The expression as 3f – 2.
The value when f = 4.5 is 11.5.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario
Two less than the product of a number and three will be:
(3 × f) - 2
= 3f - 2
When f = 4.5
(3 × 4.5) - 2
= 11.5
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let s 5 {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s. must there be two integers whose sum is 15? why?
The given set have two integers whose sum is 15 because if we selcet the element from the given set then there sum is equal to 15.
In the given question, let s = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s.
We have to check there be two integers whose sum is 15.
As we know that,
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The letter Z or the chalkboard Z is frequently used to represent the set of integers in mathematical terminology.
There are total 10 elements.
We have to choose two element from the given set which sum is equal to 15.
If we choose 3 and 12 then there sum is 15.
Similarly, if select (5,10), (6,9), (7,8) the sum of all these selection is 15.
So the given set have two integers whose sum is 15.
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Please answer this question ty.
Answer:
u forgot the question...........
A mathematical model was created and solved using linear programming. The optimal values were determined: x1 = 10 and x2 = 10. If one of the constraints is: 4x1 + 2x2 >= 55, you can conclude that:
A.this is a binding constraint, so there is no slack or surplus
B.there are 15 units of surplus
C.there are 15 units of slack
D.there are 5 units of slack
E.there are 5 units of surplus
In mathematics, linear programming is a technique for maximizing operations under certain restrictions.
Why does a mathematical model of a linear programming problem is important?Using the mathematical modeling technique of linear programming, a linear function is maximized or minimized depending on the restrictions it is subjected to. This method has proved helpful for directing quantitative judgments in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.
In mathematics, linear programming is a technique for maximizing operations under certain restrictions. Maximizing or minimizing the numerical value is the primary goal of linear programming. It comprises of linear functions that are subject to restrictions in the form of inequalities or linear equations.
Therefore, the correct answer is option A. this is a binding constraint, so there is no slack or surplus.
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Classify the triangle with the given side lengths as
acute, right, obtuse, or not a triangle.
5, 9, 10
The angle with sides 5, 9 and 10 is an obtuse triangle
Obtuse AngleThis is a type of angle in which the angles are less than 180 degrees but less than 180 degrees.
In this case, we can easily determine if it's an obtuse angle.
Assuming the longest side is 10 units, the sum of it's two other sides must be greater than it's longest side which is supposedly the hypothenuse.
5 + 9 = 14
14 > 10
This indicates that the triangle is an obtuse triangle.
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Someone please help I can’t figure out 11, 13, or 15 I just need an explanation and how to set the equation up!!??
The solution to each of the system of equations is given as follows:
11. (1,-1).
13. (-6,-5).
15. (-4,3).
What are the solutions to the system of equations?For item 11, the system is given as follows:
5x = y + 6.5x + 2y = 3.The variable x can be isolated as follows:
5x = y + 6.5x = 3 - 2y.Then the solution for y is given as follows:
y + 6 = 3 - 2y
3y = -3
y = -1.
Then the solution for x is of:
5x = -1 + 6
5x = 5
x = 1.
Following the same procedure, in item 13, we have that:
3y = 6x + 21.3y = 4x + 9.Hence the solution for x is of:
6x + 21 = 4x + 9
2x = -12
x = -6.
The solution for y is of:
3y = 4(-6) + 9
3y = -15
y = -5.
For item 15, we have that:
x = 5 - 3y.x = -6y + 14.Hence the solution for y is of:
5 - 3y = -6y + 14
3y = 9
y = 3.
Then the solution for x is of:
x = 5 - 3(3)
x = 5 - 9
x = -4.
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how to find slope of negative line
Answer: The slope of a negative line can be calculated using (y2 - y1)/(x2 - x1)
Step-by-step explanation:
Example:
(2, -4) (3, -5)
(y2 - y1)/(x2 - x1)
-5 - -4 / 3 - 2
-1/1
Slope = -1
(d)
Most of the kinetic energy of the diver is transferred to the water.
How does this affect the thermal energy of the water?
Tick (✓) one box.
The thermal energy decreases.
The thermal energy stays the same.
The thermal energy increases.
Most of the kinetic energy of the water is transferred into the water, then the thermal energy will increase. Hence, option C is correct.
What is kinetic energy?Kinetic energy is the term used in physics to describe the force that a moving item has. It is described as the amount of effort necessary to accelerate anybody with a particular mass from rest to a given velocity. Except variations in speed, the body retains the kinetic energy it gains during acceleration.
The body uses exactly the same amount of energy when slowing down from its current rate to a state of rest. Formally, kinetic energy refers to any term in a system's Lagrangian that has a derivative with respect to time.
As per the given information in the question,
When the kinetic energy of the diver is transferred into the water, the thermal energy will increase.
The entity's thermal energy grows as the average kinetic energies of its particles rise. As a result, an object's thermal energy rises as its temperature does.
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A salesperson at a jewelry store earns 6% commission each week. Last week, jarrod sold $680 worth of jewelry. How much did make in commission? How much did the jewelry store make from sales?
Answer:
1/ $ 4.08
2/ $675.92
Step-by-step explanation:
Take 68 times 0.06% = $4.08
680 - 4.08= 675.92
Answer:
Step-by-step explanation:
40.80 it told me the answer
what is the rate of change?
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{50}~,~\stackrel{y_1}{45})\qquad (\stackrel{x_2}{70}~,~\stackrel{y_2}{61}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{61}-\stackrel{y1}{45}}}{\underset{run} {\underset{x_2}{70}-\underset{x_1}{50}}} \implies \cfrac{ 16 }{ 20 } \implies {\Large \begin{array}{llll} \cfrac{4 }{ 5 } \end{array}}[/tex]
the royal fruit company produces two types of fruit drinks. the first type is 60% pure fruit juice, and the second type is 85% pure fruit juice. the company is attempting to produce a fruit drink that contains 75% pure fruit juice. how many pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 75% pure fruit juice?
The pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 75% pure fruit juice is 72 and 108 pints respectively.
Let juice A = a
60% pure fruit juice
Let juice B = b
85% pure fruit juice
We need to make 180 pints of juice from both
a + b = 180
represented in terms of pure fruit
a = 0.60; b = 0.85 ;
Our mixed fruit juice from a and b should be 75% pure fruit = 0.75
Mathematically,
0.60a+ 0.85b = 180(0.75)
0.60a + 0.85b =135
Multiply this equation by 100
60a+ 85b = 13500
Now we have two equations for two variables,
a + b = 180 and
60a+ 85b = 13500
Multiply equation 1 by 60,
we get,
60a + 60b = 10800
On solving these equations we get,
b = 108
Substitute b = 108 into the second equation
60a+ 85(108)= 13500
60a+ 9180 = 13500
a = 72
Therefore , the pints of juice A required is 72 pints and the pints of juice B required is 108 pints.
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Answer:
Step-by-step explanation:
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of the two existing types of drink must be used to make 60 pints of a mixture that is 75% pure juice?
Suppose you deposit 1,000$ in a savings account that pays interest at an annual rate of 6%. If no money is added or withdrawn from the account, answer the following questions.
a. How much will be in the account after 4 years?
b. How much will be in the account after 17 years?
c. How many years will it take for the account to contain 1,500$?
d. How many years will it take for the account to contain 2,000$?
Answer:
a. $1240
b. $2020
c. 8.3 years
d. 16.7 years
Step-by-step explanation:
Using the simple interest formula, I = Prt, we solve as follows.
a.
I = 1000 × 0.06 × 4 = 240
1000 + 240 = 1240
Answer: a. $1240
b.
I = 1000 × 0.06 × 17 = 1020
1000 + 1020 = 2020
Answer: b. $2020
c.
$1500 - $1000 = $500
Interest is $500
500 = 1000 × 0.06 × t
t = 8.3
Answer: c. 8.3 years
d.
$2000 - $1000 = $1000
Interest is $1000
1000 = 1000 × 0.06 × t
t = 16.7
Answer: d. 16.7 years
Answer:
Please note I have assumed the interest is compounded annually.
a) $1,262.48
b) $2,692.77
c) 7 years
d) 12 years
Step-by-step explanation:
Assuming the interest is compounded annually.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
P = $1,000r = 6% = 0.06Substitute the given values into the formula to create an equation for A in terms of t:
[tex]\implies A=1000(1+0.06)^t[/tex]
[tex]\implies A=1000(1.06)^t[/tex]
Part (a)To calculate how much will be in the account after 4 years, substitute t = 4 into the equation:
[tex]\implies A=1000(1.06)^4[/tex]
[tex]\implies A=1000(1.2624769...)[/tex]
[tex]\implies A=1262.4769...[/tex]
Therefore, there will be $1,262.48 in the account after 4 years.
Part (b)To calculate how much will be in the account after 17 years, substitute t = 17 into the equation:
[tex]\implies A=1000(1.06)^{17}[/tex]
[tex]\implies A=1000(2.69277278...)[/tex]
[tex]\implies A=2692.77278...[/tex]
Therefore, there will be $2,692.77 in the account after 17 years.
Part (c)To calculate how many years it will take for the account to contain $1,500, substitute A = 1500 into the equation and solve for t:
[tex]\implies 1500=1000(1.06)^t[/tex]
[tex]\implies 1.5=(1.06)^t[/tex]
[tex]\implies \ln 1.5=\ln (1.06)^t[/tex]
[tex]\implies \ln 1.5=t \ln (1.06)[/tex]
[tex]\implies t=6.95851563...[/tex]
Therefore, it would take 7 years for the account to contain $1,500.
Part (d)To calculate how many years it will take for the account to contain $2,000, substitute A = 2000 into the equation and solve for t:
[tex]\implies 2000=1000(1.06)^t[/tex]
[tex]\implies 2=(1.06)^t[/tex]
[tex]\implies \ln 2=\ln (1.06)^t[/tex]
[tex]\implies \ln 2=t \ln (1.06)[/tex]
[tex]\implies t=11.8956610...[/tex]
Therefore, it would take 12 years for the account to contain $2,000.
Classify the triangle shown by sides and angles.
Answer:
Acute Scalene Triangle
Step-by-step explanation:
Look at all three angles of the triangle they are all acute. In addition, all of the angles on the triangle are different making it scalene.
Aiyub vai loves to eat apples. He eats apples in an interesting way. After buying apples, on the first day, he eats 1 apple; on second day, he eats 2 apples; on the third day, he eats 3 apples. For the next few days he eats apples in a way such that, on day N , he eats n apples more than that he ate 3 days before. How many apples will he eat more in day 99 than that of in day 98?
Answer:
33
Step-by-step explanation:
Difference from
Day Number of apples previous day
1 1 -
2 2 1
3 3 1
4 5 2
5 7 2
6 9 2
7 12 3
8 15 3
9 18 3
10 22 4
11 26 4
12 30 4
13 35 5
14 40 5
15 45 5
16 51 6
17 57 6
18 63 6
19 70 7
20 77 7
21 84 7
The differences between consecutive days started at 1, then 2, then 3, etc. The last day of any specific difference is a multiple of 3.
For example, day 3 was the last day of a difference of 1.
Day 6 was the last day of a difference of 2.
Day 9 was the last day of a difference of 3.
Day 12 was the last day of a difference of 4.
In each case, 6/2 = 3; 9/9 = 3; 12/4 = 3.
99 is a multiple of 3, so it will be the last day with a difference of 99/3 = 33
Answer: 33
which of the following is the best description of a simple random sample of size n
A) Any method of sampling in which individuals are selected in a completely haphazard fashion.
B) Any method of sampling in which every group of individuals of size n is equally likely to be selected.
C) Any method of sampling in which every individual is equally likely to be selected.
D) Any method of sampling in which each individual has a probability of n/N of being selected.
Any method of sampling in which every individual is equally likely to be selected.
What does "simple random sampling" mean?
Simple random sampling is a sort of probability sampling in which a subset of participants from a population is randomly chosen by the researcher.
There is an equal opportunity for selection for every person in the population. Then, data are gathered from as many of the individuals in this chosen subset as is feasible.
A simple random sampling is a method of sampling where each potential participant has an equal chance of being chosen. In other words, the likelihood that any given person will be chosen is 1/n if there are n people.
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the edison electric institute has published figures on the number of kilowatt hours used annually by various home appliances. it is claimed that a vacuum cleaner uses an average of $46$ kilowatt hours per year. if a random sample of $12$ homes included in a planned study indicates that vacuum cleaners use an average of $42$ kilowatt hours per year with a standard deviation of $11.9$ kilowatt hours, do these data suggest that at the $0.05$ significance level the mean annual usage of vacuum cleaners is less than $46$ kilowatt hours? assume the population distribution of usage in kilowatt hours to be normal.
The test statistic is less than - 1.796
Hypothesisi test
H0: μ = 46
Ha: μ < 46
This is a lower tailed test
mean = 42
standard deviation = 11.9
sample size n = 12
The level of significance α = 0.05
degree of freedom df = n - 1 = 12 - 1 = 11
Test statistic = (x - mean)/(standard deviation / √n) = (42 - 46)/(11.9 / √12) = - 1.164
Test statistic = - 1.164
Using t- table, we can observe that the p - value is between 0.10 and 0.15
Using excel we find p - value = P(t < - 1.796)
p value = 0.1344
H0: μ < 46, rejection rule is
Reject H0 if test statistic < - 1. 796
Therefore, we reject the hypothesis as the test statistic is less than - 1.796
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Ava made 5% of her free throws over the season. If she shot 120 free throws,
how many did she make?
The free throws she made by an accuracy of 5% in 120 is a total of 6
How to determine how many of the free throws she make?The given parametes from the question are
Free throw made = 5%
Total number of free throws = 120
The above means that we multiply the percentage of free throws made by the total number of free throws to determine the count of free throws made
Having mentioned that, we have
Free throw made = 5% * Total number of free throws
So, we have
Free throw made = 5% * 120
Evaluate
Free throw made = 6
Hence, she made 6 of 120 free throws
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Find the two numbers which on multiplication with √360 gives a rational number. Are these numbers rational or irrational?
Answer:
The two numbers we are looking for are a rational number and an irrational number.
Step-by-step explanation:
To find the two numbers that, when multiplied by the square root of 360, give a rational number, we can consider the prime factorization of 360. 360 can be written as 2^3 * 3^2 * 5, so the square root of 360 is equal to √(2^3 * 3^2 * 5) = 2√(3 * 5) = 2√15.
Now, suppose we want to find a rational number that is equal to x * √15. We can rewrite this expression as x * √(3 * 5) = x * √3 * √5. For this expression to be rational, both x and √3 must be rational or both must be irrational.
If x is rational, then the expression x * √3 * √5 is rational. Therefore, one of the two numbers we are looking for is x, which is a rational number.
If x is irrational, then the expression x * √3 * √5 is irrational. Therefore, the other number we are looking for is √3, which is an irrational number.
Therefore, the two numbers we are looking for are a rational number and an irrational number.
Create a binomial probability experiment with the data from the public opinion poll experiment. Use the probability of success and failure from the experiment. Calculate the probability of the number of successes in 100 random tests. For example, if the probability of success is 0.20 and the number of trials is 100, then the number of successes is 20.
Please give and answer my grade has never depended on something more. thank you.
Binomial probability distribution for the given set of data is
[tex]100C_x (0.20)^x (0.80)^{100-x}[/tex]
What is binomial probability distribution?
"Binomial probability distribution is the representation of a probability with only two outcomes success and failure under given number of trials."
Binomial probability distribution is given by
[tex]nC_x p^x q^{n-x}[/tex]
n= number of experiments
x = 0, 1, 2, 3,.......
p = probability of success
q = probability of failure
According to the given question
Number of trials 'n' = 100
Probability of success 'p' = (20 / 100)
= 0.20
Probability of failure 'q' = 1 - p
= 1 - (20/100)
= (80 / 100)
Substitute the value in the formula we get
Required probability = [tex]100C_x (0.20)^x (0.80)^{100-x}[/tex]
Example:
Tossing a coin 6 times getting exactly two heads.
Number of trials 'n' = 6
Number of heads 'x' =2
Only two possible outcomes head or tail
Probability of getting head 'p' = 1 / 2
Probability of not getting head 'q' = 1 /2
Required probability = [tex]6C_2[/tex] (1/2)²(1/2) ⁶⁻²
= [tex]6C_2\\[/tex] (1/2)⁶
Hence, binomial probability distribution for the given set of data is
[tex]100C_x (0.20)^x (0.80)^{100-x}[/tex]
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y=-1/2X
thank you for your time
Kiki runs 437 miles during the first week of track practice. She runs 623 miles during the second week of track practice.
How much longer does Kiki run during the second week of track practice than the first week of track practice?
1521 mi
125 mi
2521 mi
225 mi
QUICK PLEASE!!!!!!
Answer:
186- none of those answers are correct, the right answer is one hundred eighty six miles
Step-by-step explanation:
623
-437
____
186
Answer:
The difference in the number of miles run by Kiki during practice is 186 miles.
Step-by-step explanation:
Given that Kiki runs 437 miles during the first week of track practice and she runs 623 miles during the second week of track practice.
The difference in miles will be:
= 623 - 437 = 186 miles.
A line segment has endpoints R (-3,-3) and S (5.2). What is the x-coordinate of the point that is 3/4 of the way from R to S on this line segment?
The x-coordinate of the point i.e. 3/4 of way from R to S is 3/7, using the segment formula.
What is segment formula ?
Segment formula is the easiest way to find x and y coordinate of a point when ratio of distances over end point is given i.e.:
Let the coordinate of point P(x, y) dividing the line segment joining the points A(x1 , y1) and B(x2 , y2) internally in ratio m1:m2 then
x= [tex]\frac{m1x2+m2x1}{m1+m2}[/tex]
y = [tex]\frac{m1y2 + m2y1}{m1+m2}[/tex]
using given information,
Let R is 1st point and S is 2nd point ,
3/4 is the ratio so,
m1 = 3,
m2 = 4
x1 = -3
x2 = 5
y1 = -3
y2 = 2
Putting values in above formula for x,
we get
x = 3/7
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The angle measures of an isosceles triangle are (4x + 5)°, (4x + 5)°, 10°.
What is the measure (in degrees) of an exterior angle supplementary to one
of the base angles?
The measure of an exterior angle supplementary to one of the base angles of this isosceles triangle is 2 * (4x + 5)° = 8x + 10°.
What is an isosceles triangle?
An isosceles triangle, therefore, has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (leg)
In an isosceles triangle, the two base angles are equal. Therefore, the measure of each base angle is (4x + 5)°.
An exterior angle of a triangle is supplementary to one of the base angles if it forms a straight line with the base angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two base angles.
Therefore, the measure of an exterior angle supplementary to one of the base angles of this isosceles triangle is 2 * (4x + 5)° = 8x + 10°.
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1. The line of best fit for a data set is y = 1.1x + 3.4. Find the residual for each of the coordinate pairs, (x, y).
a. (5,8.8)
b. (2.5,5.95)
c. ((0,3.72)
d. (1.5,5.05)
e. (-3,0)
f. (-5,-4.86)
The residual for each of the coordinate pairs, (x, y) are-
a) -3.1; b) -0.2; c) 0.32; d) 0; e) -0.1; f) -6.96.
Explain the term line of best fit?A straight line which minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis as well as a tool for forecasting indicators and price changes.For the stated question;
Data is given by the line of best fit as;
y = 1.1x + 3.4
Then, the residual for the given coordinates are found as;
Residual = y - (1.1x + 3.4)
a. (5,8.8)
Residual = 5.8 - (1.1(5) + 3.4)
Residual = -3.1
b. (2.5,5.95)
Residual = 5.95 - (1.1(2.5) + 3.4)
Residual = -0.2
c. ((0,3.72)
Residual = 3.72 - (1.1(0) + 3.4)
Residual = 0.32
d. (1.5,5.05)
Residual = 5.05 - (1.1(1.5) + 3.4)
Residual = 0
e. (-3,0)
Residual = 0 - (1.1(-3) + 3.4)
Residual = -0.1
f. (-5,-4.86)
Residual = -4.86 - (1.1(-5) + 3.4)
Residual = -6.96
Thus, the residual for each of the coordinate pairs, (x, y) are found.
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a ________ value in a loop can be either a positive or a negative number.
A Increment value in a loop can be either a positive or a negative number.
Positive Increment: A positive increment is when the value of the loop increases on each iteration.
Negative Increment: A negative increment is when the value of the loop decreases on each iteration.
In a step value, the counter variable is either an increment or a decrement every time the loop is executed. If the counter variable is decreased, it can go as low as a negative number, whereas with an increment, the counter variable can be either negative or positive with each loop executed increased.
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Which scatter plot shows the best line of fit?
Multiple choice question.
A)
B)
C)
D)
Answer:
D
Step-by-step explanation:
The line of best fit is a line that represents the “average” between all of the points. It’s typically in the middle of all of the points. In this case, I’d go with D because 4 points lie on the line of best fit and the line trends sharply upwards, following the general direction of the points.
Find an explicit rule for the nth term of the arithmetic sequence. -20, -14, -8, -2, ... A. an = -20 + 6(n+2) B. an = -20 + 6(n-1) C. an = -20 Ã 6(n-1) D. an = -20 + 6(n+1)
the explicit rule of the nth term of the arithmetic
sequence is A. aₙ = 6n-8
B. aₙ = 6n-26
C. aₙ= 6n-26
D. aₙ =6n-14
What is arithmetic sequence?the sequence of numbers having constant differences between two successive numbers.
why explicit formula for arithmetic sequence is used?the explicit formula is used for determining any term of an arithmetic sequences directly in where only the first term and differences between two consecutive terms are needed to know.
Given, -20,-14,-8,-2,...are the terms. an explicit rule for the nth term of the arithmetic sequence is given by the formula, aₙ=a₁+(n-1) d
where, a₁ is the first term, aₙ is the nth term, d is the difference between two terms, n is the number of terms.
as per question a₁= -20, d= 6
now A. aₙ = -20+6(n+2)
aₙ = 6n-8
B. aₙ= -20+6(n-1)
aₙ = 6n-26
C. aₙ =-20+6(n-1)
aₙ = 6n-26
D. aₙ= -20+6(n+1)
aₙ = 6n-14
the above are the explicit rules for the arithmetic sequence.
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Priya invests a sum of money at an interest rate of 8% per year.
At the end of one year, the interest she receives is 1800 rupees.
Work out the value of Priya’s investment at the end of one year.
The value of Priya's investment at end of the year is Rs. 24300.
Simple Interest:The formula for simple interest is given by
Simple interest, I = PTR/100Where, P = Principal amount, T = Time period, and R = Rate of interest
And the formula for the Amount at end of the time period is given by
Amount, A = P + IHere we have
Priya invests a sum of money at an interest rate of 8% per annum
The interest that she gained after 1 year = 1800 Rs.
Let P be the principal amount i.e Priya's investment
Then calculate Simple interest on P at 8% for 1 year
As we know Simple interest = PTR/100
Interest on P = P(1)(8)/100 = 0.08P
From the given data, interest at end of the year = Rs. 1800
=> 0.08P = 1800
=> P = 1800/0.08
=> P = 22500
The amount that Priya invested = Rs. 22500
As we know Amount = Principal amount + interest
= Rs. 22500 + Rs. 1800
= Rs. 24300
Therefore,
The value of Priya's investment at end of the year is Rs. 24300.
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Graph shows two lines on a coordinate plane. A line labeled p goes through (2, 2) and (0, minus 4). Another line labeled q goes through (0, 2) and (2, minus 4). Both lines intersect at X-axis at 1 and Y-axis at minus 1. The slope of line p is , and the slope of line q is .
The slope of line p is 3, and the slope of line q is -3
How to determine the slopes of the lines?From the question, we have the points that can be used in our computation:
Line p
From the line p, we have the following ordered pairs
(2, 2) and (0, -4)
Line q
From the line p, we have the following ordered pairs
(0, 2) and (2, -4)
Rewrite the above points properly
So, we have the following ordered pairs
Line p, (x, y) = (2, 2) and (0, -4)
Line q, (x, y) = (0, 2) and (2, -4)
The slopes of the lines are then calculated using the following slope equation
slope = (y₂ - y₁)/(x₂ - x₁)
Substitute the known values in the above equation
So, we have the following equation
Slope of line p = (-4 - 2)/(0 - 2)
Evaluate
Slope of line p = 3
Slope of line q = (-4 - 2)/(2 - 0)
Evaluate
Slope of line q = -3
Hence, the slopes are 3 and -3, respectively
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Can square root of 34 be simplified?
Answer:
are you stupif? no dumas
Step-by-step explanation:
does someone mind helping me with this problem? Thank you!
Answer:
Below
Step-by-step explanation:
Point slope form of the new line would be
(y -2) = m (x-3) from the given formula
From the GIVEN line....its slope, m , is 1/2
perpendicular slope is - 1/m = -2 ( this is something you have to remember/learn)
then the NEW Line becomes
(y-2) = -2 ( x-3) expand and simplify
y-2 = -2x+ 6
y = -2x + 8 Done !
Answer:
y = - 2x + 8
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{1}{2}[/tex] x - 9 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/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{1}{2} }[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute the point (3, 2 ) into the partial equation
2 = - 2(3) + c = - 6 + c ( add 6 to both sides )
8 = c
y = - 2x + 8 ← equation of perpendicular line
