = }\frak{\ \dfrac{9}{4}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
When Roberto got a puppy from the shelter, it weighed 10.5Ibs. The puppy gained 40% of its original weight in the first month that Roberto had him. How much did the puppy weight after the first month?
Answers
Select the correct answer. A linear function on a coordinate plane. A line passing through (1, 4), (minus 2, minus 2), intersects the y- axis at 2 units and intersects the x-axis at (minus 1, 0) to form shaded portions on the left side of the line. Which of the following inequalities is graphed on the coordinate plane? A. y ≤ 2 x + 2 B. y ≥ 2 x + 2 C. y < 2 x + 2 D.
Answers
Considering the given linear function, the inequality graphed is:
B. [tex]y \geq 2x + 2[/tex].
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:
m = (4 - 2)/(2 - 1) = 2.
Thus the equation of the line is:
y = 2x + 2.
The left-side of the line is the values above the line, hence the inequality is:
B. [tex]y \geq 2x + 2[/tex].
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This spinner has 6 equal sections. In simplest form, what are the odds in favor of spinning blue or green?
A. 1:2
B. 1:3
C. 3:1
D. 2:1
Answers
The length of each edge of a cube is decreased by $40\%$. By what percent does the volume of the cube decrease
Answers
Now simplify the y-terms to get the equation of the parabolic path. You do not need to expand the x-term. (2 points) Hint: Square both sides to get rid of the square roots
Answers
The simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
How to determine the simplified equation?The complete question is added as an attachment
The equation is given as
[tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex]
Subtract (x - 10)^2 from both sides
[tex](y- 6)^2 = 4^2 - (x - 10)^2[/tex]
Evaluate 4^2
[tex](y- 6)^2 =16 - (x - 10)^2[/tex]
Take the square root of both sides
[tex]y- 6= \sqrt{16 - (x - 10)^2}[/tex]
Add 6 to both sides
[tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
Hence, the simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
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Question 15 of 46
Which of the following statements about the polynomial function
F(x) = 2x³ - 2x² +1 is true?
Answers
The given polynomial function has 1 relative minimum and 1 relative maximum.
What are the relative minimum and relative maximum?The relative minimum is the point on the graph where the y-coordinate has the minimum value.The relative maximum is the point on the graph where the y-coordinate has the maximum value.To determine the maximum and the minimum values of a function, the given function is derivated(since the maximum or minimum is obtained at slope = 0)Calculation:The given function is
f(x) = 2x³ - 2x² + 1
derivating the above function,
f'(x) = 6x² - 4x
At slope = 0, f'(x) = 0 (for maximum and minimum values)
⇒ 6x² - 4x = 0
⇒ 2x(3x - 2) = 0
2x = 0 or 3x - 2 = 0
∴ x = 0 or x = 2/3
Then the y-coordinates are calculated by substituting these x values in the given function,
when x = 0;
f(0) = 2(0)³ - 2(0)² + 1 = 1
So, the point is (0, 1)
when x = 2/3;
f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27
So, the point is (2/3, 19/27)
Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.
So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.
Thus, option A is correct.
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The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments: investigate further whether the proportions of furnished apartments differ be- tween apartments with different numbers of bedrooms, it is useful to test formally whether the number of bedrooms in an apartment and whether it is furnished or not are independent (a) State the null hypothesis the relevant form of the test statistic and the approximate distri- bution of the test statistic for carrying out this text (b) Provide cross-tabulation of the apartment data by these two factors (you should generate this table using R)
(c) Carry out a formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv. the resulting p-value for the test, or rejection region You should also ensure that you conclude your formal test by interpreting the p-value (or rejection region and your observed test statistic) in terms of the original question discussed above:'
Answers
The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000
formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv
500x + 900y + 1500z = 750,000 - - - (1)
x + y + z = 1000 - - - - (11)
x = 200 + y + z - - - - (111)
x + 2y + 3z = 1550 - - - (1V)
I bedroom = x
2 bedroom = y
3 bedroom = z
All the condition s gjvbbs'
500x + 900y + 1500z = 750,000 - - - (1)
x + y + z = 1000 - - - - (11)
x = 200 + y + z - - - - (111)
x + 2y + 3z = 1550 - - - (1V)
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I need help please. Does any one know how to do this
Answers
The probability that a randomly selected muffin will be a banana nut muffin is; P(banana nut muffin) = 0.5
What is the probability of selection?From the table in the question, we are given;
Number of blackberry muffins = 10
Number of banana nut muffins = 25
Number of Chocolate chip muffins = 1
Number of blueberry muffins = 11
Number of pumpkin spice muffins = 3
Total number of muffins = 10 + 25 + 1 + 11 + 3
= 50
Probability = number of successful outcomes/Total number of outcomes
Thus;
P(banana nut muffin) = 25/50
= 0.5
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A shopkeeper buys a quantity of oranges. On Thursday 2/7 were sold, on Friday 3/8 and on
Saturday 1/5. If 156 oranges remain unsold, how many were sold on Friday? *
Answers
There is a total of 420 Oranges were sold on Friday.
What is a fraction?
A fraction is a mathematical expression that represents a ratio of two numbers. It is written as a ratio of two integers, with the numerator (top number) representing the number of parts being considered and the denominator (bottom number) representing the total number of parts in the whole. The fraction can be written with a slash (/) or a horizontal line.
let the original number of orange be x
total orange sold = 2x/7 + 3x/8 + x/5 = 241x/280
Oranges left = x - 241x/280 = 39x/280
now, 39x/280 = 156
x = 1120 were there.
According to question
number of oranges sold on Friday = 3/8 * 1120
= 420 Oranges were sold on Friday.
Hence, there is a total of 420 Oranges were sold on Friday.
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A balloon attached to an atmospheric data-gathering device must be at least 1000 m high to begin recording information. Two spotters, Mary and Nathan, walk the same distance from the launch site at an angle of 70° to each other until they are 225 m apart. From these positions, they watch the rise of the balloon with instruments that record the angle of elevation. What angles of elevation must the instruments record in order for the balloon to be at the correct height for atmospheric data gathering?
Answers
The angle of elevation that the instruments have to record to be at the correct height is given as 79°
How to solve for the angle of elevationWe have 2x + 70 = 180
We have to find the value of x
2x = 110
x = 55
y/sin x = 225/sin70
This is the use of sine rule
From here we would have
y = 225(sinx/sin70)
Remember x = 55
y = 225(sin55/sin70)
y = 196.1378
tanθ = 1000/y
tan θ = 1000/196.1378
tanθ = 5.098
θ = tan⁻¹5.098
= 78.90°
Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.
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Please help
7. There are two towns, Appleville and Bananaville. Appleville had a population of 3,000
people in the year 2000. Bananaville had a population of 1,000 in the same year.
Appleville's population has increased by 500 each year since. Bananaville's population
increases by 30% each year.
a. Write an equation to represent the population of Appleville, a, in x years after the year
2000.
b. Write an equation to represent the population of Bananaville, b, in x years after the year
2000.
c. What year will the population of Bananaville be larger than the population of Appleville?
Answers
On solving the provided question, we can say that the solution of the System of Equation 3000 + 500x = 1000*
What is System of Equation ?A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
A system of equations consists of two or more equations and looks for common answers. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."
The point provides a singular solution to the system of equations if the two lines cross at the same location. There are an endless number of solutions in the situation when the two lines meet, and there is none in the case where the two lines are parallel.
The equation for Appleville is
3000 + 500x, in x years after the year 2000
The equation for Bananaville is
1000* , in x years after the year 2000
The solution of the equations
3000 + 500x = 1000*
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help me please please please
Answers
The area and circumference of a circle are 12.56square feet and 12.56ft respectively
Area and circumference of a circleThe formula for calculating the area and circumference of a circle is expressed as:
A = πr²
C = πd
where
r is the radius and d is the diameter
Area = 3.14 * (2)²
Area = 12.56ft²
For the circumference
C = 3.14(4)
C = 12.54ft
Hence the area and circumference of a circle are 12.56square feet and 12.56ft respectively
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Okay can someone explain this?
Answers
Answer:
see below
Step-by-step explanation:
90 degree clockwise will change x, y coordinates to y, -x
point D 1,3 becomes 3,-1
point E 4, 4 becomes 4,-4
point F 4, -2 becomes -2,-4
point G 1,-1 becomes -1, -1
This question has two parts. Use the information to answer Part A and Part B.
Part A
Enter a number in the box to create an expression equivalent to 2-5.
Part B
Which expressions represent the distance between the two points on the
number line? Select all that apply.
A 2-5
B. 2+(-5)
c. 1-3-21
D. 12-(-3)
E. 1-3+(-2)|
OF. 1-3-(-2)
Answers
Taking 1 in the box it creates an expression equivalent to 2 - 5.
The expressions represent the distance between the two points on the
number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.
What is integers on number line?
Integers are represented using a number line. A straight line of numbers is shown visually as a number line. It is made up of positive integers like 1, 2, etc., negative integers like - 1, - 2, etc., and a zero that is neither positive nor negative.
Part A:
2 - 5 = -3
2 + 1 = 3
The distance on the number line between a number and 0 is its absolute value.
a. That distance is never negative.
b. The symbol for Absolute Value is “ | | ”.
Hence, by taking 1 in the box it creates an expression equivalent to 2 - 5.
Part B:
|-3 -2| = 1
This point represent distance from -3 to -2 on the number line is 1 unit.
|2-(-3)| = 5
This point represent distance from 2 to -3 on the number line is 5 units.
|-3 + (-2)| = 5
This point represent distance from -3 to -2 on the number line is 5 units.
|-3 - (-2)| = 1
This point represent distance from -3 to -2 on the number line is 1 units.
Therefore,
Taking 1 in the box it creates an expression equivalent to 2 - 5.
The expressions represent the distance between the two points on the
number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.
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show the height of the pyramid is 9 cm
Answers
The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let us assume that the pyramid has a volume of 75 cm³ and square base area of 25 cm², hence:
Volume = (1/3) * area of base * height
75 = (1/3) * 25 * height
height = 9cm
The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm
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