Answers
The desired values of a and b to conform the translation (x,y) -> (x+a, y-b) to the format of a reflection around line q preceded by a reflection across line p are a = 2x+2 and b = y.
How to get the valuesLine q is a vertical line of equation x = -1, and the reflection of any point (x, y) across it provides its mirror image on the other side. Thus, reflecting a point (x, y) across line q results in the point (-x-2, y).
Additionally, line p is a horizontal line of equation y = b. When a point (x,y) is reflected across this line, its mirror image appears on the opposite side. Therefore, reflecting a point (x, y) across line p yields the point (x, 2b-y).
Presently, we seek to ascertain whether these two reflections are equivalent to shifting a point (x,y) to another point (x+a, y-b). Consequently, let us experiment with an arbitrary point (x,y): when we reflect it across line q, then over line p, then shift it by (a,-b), we should end up at (x+a, y-b).
Applying this pathway to our chosen point (x,y) gives the resultant point of (-x-2, y); followed by (-x-2, 2b-y); and finally (-x-2+a, 2b-y-b). Hence, for the transformation (x,y) -> (x+a, y-b) to be equivalent to one reflection about line q trailed by a reflection about line p, the following equations must resolve simultaneously:
-x-2+a = x+a
2b-y-b = y-b
By solving these equations, it is revealed that the desired values of a and b to conform the translation (x,y) -> (x+a, y-b) to the format of a reflection around line q preceded by a reflection across line p are a = 2x+2 and b = y.
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Related Questions
the department of education wishes to estimate the proportion of all college students who have a job off-campus. it surveyed 1600 randomly selected students; 451 had such jobs. the population of interest to the department of education is:
Answers
The population of interest to the department of education will be all college students.
A population is a large group of individuals that have some common feature by the researcher's point of interest.
Here the Department of Education wishes to estimate the proportion of all college students who have a job off-campus.
Proportion: A proportion is an equation in which two ratios are set equal to each other. If there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4).
So , he needs data of all students to compute the exact proportion.
But instead of that he surveyed 1600 randomly selected students which determine the sample.
Sample just gives the estimate of the parameter.
Hence, the population of interest to the Department of education is " All college students" .
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Which of these expressions are equivalent to 4x+2(2x−5)−(3−5x) ? Choose the TWO correct answers.
a- 3x−13
b- 13x−13
c- 8x−5−3−5x
d- 8x−10−3−5x
e- 8x−10−3+5x
Answers
Answer:
4x+2(2x−5)−(3−5x) = 8x-10-3+5x
Step-by-step explanation:
We need to find the equivalent expression to 4x+2(2x−5)−(3−5x).
Using distributive property as follows :
a(b+c) = ab+ac
4x+2(2x−5)−(3−5x) = 4x+4x-10-3+5x
= 8x-10-3+5x
Option (e)
Hence, the correct option is (e) "8x-10-3+5x"
Write the inequality: a band will sell their CDs of the music at their concert for $5 each. The band ordered 300 CDs at a cost of $1.25 each. Which inequality represents the number of CDs, n, the band needs to sell to make a profit of at least $500
Answers
The band needs to sell at least 175 CDs to make a profit of at least $500.
The inequality that represents the number of CDs, n, the band needs to sell to make a profit of at least $500 is:
5n - 1.25(300) ≥ 500
Explanation:
- The band sells each CD for $5, so the revenue from selling n CDs is 5n.
- The band ordered 300 CDs at a cost of $1.25 each, so the total cost of the CDs is 1.25(300) = $375.
- To make a profit of at least $500, the revenue from selling the CDs (5n) must be greater than or equal to the total cost of the CDs plus $500 (375 + 500 = 875).
- Putting it all together, we get the inequality:
5n - 1.25(300) ≥ 500
Simplifying this inequality gives:
5n - 375 ≥ 500
5n ≥ 875
n ≥ 175
Therefore, the band needs to sell at least 175 CDs to make a profit of at least $500.
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Simplify 3(5y + 6) -4
Answers
Given:
To simplify 3(5y+6)-4
\(\begin{gathered} 3(5y+6)-4 \\ 15y+18-4 \\ 15y+14 \end{gathered}\)Hence the simplified value os 15y+14.
Could I please get assistance with this question. Create a mini cricket/rugby clinic explanation where you teach learners about cricket/rugby while incorporating Mathematics or English literacy. Your explanation should be informative and insightful.
Answers
Introduce the sport of cricket/rugby and explain its history and rules.
Use cricket/rugby as a context for teaching Mathematics or English literacy. For example:
Mathematics: You can use cricket/rugby statistics to teach learners about probability, percentages, and data analysis. For instance, you can ask learners to calculate the batting average of a cricket player or the conversion rate of a rugby team. You can also ask learners to solve word problems related to cricket/rugby, such as "If a cricket team scores 240 runs in 50 overs, what is their run rate per over?"
English literacy: You can use cricket/rugby as a context for teaching learners about reading comprehension, writing, and vocabulary. For instance, you can ask learners to read a cricket/rugby article and summarize it in their own words. You can also ask learners to write a persuasive essay on why cricket/rugby is the best sport. Additionally, you can teach learners cricket/rugby-specific vocabulary, such as "wicket," "boundary," "try," and "conversion."
Use cricket/rugby drills and exercises to reinforce the Mathematics or English literacy concepts you have taught. For example:
Mathematics: You can ask learners to measure the distance between the wickets or the length of the cricket pitch using a tape measure. You can also ask learners to count the number of runs scored in a cricket match or the number of tries scored in a rugby match.
English literacy: You can ask learners to write a cricket/rugby-themed story or poem using the vocabulary they have learned. You can also ask learners to read a cricket/rugby rulebook and explain the rules in their own words.
Overall, incorporating Mathematics or English literacy into a cricket/rugby clinic can make the learning experience more engaging and meaningful for learners. By using cricket/rugby as a context for teaching these subjects, learners can see the real-world applications of what they are learning and develop a deeper understanding of the concepts.
How many powers of 7 are contained in 10?
Answers
There is only 1 power of 7 contained in 10.
Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.
Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.
The digit in the tens place is the same.
The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.
The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.
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There is only 1 power of 7 contained in 10.
Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.
Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.
The digit in the tens place is the same.
The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.
The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.
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Elevando um certo numero natural,maior do que zero,ao expoente 101 encontrarmos como resposta 1. Qual é esss numero? 101 A) 0 B) 1 C) 2 D) 101 = 1
Answers
Answer:
B) 1
Step-by-step explanation:
The computation of the number is shown below:
Since the number 1 would be raised to any exponent so it always remains be 1
Like
= 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1
= 1
Therefore the option B is correct
please help asap (true or false question)
Answers
Answer:
The statement is true.
Step-by-step explanation:
Let us plug\(24=-4(8)-8\) in 8 for \(x\) and 24 for \(y\) in our equation: \(24 =-4 (8) - 8\).
Now we will solve in the order described by PEMDAS.
-4(8)=32
32-8=24
24=24
Thus, our statement is true.
Two walls of a canyon form the walls of a steady flowing river. From a point on the shorter wall, the angle of elevation to the top of the opposing wall is 20° and the angle of depression to the bottom of the opposing wall is 230 feet. Using the appropriate right triangle solving strategies, solve for the following: (Do not round intermediate calculated values. Only the final answer should be rounded to one decimal place.)
the height of the short wall (x)
the height of the tall wall (y)
the distance between the canyon walls (z)
How do I solve this and get to the answer.
Answers
We found that the height of the short wall "x" is 162.6 ft, the height of the tall wall "y" is 221.8 ft, and the distance between the canyon walls "z" is 162.6 ft.
To find the x, y, and z values we need to denote the right triangles from top to bottom as triangles 1, 2, and 3.
1. Finding the height of the short wall "x"
We can find the height of the short wall "x" (in triangle 3) with the following trigonometric function:
\( cos(\theta) = \frac{x}{H} \)
Where:
H: is the hypotenuse = 230 ft
θ: is the angle between x and H.
Knowing that the sum of θ and the angle 45° must be equal to 90°, θ is:
\( \theta = 90 - 45 = 45 \)
Hence, the height of the short wall "x" is:
\(x = cos(\theta)*H = 230cos(45) = 162.6 ft\)
2. Finding the height of the tall wall "y"
The height of the tall wall "y" is given by the sum of the bases of the two first right triangles (the right triangles 1 and 2):
\( y = y_{1} + y_{2} \)
Where y₁ and y₂ can be calculated with the tangent and sine trigonometric functions.
\(y_{1} = A*tan(20)\)
\( y_{2} = 230sin(45) \)
Where A is the adjacent side to the angle 20°.
\( y = A*tan(20) + 230sin(45) \)
Since the right triangles 2 and 3 form a square, with all the sides equals to x, we have:
\( A = z = y_{2} = x = 230cos(45) \)
We can use 230cos(45) or 230sin(45) to calculate y₂, so the height of the tall wall "y" is:
\( y = y_{1} + y_{2} = A*tan(20) + 230cos(45) = 230cos(45)tan(20) + 230cos(45) = 221.8 ft \)
3. Finding the distance between the canyon walls "z"
As we said above, the "z" value is the same as "x", then:
\(z = x = 230cos(45) = 162.6 ft\)
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What is the solution to the expression 18 ÷ 2 + (1/4) to the power of 2 • 8 × 4? PLEASE EXPLAIN
Answers
Answer:
Step-by-step explanation:
[18/2 + (1/4)]^2x8x4
There is no easy way to do this I have found.
8x2x4 = 64
18/2 + 1/4 = 9.25
If you could just put the answer as 9.25^64
However if it requires a direct answer(which I don't believe it should)
9.25^64 = 6.808805e+61 (≈6.8^61)
A torus is formed when a circle of radius 3 centered at (8,0) is revolved about the y-axis a. Use the shell method to write an integral for the volume of the ton b. Use the washer method to write an integral for the volume of the torus e. Find the volume of the torus by evaluating one of the two integrats obtained in parts (a) and (). (Hint: Both integrals can be evaluated without using the Fundamental Theorems of Cabulas) a. Set up the integral that gives the volume of the torus using the shell method. Select the correct choice below and 58 in the answer boxes to complete your choice (Type exact answers) OA de 3 OF SO b. Set up the integral that gives the volume of the torus using the washer method Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers) OAS d OB dy Time Remaining: 02:00:09 Next A torus is formed when a circle of radius 3 centered at (6,0) is revolved about the y-axis. a. Use the shell method to write an integral for the volume of the torus b. Use the washer method to write an integral for the volume of the torus. c. Find the volume of the torus by evaluating one of the two integrals obtained in parts (a) and (b). (Hint: Both integrals can be evaluated without using the Fundamental Theorem of Calculus.) у У 9- 3 X a. Set up the integral that gives the volume of the torus using the shell method. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) OAS OB. dy b. Set up the integral that gives the volume of the torus using the washer method. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) OAS dx 3 OB. dy The volume of the torus is approximately cubic units. (Round to two decimal places as needed.)
Answers
a) To find the volume of the torus using the shell method, the integral can be set up as ∫2πy(2πr)dy.
b) To find the volume of the torus using the washer method, the integral can be set up as ∫π(R²-r²)dx.
c) The volume of the torus can be found by evaluating one of the two integrals obtained in parts (a) and (b).
a) The shell method involves considering cylindrical shells with height dy and radius y. Since the torus is formed by revolving a circle of radius 3 centered at (8,0) about the y-axis, the radius of each shell is y and the height is 2πr, where r is the distance from the y-axis to the circle. Therefore, the integral to find the volume of the torus using the shell method is ∫2πy(2πr)dy.
b) The washer method involves considering infinitesimally thin washers with inner radius r and outer radius R. In the case of the torus, the inner radius is the distance from the y-axis to the circle, which is y, and the outer radius is the radius of the circle, which is 3. Therefore, the integral to find the volume of the torus using the washer method is ∫π(R²-r²)dx.
c) To find the volume of the torus, one of the two integrals obtained in parts (a) and (b) can be evaluated. The specific integral to evaluate depends on the chosen method (shell or washer). By substituting the appropriate values into the integral and evaluating it, the volume of the torus can be calculated.
Note: The specific calculations to find the volume of the torus and the corresponding numerical result were not provided in the question, so the final answer in cubic units cannot be determined without further information.
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Golf Realty let their real estate brokerage license lapse. All the sales associates working under Golf Realty continued to practice real estate for five months before the error was realized. What could each agent be charged with as a result
Answers
Each sales associate working under Golf Realty could potentially face charges related to practicing real estate without a valid license. If Golf Realty allowed their real estate brokerage license to lapse.
Real estate licensing is a legal requirement for individuals involved in real estate transactions, including sales associates. If Golf Realty allowed their real estate brokerage license to lapse and the sales associates continued to practice real estate without a valid license, they could be charged with unauthorized practice of real estate or a similar offense.
The specific charges and legal consequences may vary depending on the jurisdiction and applicable laws. In many jurisdictions, practicing real estate without a license is considered a serious offense as it undermines consumer protection and regulatory requirements. Penalties for unauthorized practice may include fines, license suspension or revocation, and potential civil liability for any harm caused to clients or parties involved in the transactions.
It is important for individuals working in the real estate industry to ensure that they maintain valid licenses and comply with all relevant regulations to avoid potential legal issues. If the sales associates were unaware of the lapsed license and can demonstrate good faith in their actions, it may be taken into consideration during any legal proceedings.
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Simplify each and state the excluded values p+4/p^2+6p+8
Answers
You are given an expression for the volume of the rectangular prism. determine an expression for the missing dimension. v=4x^3 5x^2-32x-33 and the dimensions are (x 1)and (x 3)
Answers
4x^3 + 5x^2 - 32x - 33 / x + 1
4x^2 + x - 33
4x^2 + x - 33 / x + 3
4x - 11
Hey what is the answer + explain.
Answers
The range of the exponential function graphed is defined as follows:
H. {y|y > 0}.
How to obtain the range of a function?The range of a function is the set containing all the output values that are assumed by the function.
Hence on a graph, the range of the function is given by the values of y assumed by the function, while are the values on the vertical axis of the function.
The function in this problem assumes only positive values, with y = 0 being the horizontal asymptote, meaning that the function neves assumes a value of zero, thus the range is given as follows:
{y|y > 0}.
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What is the completely factored form of
x4−16x4−16
Answers
x*4-16x*4-16
4x-64x-16
-60x-16
Idil drove 12 miles in 1/5 of an hour. On average how fast did she drive in miles per hour
Answers
If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.
To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):
Average speed = distance ÷ time
Average speed = 12 miles ÷ (1/5) hour
To divide by a fraction, we can multiply by its reciprocal, so:
Average speed = 12 miles × 5/1 hour
Average speed = 60 miles per hour
Therefore, Idil drove at an average speed of 60 miles per hour.
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Solve and write equation in Slope intercept
form (y=mxth) ! Label Slope and y intercept
1) -3x +y = 8
2) -2x + 3y = 1
3)5y +3X = 10
Answers
Answer:
Step-by-step explanation:
1. is y= 3 x +8
-3 x + y - 8= 0
y = 3x+ 8
2. is in the pictures
3.
3 X + 5 y - 10 = 0
Real solution:
y = 2 - (3 X)/5
Solution:
y = 2 - (3 X)/5
Integer solution:
X = 5 n, y = 2 - 3 n, n element Z
Solution for the variable y:
y = 1/5 (10 - 3 X)
Hi can someone help me with finding out the equation for this word problem
Answers
The equation of the word problem is x-4n.
What is word problem?A word problem is a math problem written out as a short story or scenario. This mathematical statement are interpreted into mathematical equation or expression.
Representing the total number of sheep in the flock by x and representing the number of weeks by n. Therefore the remaining sheep in the flock for the number of weeks will be expressed as
x - 4n.
Therefore the equation for the word problem is x - 4n.
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Twice during the assembly, a student is chosen at random to assist with the presentation. after the first student has finished assisting, the student returns to the group and can be chosen a second time. what is the probability that the first student chosen is a senior and the second student chosen is a sophomore?.
Answers
Using it's concept, it is found that the probability that the first student chosen is a senior and the second student chosen is a sophomore is given by:
\(p = \frac{11}{320}\)
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, we have that there are:
31 juniors, 10 sophomores, 17 juniors, 22 seniors.
Then:
Out of 31 + 10 + 17 + 22 = 80 students, 22 are seniors, hence the probability that the first student is a senior is given by \(p_1 = \frac{22}{80} = \frac{11}{40}\).All students can be chosen again, hence the probability that the second student is a sophomore is given by \(p_2 = \frac{10}{80} = \frac{1}{8}\).The events are independent, hence the probability of both is given by:
\(p = p_1p_2 = \frac{11}{40} \times \frac{1}{8} = \frac{11}{320}\)
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Find two functions F and g such that h(x) can be expressed as the function indicated. Several answers are possible. h(x) = 3x = x^2; f - g {f(x), g(x)} =
Answers
h(x) can also be expressed as f(x) - g(x) where f(x) = 3x and g(x) = x² - 3x.
What is function ?
A function is a mathematical rule or relationship between two sets of objects, often called the input and output, that assigns each input value exactly one output value. In other words, a function is a set of ordered pairs, where each input has only one output value.
For example, the function f(x) = 2x assigns to each value of x its double. If we put in x=1, the output is f(1) = 2(1) = 2. If we put in x=2, the output is f(2) = 2(2) = 4. Each input value has exactly one corresponding output value, which is the definition of a function.
Functions are often represented as graphs, with the input values on the x-axis and the output values on the y-axis. The graph of a function is a visual representation of the set of ordered pairs that define the function.
To express h(x) = 3x = x² as f - g, we need to find two functions f(x) and g(x) such that f(x) - g(x) = h(x).
One possible way to do this is to let f(x) = x² + 3x and g(x) = x². Then we have:
f(x) - g(x) = (x² + 3x) - x² = 3x = x² = h(x)
Therefore, h(x) can be expressed as f(x) - g(x) where f(x) = x² + 3x and g(x) = x².
Another possible way to do this is to let f(x) = 3x and g(x) = x² - 3x. Then we have:
f(x) - g(x) = 3x - (x² - 3x) = 6x - x² = h(x)
Therefore, h(x) can also be expressed as f(x) - g(x) where f(x) = 3x and g(x) = x² - 3x.
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Which mathematical operator is used to raise 5 to the second power in python? ^ / ** ~
Answers
In Python, the double asterisk (**) operator is used for exponentiation or raising a number to a power.
When you write 5 ** 2, it means "5 raised to the power of 2", which is equivalent to 5 multiplied by itself.
The base number is 5, and the exponent is 2.
The double asterisk operator (**) indicates exponentiation.
The number 5 is multiplied by itself 2 times: 5 * 5.
The result of the expression is 25.
So, 5 ** 2 evaluates to 25.
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y at least inequality symbol 2/3x + 2 y<-1/3x+1
Answers
After solving the given inequality question, we will get x < -9.
What is an inequality symbol?A mathematical sign for comparing two values or expressions is an inequality symbol. Inequality symbols include: (less than), > (greater than), (less than or equal to), and (greater than or equal to). Inequalities can be used to represent connections between two or more variables, for as 5 10 indicating that 5 is less than 10. Inequalities can also be used to define mathematical equations or to describe connections between variables. The equation x + 2 7 can, for example, be used to represent the relationship between x and 7, or to communicate that the value of x must be less than 5 for the equation to be true.
In the given question,
2/3x + 2y < -1/3x + 1
⇒ 2/3x + 2y - (-1/3x + 1) < 0
⇒ 5/3x + 3 < 0
⇒ 5/3x < -3
⇒ x < -9
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hich numbers are 9 units from −5 on this number line? Drag and drop all of the numbers that are 9 units from −5 to their correct position on the number line.
(IMAGE BELOW PLEASE EDIT THE IMAGE)
Answers
the numbers are 9 units from −5 on this number line are
4 14This is further explained below.
What is inequality?inequality, A statement in mathematics that establishes an order connection between two numbers or algebraic expressions, such as "greater than," "greater than or equal to," "less than," or "less than or equal to."
Generally, to know which numbers are 9 units from −5 on this number line, we mathematically compute
-5+9= 4
-5-9= -14
In conclusion, the numbers 9 units from −5 on this number line are
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Do you think that you could ever have a probability of
1110? Why or why not? Be sure to use the definition of probability
Answers
Answer:
No
Step-by-step explanation:
Probability meaning: "the extent to which something is probable; the likelihood of something happening or being the case."
Probability only is a range from 1-100 %
Probability can also be written as a percentage, which is a number from 0 to 100 percent. ... The probability of a certain event occurring depends on how many possible outcomes the event has. If an event has only one possible outcome, the probability for this outcome is always 1 (or 100 percent).
(credits to scientific american)
A rectangle with a length of (x+2) cm and a width of y cm has a perimeter of 37.5 cm. A second rectangle has twice the perimeter, with a length of (2x - 6.5) cm and a width of (x+2y) cm. Find the values of x and y.
Answers
Answer
x=10.5 , y=6.25
Step by Step ^
The solution is, the values of x and y is, x=10.5 , y=6.25.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
Perimeter refers to the total outside length of an object,
here, we have,
we know,
perimeter of rectangle is:
P = 2*( a+ b)
given that,
A rectangle with a length of (x+2) cm and a width of y cm has a perimeter of 37.5 cm.
i.e. we get,
2( x+2 + y ) = 37.5
or, 2x + 2y = 33.5 ........(1)
and, we have,
A second rectangle has twice the perimeter, with a length of (2x - 6.5) cm and a width of (x+2y) cm.
i.e. we have,
2( 2x - 6.5 + x + 2y ) = 75
or, 3x + 2y = 44.5 .....(2)
solving (1) & (2) , we get,
x=10.5 , y=6.25
Hence, The solution is, the values of x and y is, x=10.5 , y=6.25.
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In the diagram, ABCD ~ EFGH . Find the area of ABCD.
Answers
Answer:
150 in ^2
Step-by-step explanation:
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Inverses, contrapositives and converses. Below are examples of mathematical statements you’ll encounter in this class. Assume x, y, a, b, c are integers.
If the difference x − y is even then x and y are also even.
If a divides b or a divides c then a divides bc. (Note: a divides b means that the fraction b/a is an integer. For example, 3 divides 6 but 3 does not divide 7.)
If x2 ≥ 100 and x ≥ 0, then x ≥ 10.
(i) (9 pts.) State the inverse, contrapositive and converse of each statement above. When possible, avoid using the word "not." Instead, replace "not even" with "odd", etc.
Recall that for P → Q,
contrapositive: ¬Q →¬P
converse: Q → P
inverse: ¬(P → Q) = ¬(¬P ∨ Q) = P ∧ ¬Q
(ii) (3 pts.) Then indicate their truth values. Thus, for each statement you must determine whether the statement itself, its inverse, contrapositive and converse are true or false. That’s four true/false answers for each statement.
Answers
1. Statement: True
Inverse: True
Contrapositive: True
Converse: True
2. Statement: True
Inverse: True
Contrapositive: True
Converse: True
3. Statement: True
Inverse: True
Contrapositive: True
Converse: True
(i)
Statement: If the difference x - y is even, then x and y are also even.
Inverse: If x and y are not even, then the difference x - y is not even.
Contrapositive: If x and y are not even, then the difference x - y is not even.
Converse: If x and y are even, then the difference x - y is even.
Statement: If a divides b or a divides c, then a divides bc.
Inverse: If a does not divide b and a does not divide c, then a does not divide bc.
Contrapositive: If a does not divide b and a does not divide c, then a does not divide bc.
Converse: If a divides bc, then a divides b or a divides c.
Statement: If x^2 ≥ 100 and x ≥ 0, then x ≥ 10.
Inverse: If x^2 < 100 or x < 0, then x < 10.
Contrapositive: If x^2 < 100 or x < 0, then x < 10.
Converse: If x ≥ 10, then x^2 ≥ 100.
(ii)
For each statement, we need to evaluate the truth values of the statement, inverse, contrapositive, and converse.
Statement: True
Inverse: True
Contrapositive: True
Converse: True
Statement: True
Inverse: True
Contrapositive: True
Converse: True
Statement: True
Inverse: True
Contrapositive: True
Converse: True
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The table of values below represent an exponential function. Write an exponential equation that models the data. X y -2 26 -1 18. 2 0 12. 74 1 8. 0918 2 6. 2426 a. Y = 18. 2 (1. 7) Superscript x c. Y = 26 (0. 7) Superscript x b. Y = 12. 74 (1. 3) Superscript x d. Y = 12. 74 (0. 7) Superscript x.
Answers
The given table of values represents an exponential function. We need to write an exponential equation that models the given data .The exponential function can be represented as :y = ab ^x where y is the dependent variable, a is the initial value, b is the base, and x is the independent variable.
The given table of values :X y-2 2618 20 12.74 18.0918 26.2426We are required to find the equation that models the data. Therefore, we use the given data to find the initial value and base of the exponential function .Initial value: The initial value is the value of y when x = 0. From the table, we can observe that y = 20 when x = 0. Therefore, a = 20.Base:The base of an exponential function can be determined by the ratio of two consecutive values of y. We can calculate the base of the function as follows:\[\frac{y}{x} = b\]Taking the ratio of y for two consecutive values of x:\[\frac{18}{20} = 0.9\]Similarly,\[\frac{12.74}{18} = 0.7072\]Therefore, the base of the exponential function is 0.9.Substituting the initial value and base in the equation :y = ab ^x we get the required exponential equation as:y = 20(0.9)^x Therefore, the option is (b) Y = 12.74 (1.3)^x.
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5 a. how to convet 2 hour to second
Answers
Answer:
Step-by-step explanation:
2 hour
To seconds = 7200
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Mark brainliest