Find the values of the power in the following pattern: (10)1, (10)2, (10)3, (10)4....Describe the pattern, and use it to evaluate (10)6 without using multiplication
Prove the divisibility of the following numbers:
51^7-51^6 by 25
To prove the divisibility lets expand each number first to get the complete picture of the problem
51^7 = 8.974106779 . 10^11
51^6 = 1.75962878 . 10^10
(51^7 - 51^6) = 8.974106779 . 10^11 - 1.75962878 . 10^10
= 8.798143901. 10^11
[tex]\frac{8.798143901. 10^11}{25}[/tex]
= 3.51925756. 10^10
That is the answer expressed in scientific notation
= 35192575600
Which means the divisibility is proven
Step-by-step explanation:
[tex]51^7-51^6=51^{6+1}-51^6\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=51^6\cdot51^1-51^6\cdot1\\\\\text{use the distributive property}\ a(b-c)=ab-ac\\\\=51^6\cdot(51-1)=51^6\cdot50=51^6\cdot(2\cdot25)=25\cdot(51^6\cdot2)[/tex]
[tex]\text{One of the factors of the product is the number 25.}\\\\\bold{CONCLUSION:}\\\\\text{The whole product is divisible by 25.}[/tex]
[tex]\text{Therefore}\ 51^7-51^6\ \text{is divisible by 25.}[/tex]
cody spent $144 on shirts. fancy shirts cost $23 and plain shirts cost $13. if he bought a total of 8 then how many of each kind did he buy?
Last year the attendance at the homecoming football game was 300.This year 360 people attended.What was the percent increase from last year to this year
Multiply r2+7r+10/3 by 3r-30/ r2-5r-50
help with homework. show work
Some students were surveyed about how much time they spent playing video games last week and their overal test average.
Find the equation of the least-squares line.
Interpret the meaning of the slope.
Interpret the meaning of the y-intercept mathematically.
State the correlation coefficient. Describe any possible correlation for the data set. Use the correlation coefficient to support your answer.
Use the equation of the least-squares line from part a to predict the test average for someone who plays 5 hours of video games a week.
If you take a certain number 2.5 times then add 1.75 and divide the result by 0.8, you’ll get 37.5. What was the original number?
Answer:
The original number is 11.3
Step-by-step explanation:
Let the number is x and then we form the equation to solve it for the value of x.
1- Number is multiplied by 2.5 then it becomes = 2.5x
2- Then we add 1.75 to the expression then new expression will be = 2.5x + 1.75
3- We divide the result by 0.8 then expression will be = [tex]\frac{2.5x + 1.75}{0.8}[/tex]
4- Now the final expression is equal to 37.5 so the equation will be
[tex]\frac{2.5x + 1.75}{0.8}[/tex] = 37.5
Now we multiply 0.8 in both the sides of the equation
[tex]\frac{2.5x + 1.75}{0.8}[/tex]×0.8 = 37.5×0.8
2.5x + 1.75 = 30
2.5x = 30 - 1.75
2.5x = 28.25
x = 28.25/2.5 = 11.3
Answer:
11.3
Step-by-step explanation:
I need to hurry so I don't have enough time to write this down.
What geometric shape may describe a quadrilateral that has exactly two pairs of parallel sides and no right angles? (If you don’t know that don’t answer...otherwise I will report you from the system)
Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual simple interest rate of 9%. After 8 years, the interest earned on the account was $1,440. How much money did Mike's grandmother deposit in the account?
Owen used these steps to solve the equation 4x+7=1+2(2x+3) . Which choice describes the meaning of his result, 7=7 ?
a.The result is not correct because Step 2 has an error.
b.The solution is x=7.
c.No values of x make the equation true.
d.All values of x make the equation true.
The choice that describes the meaning of the result is,
all values of x make the equation true.
The correct option is d.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
Owen used these steps to solve the equation,
4x+7 = 1+2(2x+3).
Simplifying,
4x + 7 = 1 + 4x + 6
4x + 7 = 4x + 6 + 1
4x + 7 = 4x + 7
Subtract 4x to both sides,
7 = 7.
That means, the equation has infinitely many solutions.
Therefore, all values of x make the equation true.
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The table given are for the linear functions f(x) and g(x) what is the input value for which f(x) = g(x) is true ?
x=
The functions f(x) and g(x) will be equal at x = -1 the input value will be -1.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Two function f(x) and g(x) shown in the table.
From the table:
At x = -1
f(-1) = 3
At x = -1
g(-1) = 3
f(-1) = g(-1)
or
f(x) = g(x) at x = -1
Thus, the functions f(x) and g(x) will be equal at x = -1 the input value will be -1.
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The graph represents function 1, and the equation represents function 2:
A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 3.
Function 2
y = 5x + 4
How much more is the rate of change of function 2 than the rate of change of function 1?
I'll give brainliest if you show your work. Plz answer quickly in less than 45 minutes.
Which two points should the line of best fit go through to best represent the data in the scatterplot?
(1, 16) and (2, 15)
(1, 16) and (6, 1)
(2, 15) and (4, 9)
(5, 8) and (6, 1)
Answer:
2,15 and 4,9
Step-by-step explanation:
this is because these two points are in between the other two sets of points.
Plot the x- and y-intercepts to graph the equation. y=13x−1 .
PLEASE plot it on a graph PLEASE and i will get you brainly and 15 points
Answer:
Given the equation: [tex]y = \frac{1}{3}x -1[/tex] .....[1]
To find the intercepts:
x-intercepts states that the graph cross the x-axis.
Substitute the value of y = 0 in [1] to solve for x;
[tex]0 = \frac{1}{3}x-1[/tex]
Add 1 to both sides we get;
[tex]1 = \frac{1}{3}x[/tex]
Multiply both sides by 3 we get;
[tex]3 = x[/tex]
x-intercepts = (3, 0)
y-intercepts states that the graph cross the y-axis
Substitute the value x = 0 in [1] to solve for y;
[tex]y = \frac{1}{3}(0) -1[/tex]
Simplify:
y = -1
y-intercept = (0, -1)
Now, using these x- and y--intercepts points to graph the given equation [tex]y = \frac{1}{3}x -1[/tex] as shown below.
Maggie and her friend visit a beach that has a shoreline 2 2/5 kilometers long. They walk along 2/3 of it. How many kilometers of the beach shoreline do they walk?
To find out how many kilometers of the beach shoreline Maggie and her friend walk, we need to multiply the length of the shoreline by the fraction they walk along. Maggie and her friend walk 8/5 kilometers of the beach shoreline.
Explanation:To find out how many kilometers of the beach shoreline Maggie and her friend walk, we need to multiply the length of the shoreline by the fraction they walk along.
First, we need to convert the mixed number 2 2/5 to an improper fraction. We can do this by multiplying the whole number (2) by the denominator (5) and adding the result to the numerator (2), then putting the new numerator over the denominator. So, 2 2/5 is equal to (2 * 5 + 2) / 5 = 12/5.
Next, we can multiply the length of the shoreline (2 2/5) by the fraction they walk along (2/3). Multiply the whole number and numerator separately, then add the products and put the result over the denominator.
So, (12/5) * (2/3) = (12 * 2) / (5 * 3) = 24/15 = 8/5.
Maggie and her friend walk 8/5 kilometers of the beach shoreline.
how do you find the equation of a linear model when given the graph but not the equation
We want to see how to find a linear equation by only looking at the line graph.
First, a general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Then the line is something like:
[tex]y = (\frac{y_2 - y_1}{x_2 - x_1})*x + b[/tex]
To get the value of b, we use the fact that if the function passes through (x₁, y₁), it means that when x = x₁ we also must have y = y₁, replacing that in the equation we get:
[tex]y_1 = (\frac{y_2 - y_1}{x_2 - x_1})*x_1 + b\\\\y_1 - (\frac{y_2 - y_1}{x_2 - x_1})*x_1 = b[/tex]
Then the linear equation is:
[tex]y = (\frac{y_2 - y_1}{x_2 - x_1})*x + y_1 - (\frac{y_2 - y_1}{x_2 - x_1})*x_1[/tex]
So what we need to do is just look at the graph and find two points, then you can use the above guide to find the linear equation.
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Which property changes when a figure is translated
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below.
Survey responses of "yes comma " "no comma " and "no opinion"Survey responses of "yes," "no," and "no opinion"
Choose the correct answer below.
A.
The nominalnominal level of measurement is most appropriate because the data cannotcannot bebe ordered.ordered. nothing nothing nothing nothing nothing nothing nothing nothing nothing nothing
B.
The intervalinterval level of measurement is most appropriate because the data can becan be ordered comma differences left parenthesis obtained by subtraction right parenthesis can be found and are meaningful comma andordered, differences (obtained by subtraction) can be found and are meaningful, and there is no natural starting point.there is no natural starting point.
C.
The ratioratio level of measurement is most appropriate because the data can be ordered commacan be ordered, differences left parenthesis obtained by subtraction right parenthesis can be found and are meaningful comma and there is adifferences (obtained by subtraction) can be found and are meaningful, and there is a natural starting point.natural starting point.
D.
The ordinalordinal level of measurement is most appropriate because the data can becan be ordered comma but differences left parenthesis obtained by subtraction right parenthesis cannot be found or areordered, but differences (obtained by subtraction) cannot be found or are meaningless.
Can someone help me with number 33 please
Jeff purchased 5 items at the same price and 1 item for $2.95. What was the individual price of the 5 items if Jeff's total was $18.90 before tax? a. $3.19 b. $2.95 c.$4.37 d. $15.95
Answer:
3.19
Step-by-step explanation:
determine the area of the composite figure shown below
Which rules of exponents will be used to evaluate this expression? Check all that apply. [(-8)^4]-5 (-8)6
product of powers
quotient of powers
power of a power
power of a product
negative exponent
zero exponent
Answer:
the answers are
b,c,e
quotient of powers, power of a power, and negative exponent
got it right on the quiz
Step-by-step explanation:
Answer:
B,C,E
Step-by-step explanation:
edge 2022
Light travels at a speed of about 3.0x10^8 meters per second. How far does light travel in 4,500 seconds You Would Get __ E __
light would travel approximately [tex]\( 1.35 \times 10^{12} \)[/tex] meters in 4,500 seconds.
To find out how far light travels in 4,500 seconds, we can use the formula:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]
Given that the speed of light is approximately [tex]\( 3.0 \times 10^8 \)[/tex] meters per second and the time is 4,500 seconds, we can plug these values into the formula:
[tex]\[ \text{Distance} = 3.0 \times 10^8 \text{ m/s} \times 4,500 \text{ s} \][/tex]
Calculating this gives us:
[tex]\[ \text{Distance} = 1.35 \times 10^{12} \text{ meters} \][/tex]
So, light would travel approximately [tex]\( 1.35 \times 10^{12} \)[/tex] meters in 4,500 seconds.
the measure of an angle is 34 degrees what is the measure of its supplement
The measure of the supplement angle is 146 degrees.
What are supplementary angles?The supplementary angles is defined as when pair of angles addition to 180° then they are called as supplementary angles. There are two types of supplementary angles.
What are Adjacent angles?Adjacent angles is the type of supplementary angles. Adjacent angles have a common side and vertex, for example a corner point. Their points do not overlap in any way. In other terms, adjacent angles is pair of two angles next to each other
Given that the measure of an angle is 34 degrees
Let x = the measure of the supplement angle.
Two angles whose sum is 180 degrees are supplementary.
∴ x + 34 = 180
Then, (180 -34 ) is the supplement of that angle.
The measure of the supplement angle = 146 degrees
Hence, the measure of the supplement angle is 146 degrees.
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Help please? I don't understand..!
63,360, 63,366, 63,372, 63,378, 63,384, ... What is Barry's altitude above sea level, in inches, when he is standing on the 65th step above the one-mile step (counting the one-mile step itself as step #1)?
Please give answer and explain please.
you suspect that an unscrupullous employee at a casino has tampereed with a die. that is, he is using a loaded die. In order to test this claim you roll it 258 times and obtain the folllowing frquencies Category 1 2 3 4 5 6 Frequency 48 52 51 34 48 25 a. Choose the approp. alternative hypotheses to test if the population proportion differ a/all population proportion differ from 1/6 b/ Not ll population proportion are equal to 1/6 b-1 calculate the value of the test statistic(round to at last 4 decimal places) b-2 Approx. the p-value c. at the 10% signifigance level. can you conclude that the die is loaded?
find the solution of the equation: x2 = 30 -13x