Answer:
5.291 x 10⁶
Step-by-step explanation:
Why is 5,291,000 written as 5.291 x 106 in scientific notation?
The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.
Calculating scientific notation for a positive integer is simple, as it always follows this notation:
a x 10b
Follow the steps below to see how 5,291,000 is written in scientific notation.
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 5,291,000
New Number: 5.291000
Step 2
Now, to find b, count how many places to the right of the decimal.
New Number: 5 . 2 9 1 0 0 0
Decimal Count: 1 2 3 4 5 6
There are 6 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10b
a = 5.291 (Please notice any zeroes on the end have been removed)
b = 6
Now the whole thing:
5.291 x 10⁶
Step 4
Check your work:
10⁶ = 1,000,000 x 5.291 = 5,291,000
A closet is in the shape of a rectangular prism. It is 214feet long, 3 feet wide, and 4 feet tall.
What is the volume of the closet?
7
f(x) = 3x2 + 4x – 7
g(x) = 2x – 11
Answer:
g[f(x)] = 6x² + 8x - 25
Step-by-step explanation:
g[f(x)] = g(3x² + 4x - 7)
= 2(3x² + 4x - 7) - 11
= 6x² + 8x - 14 - 11
= 6x² + 8x - 25
4. Find the arc length.
Find the circumference:
8km x 2 x 3.14 = 50.24 km
Arc length = 50.24 x 225/360 = 31.4 km
answer: C. 10 pi or 31.4 km
What scientific value for n will make this equation true? (4.8 × 10–3)(n) = 9.6 × 109 2.0 × 10–6 2.0 × 10–3 2.0 × 103 2.0 × 1012
The scientific value for n that will make the equation (4.8 × 10^(-3))(n) = 9.6 × 10^9 true is given by: Option D: 2.0 × 10^(12)
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
Scientific notations have some of the profits as:
Better readability due to compact representation
Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
Finding the value of n from the given equation:
[tex](4.5 \times 10^{-3}) \times n = 9.6 \times 10^9\\\\\text{Dividing both the sides by } (4.5 \times 10^{-3}) \\\\n = \dfrac{9.6 \times 10^9}{4.5 \times 10^{-3}} = \dfrac{9.6}{4.5} \times \dfrac{10^{9}}{10^{-3}}\\\\n \approx 2.1333 \times 10^{9-(-3)} = 2.1333 \times 10^{12} \approx 2.0 \times 10^{12}[/tex]
Thus, the scientific value for n that will make the equation (4.8 × 10–3)(n) = 9.6 × 10^9 true is given by: Option D: [tex]2.0 \times 10^{12}[/tex]
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Answer: D
Step-by-step explanation:
what is the constant of proportionality of the below
Answer:
Proportionality constant k
When two variables are directly or indirectly proportional to each other, then their relationship can be described as y = kx or y = k/x, where k determines how the two variables are related to one another. This k is known as the constant of proportionality.
Answer: Proportionality constant k
Step-by-step explanation:
below?
HELP I NEED THESE FOR TODAY MOST BRAINIEST FOR THE FIRST :)!!
The function f(x) is shown on the graph.
The graph shows three pieces of f of x. One piece is curved in quadrant three increasing from the left and turning at approximately negative 3.8 comma negative 5.5 to then decreases and is asymptotic to the line x equals negative 2. Another piece is an upward opening u-shaped curve, which is asymptotic to the line x equals negative 2 and x equals 2 with a minimum at approximately negative 0.3 comma 2.4 3.24. Another piece is asymptotic to the line x equals 2 and is increasing from the left and passes through the point 3 comma 2 and continues to increase in quadrant one.
Which type of function describes f(x)?
Exponential
Logarithmic
Polynomial
Rational
Question 2(Multiple Choice Worth 2 points)
(07.04 MC)
The table of values represents a continuous function.
x
–3
–1
1
3
5
7
9
g(x)
0.375
0.75
1.5
3
6
12
24
Which type of function describes g(x)?
Exponential
Logarithmic
Polynomial
Rational
Question 3(Multiple Choice Worth 2 points)
(07.04 MC)
Which of the following is an example of a polynomial function?
f(x) = 5x3 + 2x2 – 6x + 7
g of x equals the quantity x squared plus 2x minus 3 end quantity divided by the quantity x minus 4 end quantity
h(x) = 750(1.04)x
p(x) = log3(x)2
Question 4(Multiple Choice Worth 2 points)
(07.04 MC)
Given a polynomial function f(x) = 2x2 + 7x + 6 and an exponential function g(x) = 2x + 5, what key features do f(x) and g(x) have in common?
Both f(x) and g(x) increase over the interval of [–4 , ∞)
Both f(x) and g(x) have the same x-intercepts of (–2, 0) and (–1.5, 0).
Both f(x) and g(x) have the same y-intercept of (0, 6).
Both f(x) and g(x) have the same range of (–∞, 0].
Question 5(Multiple Choice Worth 2 points)
(07.04 MC)
What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common?
Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.
The table of values of function g(x) and the function f(x) = 5x3 + 2x2 – 6x + 7 are illustrations of exponential functions and polynomial functions
2. The type of function g(x)The values on the table can be represented as:
(x, g(x)) = (-3, 0.375) (-1, 0.75) (1, 1.5) (3, 3) (5, 6) (7,12) (9, 24)
The above values show that as the values of x increases by 2, the values of function g(x) doubles.
Only an exponential function has this property.
Hence, the table of values represents an (a) exponential function.
3. Example of a polynomial functionA polynomial function is represented as:
y = ax^n + bx^n-2 + .......... + d
Using the above format, the function that is a polynomial function is (a) f(x) = 5x3 + 2x2 – 6x + 7
4. Key features in the functionsThe functions are given as
f(x) = 2x2 + 7x + 6
g(x) = 2x + 5
Set x to 0 to calculate the y-intercept
f(0) = 2(0)2 + 7(0) + 6 = 6
g(x) = 2^0 + 5 = 6
Hence, both functions have the same (c) y-intercept
Questions 1 and 5 are not properly presented
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Answer:
exponential function
Step-by-step explanation:
HS Teacher
Jacob spent $34 on a magazine and seven notepads. if the magazine cost $6, then how much was each notepad?
Step-by-step explanation:
first you subtract 34 and 6 to get 28
now its 7 multiplyed by some number
each notepad 4 dollars cause 7x4=28
Answer:4 dollars
Classify the following triangle. Check all that apply
Answer:
The answer is F, A
Step-by-step explanation:
It is a right and isosceles triangle
Answer:
right and isosceles
Step-by-step explanation:
the sum of the degree measurement of all triangles is 180
given are 45 and 45
45 + 45 = 90 so the other angle must be 90
a triangle with an angle of 90 degrees is always a right triangle
also
8^2 + 8^2 = 11.3^2
64 + 64 = 127.69
this is close enough to being true
an isosceles triangle is a triangle with 2 equal side lengths
this is an isosceles triangle because 8 = 8
Compare learning about functions to learning a new language. How are they similar?
Answer:
Similarities
They both follow strict laws (typically stricter for math).
Practice makes perfect: both can be learned to points of practical perfection.
The brain must first attribute meaning or value to elements of either in order to build a learning pattern.
Differences:
Math is learned under assumptions of perfection (2 + 2 = 4 ALWAYS); whereas, language is learned under assumptions of reality (2 + 2 may be 5 for significantly larger values of 2). In other words, 2 average sized men plus 2 average sized Texans would more likely equal 5 or more average sized men.
Math is logical and language is largely artistic.
There is only one solution (or specific set of solutions) to every math problem. On the other hand, there are at least 100 different ways to express the same idea using language.
Step-by-step explanation:
Answer:
Language rules could be compared to syntax rules that govern the writing and scripting of a function. Language-based rules could be compared to syntax rules when writing functions, such that when the guiding syntax is correctly displayed, the function is clear and easy to read.
Suppose a line, with a slope of -3 and a y-intercept of 4, is translated -4 units along the x-axis and 6 units along the y-axis. What is the equation of this new line?
Answer:
[tex]y=-3x-2[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation: [tex]y=mx+b[/tex]
where:
[tex]m[/tex] is the slope[tex]b[/tex] is the y-interceptGiven:
slope (m) = -3y-intercept (b) = 4Equation of line: [tex]y=-3x+4[/tex]
If the line is translated -4 units along the axis, we need to substitute
[tex]x \rightarrow (x+4)[/tex]
If the line is translated 6 units along the y-axis, we need to add 6 to the equation:
[tex]\implies y=-3(x+4)+4+6[/tex]
[tex]\implies y=-3(x+4)+10[/tex]
[tex]\implies y=-3x-12+10[/tex]
[tex]\implies y=-3x-2[/tex]
Answer:
y = -3x - 2
Step-by-step explanation:
Rules to remember :
f(x + a) = translated 'a' units leftf(x - a) = translated 'a' units rightStandard form of the original equation
y = mx + bhere m = slope and b = y-intercept⇒ y = -3x + 4Translating -4 units along the x-axis
y = -3(x + 4) + 4y = -3x - 12 + 4y = -3x - 8Translating 6 units along the y-axis
y = -3x - 8 + 6y = -3x - 2Maddy has a coupon for bananas. Bananas normally
cost $0.49 per pound. Maddy wants to buy 8
pounds of bananas for her team. She has a coupon
for 5 cents off per pound.
If she uses the coupon, how much will she pay?
Answer:
$3.52
There are two ways you can solve this problem.
1. Take 5 cents off before multiplying.
Since the coupon takes 5 cents off per pound, you can subtract 5 cents off 49 cents.
$0.49-$0.05= $0.44
Now multiply $0.44 by the 8 pounds.
$0.44 (8) = $3.52
2. Take the 5 cents off after multiplying
You can multiply the 5 cents by 8, to find the total money off the bananas. Then subtract that from the total cost.
$0.49 (8) = $3.92 -> Total cost with no coupon
$0.05 (8) = $0.40 -> Total money off
Subtract the two totals.
$3.92 - $0.40 = $3.52
Answer:
I believe the answer is 3.42.
Find the number that makes the ratio equivalent to 1:9.
7:
Answer:
7:63
Step-by-step explanation:
It's a 1 to 9 ratio, which means the second number is 9 times bigger.
To make it equivalent, you need to make 7 9 times bigger as well.
7x9=63
Answer: 7:63
Paul is making grey paint. He mixes black and white paint in the ratio 1:3. He makes 35 litres of grey paint. How much white paint does he use?
The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.15x2 − 6x + 400
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
The function of the production cost is a quadratic function, and the maximum production cost of the company is $340
How to determine the maximum production cost of the company?The function of the production cost is given as:
f(x) = 0.15x² - 6x + 400
Differentiate the function
f'(x) = 0.3x - 6
Set the function to 0
0.3x - 6 = 0
Add 6 to both sides
0.3x = 6
Divide both sides by 0.3
x = 20
Substitute x = 20 in f(x) = 0.15x² - 6x + 400
f(20) = 0.15 * 20² - 6 *20 + 400
Evaluate
f(20) = 340
Hence, the maximum production cost of the company is $340
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i need help 9y grade math
Answer:
17x+7
Step-by-step explanation:
(10x+3)-(-7x-4)
Done!
Solve for x and y
7y - 5x = 45
x = 8 – 2y
Answer:
Hope the pictures will help you.
The solution to the system of equations is x = -2 and y = 5.
What is the solution to the system of equations?Given the parameters:
7y - 5x = 45
x = 8 - 2y
To solve the system of equations, substitute the expression for x from the second equation into the first equation.
7y - 5x = 45
Plug in x = 8 - 2y:
7y - 5( 8 - 2y) = 45
7y - 40 + 10y = 45
Collect and add like terms:
7y + 10y = 45 + 40
17y = 85
y = 85/17
y = 5
Plug the value of y into the second equation and solve for x:
x = 8 - 2y
Plug in y = 5:
x = 8 - 2( 5 )
x = 8 - 10
x = -2
Therefore, the value of x is -2 and y is 5.
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Consider parallelogram VWXY below.
Use the information given in the figure to find m∠YXV, m∠Y, and x.
note:Parallelogram WXYZ not VWXY & I will answer the questions in the image b'cos I don't get your question.
Answers:
a.(i.)Slope of line YZ = 4/5
(ii.)Line adjacent line YZ is line YX,slope of YX =5/4
b.(i.)Length of line YZ =√41 units
(ii.)Length of line YX =√41 units
c.WXYZ is a rhombus.
Step-by-step explanation:
a.Slope=gradient(m)=(y₂-y₁)/(x₂-x₁)
(i.)m of line YZ=(y₂-y₁)/(x₂-x₁) where Y(-6,-1) & Z(-1,3)
(I believe you know what the y₂,y₁,x₂ & x₁ stand for.)
So m=(y₂-y₁)/(x₂-x₁),=(3-(-1))/(-1-(-6) =(4)/(5)=4/5
∴m of line YZ is 4/5
(ii.)m of line YX=(y₂-y₁)/(x₂-x₁) where Y(-6,-1) & X(-2,4)
So m=(y₂-y₁)/(x₂-x₁),=(4-(-1))/(-2-(-6) =(5)/(4)=5/4=1.25
∴m of line YX is 5/4
b.(i.)To find the length of line YZ,we have to express it as column vector YZ.
Vector YZ=OZ-OY,Z-Y=(-1,3)-(-6,-1)=(5,4)
Length=√x² plus y²=√5² plus 4²=√25 plus 16=√41 units
∴The length of line YZ is √41 units.
(ii.)To find the length of line YX,we have to express it as column vector YZ.
Vector YX=OX-OY,X-Y=(-2,4)-(-6,-1)=(4,5)
Length=√x² plus y²=√4² plus 5²=√16 plus 25=√41 units
∴The length of line YX is √41 units.
c.WXYZ is a rhombus.
y=4x+3 system of equations
Step-by-step explanation:
y=4x + 3
it should have another one
Turner works a part-time job at a video game shop. He makes $12.30 per hour. If he works 22.5 hours this week, how much will he earn?
Answer:
Step-by-step explanation:
You multiply 12.30 x 22.5 and that = $276.75
X/3+7=12
Help :)
I need to write more to send it so…
Answer:
15
Step-by-step explanation:
To solve you have to get x by itself on one side.
x/3+7=12
First, you move the seven over.
x/3+7-7=12-7
Simplify.
x/3=5
Now to get x by itself you can multiply both sides by 3.
x/3*3=5*3
Simplify.
x=15
Answer:
x = 15
Step-by-step explanation:
x/3 + 3⋅7/3 = 12
x+3⋅7/3=12
x+21/3
X=15
if you answer this. i will forever love you. foreverrrrrrr
Answer:
Step-by-step explanation:
The Mean Value Theorem says that for continuous and differentiable function f(x) on the interval ( a, b ) there is number c ∈ ( a, b ) that
f'(c) = [tex]\frac{f(b)-f(a)}{b-a}[/tex] ....... (1)
~~~~~~~~~~~~~~~~
f(5) = 44
f(0) = - 1
5 - 0 = 5
f'(x) = 2x + 4 ⇒ f'(c) = 2c + 4
2c + 4 = [tex]\frac{44+1}{5}[/tex]
2c + 4 = 9 ⇒ c = [tex]\frac{5}{2}[/tex] (D).
PLEASE HELP! PLEASE HELP! I NEED TO GET THIS RIGHT! PLEASE ANSWER FULLY!
Answer:
what do you need help with
manatees are large, gentle, slow-moving sea creatures found along the coast of florida. many manatees are injured or killed by boats. here is a scatterplot showing the relationship between the number of boats registered in florida (in thlusands) and the number of manatees killed by boats for the years 1977 to 2015. is r>0 or r<0? closer to r=0 or r=+- 1? explain your reasoing
Using correlation coefficients, it is found that the value of r is greater than 0 and close to 1, as the scatter-plot is increasing linearly.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.Researching the problem on the internet, it is found that the relation is modeled by an increasing scatter-plot, hence r > 0. There are very few points in which there are oscillations, which indicate a strong relationship, hence r is closer to 1.
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A rectangular piece of poster board measures 60 centimeters by 80 centimeters. Linn draws the net of a box on the poster board and cuts it out. If the box measures 10 centimeters by 16 centimeters by 27 centimeters, what is the area of the poster board left?
A cone has a
volume of 3511
cubic feet and a
height of 13 feet.
Find the diameter
of the cone.
Answer:
Ah cgej4
YTL bebekte gt ydd
Step-by-step explanation:
(8=6'+)9*3-6
I NEED HELP ASAP find the lateral area and surface area of a triangular prism (a, 12^{2} 15^{2}) the height is 20. PLEASE HELP
Answer:
Step-by-step explanation:
The sum of two consecutive odd numbers is 24. Find the numbers.
Answer:
numbers = 11, 13
Explanation:
Let the two consecutive odd numbers be: n and n + 2
==========
n + n + 2 = 242(n) + 2 = 242(n) = 24 - 22(n) = 22n = 11⇒ One number: 11
⇒ Another number: 11 + 2 = 13
The sum of two consecutive odd numbers is 24. Find the numbers .
Given : -Sum of two consecutive odd no. = 24To Find : -We have to find the numbers .
Concept : -In this question we have to find the numbers by assuming the numbers and forming equations to finally get the appropriate answer .
To Assume : -Let first odd no. be x .Let second odd no. be x + 2So let's get started by solving : -[tex] \longrightarrow \: x + 2 + x= 24[/tex]
Now adding them ,
[tex] \longrightarrow \: 2x + 2 = 24[/tex]
Now taking 2 common ,
[tex] \longrightarrow \: 2(x + 1) = 24[/tex]
Now dividing 24 by 2 ,
[tex] \longrightarrow \: x + 1 = \frac{24}{2} [/tex]
We get ,
[tex] \longrightarrow \: x + 1 = 12[/tex]
Now transposing 1 to right hand side ,
[tex] \longrightarrow \: x = 12 - 1[/tex]
So ,
[tex] \longrightarrow \: \boxed{\bold{ x = 11}}[/tex]
Therefore value of first number is 11 .
Now , other consecutive no. be x + 2 . So
11 + 213Therefore value of second number is 13 .
Verifying :According to question sum of two consecutive no. is 24. So :
11 + 13 = 2424 = 24L.H.S = R.H.S Hence , Verified .Therefore our answer is valid .# [tex] \sf{Keep \: Learning}[/tex]HELP PLEASE URGENT, ASAP. GRADE 11 TRIGONOMETRY MATH, ill give brainliest.
Answer:
deedww
Step-by-step explanation:
A pet store has 4 tanks of fish. Each tank has 32 fish. How many fish does the store have?
Answer:
128
Step-by-step explanation:
32 × 4 = 128
Each tank has 32, and there are four, so 32 times 4.
The store has 128 fish in the tank.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that pet store has 4 tanks of fish. Each tank has 32 fish.
Therefore,
Total fish = Number of fish that a tank can hold x Number of tanks
32 × 4 = 128
Hence, we get 32 for each tank, and there are four,
Thus, 32 times 4.
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1.what is the measure in degrees of angle x.
2.what is the measure in degrees of angle y
Show your work
⠀
1. Here,
⠀
[tex] \sf \longrightarrow x + 45^\circ = 180^\circ [/tex] ( Linear pair of angles measure upto 180° )
⠀
Thus,
⠀
[tex] \sf \longrightarrow x + 45^\circ = 180^\circ \\ \\ \\ \sf \longrightarrow x = 180^\circ - 45^\circ \\ \\ \\ \sf \longrightarrow \underline{ \boxed{ \frak{ \blue{ x = 135^\circ }}}} \: \star \: \: \: \: \: \: \: \\ \\ [/tex]
⠀
Now, for y,
⠀
[tex] \sf \longrightarrow \underline{ \boxed{ \sf{ \orange{y = 45^\circ}}}} \: \star [/tex] ( Vertically Opposite Angles)
⠀
[tex] \underline{\rule{230pt}{2pt}} [/tex]
⠀