Given : A inequality is given to us . The inequality is 19 ≥ t + 18 ≥ 11 .
To Find : The correct option between the given ones . To write the compound inequality with integers .
Solution : The given inequality to us is 19 ≥ t + 18 ≥ 11 . Let's simplify them seperately .
\(\red{\tt Case\:1}\)
⇒ 19 ≥ t + 18 .
⇒ t + 18 ≤ 19 .
⇒ t ≤ 19 - 18 .
⇒ t ≤ 1 = 1 ≥ t . ..................(i)
\(\red{\tt Case\:2}\)
⇒ t + 18 ≥ 11 .
⇒ t ≥ 11 - 18.
⇒ t ≥ -7 . ....................(ii)
On combing (i) & (ii) .
\(\Large\boxed{\green{\bf \red{\longmapsto} 1 \geqslant t \geqslant -7 }}\)
This means that t is less than or equal to 1 but greater than or equal to (-7) .
10000000000000023486851765498487984 + 189454+818945184654988484
Which statement best describes this graph?
Answer:
the 3rd option
Step-by-step explanation:
the x intercept is where the graph crosses. The x axis. Here the slope is negative one half. Count rise over run between two points. Use the ones on the grid
A relatively prime date is a date for which the number of the month and the number of the day are relatively prime. For example, June 17 is a relatively prime date because the greatest common factor of 6 and 17 is 1. How many relatively prime dates are in the month with the fewest relatively prime dates
There are 11 prime dates in it.
The prime numbers between 1 and 30 are 1, 2,3,5,7,11,13,17,19,23,29
Relative prime:
Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.
Hence There are 11 prime dates in the month of June.
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Answer: 10
Step-by-step explanation:
Since exactly 1 in every $n$ consecutive dates is divisible by $n$, the month with the fewest relatively prime days is the month with the greatest number of distinct small prime divisors. This reasoning gives us June ($6=2\cdot3$) and December ($12=2^2\cdot3$). December, however, has one more relatively prime day, namely December 31, than does June, which has only 30 days. Therefore, June has the fewest relatively prime days. To count how many relatively prime days June has, we must count the number of days that are divisible neither by 2 nor by 3. Out of its 30 days, $\frac{30}{2}=15$ are divisible by 2 and $\frac{30}{3}=10$ are divisible by 3. We are double counting the number of days that are divisible by 6, $\frac{30}{6}=5$ days. Thus, June has $30-(15+10-5)=30-20=\boxed{10}$ relatively prime days.
APPLICATION (16 MARKS) #3. Calculate the area of the composite shape. Use complete and subtract. 7x-4 5x+2 #4. Factor fully. (First factor out the GCF) a) 12a² 75 - (GCF and DOS) b) 6x² 18x - 24 (GCF and P & S) (2%] [23] 2x+3 3x-2 (8 Marks)
The area of the composite shape cannot be determined without further information or a diagram provided.
To fully factor the given expressions:
(a) 12a² + 75 can be factored by finding the greatest common factor (GCF) and applying the difference of squares (DOS):
GCF: The GCF of 12a² and 75 is 3.
DOS: We can rewrite 75 as (5²)(3), so the expression becomes:
3(4a² + 25).
(b) 6x² + 18x - 24 can be factored by finding the GCF and using the process of factoring by grouping:
GCF: The GCF of 6x², 18x, and -24 is 6.
Factoring by grouping: We group the terms as follows:
6x² + 18x - 24 = 6(x² + 3x - 4).
Now we need to factor the quadratic expression in the parentheses. We can use the product and sum method or the quadratic formula to find the factors:
The factors of x² + 3x - 4 are (x + 4)(x - 1).
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last week , tina worked 35 hours in 5 days she worked the same number of hours each day , How many hours did she work each day
Enter the correct answer in the box. What is this expression in simplified form?
3\sqrt{88}
Answer: \(12\sqrt{5}\)
Step-by-step explanation:
\(3\sqrt{88}\)
88 can be rewritten as 8 x 10 and 8 can be rewritten as \(2^2*2\) making a 2 come out of the root.
\(3\sqrt{2^2*2*10}\\ 3*2\sqrt{2*10}\\6\sqrt{2*10}\)
10 can be rewritten as 2 x 5.
\(6\sqrt{2*2*5}\)
2*2 can also be rewritten as \(2^2\) making a 2 come out of the root.
\(6\sqrt{2^2*5}\\ 6*2\sqrt{5}\\ 12\sqrt{5}\)
We can't keep simplifying the root.
Solve the system 2x + 2y = -6 and 3x - 2y = 11 by using graph paper or graphing technology. What is the solution to the system?
Answer:
the solution is (1,-4)
Step-by-step explanation:
5 divided by 9/10 as a fraction!
Answer:
the answer is 50/9
Step-by-step explanation:
5 : 9/10 = 5 : 10/9 = 5×10/9 = 50/9
The number 5 divided by the fraction \(\dfrac{9}{10}\) gives the mixed fraction \(5\dfrac{5}{9}\).
In mathematics, a fraction is an expression that shows a portion or a division of a whole number. It's applied to portray numbers that are not whole numbers or integers. A fraction consists of two factors, that are:
1. Numerator: The numerator is the number on the top of the fraction. It represents the quantity or proportion of the total being considered.
2. Denominator: The denominator is the number at the bottom of the fraction. It represents the complete number of equal parts into which the total is divided.
\(5\ \div\ \dfrac{9}{10}\\= 5\ \times\ \dfrac{10}{9}\\= \dfrac{50}{9}\\\\= 5\dfrac{5}{9}\)
Thus, the fraction obtained by dividing 5 by \(\dfrac{9}{10}\) is \(5\dfrac{5}{9}\).
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What number belongs in the box?
Answer:
16
Step-by-step explanation:
15+23= 38
38-22=16
Therefore the answer is 16. LMK if you need anymore help
Answer:
16
Step-by-step explanation:
\(15+23=x+22\\38=x+22\\x=38-22\\x=16\)
expand and simplify (x - 2)(x + 1)
Answer:
X^2 - X - 2
Explanation:
multiply X by X, then X by 1, then -2 by X, and lastly -2 by 1 and combine like terms (X and -2X)
Find the slope of the line between the two points.
The slope of the line between the two points is - 2 / 3.
How to find the slope of a line?The slope of a line is the change in y coordinate with respect to the change in x coordinate.
The slope of a line is rise over run.
The slope of a line can be express as follows:
slope = y₂ - y₁ / x₂ - x₁
using two coordinates (3, 1)(0, 3)
where
x₁ = 3
x₂ = 0
y₁ = 1
y₂ = 3
Therefore,
slope = 3 - 1 / 0 - 3
slope = 2 / -3
slope = - 2 /3
Therefore, the slope of the line is - 2 / 3.
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Use cylindrical coordinates to find the volume of the region E that lies between the paraboloid x² + y² - z=24 and the cone z = 2 V x² + y².
The volume of the region E is zero.
How to find volume using cylindrical coordinates?Using cylindrical coordinates, we can express the given surfaces as:
Paraboloid: ρ² - z = 24
Cone: z = 2ρ²
To find the volume of the region E enclosed between these surfaces, we need to determine the limits of integration in the cylindrical coordinate system.
The paraboloid and cone intersect when their corresponding equations are satisfied simultaneously. Substituting the equation of the cone into the paraboloid equation, we get:
ρ² - (2ρ²) = 24
-ρ² = 24
ρ² = -24
Since ρ² cannot be negative, this implies that there is no intersection between the paraboloid and the cone. Therefore, the region E does not exist, and the volume is zero.
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What combination of transformations is shown below?
Answer:
Reflection and Translation
Step-by-step explanation:
1 is reflected to 2, and then 2 is translated to 3
An ordered pair is a(n) ________ of an equation in two variables if replacing the variables by the coordinates of the ordered pair results in a true statement.
An ordered pair is a solution of an equation in two variables if replacing the variables by the coordinates of the ordered pair results in a true statement.
In mathematics, an equation in two variables represents a relationship between two quantities. An ordered pair consists of two values, typically denoted as (x, y), that represent the coordinates of a point in a two-dimensional plane.
When these values are substituted into the equation, if the equation holds true, then the ordered pair is considered a solution or a solution set to the equation. This means that the relationship described by the equation is satisfied by the values of the ordered pair. In other words, the equation is true when evaluated with the values of the ordered pair.
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I usually walk at a speed of 0.75 miles per 30 minutes. How long will it take me to walk from my house to the supermarket 1.5 miles down the road?
Answer:
It will take you 1 hour to walk 1.5 miles.
Step-by-step explanation:
Which equation represents a line which is perpendicular to � = 0 x=0? � = − � x=−y � = − 5 x=−5 � = � + 2 y=x+2 � = 1 y=1
The equation y=1 represents a line Perpendicular to x=0.
The equation x=0 represents a vertical line passing through the point (0,0) on the x-axis. A line perpendicular to this line will be a horizontal line passing through the point (0, c) where c is a constant.
So, the equation of the line perpendicular to x=0 is y = c, where c is any constant.
Among the given options, the equation that represents a horizontal line is:
� = 1 y=1
Therefore, the equation y=1 represents a line perpendicular to x=0.
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i need this asap so can someone answer
I just need help please
A proportion is a fraction of a total amount, that can also be interpreted as a percentage, and is used along with the basic arithmetic operations, especially multiplication and division, to obtain the desired measures in the context of a problem.
To obtain the amount relative of a percentage, we multiply the decimal equivalent of the percentage by the total amount.
The amounts in this problem are obtained as follows:
25% off $60: 0.75 x 60 = $45. -> 25% off means that the discount is of 25%, hence 75% of the total price is paid.15% off then 10% off: 0.85 x 0.9 x $60 = $45.9 -> the same logic is applied, just now we have two consecutive discounts.As the prices are different, it means that Jeremy cannot simply add these percentages.
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What is the greatest common factor of -18x4y - 9xy3 + 3xy2? a. 3x4y3 b. 3xy c. xy d. 3xy2
The greatest common factor of -18x^4y - 9xy^3 + 3xy^2 is 3xy. So, correct option is B.
To find the greatest common factor (GCF) of -18x4y, -9xy^3, and 3xy^2, we can factor out the common variables and their corresponding exponents.
First, we can factor out -3xy from each term, as it is a common factor:
-18x^4y - 9xy^3 + 3xy^2 = 3xy(-6x^3 - 3y^2 + y)
Now, we can simplify the expression by factoring the polynomial -6x^3 - 3y^2 + y further. We can see that 3 is a common factor of all the terms in the polynomial, so we can factor out a 3:
-6x^3 - 3y^2 + y = 3(-2x^3 - y^2 + 1/3 y)
Now, we can see that the GCF of the original terms is 3xy times the expression in the parentheses, which is -2x^3 - y^2 + 1/3 y.
Therefore, correct option is B.
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Answer:
3xy
Step-by-step explanation:
First, we need to factor out the greatest common factor from the given terms.
The terms have an x, a y, and a 3 in common.
So, we can factor out 3xy from each term:
−18x4y − 9xy3 + 3xy2 = 3xy(-6x3 - 3y2 + y)
Now, we can see that there are no other factors that can be removed from the expression.
Therefore, the greatest common factor of −18x4y − 9xy3 + 3xy2 is 3xy.
So, the correct answer is 3xy.
Where will the reflection on the x-axis be?QuadrantiQuadrant ilQuadrant IVQuadrant(-6,-7)
The reflection will be on Quadrant II
Explanation:The rule for reflection on the x-axis is to negate the y-values but leave the x-values the same.
(-6, -7) becomes (-6, 7)
This would reflect on Quadrant II
8x+5 with an explanation
Answer:
8x+5
Step-by-step explanation:
it would be 8x+5.
this is because 8x and 5 are not like terms so they cannot be collected which means that the answer is 8x+5
Please help me this is my last question
Answer:
5.831
Step-by-step explanation:
Pythagoras says RS = √(5²+3²) = √34 ≈ 5.831
Answer:
RS ≈ 5.83 units
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
Here RS is the hypotenuse and the legs have measure 5 and 3, thus
RS² = 5² + 3² = 25 + 9 = 34 ( take the square root of both sides )
RS = \(\sqrt{34}\) ≈ 5.83 ( to 3 significant figures )
What is 3n + 1 when n =4
Answer:
13
Step-by-step explanation:
3n+1
Let n= 4
3(4)+1
12+1
13
Answer:
\({ \tt{f(n) = 3n + 1}} \)
» When n is 4, f(n) is f(4);
\({ \tt{f(4) = 3(4) + 1}} \\ { \tt{f(4) = 12 + 1}} \\ { \underline{ \tt{ \: f(4) = 13 \: }}}\)
i need help on this probability question
The probability that Keiran saw exactly one animal which is a lion will be 1/3.
What is probability?The chance of the event to happen is given as,
P = (Favorable event) / (Total event)
The probability that Keiran saw a lion is 2/5.
The probability that Keiran saw a rhino after watching a lion is 5/6.
The probability that Keiran saw a rhino without watching a lion is 4/9.
The probability that Keiran saw exactly one animal which is a lion is given as,
P = (2/5) x (5/6)
P = 2 / 6
P = 1/3
The probability that Keiran saw exactly one animal which is a lion will be 1/3.
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What makes a point a solution to a system of equation? 55 points
Answer:
A solution to a system of equations means the point must work in both equations in the system
Answer:
The point must work in both equations in the system, therefore, when we test the point in both equations, it must be a solution for both.
Step-by-step explanation:
help on 5 . find the value of x
Answer:
The choice B. 5°
Step-by-step explanation:
The angle in the figure is 90°
\(36 + (11x - 1) = 90 \\ 36 + 11x - 1 = 90 \\ 11x + 35 = 90 \\ 11x = 90 - 35 \\ 11x = 55 \\ \\ x = \frac{55}{11} \\ \\ x = 5\)
Write a true equation based on this diagram
A number m plus 4 is greater than or equal to 9
Answer:
5
Step-by-step explanation: If M is 4, 4 + 5 = 9
Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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NOBODY RESPONDED ON MY LAST QUESTIONS BUT I NEED HELP!!!!
Answer:
Step-by-step explanation:
4a:(3)
4b: d=don dx3=