The linear inequality represented by the graph is defined as follows:
y ≥ -2x + 1.
The ordered pairs that are solutions to the inequality x < -3 are given as follows:
(-5,5).(-4,-3).(-105,0).How to obtain the linear inequality?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the coefficients are given as follows:
m is the slope, representing the rate of change.b is the y-intercept, which is the value of y when the graph of the function crosses the y-axis.The function in this problem crosses the y-axis at y = 1, hence the intercept b is given as follows:
b = 1.
When x increases by one, y decays by two, hence the slope m is given as follows:
m = -2.
The shaded region, considering the solid line, is given by the values to the right of the line, hence the inequality is defined as follows:
y ≥ -2x + 1.
How to obtain the ordered pairs that are solution to the inequality?The inequality for this problem is defined as follows:
x < -3.
The ordered pairs have the following format:
(x,y).
Hence all the ordered pairs that have x < -3, no matter the coordinate of y, are solutions to the inequality.
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After playing 5 games, you have 33 credits left. You play 4 more games and have 21 credits left. Write an equation that represents the number of credits y on the card after x games
Answer:
5x=33y,4x=21y I hope this is helpful
What is AE?
Enter you answer in the box.
Answer:It means almost everywhere
Step-by-step explanation:
The value of AE is, 10 units.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Here, From the given figure we can see that two triangle ABE and DEC are similar.
Therefore, The ratio of corresponding sides are equal.
Hence, From figure we get,
⇒ ED/AE = CD/AB
Substitute all the values, we get;
⇒ (x + 6)/(2x + 6) = 8/10
⇒ 10(x + 6) = 8(2x + 6)
⇒ 10x + 60 = 16x + 48
⇒ 16x - 10x = 60 - 48
⇒ 6x = 12
⇒ x = 2
So, The value of AE is,
AE = 2x + 6
AE = = (2 × 2 ) + 6
AE = 4 + 6
AE = 10
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When a number is decreased by 10% of itself, the result is 99. What is the number?
Answer:990
Step-by-step explanation:10%=0.1
X*0.1=99
99/0.1=990
x=990
What Income tax should be on 400 naira at the rate of 2¹/2 kobo per Naira? A. 2 Naira B. 4 Naira C. 5 Naira D. 10 Naira E. 15 Naira
Step-by-step explanation:
A. Hawa Enterprise is a small retail business located in Changlun, Kedah. Follows are information on bank transactions of Hawa Enterprise as at 31 July 2022:
a. Cash on the book was RM34,635.
b. Cash as shown on the bank statement was RM35,296.
c. A deposit of RM3,500, representing cash receipts on 31 July, did not appear on the bank statement.
d. Outstanding cheque include cheques No 2031, No 2558, and No 2783 with the amount respectively RM530, RM1,551 and RM2,100.
e. The bank collected RM810 on a note receivable for Hawa Enterprise. The bank charged a collection fee of RM10 which was credited to Hawa Enterprise’s account.
f. An NSF cheque for RM950 from a customer, En Mansor, was returned with the bank statement.
g. The bank paid correctly an amount of RM3,680 for cheque No 2805 which was recorded in a book as RM3,860. h. Bank service charges for July 2022 amounted to RM50.
REQUIRED:
Prepare the bank reconciliation statement for Hawa Enterprise as at 31 July 2022.
B. Beginning July 2022, Hawa Enterprise has established a petty cash fund for its small expenditures. The following transactions took place during the month of July:
5/7 Established a RM300 petty cash fund with cash withdrawn from the company’s current account.
30/7 The petty cash fund has RM12 remaining and is replenished. Expenditures for July were RM75 for supplies, RM60 (meals), RM80 (postage), RM50 (amenities) and RM25 (freight-in).
REQUIRED:
Prepare the journal entries for the above transactions.
The debt-to-assets ratio formula is: Debt-to-assets ratio = total liabilities/total assets. If your total liabilities are $3,228 and your total assets are $5,091. What is your debt-to-assets ratio?
The debts to assets ratio is 0.63
How to calculate the debts to assets ratio ?The formula for calculating debts to assets ratio is
total liabilities/total assets
The total liabilities is $3,228
The total assets is $5,091
Therefore the debts to assets ratio is
3228/5091
= 0.63
Hence the debts to assets ratio is 0.63
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Match the image to the scale factor from FG to F'G'.
Image 1
F
F
Image 2
F'
F
Image 3
F'
F
F
Image 4
F
F
Image 5
F'
12
12
8
6
18
12
12
12
12
24
G'
G
G
G'
G
G'
G
F
The scale factor for each of the dilation is given as -
K₁ = 18/12 = 3/2K₂ = 8/12 = 2/3K₃ = 12/12 = 1K₄ = 6/12 = 1/2What is scale factor?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor. It also tells by how many times is {y}, greater than {x}.
Given is a line segment and its dilated image.
The scale factor is given by -
K = y/x
[1] -
K₁ = 18/12 = 3/2
[2] -
K₂ = 8/12 = 2/3
[3] -
K₃ = 12/12 = 1
[4] -
K₄ = 6/12 = 1/2
Therefore, the scale factor for each of the dilation is given as -
K₁ = 18/12 = 3/2K₂ = 8/12 = 2/3K₃ = 12/12 = 1K₄ = 6/12 = 1/2To solve more questions on direct variation, visit the link below -
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The range of the function f (x) =√x^2−4
is (−∞, −1) ∪ (1, ∞). To explain
why this is true, you have to do two things:
(a) Show that if f (x) = y for some x, then either y > 1 or y < −1.
(b) Show that if y < −1 or y > 1, then the equation f (x) = y has a solution in x.
The solutions for the given function are (-2, 0) and (2, 0).
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
The given function is f(x)=√(x²-4).
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,−2]∪[2,∞),{x|x≤−2,x≥2}
Range: [0,∞),{y|y≥0}
Therefore, the solutions for the given function are (-2, 0) and (2, 0).
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Write the sentence as an equation.
106 more than the quantity 68 times y is the same as 36 decreased by y
Answer: 68y+106=36-y
Is 6 inches in 10 seconds proportional to 12 inches in 60 seconds?
Answer: No
Step-by-step explanation:
to be proportional, both numbers have to increase by the same number
because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in
Place value of the 4 in 2, 487, 492
Jasmine claims “to find the lowest common multiple of two numbers, you can multiply them together. For example, 5 × 8 = 40 and the LCM of 5 and 8 is 40”
Is Jasmine correct? Justify your answer.
Answer:
No, Jasmine is not correct. The Lowest Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. Multiplying the two numbers together is not always the correct method to find the LCM.
For example, the LCM of 5 and 8 is 40, but the product of 5 × 8 = 40 is not the LCM.
A more accurate way of finding the LCM is by using the prime factorization of the numbers. By finding the prime factorization of the two numbers, you can take the highest exponent of each prime factor and multiply them together. The result of that multiplication is the LCM of the two numbers.
In this case, the prime factorization of 5 is 5 and 8 is 2^3. The LCM of 5 and 8 is 2^3*5 = 40. So Jasmine's claim that 5 x 8 = 40 and the LCM of 5 and 8 is 40 is not correct.
There are 135 people in a sport centre.
73 people use the gym.
73 people use the swimming pool.
67 people use the track.
36 people use the gym and the pool.
35 people use the pool and the track.
32 people use the gym and the track.
14 people use all three facilities.
How many people use exactly one of these facilities?
The number of people that uses exactly one of gym, swimming pool and track is 49people
What is set?A set is the mathematical model for a collection of different things. A set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
The number of people that uses gym= 73- ( 32-14+ 36-14 + 14)
73-(18+22+14)
73 - (54) = 19 people
The number of people that use pool only = 73-(36-14+35-14+14)
= 73-(22+21+14)
= 73-(57)
= 16people
The number of people that use track only = 67-(32-14+35-14+14)
= 67-(18+21+14)
= 67-53
= 14people
therefore the number of people that use one of the facility is 19+16+14 = 49people
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Gershon Smudgenick had 4 pounds of broccoli sprouts. He
went to Joe's Discount Bonanza and got some more. He ended up
with 11 pounds of broccoli sprouts. What is the fractional increase
in Gershon's broccoli sprouts? What is the percent increase in
Gershon's broccoli sprouts?
Answer: The fractional increase in Gershon's broccoli sprouts is 7/4 and the percent increase in Gershon's broccoli sprouts is 175%.
Step-by-step explanation:
The fractional increase in Gershon's broccoli sprouts is the difference between the final amount and the initial amount divided by the initial amount.
So in this case, it would be (11 - 4) / 4 = 7 / 4.
The percent increase in Gershon's broccoli sprouts is the fractional increase multiplied by 100.
So, it would be (7 / 4) * 100 = 175%.
It means Gershon's broccoli sprouts increased by 175% from 4 pounds to 11 pounds.
What is the correct solution set for the following graph?
{ } or empty set
{point in Quadrant II}
{point in Quadrant IV}
{infinite set of points on the line}
The correct solution set for the given graph include the following: D. {infinite set of points on the line}.
What is a quadrant?In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.
This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:
Quadrant IQuadrant IIQuadrant IIIQuadrant IVGenerally speaking, the solution set of a graph simply refers to all of the points that lie on its line. By critically observing the graph of lines a and b, we can reasonably infer and logically deduce that they both have the same slope, solution set, as well as increasing and decreasing infinitely.
In this context, the correct solution set lies in both Quadrant II and Quadrant III because both lines move towards negative and positive infinity i.e [-∞, ∞].
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how do you find the distance formula to find the distance between each of the specified points. (ie pythagorean theorem)?
Answer: The distance formula is a mathematical formula used to find the distance between two points in a plane. One way to find the distance formula is by using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The distance formula can be derived from the Pythagorean theorem by considering the two points as the two endpoints of a line segment. The formula is as follows:
Distance = √(x2 - x1)^2 + (y2 - y1)^2
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this formula, the difference in the x-coordinates is squared and the difference in the y-coordinates is also squared. Then, these two values are added and the square root of the result gives the distance between the two points.
For example, if we have two points (x1, y1) = (2, 3) and (x2, y2) = (5, 8), we can use the distance formula to find the distance between these two points:
Distance = √((5 - 2)^2 + (8 - 3)^2)
Distance = √(3^2 + 5^2)
Distance = √(9 + 25)
Distance = √(34)
Distance = 5.83
Therefore, the distance between the two points is 5.83 units.
Step-by-step explanation:
Consider parallelogram JKLM below.
Use the information given in the figure to find mLNJK, x, and mLNKJ.
K
N
4x - 3
13
AL
50°
42°
M
Answer:
∠NJK = 50°x = 4∠NKJ = 42°Step-by-step explanation:
You want a couple of interior angles and the value of x given the parallelogram in the figure.
AnglesThe diagonals of a parallelogram bisect each other, and divide the figure into two pairs of congruent triangles. Here, the congruent triangles of interest are ...
∆NKJ≅∆NML
In these triangles, that means ...
∠J ≅ ∠L = 50° = ∠NJK
∠K ≅ ∠M = 42° = ∠NKJ
SegmentsThe halves of diagonal JL are congruent, so we have ...
4x -3 = 13
4x = 16 . . . . . . . . add 3
x = 4 . . . . . . . . . divide by 4
Find the measure of < 6.
Answer:
Angle 6 = 70
Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.
Please answer:
The fraction 1/7 is equal to the repeating decimal 0.142857 . Which digit occurs in the 2023rd place after the decimal point?
The digit that occurs in the 2023rd place after the decimal point is; 1
How to Interpret Repeating Decimals?A repeating decimal has another name called a recurring decimal, and it is defined as a number whose decimal representation eventually becomes periodic
Now, we are given the fraction as 1/7 which is a repeating decimal because its decimal representation is periodic for every 6 decimal units as shown below; 1/7 = 0.142857142857...
Now, the digits are repeated after every 6 digits and as such to get the digit in the 2023rd place;
2023/7 = 337 remainder 1
Thus, the sequence 142857 would be repeated 337 times after which the next digit which is the 2023rd digit will be 1.
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Write and solve an equation.
A drink and 7 pizzas cost $94.25. The cost of the drink was $1.50. What was the cost, c, of one pizza?
Answer:
13.25
Step-by-step explanation:
1. you have to subract the cost of the drink:
94.25-1.50=92.75
2.you have to divide to get the individual cost of pizzas by doing
92.75÷7=13.25
so therefore your answer is 13.25 per pizza
Recall that during the 2013-2014 academic year, the school board in Wichita Falls, Texas, began planning for new and renovated high school facilities. A committee of community members was formed to explore various options for a bond proposal to pay for the plan¹. The committee presented three options to the board of trustees
Plan A has the majority of votes.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given this, the school board in Wichita Falls, Texas, began planning for new and renovated high school facilities.
There is a total of 3 + 3 +1 = 7 votesthus we can say the total number of members who voted is 7.
For the majority, more than 50% of votes are required. In this case, 50% of 7 = 3.5Therefore, 4 votes are required for the majority.
Here, no plan received 4 Ist choice votes.Therefore, there is no plan that receives a majority of votes.
In the instant run-off method, the candidate with the lowest 1st choice votes is eliminated and his votes are transferred to the candidate of the next choice. This process continues till a majority winner is found. In the initial table:1st choice votes to A=3
1 choice votes to B=3 1st choice votes to C=1
So, C is to be eliminated and his 1 vote is to be transferred to A (as A is the next choice after C in column 3 of the table)
First choice vote to A = 3 + 1 = 4
First choice vote to B = 3
Since A gets the majority of votes A is the winner
Thus, Plan A has the majority of votes.
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Complete question:
What is the equation of this line? y>1/2x−3 y<1/2x−3 y>2x−3 y<2x−3
Answer:
The equation of this line is y>1/2x-3
Step-by-step explanation:
This is an inequality equation that represents a line that is greater than 1/2x-3. The inequality symbol ">" indicates that all the y-coordinates that are on the same side of the line as the y-axis are greater than 1/2x-3.
In other words, all the points that lie above the line will satisfy the inequality, while all the points that lie below the line will not.
It's worth noting that the line y<1/2x-3 represents the same line but the inequality symbol "<" indicates that all the y-coordinates that are on the same side of the line as the x-axis are less than 1/2x-3.
y>2x-3 and y<2x-3 represent different lines, the first one represents a line with a slope of 2 and the second one represents a line with a slope of -2.
How do I divide with rational expressions.
The value of the rational expression is q⁴ / 14p⁴
What are rational expressions?A rational expression is the ratio of two polynomials. If f is a rational expression, then f can be written in the form p/q where p and q are polynomials.
Given are rational expressions,
5pq / 16p³ ÷ 35p²q² / 8q⁵
Using identity, a/b ÷ c/d = a/b × d/c
5pq / 16p³ × 8q⁵ / 35p²q²
= 40q⁴ / 560p⁴
= q⁴ / 14p⁴
Hence, the value of the expression is q⁴ / 14p⁴
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0.15 | 0.3 | 1 | 2 | 2.7 | 5.4 | 6.4 | ? | ?
A 12.2, 12.9
B 9.5, 13.6
C 7.1, 8.6
D 6.8, 7.5
The next two numbers on the number pattern will be 12.2, 12.9 the correct option is A
How to obtain the next two points on the number pattern?To obtain the next two points on the number pattern, first we must identify what is the meaning of pattern.
The pattern is given as follows;
The double of an amount is calculated.
Now 0.7 is increased to double the amount, and we return to step 1, doubling the value.
The final term is 6.1, which is obtained after the addition of 0.7 to 5.4. Double 6.1 is obtained multiplying the number by 2, as follows;
2 x 6.1 = 12.2.
Then the number obtained after 0.7 is added to 12.2 is given as follows;
0.7 + 12.2 = 12.9.
It implies that the correct answer of the given number pattern is 12.2, 12.9
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Simplify the following expression.
4√72
O A. 6√24
B.
144√6
OC. 24√6
D. 24√/2
O D.
The expression 4√72 can be simplified by first taking the square root of both sides, which gives us 2√72. Then, we can factor out a 6 from both sides, which gives us 24√6. Therefore, the simplified expression is 24√6.
What is expression?Expression is the process of conveying one’s thoughts, emotions, ideas, and beliefs through speech, writing, art, or any other form of communication. Expression is a form of communication that allows people to express themselves in a way that is meaningful and personal to them. It is a powerful way for individuals to express their thoughts, feelings, and opinions without fear of judgement or criticism. Expression is an important part of self-expression, and it can be used to connect with others through shared experiences, to create a sense of community, and to grow and learn from one another. Expression is an invaluable tool for self-expression, creativity, and communication.
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3) The area and
diagonal of a
Kite are 144cm and 8cm respectively, find the other diagonal
Answer:
Step-by-step explanation:
Let the other diagonal be d.
From the Pythagorean theorem,
d2 = 82 + 1442
d2 = 64 + 20736
d2 = 20800
d = √20800
d = 144 cm
You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 500 eggs and 1,050 cups of cream. How many quarts of each flavor should you make in order to use up all the eggs and cream?
Creamy Vanilla
qt
Continental Mocha
qt
If I manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. Where I have in stock 500 eggs and 1,050 cups of cream. The number of quarts of each flavor that I would make in order to use up all the eggs and cream is: 150 quarts of Vanilla and 200 Quarts of Mocha.
Let x and y be the number of Quarts of Vanilla and Mocha respectively.
The total number of eggs used is given as:
2x+y = 500
And the total cups of cream is:
3x + 3y = 1050
Removing the second equation from three times the first, we get:
3(2x + y) - (3x + 3y) = 3(500) -1050
6x + 3y - 3x - 3y = 1500 - 1050
⇒ 3x = 450
⇒ x = 450/3
x = 150
By substituting x back in tot he first equation we find:
2x+y = 500
2 (150) + y = 500
300 + y = 500
y = 500 - 300
y = 200.
Thus, to use up al the eggs and cream, 150 quarts of Vanilla and 200 quarts of Mocha should be produced.
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5. An engineer typically makes 50% more than a school teacher. What is the engineer's income as a percentage of the school teacher's income. How many times as large as the teacher's income is the engineer's?
Answer:
If an engineer typically makes 50% more than a school teacher, then the engineer's income is 150% of the school teacher's income. Because 100% represents the school teacher's income, and 50% represents the engineer's additional income, the sum is 100%+50% = 150%.
The engineer's income is also 1.5 times as large as the school teacher's income. This can be found by dividing the engineer's income percentage (150%) by the school teacher's income percentage (100%), which gives 150% / 100% = 1.5.
So the engineer's income is 150% of the school teacher's income, and it is 1.5 times as large as the school teacher's income.
- C
Twenty less than a number is more than twice the same number . Find the smallest possible value of the number.
The smallest possible value of the number that is an integer is -21
Determining the value of a numberFrom the question, we are to determine the smallest possible value of the number
From the given information, we have that
"Twenty less than a number is more than twice the same number"
Let the number be x
Then,
we can write that
x - 20 > 2x
Now, we will solve for x
x - 20 > 2x
-20 > 2x - x
-20 > x
Therefore,
x < -20
The possible integers are -21, -22, -23, -24, -25, -26, ...
Then,
The smallest integer is -21
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Serena added 10 grams of sugar to 20 grams of water.
She made
grams of
%
sugar syrup.
Serena added 10 grams of sugar to 20 grams of water to make a sugar syrup.
The total amount of sugar syrup made is the sum of the weight of sugar and the weight of water, so:
10 grams (sugar) + 20 grams (water) = 30 grams (sugar syrup)
To find the percentage of sugar in the syrup, we can divide the weight of the sugar by the total weight of the syrup and multiply by 100.
% sugar = (weight of sugar / total weight of syrup) * 100
% sugar = (10 / 30) * 100 = 33.333 %
So the sugar syrup made by Serena contains 33.333% sugar by weight.
It's important to note that the sugar syrup doesn't have only sugar, it also have water, the sugar is just the main ingredient and the percentage of sugar is just the proportion of sugar within the syrup.
Erica earned a total of 67,160 last year from her two jobs. The amount she earned from her job at the store was 1,550 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college
Answer:
Let's call the amount Erica earned from her job at the college "x". We know that:
Total income = $67,160
Income from store = 3x + 1,550
Total income = Income from store + Income from college
67,160 = 3x + 1,550 + x
67,160 = 4x + 1,550
Now we can solve for x:
67,160 - 1,550 = 4x
65,610 = 4x
x = 16,402.5
Erica earned $16,402.50 from her job at the college.