The product of 4.5 x 1012 and 5.12 x 109 written in scientific notation is 23.04 x 110308
It is given that,
Two numbers are 4.5 x 1012 and 5.12 x 109
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 X 10^8 in scientific notation.
We need to find the product of both numbers and then find the final answer in scientific notation form
(4.5 x 1012) x ( 5.12 x 109 )
(4.5 x 5.12) x ( 1012 x 109)
23.04 x 110308
Hence, the product of 4.5 x 1012 and 5.12 x 109 written in scientific notation is 23.04 x 110308
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In Problem 17, verify that the functions fand g are inverses of
each other by showing that (f o g) (x) = x and (g o f) (x) = x.
Problem 17:
f(x) = 1/x g(x) = 1/x
Answer:
you are very very very correct
The number line shows the distance in meters of two birds, A and B, from a worm located at point X:
Part A: Expression for the distance in meters between given two birds using subtraction = 2.5 - (-2.5)
Part B: The distance between two birds using additive inverse 2.5- (-2.5) =5 meters
What is an expression and additive inverse?An expression is an combination of numbers and mathematical operations such as addition, subtraction, division and multiplication with equating any two terms.
Additive inverse : Additive inverse of an number a is the number that when adds to a gives zero .
Let b be additive inverse of a, then a + b =0
Then, b = -a
Given two birds A and B are at points x= -2.5 and y = 2.5 respectively
Therefore, the expression for the distance in between given two birds
= y - x = 2.5- (-2.5)
We an clearly see that -2.5 is additive inverse of 2.5
Distance between the two birds = 2.5 -(-2.5) =2.5 +2.5 = 5 meters
Therefore, the expression for distance between the two birds A and B is 2.5-(-2.5) and the distance is 5 meters.
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A trapezoid has sides of length 19.5 centimeters, 16.9 centimeters, 19.5 centimeters, and 18
centimeters. What is the perimeter?
centimeters
the answer is correct because you gave text evidence
Evaluate the expression 2x² - 4 when x = -3.
Answer: 32
Step-by-step explanation: 2(-3)2. -4
A car tire has a radius of 1.5 feet. if the tire is rotating at 800 rpm, what is the speed of the car in miles per hour (1 mile = 5,280 feet)? round the answer to the nearest tenth. the car is traveling approximately miles per hour.
Answer:85.7 miles per hour
Step-by-step explanation:
In advertising, the decay factor describes how an advertisement loses its effectiveness over time. In math, would you expect a decay factor to increase or decrease the value of y as x increases?
When the value of x will increase then decay factor will decrease the value of y.
Given that the decay factor describes how an advertisement loses its effectiveness over time.
Exponential decay will tell us the process of reducing an amount by a consistent percentage of rate over a particular period of time. Exponential decay is the reciprocal of exponential growth when a quantity decreases by the same factor in equal intervals of time, the constant coefficient of the exponential decay function is less than 1. This can be expressed as (1 - r) and is called the decay factor.
According to the definition of the decay factor, its say that when the value of x increases then the decay factor of the value of y will decrease.
Hence, the value of x will increase then decay factor will decrease the value of y.
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Rate my art HONESTLY
It’s Queen Elizabeth II pointillism
Any tips on how to fix her neck are appreciated
I would say avoid adding any more detail to the eyes and facial features. normally pointillism uses alot more dots and makes them most concentrated in darker areas. i would recommend trying to add shadows to most of it or adding more detail to the hat. Ii think her neck looks ok but there isn't really a way to get rid of the diagonal that you made.
Answer:
I think its great! I think add more hair to the side of head there. other than that it resembles her quite nicely!
Step-by-step explanation:
Vertical 1.
3+ 12, an incomplete mathematical sentence.
Addition 3+ 12, an incomplete mathematical sentence. 1.3+ 12=13.3
Addition is a mathematical procedure that is used to add numbers. The sum of the given numbers is the result of adding the given numbers. For instance, if we add 2 and 3, (2 + 3), the result is 5. We used the addition function on two numbers, 2 and 3, to produce the sum, 5
Symbol for Addition
Different symbols are used in mathematics. One of the most used arithmetic symbols is the addition symbol. We read about adding two numbers, 2 and 3, in the definition of addition above. If we look at the addition pattern (2 + 3 = 5), the symbol (+) joins and completes the two integers.
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Evaluate the expression A=3, b=1/2.and c=4
8ab/2bc
Answer: 3
Step-by-step explanation:
First substitute values in :
8(3)(1/2)/ 2(1/2)(4)
Then simplify :
12/ 4
3
Find the coordinates of the point where y - 4x = 1 crosses the y-axis
Step-by-step explanation:
to cross the y-axis x must be 0.
so,
y - 4×0 = 1
y = 1.
so, the point is
(0, 1)
Elena’s father put $460 into a savings account for her. The account pays 2.5% simple interest each year. If he neither adds nor withdraws money from the account, how much interest will the account earn after 4 years? Round to the nearest cent.
Answer:
$46
Step-by-step explanation:
So, the principal amount, P = $460
Yearly simple interest, R = 2.5% which equals 0.025
Time(T) which is 4 years.
The interest(I) for the amount, P at the rate of R yearly, after T years,
Elena's account will earn $46.
I need help. 2(x + 6) = 2x + 12
please help!! 10 points+ brainlist!!
Answer:
Mean - 67 inches
Median - 67 inches
Mode - 68 inches
Step-by-step explanation:
Definitions of the words:
Mean - The average number of the data set.
Median - The middle number in the data set when ordered from least to greatest.
Mode - The value that appears most frequently.
Mean:
We can add them up and divide by the number of values in the set, 7.
469 / 7 = 67
Median:
We can order them from least to greatest and see which one is the 4th one.
60, 62, 66, 67, 68, 68, 78.
67 is in the middle, so that is our median.
Mode:
Only 68 is repeated twice in the set, so 68 is the mode.
Hope this helped! Have a great day!
Select the locations on the number line to plot the points −2 , −11 , and −17 .
Number Line :
In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length. A number line can be extended infinitely in any direction and is usually represented horizontally.
or
A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.
On a number line, a number on the left is always less than a number on the right. Similarly, a number on the right is always greater than a number on the left.
The Number Line app helps students visualize number sequences and illustrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing. Choose number lines labeled with whole numbers, fractions, decimals, or negative numbers. Or use a custom number line, with or without tick marks, and set your own interval.
Show intervals between points on the line using forward or backward jumps above and below the line. Jumps can also be labeled with their values or left blank. Add custom tick marks to the number line to show equivalence or compare number values.
Basic Number Line Skills:
1. Find the dot marked on a number (and name the dot)
2. Place a dot at the desired location
3. Find the desired number below the number line’s tick mark*
-17 -11 -2 0
-----|-----------------|----------|----------------|-----------------------------------------------Number line
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The table shows the total distance that Myra runs over different time periods.
A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0.0, 0.4, 0.8, 1.2, 1.6.
Which describes Myra’s distance as time increases?
increasing
decreasing
zero
constant
The option that describes Myra’s distance as time increases is increasing.
What is the change in Myra's distance?
Looking at the table provided, it can be seen that as time passes, the distance ran by Myra increases. It can be seen that distance increases from 0.4miles to 0.8 miles when time increases from 2 seconds to 4 seconds.
Change in distance run per time = change in distance / change in time
(0.4 - 0) / (2 - 0)
0.4 / 2 = 0.2
Myra's distance increases by 0.2 per second. This means that Myra is running at a constant speed. Thus, the rate of the increase in the distance run by Myra is a constant 0.2 per second.
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Answer:
the answer is increasing
Please help. Can you also please put the explanation?
Answer: she spent 40 minutes answering the phone calls
Step-by-step explanation:
Its 40 minutes because she spends 20 minutes delivering flowers and she worked at the hospital for 60 minutes that day. So, if you take away the 20 minutes for the 60 minutes, she spent she will only have 40 minutes left to answer calls.
There are 100 people on the swim team.today, they are going to a big swim meet on the other side of town. if each minivan can take 15 people how much minivans will they need.
Using the mathematical operation such as division, the swim team, which has 100 people on it, needs 7 minivans to take them on the other side of town.
If there are 100 people on the swim team that will be divided into minivans that can only occupied by 15 people, divide 100 by 15 to know how many vans they will need.
100 people ÷ 15 people/minivan
100 ÷ 15 = 6 r 10
This means that the swim team will need 6 minivans and still, 10 people don't belong to any minivan yet. So, 1 additional minivan will be needed for the remainder of 10 people.
Hence, the swim team will be needing 7 minivans to cater 100 people on their team.
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Put the correct number in each box
1/7=4/? = ?/56
y varies directly with x .
If x=2 when y=4 , find y when x=5 .
After direct variation y =10 when x = 5.
What specifically do we mean by "direct variation"?Direct variation equations use the same phrase to give the reader a hint.The phrase is either "directly proportional" or "directly varies."The area of a square, for instance, is proportional to the square of its side.If y varies directly as x and y = 6 when x = 2, the variational constant is k = 3.As a result, the direct variation equation is y = 3x.So,
The initial statement is y = kx
Then to find y when x = 5.
K constant will be y/x ⇒ 4/2That is y = kx ⇒ y = 4/2 × xWhen x = 5:
y = 4/2 × 5 ⇒ y = 10Therefore, after direct variation y =10 when x = 5.
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Does the table represent an exponential function
x1234
y 39 27 81
Ono
Oyes
Answer:
No.
Step-by-step explanation:
If lindley requests an extension to file her individual tax return in a timely manner, the latest she could pay her tax due without penalty is::_________
If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
What is an individual tax return?A person or married couple must submit an official form known as an individual tax return to a federal, state, or local taxing authority in order to record any taxable income they received within a certain time period, typically the previous year.
This document is used to determine how much tax was paid in excess of what was required during that time period.
In this case, if Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
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If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is:
April 15th.
October 15th.
August 15th.
November 15th.
None of the choices are correct.
Need help ez question
Answer:
x = 0.25
Step-by-step explanation:
[tex]9\sqrt{x} =5-2x[/tex]
[tex]81x = 25 - 20x + 4x^{2}[/tex]
[tex]0=4x^{2} -101x+25[/tex]
[tex]0 = 4x^{2} -1x-100x+25[/tex]
[tex]0=x(4x-1)-25(4x-1)\\0=(x-25)(4x-1)[/tex]
[tex]x=25,\frac{1}{4}[/tex]
[tex]2*25+9\sqrt{25} =5\\50+9*5=5\\50+45=5\\95=5[/tex]
[tex]2*\frac{1}{4}+9\sqrt{\frac{1}{4} } =5 \\0.5+9*\frac{1}{2} =5\\0.5+4.5=5\\5=5[/tex]
Answer:
[tex]x=\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given equation:
[tex]2x+9\sqrt{x}=5[/tex]
Subtract 2x from both sides to isolate the square root:
[tex]\implies 2x+9\sqrt{x}-2x=5-2x[/tex]
[tex]\implies 9\sqrt{x}=5-2x[/tex]
Square both sides to eliminate the square root:
[tex]\implies (9\sqrt{x})^2=(5-2x)^2[/tex]
[tex]\implies 81x=(5-2x)(5-2x)[/tex]
[tex]\implies 81x=25-20x+4x^2[/tex]
Subtract 81x from both sides:
[tex]\implies 81x-81x=25-20x+4x^2-81x[/tex]
[tex]\implies 0=25-101x+4x^2[/tex]
[tex]\implies4x^2-101x+25=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]\implies ac=4 \cdot 25=100[/tex]
[tex]\implies b=-101[/tex]
Therefore, the two numbers are -1 and -100 as:
[tex]\implies -1 \cdot -100=100=a[/tex]
[tex]\implies -1+(-100)=-101 =b[/tex]
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies4x^2-x-100x+25=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(4x-1)-25(4x-1)=0[/tex]
Factor out the common term (4x - 1):
[tex]\implies (x-25)(4x-1)=0[/tex]
Apply the zero-product property:
[tex](x-25)=0 \implies x=25[/tex]
[tex](4x-1)=0 \implies x=\dfrac{1}{4}[/tex]
Input each solution into the original equation to check its validity:
[tex]\begin{aligned}x=25 \implies 2(25)+9\sqrt{25}&=5\\50+9(5)&=5\\50+45&=5\\95 & \neq 5\end{aligned}[/tex]
Therefore, x = 25 is not a valid solution.
[tex]\begin{aligned}x=\dfrac{1}{4}\implies 2\left(\dfrac{1}{4}\right)+9\sqrt{\dfrac{1}{4}}&=5\\\dfrac{1}{2}+9(\dfrac{1}{2})&=5\\\dfrac{1}{2}+\dfrac{9}{2}&=5\\\dfrac{10}{2}&=5\\5 & = 5\end{aligned}[/tex]
Therefore x = ¹/₄ is a valid solution.
Therefore, the only valid solution to the equation is x = ¹/₄.
Expand each logarithm.
log₈8 √3a⁵
The expansion of the expression log₈8 √3a⁵ is
1+ log 3/2log 8 +5 log a/ log 8.
Given that the expression is log₈8 √3a⁵.
We are required to expand the expression.
The change of base formula is used to write a logarithm operation again as a fraction of logarithms with a new base.
The expression is log₈8 √3a⁵.
log₈8 √3a⁵= (log 8 +log [tex]\sqrt{3}[/tex] +log [tex]a^{5}[/tex])/log 8
=1+ log 3/2log 8 +5 log a/ log 8 (We know that log [tex]m^{n}[/tex]=n log m)
Hence the expansion of the expression log₈8 √3a⁵ is
1+ log 3/2log 8 +5 log a/ log 8.
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What is the factored form of 2 x³+5 x²-12 x ?
(F) x(2 x-3)(x+4) (H) x(2 x+4)(x-3) (G) (2 x²-3)(x+4) (I) (2 x-4)(x+3)
After solving, the factors of equation 2x³+5x²-12x are:
(F) x(2x-3)(x+4)What basically is an equation?An equation is a mathematical statement composed of two representations joined by an equal sign.An example of an equation is 3x - 5 = 16. After attempting to solve this equation, we get the value for the variable x as x = 7.So,
Given the equation: 2x³+5x²-12x
Then,
2x³+5x²-12xx[2x²+5x-12]x[2x²+x( - )-12]x[2x²+x(8-3)-12]x[2x²+8x-3x-12]x[2x(x+4)-3(x+4)]Factors are: x(2x-3)(x+4)
Therefore, after solving, the factors of equation 2x³+5x²-12x are:
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The scale of a map is 2.6 ft = 89
miles
Map: 5.6 ft
Actual:
miles
Actual miles is [tex]\frac{2492}{13}[/tex]
According to the question,
Given that,
Map is 5.6 ft
scale of Map is 2.6 ft which is equal to 89 miles
Actual miles = [tex]\frac{5.6 * 89}{2.6}[/tex]
= [tex]\frac{498.4}{2.6}[/tex]
multiply both the numerator and denominator with the same integer
= [tex]\frac{4984}{26}[/tex]
= [tex]\frac{2492}{13}[/tex]
Actual miles is [tex]191\frac{9}{13}[/tex] ≈ 1.916923 ×[tex]10^{2}[/tex]
Definition of miles per hour unit: ≡ 1 mi / 3600 s = 1609.344 m / 3600 s. In American public life, this is the most commonly used speed unit. Cars speeds are measured in mpg. Interpretation: The speed at which the body moves 1 mile (or 1609.344 metres) in 1 hour.
Definition of feet per second unit: ≡ 1 ft / 1 s = 30.48 cm / 1 s. Abbreviation is fps. In America, perhaps this is the second most commonly used speed unit in public life (after miles per hour). Definition: The speed at which the body moves 1 foot (or 30.48 centimetres) in 1 second.
Convert Miles to Feet
Multiply your speed in miles per hour by 5,280. This is the number of feet in a mile. The result is your speed in feet per hour. For example, 60 miles per hour times 5,280 feet per mile is 316,800 feet per hour.
Convert to Feet per Minute
Divide your speed in feet per hour by 60. This is the number of minutes in an hour. Therefore, the result is your speed in feet per minute. For example, 316,800 feet per hour divided by 60 minutes per hour is 5,280 feet per minute.
Convert to Feet per Second
Divide your speed in feet per minute by 60. This is the number of seconds in a minute. Therefore, the result is your speed in feet per second. For example, 5,280 feet per minute divided by 60 seconds in a minute equals 88 feet per second.
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Factor each expression.
9 x²-25
After factorization of the expression 9x²-25, the answer comes to:
(3x - 5)²What do we mean by an expression?An expression or mathematical expression is a finite mixture of symbols that is well-formed according to context-dependent rules. To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.Many authors differentiate between an expression and a formula, with the former referring to a mathematical object and the latter referring to a statement about mathematical objects.So,
The given expression is: 9x²-25
Then,
9x²-253²x²-5²(3x)²-(5)²(3x - 5)²Therefore, after factorization of the expression 9x²-25, the answer comes to:
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What is the equation of a line that passes through the point (2,−2) and is perpendicular to y=x4−3 ?
The equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2
How to find the equation of the perpendicular line?The equation of the line is given as
y = 4x - 3
Rewrite the equation as
y = 4x - 3
A linear equation is represented as
y = mx + c
Where
Slope = m
So, we have
m = 4
The slopes of perpendicular lines are opposite reciprocals
This means that
m2 = -1/m1
So, we have
m = -1/4
Evaluate
m = -1/4
The equation of the perpendicular line is then calculated as
y = m(x - x1) + y1
Where
(x1, y1) = (2, -2)
This gives
y = -1/4(x - 2) - 2
Evaluate
y = -1/3x + 1/2 - 2
Evaluate the sum and the difference
y = -1/3x - 3/2
So, the equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2
Hence, the required equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2
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Find the solution(s) to the system of equations. Select all that apply. y=x²-5 y=x-3
Answer:
x = 2, y = -1
x = -1, y = -4
Step-by-step explanation:
Both equations are equal to y, so just set x - 3 = x^2 - 5 and solve.
This diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other. A rhombus is a quadrilateral with 4 congruent sides
Answer:
Step-by-step explanation:
Answer:
This diagram is a straight edge and compass construction . A is the centerof one circle , and B is the centre of the other . A rhombus is a quadrilateral with 4 congruent sides
Step-by-step explanation:
To rationalize the denominator of 4√4/25, by what number would you multiply the numerator and denominator of the fraction?
Rationalization is multiplying a surd by another similar surd to obtain a rational number. In mathematics, a surd is an expression involving a square, cube, or another kind of root symbol. The surd used for multiplication is called the rationalization factor (RF). Rationalize the denominator to make it easier to perform calculations with rational numbers. Rationalizing a denominator with a fraction removes all root terms, such as square roots and cube roots, from the denominator.
[tex]\frac{4}{\sqrt{\frac{4}{25}}}[/tex]
[tex]\begin{aligned}&\frac{4}{\frac{\sqrt{4}}{\sqrt{25}}}\\&\frac{\frac{4}{\sqrt{2^2}}}{\sqrt{5^2}}\end{aligned}[/tex]
[tex]\frac{4}{\frac{\sqrt{2^2}}{\sqrt{5^2}}}[/tex]
[tex]\frac{4}{\frac{2}{5}}[/tex]
[tex]\begin{aligned}&4 \div \frac{2}{5} \\&4\left(\frac{5}{2}\right) \\&\frac{4 \cdot 5}{2} \\&2 \cdot 5\end{aligned}[/tex]
[tex]10[/tex]
And if the question is like this,
[tex]$\frac{4 \cdot \sqrt{4}}{25}$$\frac{4 \cdot \sqrt{2^2}}{25}$$\frac{8}{25}$[/tex]
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