By using some exponent properties, we will find the equivalent expression:
(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²
How to find an equivalent expression?Here are some exponent properties that we need to use:
(aⁿ)ˣ = aⁿ*ˣ
(a⁻ⁿ) = (1/a)ⁿ
Here we have the expression:
(m⁻²*n⁻³)⁻⁴
The exponents can be distributed under multiplication, then:
(m⁻²)⁻⁴*(n⁻³)⁻⁴
Now we can use the first property so we get:
(m⁻²)⁻⁴*(n⁻³)⁻⁴ = m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾
m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾ = m⁸*n¹²
That is the equivalent expression.
(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²
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what is s for the following function
Answer:
S = 3
S = 5
S = 7
S = 9
Step-by-step explanation:
t = 3s + 2
when t = 11
11 = 3s + 2
11 – 2 = 3s
9 = 3s
s = 3
t = 3s + 2
when t = 17
17 = 3s + 2
17 – 2 = 3s
15 = 3s
s = 5
t = 3s + 2
when t = 23
23 = 3s + 2
23 – 2 = 3s
21 = 3s
s = 7
t = 3s + 2
when t = 29
29 = 3s + 2
29 – 2 = 3s
27 = 3s
s = 9
I HOPE ALL THIS HELPS
RATE AS BRAINLIEST PLS
Find domain and range. Due tmrw!
The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).
How to find the domain and range of a function?The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
For the graph given, the domain lie across the x-axis.
The range is possible y values. Since we can use negative x values, if we plug in x values for the function, we are going to get positive numbers, as we plug in higher negative numbers, our range is bigger.
The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).
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Answer:
answer is in explanation
Step-by-step explanation:
The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).
How to find the domain and range of a function?
The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
For the graph given, the domain lie across the x-axis.
The range is possible y values. Since we can use negative x values, if we plug in x values for the function, we are going to get positive numbers, as we plug in higher negative numbers, our range is bigger.
The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).
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On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.
Complete the relative frequency table, showing all necessary calculations.
By using the tabular data given , the complete relative frequency table has been shown below
What is tabular data?
Data given in the form of rows and columns is known as tabular data.
The relative frequency table has been shown below
Frequency of students who like to like to fly and can drive = 0.32
Total frequency of students who like to fly = 0.70
Frequency of students who like to like to fly cannot drive = 0.70 - 0.32 = 0.38
Frequency of students who can drive = 0.45
Frequency of students who cannot drive = 0.55
Frequency of students who do not like to fly can drive = 0.45 - 0.32 = 0.13
Frequency of students who do not like to fly cannot drive = 0.55 - 0.38 = 0.17
Total frequency of students who do not like to fly = 0.13 + 0.17 = 0.30
The complete relative frequency table is
Can drive Cannot drive Row totals
Like to fly 0.32 0.38 0.70
Do not like to fly 0.13 0.17 0.30
Column totals 0.45 0.55 1
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what is the purpose of statistical inferences? to estimate mean, median, mode, variance, and skewness of large sample data to make generalizations about population characteristics from sample results to study characteristics of binomial or poisson random variables to fully describe the characteristics of the population
The main purpose of statistical inferences is to make generalizations about a population from a small sample result.
What is the meaning of statistical inference?Whenever we chart graphs, we try to represent raw data in tabular form. This data is mainly collected by us through surveys conducted on a small group of people, maybe our friends, family or anyone random. Through the data we receive, we can evaluate it to know results of out particular survey topic. Now, if we use this result to draw generalized conclusions about the whole population, then it is known as "inference" statistics. In inference statistics we donot limit the data to our sample size but rather use it to make predictions about the population.
For example: if we want to know the effictivity of a particular drug, we test it on a group of let's say, 100 people. The results show that about 75 treated got cured of the disease for which the drug was made to combat. Using statistical inference, we can conclude that in a population, the drug has an effictivity of 75%.
Further hypothesis can be conducted on the data using inferential statistics.
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m×n , when m=13 and n=12
Answer:
156
Step-by-step explanation:
mxn
13x12= 156
......
If g=2 r=3 and t=11 solve
(2t+3g) divided by 4
The results of the evaluation of the given expression; (2t+3g) divided by 4 as required is; 7.
What is the result of the evaluation of the expression?It follows from the task content that the result of the evaluation of the given expression is to be determined according to the information provided.
Therefore, since the expression to be evaluated is; ( 2t + 3g ) / 4.
Where; g = 2, r = 3 and t = 11.
Therefore, we have;
( 2(11) + 3(2) ) / 4
= ( 22 + 6 ) / 4
= 28 / 4
= 7.
Therefore, the result of the expression evaluation is; 7.
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true or false considered multiple regression which is a sample at 36 observations for a given eggs and fitted why the 95% approximate prediction interval for individual why is wider than the corresponding approximate 95% confidence interval for the conditional mean a y
The statement "considered multiple regression which is a sample at 36 observations for a given eggs and fitted why the 95% approximate prediction interval for individual why is wider than the corresponding approximate 95% confidence interval for the conditional mean" is false.
Here we have given the statement and we need to identify whether this one is true or not.
As we all know that then Confidence interval is narrower than the prediction interval because Prediction intervals must account for both the uncertainty in estimating the population mean, plus the random variation of the individual values.
Therefore the prediction interval is always wider than a confidence interval.
And also here the prediction interval will not converge to a single value as the sample size increases.
Therefore, the statement is incorrect.
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solid fats are more likely to raise blood cholesterol levels than liquid fats. suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results: we want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. what is the test statistic? (assume the population data is normally distributed)
The test statistic would be a two-sample t-test, which compares the means of two independent samples by calculating the difference in means between the two samples and dividing the difference by the standard error of the difference.
How does math define a percent?In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).
Describe a percentage example.
The hundredth component, one percent (symbolized as 1%), is expressed as 100 percent, and 200 percent denotes double the quantity specified. For example, 1% of 1,000 chickens equals 1/100 of 1,000, or 10 chickens, and 20% of the total is equal to 20% of 1,000, or 200.
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In the given figure, write the relation between AB and CD as well as AB and AE.
Answer:
A point and C point are correspondingC and D point are parallel linesI'm not really sure about this one but I think A and E point are also parallel as there is a straight lineHope this Helps!!!
p,3,5,7,q,13 is a sequence of prime numbers.Find the value of p+q.
A.10
B.12
C.13
D.14
Answer: P is 1 and q is 11, making your answer 12.
Step-by-step explanation:
If the chart is displaying prime numbers in order from 1 to 13, list all of the prime numbers. We would start with '1' because '1' is a prime and the first one on the list, thus followed by 3, then 5, then 7, then 11 because the only prime number between 7 and 13 is 11.
Then, add your P and q together, 1 and 11 in this example, to get your final answer of 12.
What is the slope-intercept equation for the linear function represented by the
table?
Answer: y= 3/2x - 6
Step-by-step explanation:
The equation is y=mx + b
The y-intercept is when x = 0, so on the table y-intercept = -6
The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2
to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}[/tex]
now, the y-intercept occurs when x = 0, recheck the picture below.
Which statement correctly compares the function on this graph with the function y=2x-5?
The statement that correctly compares the function of the given graph with the function y = 2x - 5 is; Option C: The function shown on the graph has a greater rate of change and a higher starting point.
What is the rate of change of the function?The rate of change of function is defined as the change in the value of the function with respect to x value.
Rate of change of function f(x) is;
f'(x) = df(x)/dx
The given function is; y = 2x - 5
Thus;
Rate of change of function = f'(x) = df(x)/dx = dy/dx = d(2x - 5)/dx = 2
The starting point of the function f is the y-intercept of the function.
The y-intercept of the function is the point where the function touches the y-axis which can be calculated by putting x value is equals to 0.
Thus; y = 2*0 - 5
y= -5
The starting point of function is -5.
Slope = (y intercept)/(x - intercept)
Slope = 4/1 =4
Thus, the rate of change of the graph = slope of the graph= 4
The y-intercept of the graph is equal to the starting point of the graph which is -5
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input
SOLIS
Output
4
S
7
Which ordered pair needs to be removed in order for
the mapping to represent a function?
By using the concept of function, it can be concluded that (-2, -1) needs to be removed to make the given relation a function
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here, from the figure, it can be seen that -2 has two images,
2 and -1
So from the options given, the point (-2, -1) needs to be removed to make the given relation a function
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Complete Question
Input Output Which ordered pair needs to be removed in order for the mapping to represent a function? O (-3, -4) O (-2, -1) O (1, -3) O (3,7)
(1 point) how many strings of 4 lower case english letters are there that have the letter x in them somewhere? here strings may use the same letter more than once. (hint: it might be easier to first count the strings that don't have an x in them.) your answer is:
Therefore, number of strings can be made by using 4 lower case english letters is 66,351 strings.
What is combination?Combination refers to an arrangement of objects where the order is not crucial. Contrary to permutation, where the order is important. Consider how the letters A, B, and C would be arranged. ABC and ACB are not the same arrangement in a permutation.
Here,
Repetition is permitted as long as we're only looking at lowercase letters.
Number of strings of length 4=[tex]26^{4}[/tex]
Other than x, how many strings of length 4 exist=[tex]25^{4}[/tex]
[tex]26^{4}[/tex]- [tex]25^{4}[/tex]=66,351 strings.
Therefore number of strings can be made by using 4 lower case english letters is 66,351 strings.
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Iliana plays a video game that awards experience points, called "XP", based on how long she plays. She made this graph to study how her playing time relates to XP:
How many hours will it take Iliana to get 200 total XP?
____ hours
Answer:
It will take Iliana 16 hours to get 200 total XP.
Step-by-step explanation:
To project a value on a graph, we need to first find the equation of the graph.
The graph makes the shape of a line. Therefore, the equation of a graph is a linear equation.
⭐What is a linear equation?
a linear equation is an equation where each y-value increases by an additive, constant valuewhen graphed, linear equations look like a straight lineequation: [tex]y = mx + b[/tex]m = the slope (the additive, constant value)b = the y-intercept (the y-value for when x=0)To make the equation for this graph, we need to find the value of the slope and the y-intercept and substitute it into the equation.
The equation for this graph will be called P(t).
⭐How do we find the slope?
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex][tex](x_1,y_1)[/tex] is a coordinate you are given[tex](x_2,y_2)[/tex] is another coordinate you are givenPick 2 coordinates you are given. I am going to use (2,25) and (4,50).
Substitute these coordinates into the slope formula.
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\[/tex]
[tex]m = \frac{50-25}{4-2}[/tex]
[tex]m = \frac{25}{2}[/tex]
⭐How do we find the y-intercept?
look at the graph and find the corresponding y-value for when x=0or: for every coordinate, move up/down and left/right by the slope until you get to x=0, and find the y-coordinate for when you get to x=0Since we aren't given the corresponding y-value for when x=0, we have to do the second option stated.
m = 25/2 is the same thing as m = -25/-2, because:
negative/negative = positive
positive/positive = positive
Thus, we can move down from point (2,25) 25 units and left 2 units to get to point (0,0).
[tex]y-intercept = 0[/tex]
Now, substitute the values of the y-intercept and the slope into the equation for the graph.
[tex]P(t) = mt + b[/tex]
[tex]P(t) = \frac{25}{2}t[/tex]
Next, to project a value on the graph, we need to substitute the y-value into the equation to find its corresponding x-value.
The y-value we want to find is 200 XP.
[tex]200 = \frac{25}{2}t[/tex]
Multiply LHS and RHS by [tex]\frac{2}{25}[/tex] to isolate t.
[tex]\frac{2}{25}(200) = \frac{2}{25}(\frac{25}{2}t)[/tex]
[tex]\frac{400}{25} = t[/tex]
[tex]16 = t[/tex]
∴ It will take Iliana 16 hours to get 200 total XP!
⭐if this response helped you, please mark it the "brainliest"!⭐
Answer:
it would take her 16 hours to get 200 XP
you could see how much XP she gets in a hour and it would help you understand it better
HOURS ( 1 2)
TOTAL XP( 12.5 ÷2)
so according to the small little graph 1 hour is 12.5 XP so you could type how much she gets for any number of hours
EQUATIONS
p=12.5t you could make (t) time by itself
t = p/12.5
HOW LONG TO GET 200 XP
you need t get the value of t cause p = to 200
t= p/12.5
since p is = to 200 p is 200 and you can replace it
t= 200/12.5
so all you have to do it the math!
t = 16
ANSWER
it takes her 16 hours to get 200 XP
balls labeled 1 through 9 are placed in a knapsack. two balls are selected from the knapsack, one at a time without replacement. the first ball we draw is even. what is the probability that the second ball is greater than the first ball?
The probability that the second ball is greater than the first ball is 5/8
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
As to even odd
first ball can be anything. Second would have to be the first is not thus 5/9.
As second smaller than first
if first is 9, probability is 8/8, 100%, if 7 probability s 6/8 so in general take first ball, value k,
then the probability is sum (k - 1) / (n = 10 - 1) for k=1,2,…,9 so that’s all in 45/8 times 1/9 so 45/72 or 5/8.
Even a clear ball has Color so unless you have an invisible ball in your collection, both balls will be some amount of color or color.
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the points (16, 12) and (12, 9) fall on a particular line. what is its equation in slope-intercept form?
Answer: y=3/4x
Step-by-step explanation:
1. Find slope using slope formula
2. Find b value by plugging a point to solve for b with
Calculator © Cymath | Mathema X ourses/_76146_1/cl/outline Course Home Remaining Time: 1 hour, 13 minutes, 39 seconds. * Question Completion Status: QUESTION 11 An augmented matrix of a system of equations has been transformed by row operations into the 3 equations in 3 variables matrix below. State the solution to this system as (x,y,z) Enter your answer as an ordered triple within parenthesis separated by commas (x,y,z). Avoid entering spaces and decimal points Use fractions if relevant. [100 : -3 010: بی N| بااح 001 QUESTION 12 Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answ
The solution to this system of equations is (3,1,-2) which are represented by matrix.
This system of equations can be represented by the augmented matrix:
[tex]\begin{bmatrix}100 & -3 & 0 \\010 & 0 & 1 \\001 & 0 & -2\end{bmatrix}[/tex]
The augmented matrix can be transformed into an upper triangular matrix using row operations:
[tex]\begin{bmatrix}100 & -3 & 0 \\000 & 3 & 1 \\000 & 0 & -2\end{bmatrix}[/tex]
Now, we can use back substitution to solve for the unknowns.
From the bottom row, we can see that z = -2.
From the second row, we can see that y = 1.
Using the top row and the values for y and z, we can solve for x:
100x - 3(1) + 0(-2) = 0
100x - 3 + 0 = 0
100x = 3
x = 3
Thus, the solution to this system of equations is (3,1,-2).
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Christopher invested $1500 at 5% compounded semi-annually for 10 years. What is the amount of the investment at maturity?
The amount of the investment at maturity is $2443.341
Compound interest is the interest on the initial principal plus the interest which has been accumulated.
Given,
Principal amount (P)= $1500
Rate of interest(R)= 5% = 5/100 = 0.05%
Time(T)= 10 years
The formula for annual compound interest is as follows:
FV = P (1+ r/m)^mt
Where:
FV - the future value of the investment, in our calculator it is the final balance
P - the initial balance (the value of the investment)
r - the annual interest rate (in decimal)
m - the number of times the interest is compounded per year (compounding frequency)
t - the number of years the money is invested for
FV = 1500*(1+0.05/1)^(10*1) = 2443.341
The value of the investment after 10 years will be $2443.341.
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Passes through the point (-4, -3) and is perpendicular to the line -3x - 4y = 12.
Answer:
y= [tex]\frac{4}{3}[/tex] x+ [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
-3x-4y=12
1. First we need to get the equation in the form of y=mx+c to do this we add 3x to both sides and then divide it by -4 on each side to get
(add 3x to both sides) = -4y=3x+12
(divide each side by -4)= y= -[tex]\frac{3}{4}[/tex] x -3
2. to find the perpendicular gradient we find the reciprocal of the original gradient
the reciprocal of -[tex]\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex]
3. we can check this by multiplying them and seeing of we get -1
-[tex]\frac{3}{4}[/tex] x [tex]\frac{4}{3}[/tex] = = -1
4. we then sub in the gradient [tex]\frac{4}{3}[/tex] in y=mx+c this gives us
y= [tex]\frac{4}{3}[/tex]x +c
5. to find the value of c we substitute the coordinates into the equation to get ( we do this by expanding the brackets and getting c on it own)
-3= [tex]\frac{4}{3}[/tex](-4) +c
-3= -[tex]\frac{16}{3}[/tex] +c
[tex]\frac{7}{3}[/tex]=c
6. we sub [tex]\frac{7}{3}[/tex]=c back into y= [tex]\frac{4}{3}[/tex]x +c this gives us
y= [tex]\frac{4}{3}[/tex]x + [tex]\frac{7}{3}[/tex]
7. Therefore our final answer is
y= [tex]\frac{4}{3}[/tex]x + [tex]\frac{7}{3}[/tex]
help please i need to answer it
Answer: 4ft/s
Step-by-step explanation:
I think
2 + 6 = 8
8 / 2 = 4
f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]f(x)= 2x^2 + 12x +16 \qquad \begin{cases} x_1=-3\\ x_2=-2 \end{cases}\implies \cfrac{f(-2)-f(-3)}{-2 -( -3)} \\\\\\ \cfrac{[2(-2)^2 + 12(-2) + 16]~~ - ~~[2(-3)^2 + 12(-3) + 16]}{-2+3} \\\\\\ \cfrac{[8-24+16]~~ - ~~[18-36+16]}{1}\implies 0-(-2)\implies \text{\LARGE 2}[/tex]
The vertices of a triangle are P(3,-2), Q(-1, -2), and R(2, 7). Name the vertices of APQR after a reflection over the y axis.
P'(3,-2). Q'(-1,-2), R'(2,7)
P'(-3, 2), Q'(1, 2), R'(-2,-7)
P'(-3,-2). Q'(1, -2), R'(-2,7)
P'(3, 2), Q'(-1,2), R'(2-7)
The reflection of triangle with respect to y axis is P'(-3,-2). Q'(1, -2), R'(-2,7)
How does reflection relate to the y axis?
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
What does a reflection mean in mathematics?
A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
For the reflection we need to see first the axis then we will fix that coordinate of the axis like in this case we have y axis so y coordinates will be fix and for x coordinate we will do in opposite direction like for 3 it will be -3 , for -1 it will be 1 and for 2 it will be -2
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..................................
Answer:
what are you asking?!?
Step-by-step explanation:
find the equation of the line that contains the point p(4, 5) and is perpendicular to the graph of y = 5/4 x − 1.
Answer:
y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{5}{4}[/tex] x - 1 ← is in slope- intercept form
with slope m = [tex]\frac{5}{4}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex] , then
y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (4, 5 ) into the partial equation
5 = - [tex]\frac{16}{5}[/tex] + c ⇒ c = 5 + [tex]\frac{16}{5}[/tex] = [tex]\frac{25}{5}[/tex] + [tex]\frac{16}{5}[/tex] = [tex]\frac{41}{5}[/tex]
y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex] ← equation of perpendicular line
Lillian bought snacks for her team's practice. She bought a bag of apples for $2.36 and a 4-pack of juice bottles. The total cost before tax was $6.48. How much was each bottle of juice?
The price of each bottle of juice is $1.03
What is an equation?
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
Let 'x' be the price of each bottle of juice. Then,
According to the question,
2.36 + 4x = 6.48
or, 4x = 6.48 - 2.36
or, 4x = 4.12
or, x = 4.12/4
or, x = 1.03
Hence, the price of each bottle of juice is $1.03
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what performs all arithmetic operations (for example, addition and subtraction) and all logic operations?
An arithmetic logic unit (ALU) performs all arithmetic operations (for example, addition and subtraction) and all logic operations.
An arithmetic logic unit (ALU) is a digital circuit used to perform arithmetic and logic operations. It represents the fundamental building block of the central processing unit (CPU) of a computer. Modern CPUs contain very powerful and complex ALUs. In addition to ALUs, modern CPUs contain a control unit (CU).
Basic arithmetic and logical operations are carried out using an ALU. Addition, subtraction, multiplication, and division are a few examples of arithmetic operations.
Binary numbers, or 0 and 1, are used to store and modify every piece of data in computers. Since a switch has just two possible states—open or closed—transistor switches are used to alter binary numbers. An open transistor, through which no current flows, is equivalent to a 0. A closed transistor with a current flowing through it symbolizes a 1.
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is the line through (-4, 26, 1) and (-2, 0, -3) parallel to the line through (10, 18, 4) and (5, 3, 14)?
No, the line passing through (-4, 26) and (-2, 0) is not parallel to line passing through (10, 18) and (5, 3) because slopes of both lines are different.
Line is possible in 2-d forms so, it has only x and y-co-ordinates. Z-co-ordinates is not possible.
We know very well that to prove any two lines are parallel to each other we need to prove only whether their slopes are equal or not.
Now, talking about the slopes we know that if any line is passing from point(x₁,y₁) and again passing from other point(x₂,y₂) then slope(m) of that line is given by the formula=(y₂-y₁) / (x₂-x₁)
So, for first line we have (x₁, y₁)=(-4,26)
and (x₂, y₂)=(-2,0)
So, slope(m₁) of first line is =(0-26)/(-2 - (-4))
=>m₁ = -26/2
=>m₁ = -13 ----(eq1)
Similarly, for second line, we have (x₁, y₁)=(10,18)
and (x₂, y₂)=(5,3)
So, slope(m₂) of second line is =(3-18) / (5-10)
=>m₂ = -15/-5
=>m₂= 3 -------(eq2)
On comparing eq1 and eq2,we get
=>m₁≠m₂.
Hence, the given lines are not parallel.
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(Complete question) is:
Is the line through (-4, 26) and (-2, 0) parallel to the line through (10, 18) and (5, 3)?
In July, the price of a gallon of gasoline rose 12%. In August it fell 15% of its final July price, ending
the month at $1.19. What was its price at the beginning of July
Price of a gallon of gasoline at the beginning of July was $2.41
What is percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.
According to the question:
In July, the price of a gallon of gasoline rose=12%
In august, it fell 15% of its final July price,
Ending the month at 1.19 rupees
Let us consider,
x is the original price at the beginning of July,
then the price of gasoline rose is 112%
=100+2
=112%
=112/100
=1.12
In august it fells 15%=100-15%
=.85%
With the help of given data
the original price is---- x
(1.12) × (.85) x = 2.29
find the value of x
x = 2.29/0.952
x=2.41
x=2.41 was its price at the beginning of July.
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i need help, i don’t understand
Answer:
x = 2; y = 10
Step-by-step explanation:
y = 5x
2x + 3y = 34
You have a system of equations. Since the first equation is already solved for y, we can easily use the substitution method. Substitute 5x for y in the second equation.
2x + 3y = 34
2x + 3(5x) = 34
2x + 15x = 34
17x = 34
x = 2
Now substitute 2 for x in the first equation.
y = 5x
y = 5(2)
y = 10
Solution: x = 2; y = 10
