This triangle is not a right triangle because the sum of the squares of the two smaller sides is not equal to the square of the largest side.
To determine if a triangle is a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two smaller sides is equal to the square of the largest side.
In this case, we can compare the squares of the sides with lengths of 33 km and 72 km, and the square of the side with length 78 km:
33^2 + 72^2 = 5184 + 5184 = 10368
78^2 = 6084
Since 10368 is not equal to 6084, we can conclude that this triangle is not a right triangle.
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How many inches is 5 3 height?
Height is 63 inches, or 5 3 inches.
Explain about the inches?A measurement of distance or length in US units. A foot is 12 inches long and a yard is 36 inches long. 2.54 cm are exactly one inch.
A measurement of 1 inch is about equivalent to 2.54 cm. Add 2.54 cm to the provided inch number to convert it to centimetre values. 0.393701 inches are equal to 1 centimetre.
The smallest length you can measure with a ruler is 1/16 inch since each inch is divided into 16 lines, each of which is 1/16 inch long.
If you don't have a measuring device around, use the top of your thumb or another item that is roughly the same length to estimate measurements in inches. A foot is made up of 12 inches.
= (5 x 12) + 3.
= 60 +3
= 63
You now have 63 inches altogether.
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predict the sign of δsol for the solution
The sign of δsol for the solution will depend on the concentration of the solute and the temperature.
The sign of δsol for the solution will depend on two main factors: the concentration of the solute and the temperature. If the concentration of the solute is increased, the solute's tendency to dissolve in a solvent will also increase, resulting in a higher solubility. This increase in solubility will cause the sign of δsol to be positive. On the other hand, if the temperature is increased, the solubility of the solute will decrease, resulting in a decrease in the solubility. This decrease in solubility will cause the sign of δsol to be negative. Therefore, the sign of δsol for the solution will depend on the concentrations of the solute and the temperature. If the concentration of the solute is increasing, the sign of δsol will be positive; if the temperature is increasing, the sign of δsol will be negative.
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Pls Help will give brainlyest (15 pts)
Answer:
r ≥2, r<0
Step-by-step explanation:
1st blank:
1. Multiply both sides by 2
2. Simplify. 7r-20≥ -6
2nd blank:
1. multiply both sides by 2 to get (2(r+14))/2 < 7*2.
2. Simplify. You should get r+14 <14
3. Subtract 14 from both sides to isolate r.
4. Answer is r<0
Able, Baker, and Charlie are the only three stocks in an index. The stocks sell for $37, $312, and $94, respectively. If Able undergoes a 3-for-4 reverse stock split, what is the new divisor?
In order to calculate the new divisor for a 3-for-4 reverse stock split, we must first calculate the new share price for Able. Since 3/4 of the shares are being replaced with just 1/4 of the old shares, the new price for Able will be $111 (3 x $37 = $111).
The divisor is used to calculate the new index value by dividing the sum of the new share prices by the divisor. Therefore, the new divisor will be 1.33 ($111 + $312 + $94 = $517 / 1.33 = $389.28). This is because the new share prices will total $517 and when you divide that by the divisor, the index value will be $389.28.
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What kind of transformation is the function h(n) = 2(0. 8)n from the original function, h(n) = 10(0. 8)n?
A a vertical compression
B a vertical stretch and reflection
C a vertical stretch
D a vertical compression and reflection
The transformation of h(n) = 2(0.8)n from the original function, h(n) = 10(0.8)n, is a vertical compression.
Hence, option (a) is correct choice.
In a vertical compression, the graph of the transformed function is obtained by multiplying the y-coordinates of the points on the graph of the original function by a constant factor less than 1.
In this case, the factor is 2/10 = 1/5, which is less than 1, so the transformation is a vertical compression.
It is not a vertical stretch and reflection because the factor is less than 1, so it is not stretching the graph.
It is not a vertical stretch because the factor is less than 1, so it is not stretching the graph.
It is not a vertical compression and reflection because the factor is positive, so it is not reflecting the graph.
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When angle of elevation of the Sum is 45°, the shadow of a coconut tree is 15 m in length. What is the height of the coconut tree?
When the angle of elevation of the Sun is 45° and the shadow of a coconut tree is 15 m in length, the height of the coconut tree is 15 meters.
We have,
Denote the height of the coconut tree as AB.
A right triangle is formed by the coconut tree, its shadow, and the line connecting the top of the tree to the tip of the shadow.
From the figure,
tan(45°) = AB / 15
tan 45 = 1
So,
1 = AB / 15
Therefore,
The height of the coconut tree is 15 meters.
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What is the volume of the following rectangular prism? Volume ==equals units^3 3 cubed
Answer:
To find volume of rectangular prism you must find the length, width, and height!
Step-by-step explanation:
Volume = (Width) (height) (length)
Volume= Width x height x Length
you must multiple the length, width, and height together to get VOLUME:)
HOPE THIS HELPS :)
Combine like term (combine the poitive term and combine the negative term). 18-6-155-91
The combined like terms are -234.
Combining like terms means adding or subtracting any expressions that have the same variable. For example, in the expression:
2x + 3xThe terms 2x and 3x have the same variable (x), so they can be combined to form 5x.
Similarly, in the expression:
4y - 7yThe terms 4y and -7y have the same variable (y), so they can be combined to form -3y. The goal of combining like terms is to simplify expressions and make them easier to understand and manipulate.
In this case, the first two terms, 18 and -6, have no variable, so they can be combined to form 12. The next two terms, -155 and -91, also have no variable, so they can be combined to form -246. Finally, the combined terms, 12 and -246, can be combined to form -234. So, the final result is:
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approximate the sum of the series correct to four decimal places. [infinity] (−1)n 2nn! n = 1 s ≈
The sum of the series correct to four decimal places is 7.0000
To approximate the sum of the series, we can use the ratio test. The ratio test states that if the limit of the ratio of consecutive terms approaches a number L, then the series converges if |L| < 1 and diverges if |L| > 1.
The nth term of the series is given by
[tex]T_n = (-1)^n (3n)(n!)[/tex]
The consecutive terms is
[tex]R_n = T_{n+1}/T_n = (-1)^{n+1} (3n+3)(n+1) / (-1)^n (3n)(n!) \\= (-1)^{n+1} * 3 * (n+1) / (n!)[/tex]
Taking the limit as n approaches infinity:
[tex]L = lim_{n - > \infty} \ R_n = lim_{n - > \infty} (-1)^{n+1} * 3 * (n+1) / (n!)[/tex]
Since [tex](-1)^{n+1}[/tex] alternates between -1 and 1, the limit approaches 0 and |L| < 1, which means the series converges.
To approximate the sum of the series, we can use a numerical method such as the Euler-Maclaurin formula. The formula approximates the sum of an infinite series by the sum of its first few terms and the remainder term:
[tex]\Sigma_n^\infty=1T_n \approx \Sigma_{i=1}^m T_i + R_m[/tex]
where [tex]R_m[/tex] is the remainder term that decreases as m increases
For example, let's choose m = 5:
[tex]\Sigma_{i=1}^5 T_i = T_1 + T_2 + T_3 + T_4 + T_5[/tex]
= -3! + (-1) * 3 * 2! + (-1) * 2 * 3 * 1! + (-1) * 3 * 4! + (-1) * 4 * 3 * 2! = -6 + 6 - 2 + 24 - 24 = -2
The remainder term [tex]R_m[/tex] can be estimated using the Euler-Maclaurin formula:
[tex]R_m = -B_{2m} / (2m)! * T_{m+1}[/tex]
where B_k are the Bernoulli numbers.
For [tex]m = 5, B_2m = B_{10} = -1/252[/tex], so
[tex]R_m = -B_{10} / (10)! * T_{m+1} = -1/252 * (-1)^6 * 3 * 6! = 1/252 * 3 * 720 = 9[/tex]
Therefore, the sum of the series is approximately
[tex]\Sigma_{i=1}^\Infty T_i \approx \Sigma_{i=1}^5 \ T_i + R_m \\= -2 + 9 = 7[/tex]
To four decimal places, this is 7.0000
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Suki typed 245 words in 3 1/2 minutes. Find the following unit rates. Write the answer as a simplified
fraction and do not forget UNITS. (Decimal answers will not be accepted. )
a. How many words per minute?
b. How many minutes per word?
A. Suki typed 175/7 words per minute. B. It takes Suki 7/490 minutes per word.
A. To find the number of words per minute, we can divide the total number of words by the total time:
words per minute = 245 words / (3 1/2 minutes)
words per minute = 245 words / (7/2 minutes)
words per minute = 245 * 2 / 7 words/minute
words per minute = 175/7 words/minute
So, Suki typed 175/7 words per minute.
B. To find the number of minutes per word, we can divide the total time by the total number of words:
minutes per word = (3 1/2 minutes) / 245 words
minutes per word = (7/2 minutes) / 245 words
minutes per word = 7/2 * 1/245 minutes/word
minutes per word = 7/490 minutes/word
So, it takes Suki 7/490 minutes to type one word.
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3 1/2 minutes at 245 words per minute.
245 syllables per minute / 7 and a half minutes.
syllables per minute are calculated as 245 * 2/7.
175/7 words per minute is the word speed.
Suki's typing speed was 175/7 lines per minute.
hours per word equals (3 1/2 hours) / 245 words
syllables per minute = (7/2 minutes) / 245
minutes per word equals 7/2 * 0.245 minutes per word.
words/minute ≈ 7/490 minutes/word
Proposed solutions for which any denominator equals ____ are excluded from the solution set of a rational equation.
Answer:
0
Step-by-step explanation:
I believe it's 0, because if the denominator is equal to 0, our answer would be undefined
How many ways can 3 baseball players and 5 basketball players be selected from 12 baseball players and 12 basketball players ?
Many ways can 3 baseball players and 5 basketball players be selected from 12 baseball players and 12 basketball players are 173040 ways.
This is a combination problem, and we want to find the number of ways to choose 3 baseball players and 5 basketball players from a pool of 12 baseball players and 12 basketball players.
The formula for combinations is: C(n, k) = n! / (k! (n - k)!).
For the baseball players, n = 12 and k = 3, so C(12, 3) = 12! / (3! (12 - 3)!) = 12! / (3! 9!) = 220.For the basketball players, n = 12 and k = 5, so C(12, 5) = 12! / (5! (12 - 5)!) = 12! / (5! 7!) = 792.The total number of combinations is the product of the number of combinations for each group, so 220 * 792 = 173040.
Therefore, there are 173040 ways to choose 3 baseball players and 5 basketball players from a pool of 12 baseball players and 12 basketball players.
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At the beginning of spring, Shaniece planted a small sunflower in her
backyard. When it was first planted, the sunflower was 25 inches tall. The
sunflower then began to grow at a rate of 0.5 inches per week. How tall would
the sunflower be after 10 weeks? How tall would the sunflower be after w
weeks?
Please help fast!!!!
The sunflower be after w weeks would be 25 + 0.5 * w inches tall.
What do you mean by algebraic expression?Let's say James and Natalie were playing with matchsticks when they had the idea to create number patterns with them. James made the number 4 with four matchsticks. In order to create a pattern with two 4s, Natalie added three extra matchsticks. They understood that they could keep adding three matchsticks each round to make an additional "four" by doing so. They deduced from this that, generally speaking, in order to create a pattern with n number of 4s, you need 4+ 3(n-1) sticks. We refer to 4+ 3(n-1) as an algebraic expression in this case.
To calculate the height of the sunflower after 10 weeks, we can use the formula:
height = starting height + growth rate * time elapsed
where the starting height is 25 inches, the growth rate is 0.5 inches per week, and the time elapsed is 10 weeks.
So the height after 10 weeks would be:
height = 25 + 0.5 * 10 = 25 + 5 = 30 inches
Therefore, the sunflower would be 30 inches tall after 10 weeks.
To calculate the height after w weeks, we can use the same formula:
height = 25 + 0.5 * w
So the height after w weeks would be:
height = 25 + 0.5 * w inches
This gives you the height of the sunflower in inches after w weeks of growth.
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use the chain rule of differentiation to find the derivative with respect to t of g(t)=cos(ωt) .
the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get: ∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2- 2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
a. The region D in the x-y plane is illustrated in the figure below.
b. ∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
a. The region D in the x-y plane is the area bounded by the two parabolas y= 2x2 and y= 1 x2. This can be seen in the sketch below.
b. To evaluate the integral ∫∫ df(x,y)dxdy, we need to evaluate the integral of the function f(x,y) = x2y over the region D. We can do this by setting up the integral as follows:
∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy
Next, we can evaluate the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get:
∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
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differentiate the function. f(z) = ez/(z − 7)
The derivative of f(z) = ez/(z − 7) is therefore f'(z) = (ez(z - 6))/(z - 7)^2.
The derivative of f(z) = ez/(z − 7) can be calculated using the quotient rule. The quotient rule states that the derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared. Therefore, the derivative of f(z) = ez/(z − 7) is equal to (ez(z - 7) - (ez)(1))/(z - 7)^2. This simplifies to ez/(z - 7)^2. Therefore, the derivative of f(z) = ez/(z − 7) is equal to ez/(z - 7)^2.
For our purposes, we can substitute in g(z) = ez and h(z) = (z − 7). Then, we can calculate the derivatives of each part. The derivative of g(z) is g'(z) = ez, and the derivative of h(z) is h'(z) = 1. Now, we can plug these values into the Quotient Rule and calculate the derivative of the function f(z) = ez/(z − 7).
f'(z) = (ez(z − 7) - ez(1))/(z − 7)^2
f'(z) = (ez(z - 6))/(z - 7)^2
The derivative of f(z) = ez/(z − 7) is therefore f'(z) = (ez(z - 6))/(z - 7)^2.
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Goran buys candy that costs $8 per pound. He will spend at least $56 on candy. What are the possible numbers of pounds he will buy?
Use P for the number of pounds Goran will buy.
Write your answer as an inequality solved for p.
The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Goran buys candy that costs $8 per pound. He will spend at least $56 on candy.
Let 'p' be the number of pounds of the candy. Then the inequality is given as,
8p ≤ 56
p ≤ 56 / 8
p ≤ 7
The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.
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what is 9 minus 9 divided by 9 plus 9 minus 9 divided by 9
What is the area formula for parallelograms?
Similar to how a rectangle's area is calculated, a parallelogram's area is calculated as base times height.
Explain about the area formula for parallelograms?The four sides of a parallelogram, a geometric shape made up of two pairs of parallel lines, are parallel. The opposite sides and angles of a parallelogram have equal lengths and measures.
By multiplying the base and altitude of a parallelogram, the area of the shape can be determined. A parallelogram's base and altitude are always parallel to one another. A parallelogram's area can be calculated using the following equation: Area of parallelogram = base height square units.
You can use the following formula to determine any parallelogram's area:
Area = base x height
It should be mentioned that a parallelogram requires a perpendicular base and height.
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Determine the sum of the solutions to:
For the quadratic equation 5x² - 16x + 3 = 0, the sum of solutions is 3.02.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The quadratic expression is given as -
5x² - 16x + 3 = 0
The expression is written in the form ax² + bx + c
Where a = 5, b = -16 and c = 3
Use the quadratic formula -
x = [-b ± √(b² - 4ac)] / 2a
Substitute the values into the formula -
x = [-(-16) ± √{(-16)² - 4(5)(3)}] / 2(5)
x = [16 ± √{256 - 60}] / 10
x = [16 ± √196] / 10
x = [16 + √196] / 10 and x = [16 - √196] / 10
x = [16 + 14] / 10 and x = [16 - 14] / 10
x = 30/10 and x = 2/10
x = 3 and x = 0.2
The solutions are x = 3 and x = 0.2.
The sum of solutions are = 3 + 0.2 = 3.02
Also, the formula for sum of solutions for a quadratic equation is -b/a.
Sum of solutions = -(-16) / 5
Sum of solutions = 16 / 5
Sum of solutions = 3.02
Therefore, the sum of solutions is 3.02.
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Complete question:
Determine the sum of the solutions to:
5x² - 16x + 3 = 0
scatterplot is the best visualization for showing which of the following (choose one or more)? group of answer choices indirect or negative relationship between two ratio variables the relationship between two interval/ratio variables correlation frequency of two nominal variables
Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
Scatterplots are best for showing:
⇒the relationship between two interval/ratio variables
⇒indirect or negative relationship between two ratio variables
Scatterplots display points on a coordinate plane, with one variable plotted on the x-axis and the other variable plotted on the y-axis. This allows us to see the pattern of relationship between the two variables. If there is a positive or negative relationship, we can see if the points tend to increase or decrease as we move from left to right or from bottom to top. If the relationship is indirect, we can see if the points tend to curve in one direction or another.
Scatterplots are not the best visualisation for showing: correlation
frequency of two nominal variables
For showing correlation, a line of best fit (regression line) can be added to a scatterplot, but other visualizations such as a correlation matrix or a heat map are more commonly used.
For showing frequency of two nominal variables, a two-way table or a mosaic plot are better suited, as they can display the count or proportion of cases for each combination of the two nominal variables.
Therefore, Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
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Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
Scatterplots are best for showing:
⇒the relationship between two interval/ratio variables
⇒indirect or negative relationship between two ratio variables
Scatterplots display points on a coordinate plane, with one variable plotted on the x-axis and the other variable plotted on the y-axis. This allows us to see the pattern of relationship between the two variables. If there is a positive or negative relationship, we can see if the points tend to increase or decrease as we move from left to right or from bottom to top. If the relationship is indirect, we can see if the points tend to curve in one direction or another.
Scatterplots are not the best visualization for showing: correlation
frequency of two nominal variables
For showing correlation, a line of best fit (regression line) can be added to a scatterplot, but other visualizations such as a correlation matrix or a heat map are more commonly used.
For showing frequency of two nominal variables, a two-way table or a mosaic plot are better suited, as they can display the count or proportion of cases for each combination of the two nominal variables.
Therefore, Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
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A sequence can be generated by using an=4an−1, where a1=7 and n is a whole number greater than 1.
What are the first 3 terms in the sequence?
4, 28, 196
7, 28, 112
4, 11, 18
7, 11, 15
Answer: 7, 28, 112
Step-by-step explanation: The first three terms in the sequence can be found by using the formula an = 4an-1, starting with the initial value a1 = 7:
a2 = 4a1 = 4 * 7 = 28
a3 = 4a2 = 4 * 28 = 112
So, the first three terms in the sequence are 7, 28, 112.
A truck that is 10 ft. by 12 ft. by 14 ft. carries cube shaped boxes that
have a length of 2.5 ft. How many of these boxes can this truck hold?
Round your answer to the nearest whole number.
*10
Answer:
108
Step-by-step explanation:
The volume of the truck is 10*12*14=1680
So, answer = the volume of the truck / the volume of a cube
answer= 1680/15.625=107.52 = 108.
if the maximum value of the function y=cos x/sin x is at x = pi/4 , what is the value of m?
The maximum value of the function y=cos x/sin x at x = pi/4 is 1, so the value of m is 1.
The maximum value of the function y=cos x/sin x is when the cos x and sin x terms have the same magnitude. This happens when x=pi/4. In this case, the function reduces to y=cos(pi/4)/sin(pi/4) = 1.
Therefore, the value of m = 1.
The maximum value of the function y=cos x/sin x at x = pi/4 is 1, so the value of m is 1.
The function y=cos x/sin x has a maximum value of 1 when x = pi/4. This is because when x = pi/4, the cos x and sin x terms have the same magnitude, and the function reduces to y=cos(pi/4)/sin(pi/4) = 1. Therefore, the maximum value of the function y=cos x/sin x is 1, and the value of m is 1. This result holds true for any value of x, and is a useful tool when working with trigonometric functions.
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How do you guess the limit of (7n^3 +8n) / (2n^3 - 31) and prove that your guess is correct using the ε-N approach?
By using the ε-N approach, the value of the function is 2.71828.
The ε-N approach is a mathematical tool used to determine the limit of a function as the independent variable approaches infinity or zero.
In this problem, we are asked to guess the limit of
=> (7n³ +8n) / (2n³ - 31)
as n approaches infinity.
To do this, we need to use the ε-N approach. The first step is to make an educated guess about the limit.
Next, we use the ε-N approach to prove our guess is correct.
This involves finding an ε (epsilon) value, which is a small positive number, and an N value, which is the input value for n, such that for all n greater than N, the absolute value of the difference between the function and the limit is less than ε.
To use various symbols to denote the Epsilon values too because Epsilon has no interest in the meaning of its own like other mathematical symbols like π(pi) and it has the value 3.14.
Here the symbol e and has value 2.71828.
This means that the function is arbitrarily close to the limit.
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6.
Parallelogram ABCD has coordinates A(1,5), B(6,3), C(3,-1), and D(-2,1).
What are the coordinates of E, the intersections of diagonals AC and BD?
a (4. 5,1)
b (2,2)
c (3. 5, 2)
d (-1,3)
help with this please
The coordinates of E, the intersections of diagonals AC and BD is; B: (2, 2)
How to find the coordinates of the diagonals?A parallelogram is simply defined as a quadrilateral with two pairs of parallel sides.
Now, the diagonals of a parallelogram usually intersect at their midpoints. Formula to find the midpoint of a line with coordinates is;
Midpoint = (x2 + x1)/2, (y2 + y1)/2
Thus;
Midpoint of AC = ((1 + 3)/2, (5 - 1)/2
= (2, 2)
Similarly,
Midpoint of BD = (6 - 2)/2, (3 + 1)/2
= (2, 2)
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Use guess and check to find an anti-derivative
F(x)
for
f(x)=sin(x)cos(x)
. Explain why you chose particular guesses, and how you checked them.
When finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation.
One approach to finding an antiderivative of a function is the method of guess and check. This involves making an educated guess for the antiderivative and then verifying it by taking the derivative of the guess and comparing it to the original function.
To find the antiderivative of f(x) = sin(x)cos(x), we can start with a guess based on the product rule for differentiation: d/dx (uv) = u * dv/dx + v * du/dx
Since f(x) = sin(x)cos(x), we can write: d/dx (sin(x)cos(x)) = cos^2(x) + sin^2(x) = 1
This suggests that the antiderivative of f(x) = sin(x)cos(x) might be: F(x) = sin(x)sin(x) + C, where C is an arbitrary constant of integration.
To check our guess, we need to take the derivative of F(x) and compare it to the original function f(x): d/dx (sin(x)sin(x) + C) = cos(x)sin(x)
If our guess is correct, the derivative of F(x) should equal f(x). However, in this case, our guess does not match the original function f(x), so we need to make another guess. A second guess could be:
F(x) = -cos(x)cos(x) + C
Taking the derivative: d/dx (-cos(x)cos(x) + C) = -sin(x)cos(x)
This time, the derivative of F(x) does match the original function f(x), so our guess is correct and the antiderivative of f(x) = sin(x)cos(x) is:
F(x) = -cos(x)cos(x) + C.
Thus, In conclusion, when finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation. By checking the derivative of the guess and comparing it to the original function, we can determine whether or not our guess is correct.
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Find an equation for the surface consisting of all points p for which the distance from p to the x-axis is 4 times the distance from p to the yz-plane.
The equation that represents the distance is -25x² + y² + z² = 0
What is an Equation in Math?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A mathematical statement called an equation demonstrates the equality of two mathematical expressions.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.Equations can be divided into the three categories of linear equations, quadratic equations, and cubic equations depending on their degree.Given data :
The distance between two points, is the number of units between them.
The equation that represents the distance is -25x² + y² + z² = 0
The distance between a point and the x-axis is represented as:
D = ( y² + x² ) [tex]\frac{1}{2}[/tex]
From the question, we have:
D = 5x
Equate both expressions for D
5x =- ( y² + z² ) [tex]\frac{1}{2}[/tex]
Square both sides
25x² = y² + z²
Equate to 0
y² + z² - 25x² = 0
Rewrite as:
-25x² + y² + z² = 0
Hence, the equation that represents the distance is -25x² + y² + z² = 0
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if x represents quantity and y represents the quantity which of the tables below represnt a direct proportion
which type of chart makes this most apparent
A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.
A bar chart would make this most apparent.
A bar chart is the best type of chart to visually represent the comparison of values over a period of time. It is simple to read, and makes it easier to compare and contrast each value.
A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.
A bar chart is the best type of chart to visually represent the comparison of values over a period of time. It is simple to read, and makes it easier to compare and contrast each value.
A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.
the complete question is :
Which type of chart makes it most apparent that one group has a significantly higher value than the other?
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Redraw the triangle with sides that are 1/3 as long as the sides of the original 15 m 9 m Original 12 m a Calculate the perimeters of BOTH triangles. Perimeter (P = s + s + s) of original Perimeter of new A b. Calculate the areas of BOTH triangles. Area (A= 1 2 b^ * h) of original Area of new A . What is the relationship between the perimeters of the triangles?
The new triangle has sides of 3m, 4m, and 5m as the attached picture below.
The perimeter of the original triangle is 36 and the new triangle is 12. The area of the original triangle is 54 and the new one is 6The new triangle's perimeter is a third of the original's perimeter, which represents the ratio of both trianglesThe new triangle has sides of 1/3 of the original. Then:
1/3 x 15 m = 5m
1/3 x 9 m = 3 m
1/3 x 12 m = 4 m
The new triangle is as the attached picture below
The perimeter of the original triangle is:
P original = 15 + 9 + 12
P original = 36 m
The perimeter of the new triangle is:
P new = 5 + 3 + 4
P new = 12 m
The area of the original triangle is:
Area original = 1/2 x 12 x 9
Area original = 54 m
The area of the new triangle is:
Area new = 1/2 x 4 x 3
Area new = 6
The relationship between both triangles' perimeter is:
P original : P new = 36 : 12
= 3 : 1 --> ratio of both triangles
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