The explicit formula of arthmetic sequence is [tex]a_{n}[/tex] = a + (n-1)d
Here is an explicit formula of the sequences 62, 59, 56, and 53...
[tex]a_{n}[/tex] = 62 + (n-1)(-3)
In the formula, n is any term number and [tex]a_{n}[/tex] is the nth term.
This formula allows us to simply plug on the number of the term we are interested in, and we will get the value of that term.
In order to find the fifth term, for example, we need to plug n = 6
[tex]a_{6}[/tex] = 62 + (6-1)(-3) = 62 + 5× -3
= 62- 15
= 47
In this way, we can find any term by using the explicit formula of an arithmetic sequence.
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Solve the inequality.
8 x+15>9 x-26
From the inequality given by 8x + 15 > 9x - 26, x is less than 41.
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
Solving the inequality,
8x + 15 > 9x - 26
Combine like terms in one side and the constants in the other side.
8x - 9x > -26 - 15
-x > -41
Divide both sides by -1.
x > 41
Note that when we multiply or divide by a negative number
we must reverse the inequality.
x < 41
Therefore, x is less than 41.
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The total payroll for a baseball team is 2.47 × 109 dollars, and the total payroll for a football team is 2.6 × 1011 dollars. How many more dollars is the football team's total payroll than the baseball team's total payroll?
A. 1.3 × 1011 dollars
B. 2.5753 × 1011 dollars
C. 2.5753 × 109 dollars
D. 0.13 × 109 dollars
Using scientific notation and subtraction between two amounts, the difference between the payrolls is given by:
B. 2.5753 x 10¹¹ dollars.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
How to find how much an amount a is more than an amount b?For any generic amounts a and b, to find how much an amount a is more than an amount b, we subtract a by b.
For this problem, the budgets are given as follows:
Football: 2.6 x 10¹¹Baseball: 2.47 x 10^9.Hence the difference is given by:
2.6 x 10¹¹ - 2.47 x 10^9
To subtract two numbers in scientific notation, they must have the same exponent, hence:
2.47 x 10^9 = 0.247 x 10^10 = 0.0247 x 10¹¹.
Then the difference is:
2.6 x 10¹¹ - 0.0247 x 10¹¹ = 2.5753 x 10¹¹ (to subtract two numbers in scientific notation, we subtract the bases and keep the exponents).
The difference between the payrolls is given by:
B. 2.5753 x 10¹¹ dollars.
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Which of the following statements are true?
I. -(-6)=6 and -(-4)>-4 II. 5+6=11 or 9-2=11 III. -(-4)<4 or -10>10-10 IV. 17>2 or 6<9
a. I and II only b. I, II, and III only c. I, III, and IV only d. III and IV only
I and IV only are statements that are true out of all the statements.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
I. -(-6)=6 and -(-4)>-4
⇒ 6 = 6 and 4 > -4
IV. 17>2 or 6<9
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An accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes. Which of the following equations can be used to describe this problem?
The equation when the accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes is 120 + 40h.
How to calculate the valueFrom the information, it should be noted that the
accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes.
Let the number of hours be represented by h.
Therefore, the expression to describe the problem will be:
= 120 + (40 × h)
= 120 + 40h
The equation is 120 + 40h.
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Square, cubes, roots
a. The square roots and square cancel each other so 5 × 3 = 15
b. The cube roots and cubes cancel each other so 9 × 30 = 270
What are square and cube roots?For math students, especially those in class 8, the square root and cube root concepts are the most crucial. In order to get the square root of any integer, we must first identify a number that, when multiplied twice by itself, equals the original number.
Similar to this, we must locate a number that, when multiplied three times by itself, equals the original number in order to get the cube root of any number.
The cube root is represented by the sign "√," whereas the square root is represented by the symbol "∛."
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4= 3/2+c pleaseeeeee
20
f(x) = 4(x + 1)
(a) Write down the value of x when f¯¹(x) = 2.
(c) Find g(x).
(b) Find fg(x). Give your answer in its simplest form.
g(x)
2
Answer(a) x =
- 1
Answer(b) fg(x)=
[1]
[2]
Answer:
The value of x is 12 if the value of f^-1(x) = 2.
Step-by-step explanation:
It is given that f(x) = 4(x + 1), which is an inverse function.
Now,
First of all, let us understand what is a function and an inverse function;
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
On the other hand;
A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1." Here, (-1) should not be confused with an exponent or a reciprocal.
Now, let us consider the first part of the question;
We have to calculate the value of x when f^-1(x) = 2 given that f(x) = 4(x+1) is the function;
=> f(x) = 4(x + 1)
=> 4(y + 1) = x
=> x = 4y + 4
=> y = (x - 4)/4
=> f^-1(x) = (x - 4)/4
Hence, f^-1(x) = (x - 4)/4 is the inverse of f(x).
Now, let us put the value of f^-1(x) = 2 in the equation so obtained;
=> f^-1(x) = (x - 4)/4
=> 2 = (x - 4)/4
=> 8 = (x - 4)
=> x = 12
Hence, the value of x is 12 if the value of f^-1(x) = 2.
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What is the slope of the line that contains these points? x = 13, 14, 15, 16 y=11, 6, 1, -4
These sites are on a line with a -5 degree slope.
What is a line's slope?The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the y-intercept for the equation y = 3x - 7 is (0, 7) and the slope is 3.
In response to the query, I see the points as
(x ,y)
(13, 11)
(14, 6)
(15, 1)
(16, -4)
(13, 11) , (14, 6), (15, 1), and (16, -4)
slope = (6 - 11) / (14 - 13)
= - 5/-1
= -5
try again: (1 - 6)/(15 -14)
= -5/1
= -5
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What are the center and radius of the circle with the given equation?
a. (x+8)²+(y+3)²=121
The equation of the circle (x + 8)^2 + (y + 3)^2 = 121 has a radius of 11 and a center located at (-8 , -3).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in standard form is (x + 8)^2 + (y + 3)^2 = 121, then
h = -8
k = -3
r = √121
r = 11
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Simplify. 3/10 . 2/9
Answer:1/15
Step-by-step explanation:
Assuming it is multiplication, multiply the numerators: 3 * 2 = 6
Multiply the denominators: 10 * 9 = 90
Put them together for 6/90 and simplify for 1/15
Cual es el 35% de 900
The percentage is the hundredth of any digit or value between 1 to 100 so 35% of 900 will be 315.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The x percentage of any random y digit is given as;
⇒ (x/100) × y
Therefore,
35% of 900 →
(35/100) × 900
⇒ 35 × (900/100)
⇒ 35 × 9
⇒ 315
Hence " The 35% percentage of the amount 900 will be 315".
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The given question is not in English, English translation follows;
What is 35% of 900?
find the equation of the line shown
John walks away from his house down a straight street. The graph shows John's distance from his house over time. Describe his trip. Find John's speed on each section of the walk.
(lol please help, I don't know how to format this-)
Answer:
First Section:4km per hour
Second Section:0km per hour
Third Section:1.5km per hour
Step-by-step explanation:
From the first section to the second section the distance remains the same therefore he didn't travel at all that's why it is 0km. For the third section he has to travel 6 kilometers in 4 hours which is 1.5.
Only answer if u are sure and make a good explanation
Answer: the third option
Step-by-step explanation: 0.66666666666 is it in decimal form, the line above the single six just means its the same number over and over again
Answer:
.67 (See explanation for why)
Step-by-step explanation:
2/3
in order to turn this into a whole number, we are going to multiply the bottom number until it becomes any number starting with 1 and ending with a zero. this isnt possible Because 3 is a number that cannot do that.
So instead, we will multiply the number by 333
2*333 = 666
3*333 = 999
666/999 = 2/3
999 is nearly 1000, so lets write the decimal point 3 spaces inwards
.666
which can become
.66
The longer decimal for this(when using a calculator)
would give you
.6666666667
And if we round,
7 is higher than 5, so it becomes .666666667
continue...
Until you have .67
Hope this helps! ^^
HELP ASAP WILL MARK BRAINLIEST IF RIGHT
Nina graphs the function y=⌊x⌋ to learn the properties of the parent floor function.
What is the value of y when x=5.7?
5
5.50
5.75
6
Answer:
the answer should be 5 sorry if wrong
Answer:
5
Step-by-step explanation:
y=xx5
Can anyone help me with this problem I'll give 100 points and 5 star if you get it correct.
Answer:
F
Step-by-step explanation:
Wrong answers
A. current price not doubled
B. price before is 150%, not current price
C. price is reduced by 33.3%, not 25%
D. price is 66.6% of price before
E. price before is 1.5 times greater, not current price
G. price is now 66.6% of price before
H price is 66.6%, not 75%
The population of the United States in July of 2007 was estimated to have surpassed 301,000,000 . At the same time the world population was estimated to be over 6,602,000,000 . What percent of the world population, to the nearest tenth, lived in the United States at this time?
F. 3.1%
G. 3.5 %
H. 4.2 %
J. 4.6 %
4.6 percent of the world population, to the nearest tenth, lived in the United States at this time.
What are examples of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.[tex]\frac{United States population}{world population} = \frac{301,000,000}{6,602,000,000}[/tex] × 100
≈ 4.6
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The length of a rectangle is 4 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the dimensions of the rectangle.
The dimensions are 3 inches, 10 inches, and 13 inches.
How to compute the value?It should be noted that the diagonal is the longest side. This will be solved by using Pythagoras theorem.
Therefore,
(2x + 6)²
4x²+ 24x + 36
Reduce to lowest term
x² + 6x + 9
x² + 3x + 3x + 9
x(x + 3) - 3(x + 3)
(x - 3) = 0
x = 0 + 3 = 3
Therefore x = 3
Therefore the dimensions will be:
x = 3
2x + 4 = 2(3) + 4 = 10
2x + 6 = 2(3) + 6 = 12
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Write it in interval notation
x ≤ 3 and x ≠ -1 or 4 ≤ x
The interval notation that expresses the expression is (-∝, 3] ∩ (-∝, -1) ∩ (-1, ∝) ∪ [4, ∝)
How to use interval notation to represent the expressions?The expression is given as:
x ≤ 3 and x ≠ -1 or 4 ≤ x
In inequality, "and" is represented with ∩, while "or" is represented with ∪
The above can be represented as:
x ≤ 3 ∩ x ≠ -1 ∪ 4 ≤ x
As an interval notation, we have (-∝, 3] ∩ (-∝, -1) ∩ (-1, ∝) ∪ [4, ∝)
Hence, the interval notation that expresses the expression is (-∝, 3] ∩ (-∝, -1) ∩ (-1, ∝) ∪ [4, ∝)
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A card is drawn randomly out of 12 cards which are numbered from 1 to 12. What is the
probability that the card drawn has a composite number written on it ?
a) 2 / 3
b) 7 / 12
c) 1 / 3
d) 1 / 2
The probability that the card drawn has a composite number written on it is 1/2
What is the probability that the card drawn has a composite number written on it?The sample space is given as
S = {1, 2....3}
The list of composite numbers from 1 to 12 is 4, 6, 8, 9, 10, 12
So, we have
Composite = 6
The probability that the card drawn has a composite number written on it is
P = Composite/Sample size
So, we have
P = 6/12
Simplify
P = 1/2
Hence, the probability that the card drawn has a composite number written on it is 1/2
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Use the Distance Formula to find the distance between the pair of points.
C(11,-12), D(6,2)
Using the distance formula, the distance between the pair of points C(11,-12) and D(6,2) is 14.86 units
Given,
The points = C(11,-12) and D(6,2)
We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Substitute the values in the equation
The distance = [tex]\sqrt{(6-11)^{2}+(2--12)^{2} }[/tex]
[tex]=\sqrt{(-5)^{2}+14^{2} } \\=\sqrt{25+196}\\ =\sqrt{221}[/tex]
=14.86 units
Hence, Using the distance formula, the distance between the pair of points C(11,-12) and D(6,2) is 14.86 units
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simplify 8(x+5)-4(x+4)
2x and 72
Step-by-step explanation:
pls don't use this I don't want you to get a bad grade if it is wrong
Answer: 4x+24
Step-by-step explanation: 8x+40-4x-16
Two spheres have volumes of 36π cubic centimeters and 288π cubic centimeters. What is the ratio of the radius of the small sphere to the radius of the large sphere?
The ratio of the radius of the small sphere with a volume of 36π cubic centimeters to the radius of the large sphere having a volume of 288π cubic centimeters is 1/2.
Given two spheres having volumes of 36π cubic centimeters and 288π cubic centimeters, solve for the radius of each sphere using the formula for the volume of sphere given by:
V = 4/3πr^3
smaller sphere :
36π cubic centimeters = 4/3πr^3
r^3 = 27
r = 3 centimeters
larger sphere :
288π cubic centimeters = 4/3πr^3
r^3 = 216
r = 6 centimeters
Getting the ratio of the radius of the small sphere to the radius of the large sphere:
ratio = radius of the small sphere / radius of the large sphere
ratio = 3 centimeters / 6 centimeters
ratio = 1/2
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Write an equation in point-slope form of the line having the given slope that contains the given point.
m=2,(4,-9)
The equation in point-slope form of the line having the given slope m = 2 that contains the given point (4, -9) is 2x - y = 17
It is given that,
Slope is the measure of the steepness of a line.
Equation is the mathematical statement made up of two expressions joined together by the equal sign. For instance 3x - 5 = 16
The slope of a one point line = m = 2
The point through which the line passes = (4, -9)
We need to find the,
The equation in point-slope form of the line having the given slope that contains the given point
The formula which will be used,
(y-y1) = m(x-x1)
where, (x1,y1) = (4, -9) and m = 2
putting the values in the formula, we get
[y - (-9)] = 2. (x-4)
y + 9 = 2x - 8
y - 2x = -17
2x - y = 17
Hence, the equation in point-slope form of the line having the given slope that contains the given point is 2x - y = 17
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select the correct choice below and feeling any answer boxes within your choice
Answer:
the answer is great Britain because
Step-by-step explanation:
it is very good for this subject
Write an explicit formula for each geometric sequence. 1,2,4,8, . . .
The explicit formula for a geometric sequence is [tex]a_{n}[/tex] =[tex]a_{1}^{r-1}[/tex]
The sequence is:
1, 2, 4, 8..........
The formula for a geometric sequence,
[tex]a_{n}[/tex] = [tex]a_{1}^{r - 1} }[/tex]
a, ar, [tex]ar^{2}[/tex], [tex]ar^{3}[/tex]
r = common ratio
n = number of sequences in a series.
Let us understand by the sequence,
Here r = 2 , a = 1
Therefore by putting these values in the equation we get,
[tex]a_{n}[/tex] = [tex]a_{1}r^{n-1} }[/tex]
= a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex], ........
1, 2, 4, 8 .........
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Multiply. Write your answer in scientific notation.
(1×103)(8×10-7)
I am so close to getting it but i am second guessing my answer
Answer:
7.519*10 power 3 is the answer.
Find the magnitude and direction of vector. →RS: R(1,0) and S(-2,3)
The magnitude of vector →RS is 3√2
And the direction of vector →RS is given by an angle 315°
Let R(1,0) = (x1, y1) and
S(-2,3) = (x2, y2)
By distance formula, the magnitude of vector is
[tex]|\vec {RS}| = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|\vec {RS}| =\sqrt{(-2-1)^2+(3-0)^2} \\\\|\vec {RS}| =\sqrt{(-3)^2+3^2} \\\\|\vec {RS}| =\sqrt{9+9}\\\\ |\vec {RS}| =3\sqrt{2}[/tex]
To find the direction of the vector RS :
[tex]tan(\theta)=\frac{y_2-y_1}{x_2-x_1} \\\\tan(\theta)=\frac{3-0}{-2-1}\\\\tan(\theta)=\frac{3}{-3}\\\\ tan(\theta)=-1\\\\ \theta=tan^{-1}(-1)\\\\\theta=45^{\circ}[/tex]
However, the angle is in the fourth quadrant, so we add 360° to obtain a positive angle.
Thus, −45° + 360° = 315° .
Therefore, the magnitude of vector →RS is 3√2
And the direction of vector →RS is given by an angle 315°
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What is his speed between 12 and 20 seconds of his journey?
Answer:
= 0.25m/s
Step-by-step explanation:
The formula of finding the speed, v is given by
[tex]v \: = \frac{change \: in \: distance \: d}{change \: in \: time \: t} [/tex]
The change in distance from the graph is
∆d = (8 - 6)
= 2 m
The change in time from the graph is
∆d = (20 - 12)
= 8s
Substituting to our formula, we have
[tex]v \: = \frac{2m}{8s} \\ = \frac{1}{4} \frac{m}{s} \\ = 0.25 {m}s^{ -1 } [/tex]
Therefore, the speed v, of the journey between 12 and 20 second is 0.25m/s.
PROOF Write the specified type of proof. flow proof
Given: ∠3 ≅ ∠5
Prove: m ∠1+m ∠2=m∠6+m∠ 7
According to the given data the m ∠1+m ∠2=m∠6+m∠ 7 proofed by symmetric property:
What is the significance of symmetric property ?The symmetric property of equality is significant in mathematics because that tells us that both sides of either an equal sign are equal regardless of which side of the section they are on.
Who invented the symmetry property?But it wasn't until the nineteenth century that mathematicians like Evariste Galois, an unhappy French genius, uncovered symmetries hidden in mathematical equation solutions.
According to the given data:Given: ∠3 ≅ ∠5
Prove: m ∠1+m ∠2=m∠6+m∠ 7
Now ,
m ∠1+m ∠2=m∠6+m∠ 7..........(1)
m∠6+m∠ 7 = ∠3 + m∠4..............(2)
m ∠1+m ∠2 = ∠3 + m∠4
(subtracting)
m∠4 +m∠3 = m ∠3 + m∠4
symmetric property:
m ∠1+m ∠2=m∠6+m∠ 7
According to the given data the m ∠1+m ∠2=m∠6+m∠ 7 proofed by symmetric property:
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