The slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.
First, let us understand the slope of a line:
A slope of a line is defined in mathematics as the change in the y coordinate with regard to the change in the x coordinate.
We are given the points:
(0, 1) and (1, -2)
We will calculate the slope of the line using the following formula:
m = (y_2 - y_1) / (x_2 - x_1)
Let x_1 = 0, x_2 = 1, y_1 = 1 and y_2 = -2.
Substitute the given values in the above formula, we will get:
m = (-2 - 1) / (1 - 0) = -3 / 1 = -3
So, the slope of the line is -3.
Thus, the slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.
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write the formula to find the sum of 1st 'n' term of a ap with and the last terma
The sum of the first 'n' terms can be expressed as [tex]S_n=\frac{n}{2}[2+(n-1)][/tex]
and the last term will be [tex]t_n = 1+(n-1)[/tex], where a is the first term of A.P. and 'd' is a common difference.
What is an arithmetic progression?
An arithmetic progression or arithmetic sequence is a number sequence in which the difference between consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15.. is an arithmetic progression with a common difference of 2.
The first 'n' terms will be 1, 2, 3, 4, 5, 6, ...., n
The above sequence is an A.P. because it has a constant common difference of '1' between each consecutive number.
So a = 1, d = 1
By using the standard formula, we get
[tex]S_n=\frac{n}{2}[2a+(n-1)d]\\\\S_n=\frac{n}{2}[2+(n-1)][/tex]
and for the last term
[tex]t_n=a+(n-1)d\\\\t_n=1+(n-1)[/tex]
Hence, the sum of the first 'n' terms can be expressed as[tex]S_n=\frac{n}{2}[2+(n-1)][/tex]
and the last term will be [tex]t_n = 1+(n-1)[/tex], where a is the first term of A.P. and 'd' is a common difference.
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Explain the error in the equation that is written in standard form.
-4x + 3y = 20
Edit:
The standard form would be:
3y = 20 - 4x
or
3y = -4x + 20
Answer/Step-by-step explanation:
Standard form of the equation should be in the form:
Ax + By = C
A, B and C must be whole numbers not fractions or decimals. B and C can be negative, but A must be positive.
Correctly written in standard form, this equation just needs one small tweak, multiply the whole thing by -1 to change all the signs so that the A will be positive.
-4x + 3y = 20
-1(-4x + 3y = 20)
4x - 3y = -20 this is proper standard form.
Haley buys 18 bars of chocolate which cost her $5.40. TO raise money for charity she sells them at 40 cents each. She manages the sell them all.what is haley's percentage profit ?
Answer:
33.333...% over the base 100% (100% is representing the $5.40)
Step-by-step explanation:
she gets $7.20 from selling the 18 chocolate bars
7.20 divided by 5.40 is 1.3333...
the 1 in 1.3333... represents the base 5.40 and the 0.3333... represents the profit
If m^n=32, where m
and n are positive integers, find n^mn
The value of [tex]n ^ {mn}[/tex] = [tex]5^{10}[/tex] or 9765625.
An index is a number that is raised to power. It is written as a small number to the right and above the base number. Other names for the index are exponent or power.
The index of a number says how many times to use the number in multiplication.
[tex]m^n[/tex]=32
m and n are positive integers.
32 = 2 x 2 x 2 x 2 x 2
32 = [tex]2^5[/tex]
hence, m = 2 and n = 5.
Now, Let's find the value of [tex](n ^ m)^n[/tex].
[tex](n ^ m)^n = n^{m*n}[/tex]
= [tex]5^{2*5}[/tex]
= [tex]5^{10}[/tex] or
= 9765625
Hence, the value of [tex]n ^ {mn}[/tex] = [tex]5^{10}[/tex] or 9765625.
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Can someone help me really quick
(Please Explain how you know this is correct.)
$0.4 is the price per gallon at Miguels gasoline station
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Six customers are buying Gasoline at Miguels gasoline station.
Gasoline bought is marked on x axis and cost on the y axis.
We need to find price per gallon at Miguels gasoline station
If gasoline bought are 4 then cost is 10
Four divided by ten is zero point four.
4/10=0.4
Hence $0.4 is the price per gallon at Miguels gasoline station
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a simple random sample of 31 observations was taken from a large population. the sample mean equals 5. five is a group of answer choices population parameter point estimate population mean standard error
If a simple random sample of 31 observations was taken from a large population. The sample mean equals 5 then the five is a point estimate
Total number of population = 31 observations
Sample mean of the population = 5
Sample mean is the average value of the sample that is selected from a large population of data.
The point estimate is defined as the single value estimate of the parameter. Point estimate is usually use when we have to choose single value from a larger population, that should be the best estimate to represents the parameter.
Here the sample mean of population is 5
Therefore, five is a point estimate
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Liz and Caroline are playing checkers. Out of 12 games, Liz wins six. At this rate, how many games will she win if they play 84 games ?
Answer:
42 games
Step-by-step explanation:
she lost 6 and won 6 so if she played 84 games she will win 42 and lose 42
I need help please Find the measure of each angle
Answer:
3.54
Step-by-step explanation:
The table shows the proportional relationship between the price for a certain number of buckets of golf balls at a driving range.
Buckets 2 5 7
Price (dollars) 14.50 36.25 50.75
Determine the constant of proportionality.
14.5
7.25
21.75
8.25
Answer:
B) 7.25Step-by-step explanation:
Proportional relationship equation:
y = kx, where k-constant of proportionalityIn the given table, number of buckets represent input values (x) and the price represents output values (y).
We have for the first column:
x = 2, y = 14.50Find the value of k by plugging in the values of x and y:
14.50 = 2kk = 14.50/2k = 7.25Same result will be obtained with the other columns, therefore the constant of proportionality is 7.25.
Answer:
b) 7.25
Step-by-step explanation:
Formula we use,
→ y = kx
→ k = y/x
Now the value of k will be,
→ k = y/x || → k = y/x
→ k = 14.5/2 || → k = 36.25/5
→ [ k = 7.25 ] || → [ k = 7.25 ]
Hence, the answer is 7.25.
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Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Lia’s parents allow her to work a maximum of 15 hours per week overall. Lia’s goal is to earn at least $120 per week.
Write a system of inequalities to represent this situation. Let r be the number of hours worked at the restaurant, and let y be the number of hours of yard work.
Graph the inequalities.
What is the maximum number of hours Lia can work at the restaurant and still meet her earnings goal? Explain.
What is the maximum amount of money Lia can earn in 1 week? Explain.
THE ASSIGNMENT IS ABOUT SYSTEMS OF INEQUALITIES
Answer:
Step-by-step explanation: (a)
(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours
(d)Maximum Earning = $160
Step-by-step explanation:
Let r be the number of hours worked at the restaurant.
Let y be the number of hours of yard work,
Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.
Since she does yard work,
Lia’s parents allow her to work a maximum of 15 hours per week overall.
Lia’s goal is to earn at least $120 per week.
The restaurant, r pays $8 per hour
Yard work, y pays $12 per hour.
Therefore:
The system of inequalities that represent this problem is therefore:
(b)The graph of the inequality is attached below
(c)When the graph is plotted, the vertices of the feasible region are:
(5,10)
(5, 6.7)
(15,0)
Where the first term is for the number of hours worked in the restaurant.
The maximum value of r possible is 15 from the three points.
Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.
(d)Maximum Amount Lia can earn in 1 Week
At (5,10), Earning=(5X8)+(10X12)=40+120=$160
At (5, 6.7), Earning=(5X8)+(6.7X12)=40+80.4=$120.4
At (15,0) Earning=(15X8)+(0X12)=$120
Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.
which statement is correct? A. ED intersects AB. B. EC is perpendicular to DB. C. AE and DB intersects at point C. D. EB is perpendicular to AC.
The only true statement is line segment ED intersects line segment AB.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
From the given diagram and going through the options we can surely conclude that line segment ED intersects line segment AB.
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If p and q vary inversely and p is 19 when q is 30, determine q when p is equal to 95.
6 is the answer.
Explanation- You have to plug in, multiply, and divide using p1q1=p2q2 formula
0.3(4 − x) = x − 1.4?
Answer:
x is equal to 2
Step-by-step explanation:
simplify the equation
distribute the 0.3
0.3*4-0.3x=x-1.4
1.2-0.3x=x-1.4
get x by itself on one side
1.2+1.4=x+0.3x
simplify
2.6=1.3x
2=x
What is the distance between the two bodies halved?.
When distance is halved, force increases by 4 times.
What is gravitational force?
Each body in the universe attracts other bodies towards itself with a force known as Gravitational Force
Gravitational force is a central force which depends only on the position of test mass from the source mass and always acts along the line joining the centres of two masses.According to Newton’s law of gravitation, “Every particle in universe attracts every other particle with a force whose magnitude is,
Directly proportional to product of their masses, i.e., F ∝ (M1M2)Inversely proportional to the square of the distance between their centre, i.e., (F ∝ 1/r²)On combining these equations, we get
F = G × [M1M2]/r²
F ∝ M1M2/r²
Now , r' = r/2 ( given)
so, F' ∝ (m1m2) / (r/2)²
F' ∝(4 m1m2) / r²
Thus F' = 4×F
So, we can conclude that, when distance is halved, force increases by 4 times.
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What is 33 1/3% of $2,940
Answer:
$980
Step-by-step explanation:
33 1/3% x
------------ = ------------- Cross multiply
100% $2,940
33 1/3 x 2,940 = 100x Multiply
98000 = 100x Divide 100 to both sides
980 = x
If you are working on the part of 5-15 minutes, time-stamping (every 30 seconds) should start at: a. [00:00:00].
A timestamp is a signal that lets us know when the pertinent text was spoken and at what time. They are displayed in the format [HH:MM:SS], where HH stands for hours, MM for minutes, and SS for seconds.
There are various types of timestamps, as follows:-
1. Periodic timestamps: These timestamps are repeated frequently. They can show up every 15 or 30 seconds, or once or twice every minute.
2. Timestamps for paragraphs
3. Timestamps of sentences
4. Timestamps for speakers
When transcribing audio recordings, the following time-stamping format is used:
[00:00:00]
in which [hour: minute: second]
Therefore, [00:05:00] is the fifth minute.
If an audio file has five to fifteen minute segment, needs to be transcribed, stamping should begin at [00:05:00].
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one card is to be selected at random from a deck of cards. find the probability that the card selected is: a) a 5 b) not a 5 c) a diamond or king d) a jack or queen e) a heart and a club f) a card greater than 6 and less than 9
The probability of outcome to be a 5 is 1/13. The probability of outcome not be 5 is 12/13. The probability of outcome to be a diamond or a king is 4/13. The probability of the outcomes to be a jack or a queen is 2/13. The probability of The outcome to be a heart and a club is 0 and the probability of the outcomes to be a card greater than 6 and less than 9 is 2/13.
A deck contains a total of 52 cards.
Total outcomes if the selected number of cards is one=52
Case A:
Each suit contain one 5 numbered card. There are four suits. Therefore, The required outcome would be 4.
Probability of an outcome is the ratio of desired outcomes to the total outcomes.
The probability of outcome to be 5, P(A):
P(A)=4/52
P(A)=1/13
Case B:
The total probability of outcomes=52/52=1
The probability of the outcome to be 5=1/13
Therefore, the probability of the outcome not to be 5, P(B):
P(B)=1-(1/13)
P(B)=12/13
Case C:
Each suit carries a king. Therefore, the probability of the outcome to be a king, P(M):
P(M)=4/52
P(M)=1/13
A suit carries 13 cards. Therefore, there will be 13 cards of diamonds.
The probability of the outcome to be a diamond, P(N):
P(N)=13/52
P(N)=1/4
The probability that the outcome is a king of diamonds, P(M[tex]\cap[/tex]N):
P(M[tex]\cap[/tex]N)=1/52
Hence, the probability that the outcome is a diamond or a king, P(M[tex]\cup[/tex]N):
P(M[tex]\cup[/tex]N)=P(M)+P(N)-P(M[tex]\cap[/tex]N)
P(M[tex]\cup[/tex]N)=(1/13)+(1/4)-(1/52)
P(M[tex]\cup[/tex]N)=16/52
P(M[tex]\cup[/tex]N)=4/13
Case D:
Each suit carries a Jack. Therefore, the probability of the outcome to be a jack, P(P):
P(P)=4/52
P(P)=1/13
Each suit carries a Queen. Therefore, the probability of the outcome to be a Queen, P(Q):
P(Q)=4/52
P(Q)=1/13
The probability that the outcome is a jack and a queen, P(P[tex]\cap[/tex]Q):
P(P[tex]\cap[/tex]Q)=0/52
P(P[tex]\cap[/tex]Q)=0
Hence, the probability that the outcome is a jack or a queen, P(P[tex]\cup[/tex]Q):
P(P[tex]\cup[/tex]Q)=P(P)+P(Q)-P(P[tex]\cap[/tex]Q)
P(P[tex]\cup[/tex]Q)=(1/13)+(1/13)-0
P(P[tex]\cup[/tex]Q)=2/13
Case E:
A card is never a heart and a club. Therefore, the probability of a card to be a heart and a club is 0.
Case F:
The numbers greater than 6 and less than 9 are the numbers between 6 and 9. The numbers between 6 and 9 are 7 and 8.
Each suit carries one 7 numbered card and one 8 numbered card. There is a total of 4 suits.
Therefore the desirable outcomes=8
The probability of the outcome required=8/52
=2/13
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Solve 24-3r≥-9.
Solution:
Graph the solution.
-10 -8
-6
-4
-2
0
2
+
4
4
Graph D represent the function.
Function is a representation of continue graph which can't be break so B and C are eliminated from the option.
1. Draw all possible linea parallel to Y- axis
2. If any line cuts the graph at two or more than two points then it is not a function
Reason:- function ka definition hai, element of A related to Only single (one/unique) element in set B.
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Graph D represent the function
Function is a representation of continue graph which can't be break so B and C are eliminated from the option.
1. Draw all possible linea parallel to Y- axis
2. If any line cuts the graph at two or more than two points then it is not a function
Reason:- function ka definition hai, element of A related to Only single (one/unique) element in set B.
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Jaida worked 21.5 hours last week. She earned $11.60 per hour of work.
How much money did Jaida earn last week?
$9.90
$249.40
$1.85
$33.10
Answer:
249.40
Step-by-step explanation:
How to calculate amount of work?
According to this question, Jaida worked 21 ½ hours last week and earned $11.60 per hour of work.
If Jaida earned $11.60 per hour, this means that Jaida earned 21.5 × 11.6 = $249.4.
Therefore, If Jaida worked 21½ hours last week and earned $11.60 per hour of work. The amount of money Jaida earned last week is $249.4.
Edward buys 6 yards of fabric for $15. How much money does it cost per
yard?
Answer:
$2.5
Step-by-step explanation:
15 divided by 6 because its asking to split into groups equally
Answer:2.5
Step-by-step explanation:
Make x the subject of the formula
X/2c = a+4
The value of x the subject of the formula is 2c(4+a)
What is meant by mathematical expression ?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Equation with Lines
More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
Given ,
X/2c = a+4 by simplifying ,
x=2c(4+a)
Therefore the value of x the subject of the formula is 2c(4+a)
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6·3+6-4+6·5
6 · 3 + 6 · 4 + 6 · 5 + 6 · 8 + 2[3 · 4+ (3 · 4)]
Answer:
6·3+6-4+6·5
6 · 3 + 6 · 4 + 6 · 5 + 6 · 8 + 2[3 · 4+ (3 · 4)]=168
Answer:
one on top is 50
Step-by-step explanation:
Find the domain values of the function f(x)= 2x + 7 when the given range are {1, -1, 3}.
Answer:
(-3,-4,-2)
Step-by-step explanation:
You are given the y-values and want to find the x-values.
1 = 2x +7
-6 = 2x
-3 = x
-1 = 2x +7
-8 = 2x
-4 = x
3 = 2x +7
-4 = 2x
-2 = x
Can someone help me with the question I will give you Brainliest so please help Asap.
Is each product less than 1, equal to 1, or greater than 1?
Place each product into the correct box.
1/2x4 1/2x1 1/4x3
The product is greater than 1 < 8.4375
Given:
In the question:
Product the following question:
1/2 x 4[tex]\frac{1}{2}[/tex] x [tex]1\frac{1}{4}[/tex] x 3
Now, According to the question;
1/2 x 4[tex]\frac{1}{2}[/tex] x [tex]1\frac{1}{4}[/tex] x 3
Solve the mixed fraction:
1/2 x 9/2 x 5/4 x 3
Write as a single fraction:
(9 x 5 x 3) / (2 x 2 x4)
Calculate the product or quotient:
= 135/ 16
= 8.4375
Hence, The product is greater than 1 < 8.4375
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A, B, C and D lie on a circle a centre O. AB=7cm BC=10cm and angle ABD=77%.
AOC is a diameter of the circle
Answer:
4
Step-by-step explanation:
1
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A line has a slope of 0 and passes through the point (3, 4) . What is its equation in slope -intercept form?
Each square below represents one whole.
(one square - all shaded in of 4)
(second square - 3 shaded in of 4)
What percent is represented by the shaded area?
Answer:
The percent being represented by the shaded area is [tex]175\%[/tex]
Step-by-step explanation:
The percent being represented by the shaded area can be calculated as follows
The first step is to evaluate the left square
Since each square represents one whole, and since the left square is all shaded in of [tex]4[/tex] then the percent being represented by the shaded area in the left square is
[tex]1=\frac{4}{4}=\frac{100}{100}=100\%[/tex]
The percent being represented by the shaded area in the first or the left square is [tex]100\%[/tex]
The second step is to evaluate the right square
Since the right or the second square is [tex]3[/tex] shaded in of [tex]4[/tex], then the fraction being represented by the shaded area in the second square is
[tex]\frac{3}{4}[/tex]
The third step is to convert [tex]\frac{3}{4}[/tex] into the percent form by the following equation
[tex]\frac{3}{4}=\frac{x}{100}[/tex]
Where [tex]x[/tex] is the percent value for the second square
Multiply both side by [tex]100[/tex] to isolate [tex]x[/tex]
[tex]\frac{3}{4}\times 100=\frac{x}{100}\times 100[/tex]
Simplify the equation
[tex]\frac{300}{4}=x[/tex]
Simplify the left side of the equation
[tex]75=x[/tex]
Since the value of [tex]x[/tex] is [tex]75[/tex], then the percent being represented by the shaded area in the second square is [tex]75\%[/tex]
The fourth step is to calculate the total percent being represented by the all shaded area
Since the total percent is the sum of the percent for the first square and the percent for the second square, then it follows
[tex]\text{Total percent}=100\%+75\%[/tex]
Simplify the equation
[tex]\text{Total percent}=175\%[/tex]
Hence the percent being represented by the shaded are is [tex]175\%[/tex]
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A publihing company find that the cot of publihing each copy of a magazine i #50,000 while the ale revenue i#80,000 per copy. Fixed cot i #600,000. How many copie mut be publihed and old in order to make profit of #1,200,000
In order to make profit of 1,200,000, the company should publish 180 copies of magazine.
The formula for the profit is given by:
Profit = revenues - total cost.
Meanwhile, the total cost consists of fixed cost and variable cost.
Total cost = fixed cost + price per unit x number of units sold
Parameters given in the problem:
Fixed cost = 600,000
variable cost = 50,000 per unit
selling price = 60,000 per copy
profit = 1,200,000
Let q be the number of copies sold, then:
Revenues = 60,000 q
Total cost = 600,000 + 50,000 q
Profit = 60,000 q - (600,000 + 50,000 q)
1,200,000 = 60,000 q - (600,000 + 50,000 q)
10,000 q = 1,800,000
q = 1,800,000 / 10,000 = 180
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