The product in scientific notation of (4.12 × 10^−9)(8.3 × 10^15) is 3.4196 * 10^7
How to evaluate the product in scientific notation?The product expression is given as
(4.12 × 10^−9)(8.3 × 10^15)
Rewrite properly as
(4.12 × 10^−9)(8.3 × 10^15) = (4.12 × 10^−9) * (8.3 × 10^15)
Evaluate the product of 4.12 and 8.3 in the above expression
So, we have
(4.12 × 10^−9)(8.3 × 10^15) = 34.196 * 10^−9 × 10^15
Evaluate the product of 10^−9 and 10^15 in the above expression
So, we have
(4.12 × 10^−9)(8.3 × 10^15) = 34.196 * 10^6
Rewrite the expression as
(4.12 × 10^−9)(8.3 × 10^15) = 3.4196 * 10^7
Hence, the product in scientific notation of (4.12 × 10^−9)(8.3 × 10^15) is 3.4196 * 10^7
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Answer:
Its B. 3.4196 x 10^7
Step-by-step explanation:
This is correct answer :))
Evaluate each expression for x=0 . 13-6.5 x
After evaluating the expression for x=0, the equation 13-6.5x = 13
⇒ 13-6.5(0)
⇒ 13 - 0
⇒ 13
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.
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The current value of a baseball card is 80 times its original value v (in dollars). The baseball card is worth $36. Write and solve an equation to find the original value of the baseball card.
The original value of the baseball in discuss according to the task content is; $0.45.
What is the original value of the baseball card?It follows from the word phrase given that; the current value of a baseball card is 80 times its original value v (in dollars) where the current value is; $36.
Therefore, we have; 36 = 80 × v
Divide both sides by 80;
Hence; v = 36/80 = $0.45.
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y varies directly with x .If y= -5/8 when x= 3/2 , find x when y=(2/5)
The required value of the constant of proportion and x is (-12 / 5) and (⅙) respectively.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of constant of variation and x
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Now, find k for, given x = 3 / 2 and y = -5 / 8, we need to put these values in equation 1, i.e.
-5 / 8 = k(3 / 2)
k = -12 / 5
Further, calculate x for given y = (⅖) and constant of proportion = -12/5 i.e.
2 / 5 = (- 12 / 5) × (x)
x = -⅙
Hence, the required value of constant of variation and z is -12 / 5 and -⅙ respectively.
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Can anyone please solve these two questions
For the function f(2) = 9:
1. The value of the output is: 9
2. The value of the input is: 2.
How to Solve a Function?The function, f(2) = 9 is interpreted as, for an input value of 2, we would get an output value of 9.
This means that, when x (independent variable or input) is 2, y (dependent variable or output) would be 9.
Thus, given the function f(2) = 9, we have the following:
1. The value of the output is: 9
2. The value of the input is: 2.
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b. Without calculating, use the pattern to predict the sum of the squares of the first ten terms of the Fibonacci sequence.
Answer:23
Step-by-step explanation:
because you add the two
Raymond A circular table of diameter 91cm was decorated all round the flowers placed at interval of 11cm.How many flowers were used?
The total flowers used = 25 flowers . To determine the number of flowers, we calculate the circular table's diameter.
What is a circle's circumference?In other words, if the circle were stretched and straightened out to a line segment, the circumference would match the circle's arc length. In general, the circumference of any closed figure is measured by the length of its arc. The term "circumference" can also refer to the circle's actual location, which corresponds to the edge of a disk.
Circumference, C = π x diameter
= 3.14 x 91
= 285.88
No. of flowers = 285.88/11 = 25.98
Hence 25 flowers were used.
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Find an expression which represents the difference when (3x+1)(3x+1) is subtracted from (-9x+1)(−9x+1) in simplest terms.
Answer:
(3/+1)= 9
Step-by-step explanation:
in simplest terms
Answer:
Step-by-step explanation:
-12x
Combine the like terms to create an equivalent expression.
8x - 1 - 2y + 4 =
pls help!!!
The equivalent expression of 8x - 1 - 2y + 4 is
8x - 2y + 3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
8x - 1 - 2y + 4
Combine the like terms.
8x - 2y + 3
Thus,
The final expression is 8x - 2y + 3.
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Question 12
Write an equation of a line that passes through (8,5) and (11, 14).
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{11}~,~\stackrel{y_2}{14})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{11}-\underset{x_1}{8}}} \implies \cfrac{14 -5}{11 -8} \implies \cfrac{ 9 }{ 3 }\implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{3}(x-\stackrel{x_1}{8}) \\\\\\ y-5=3x-24\implies y=3x-19[/tex]
Answer:
So to write this as an equation follow the steps:
1.First you take y delta divided by x delta. This means that you but in the coordinates, take them minus eachother then divided by eachother. Let me show you with maths for better understanding:
Now you have k in y=kx+m ( the equation has different letters depening on where you are from but I think you understand).
So know we just use simple algebra bu putting in the coordinates in the equation. So for this example im going to use the coordinates x= 8 and y=5
so we get:
I need help divisible rules
========================================================
Explanation:
The divisibility rule for 8 is we look at the last three digits only.
The 083 is what we focus on
Is 083, aka 83, a multiple of 8? The answer is no because 83/8 = 10.375 is not a whole number result. The closest multiples are 80 and 88.
So if the number ended with something like 080 or 088, then we would have a multiple of 8 in the much larger number.
But 083 is not a multiple of 8, so the original number isn't either.
The opposite of the difference between x and 4
Please help!!
Answer:
It would be the sum of x and 4
Step-by-step explanation:
АB=2x+6
BC=3x-6
AC=?
Answer:
they cuestion is AC=2x-6
In this problem, you will use dynamic geometric, software to investigate line and rotational symmetry in regular polygons.
a. Use The Geometer's Sketchpad to draw an equilateral triangle. Use the reflection tool under the transformation menu to investigate and determine all possible lines of symmetry. Then record their number.
The equilateral triangle has three symmetry lines.
What do we mean by rotational symmetry?In geometry, rotational symmetry, also recognized as radial symmetry, is the property that a shape has when it looks the same after a partial turn rotation. The degree of rotational symmetry of an object is the number of distinct orientations in which it appears exactly the same for each rotation.Certain geometric objects, such as squares rotated 90°, are partially symmetrical when rotated at certain angles; however, the only geometric objects that are fully rotationally symmetric anywhere at an angle are spheres, circles, and other spheroids.So,
The Geometer's Sketchpad is indeed a commercial interactive geometry software program that allows you to experiment with Euclidean geometry, algebra, calculus, and other areas of mathematics. In this question, we must draw an equilateral triangle in the Geometer's Sketchpad and then use the reflection tool from the transition menu to investigate and determine all possible lines of symmetry. Then write down their number. Now we'll draw the figures on the Geometer's Sketchpad.Step 1:
Create an equilateral triangle and label its vertices A, B, and C. Draw a perpendicular line A to BC.In the line, reflect the triangle. Display the reflected image's labels. This line is the line of reflection if the image maps to the original.Step 2:
Next, draw a line perpendicular to AC through B.In the line, reflect the triangle. Display the reflected image's labels. This line is the line of reflection if the image maps to the original.Step 3:
Draw a line C perpendicular to AB now. In the line, reflect the triangle.Display the reflected image's labels. This is the line of reflection if the image includes the original.(Refer to the graphs below)
Therefore, the equilateral triangle has three symmetry lines.
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What minimum information is sufficient to determine congruency for each of the following?
a) two squares
b) two rectangles
c) two parallelograms
Two parallelograms will be congruent only when all four corresponding sides are equal in length & one corresponding internal angle is equal.
What is mean by congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
If two line segments are the same length, they are said to be congruent.If two angles have the same measure, they are said to be congruent.If two circles have the same diameter, they are congruent.If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
Two parallelograms will be congruent only when all four corresponding sides are equal in length & one corresponding internal angle is equal.Two rectangles are congruent if both of them have the opposite sides are equal. Two squares are congruent if both of them have the same edges.To learn more about congruency refer to:
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please help will give out brainlist
Because the line PQ is perpendicular to line ST, the slope of line ST is -1
How to determine the slope of ST?The points are given as
P = (1, 4)
Q = (-2, 1)
Start by calculating the slope (m) of ST using
m = (y2 - y1)/(x2 - x1)
This gives
m = (1 - 4)/(-2 - 1)
Evaluate the difference
m = -3/-3
Evaluate the quotient
m = 1
From the question, we have
Line PQ is perpendicular to line ST
This means that
Slope of ST = -1/Slope of PQ
This gives
Slope of ST = -1/1
Evaluate
Slope of ST = -1
Hence, the slope of line ST is -1
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Write an example from daily life that uses each type of real number.
integers
Most of the numbers we work with on a daily basis are real numbers. These include the cash you have in your wallet, sports statistics and the measures we see in recipes. A fraction can be used to represent each of these numbers (whether we like it or not).
What is real numbers?The value of a continuous quantity that may be used to describe a distance along a line is known as a "real number" in mathematics (or alternatively, a quantity that can be represented as an infinite decimal expansion).In one dimension, real numbers may be used to quantify things like distance, velocity, acceleration, force, momentum, and other physical quantities that can be measured (roughly) physically.Positive and negative numbers, as well as the zero, are real numbers.Since they do not belong to the imaginary number system, they are known as real numbers. For example, the square root of -1 is an imaginary number that cannot be quantified.Most of the numbers we work with on a daily basis are real numbers. These include the cash you have in your wallet, sports statistics and the measures we see in recipes. A fraction can be used to represent each of these numbers (whether we like it or not).
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Determine whether set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 65,72,88
Given set of numbers 65, 72, 88 represent an acute triangle.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.
Now we find the type of triangle.
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
the sum of the squares of the two smaller sides is,
= 65² + 72²
= 4225 + 5184
= 9409
= 97²
And 88² = 7744
Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.
Therefore, given set of numbers 65, 72, 88 represents an acute triangle.
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Pedro and Amelia share a common investment goal and once they reach their goals, they will withdraw their money.
Amelia starts out with twice as much money as Pedro and it takes Pedro 6 times longer than Amelia to reach this goal.
They both use the same bank that provides a 4% annual interest rate compounded quarterly.
Work out how long it takes Pedro to reach his investment goal.
The number of years that Pedro took to reach his investment goal will be 52.5 years.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Amelia and Pedro have the same financial objective, and if they achieve it, they will withdraw their funds. Pedro starts off with twice as much money as Amelia, but it takes him six times as long to get there. Both of them use the same bank, which offers a 4% annual interest rate that is compounded every three months. Next, we have
n' = 4n
r/4 = 2 x 0.04 / 4 = 0.02
Let x be the amount of money invested by Pedro. Then the amount of money invested by Amilia will be 2x.
Let n be the number of years. Then for Pedro, the number of years will be 6n.
Then the equation when investment gets doubled will be
4x = 2x(1 + 0.02)⁴ⁿ
2 = 1.02⁴ⁿ
Taking log on both sides, then we have
ln 2 = 4n ln 1.02
4n = 35
n = 8.75 years
Then the number of years that Pedro took to reach his investment goal will be
6n = 6 x 8.75 = 52.5 years
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Ms Smith has 10 cubes in her hand. There are 10 students in her class. They each have 10 cubes in their hands. How many cubes do they all have?
answer choices
100
110
90
125
Answer:
110
Step-by-step explanation:
if each of the 10 students have 10 cubes, that's 100, plus the 10 cubes Ms Smith has is 110
I need help asap please!
Enter the numerator and denominator of the fraction in simplest form that is equal to the decimal number shown.
0.23=
Answer:
23/99
Step-by-step explanation:
I took the test and got it right.
Hope this helps!
If a pizza delivery van travels at 80km/h, how far will it travels in 8 hours?
Answer:
640 km
Step-by-step explanation:
80km/h, x 8 hours = 640 km
The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she knows that the paper will last about 80 days.
b. What is the equation of the line in standard form?
4y - 7x = 0 is the equation of the line in standard form.
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.
To find standard equation of a line we will use points (0,0) and (80,140)
Lets fine the slope of given data, slope, m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
m = [tex]\frac{140- 0}{80- 0}[/tex]
m = 140/80
m = 7/4
We can now make the slope intercept form that is y = mx
with the given data,
y = 7/4(x)
4y = 7x
subtract 7x both the side and we get
4y - 7x = 0
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At the farmers market, Joyce buys 2 2/10 pounds of apples. The apples cost $1.25 per pound. She pays for the apples with a $10 bill. What is the change she should receive back?
Group of answer choices
10.00
7.25
7.50
2.25
Answer: Option 2
2.2 x 1.25 = 2.75
10-2.75=7.25
What is the probability of getting a sum of 6 when rolling two number cubes?
Answer:
The probability of rolling a sum of 6 with two dice is 5/36.
here is you answer
I think you like it
How do u write and graph an inequality for
{x | x< 7}
The inequality expression x < 7 is equivalent to the given inequality expression {x | x < 7}
How to write and graph an inequality for the inequality expression?The inequality expression is given as
{x | x < 7}
When the braces are removed, the inequality expression becomes
x < 7
This means that x < 7 is equivalent to the given inequality expression {x | x < 7}
Next, we represent the inequality expression on a plot
See attachment for the graph of the inequality expression
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In a 3-digit number, the hundreds digit is four more than the units digit, and the tens digit is three less than the sum of the other two digits. If the sum of all three digits in the number is 17, find the free digits. Then find the number
Step-by-step explanation:
the number is abc
c = units digit
b = tens digit
a = hundreds digit
a = c + 4
b = (a + c) - 3
a + b + c = 17
we use the first equation in the second and get
b = (c + 4 + c) - 3 = 2c + 4 - 3 = 2c + 1
abd we use the first and the second equation more in the third and get
c + 4 + 2c + 1 + c = 17
4c = 12
c = 3
b = 2c + 1 = 2×3 + 1 = 6 + 1 = 7
a = c + 4 = 3 + 4 = 7
so, the number is
773
{3x+y=9,5x-3y=1} which first step for solving the given system using substitution results in an equation without fractions
The best first step for solving the given system using substitution while avoiding fractions: Solve for y in the first equation
What is substitution method ?The substitution method is an algebraic strategy for resolving simultaneous linear equations. This approach, as the name suggests, involves substituting the value of one variable from one equation into the second equation.
Given that: the system of equation:
( 3x + y = 9 ) .....[1]
( 5x - 3y = 1 ) .....[2]
We can write equation [1] as:
y = 9 - 3x
Using substitution substitute equation ( y = 9 - 3x ) into [2] we have;
5x - 3(9 - 3x ) = 1
Therefore, the optimum first step for applying substitution and avoiding fractions to solve the given situation is:
Solve for y in the first equation.
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find the measure of the missing angle
Answer:
47 degrees
Step-by-step explanation:
180 degrees - 90 (right angle) = 90.
90 - 43 = 47
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Find the specified term of the following geometric sequences.
A^1 = 2, r= 3 find A^8
A^1 = 0, r = 1/2 find A^8
Answer:
7374
0.
Step-by-step explanation:
a^r = a1 * r^(n-1)
So, the terms are:
2*(3)^(8-1) = 4374
and
0*(1/2)^-1/2 = 0
Simplify each expression by rationalizing the denominator.
2 / √2
The simplified expression after rationalizing the denominator is [tex]\sqrt{2}[/tex].
The given expression is,
2 / √2 equation 1
Name the given expression as equation 1.
To simplify the given expression first we need to rationalize the denominator that is [tex]\sqrt{2}[/tex] .
To rationalize the denominator we need to multiply and divide the given equation 1 by [tex]\sqrt{2}[/tex] . On multiplying and dividing the given equation 1 by [tex]\sqrt{2}[/tex] we will get,
2 / [tex]\sqrt{2}[/tex] = (2 × [tex]\sqrt{2}[/tex])/([tex]\sqrt{2}[/tex] ×[tex]\sqrt{2}[/tex] )
On further simplifying the expression , we will get
= 2[tex]\sqrt{2}[/tex] / 2
= [tex]\sqrt{2}[/tex]
So, we can conclude that the simplified expression after rationalizing the denominator is [tex]\sqrt{2}[/tex].
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