Answer:
25&36
Step-by-step explanation:
25 is a square number and so is 36 and there product is 900. They are also consecutive.
Just assemble the square numbers from the least i.e 4 and try solving as asked to see if it gives 900.
Thus you'll land on 25&36
Answer:
5² and 6²
Step-by-step explanation:
Use trial and error
Start from the product of 1² and 2²
1×2²
1×4=4
4<900 (incorrect)
2²×3²
4×9=36
36<900(incorrect)
3²×4²
9×16=144
144<900(incorrect)
4²×5²
16×25=400
400<900(incorrect) *but close
5²×6²
25×36 =900
900=900(correct)
: . 5² and 6² are the two consecutive square numbers.
e population of Matteson in t years can be m What is the population of Matteson now?
Cannot be determined
The population of Matteson can be calculated using the given formula: m(t) = 11410 + 220t. However, the current population of Matteson is not given in the question, so it cannot be calculated using the given formula. Therefore, the population of Matteson now cannot be determined based on the given information.
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In the table below, find the slope, y-intercept, and equation for each racer.
Hint: Time is going to be your independent x / the x-axis. Distance is going to be your dependent y / the y-axis.
Therefore , the solution of the given problem of slope comes out to be y = 15x + 10.
Explain slope.A line's steepness is determined by its slope. In gradient based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).
Here,
A racer:
Due to the fact that the race begins at the beginning, the y-intercept
is 0.
We can select any two locations from the table and use the following formula to determine the slope:
=> Slope Equals (Distance Change) / (change in time)
As an illustration, if we select the coordinates (1, 10) and (3, 40), we obtain:
=> slope = (40 - 10) / (3 - 1) = 30 / 2 = 15
As a result, Racer A's calculation is:
=> y = 15x
Runner B:
As an illustration, if we select the coordinates (1, 25) and (3, 55), we obtain:
=> slope = (55 - 25) / (3 - 1) = 30 / 2 = 15
As a result, Racer B's calculation is:
=> y = 15x + 20
Runner B
The race begins at a distance of 10 feet, so the y-intercept is 10.
We can select any two locations from the table and use the following formula to determine the slope:
Slope Equals (Distance Change) / (change in time)
As an illustration, if we select the coordinates (1, 35) and (3, 65), we obtain:
=> slope = (65 - 35) / (3 - 1) = 30 / 2 = 15
As a result, Racer C's equation is:
=> y = 15x + 10
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Rohana wants to find the volume of a sphere that has a radius of 10 feet. Which equation chan she use to solve for this value in cubic feet?
The equation change of volume of a sphere Rohana uses to solve for this value in cubic feet is V = (4/3)π(10)³ which gives the value 4,188.79 cubic feet.
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is a constant value approximately equal to 3.14159.
In this problem, the radius of the sphere is given as 10 feet. So, we can substitute this value into the formula to get the volume of the sphere as:
V = (4/3)π(10)³
Simplifying the right side, we get:
V = (4/3) × π × (1000)
V = (4/3) × 3.14159 × 1000
V = 4.18879 × 1000
V = 4,188.79 cubic feet
Therefore, the volume of the sphere with a radius of 10 feet is 4,188.79 cubic feet.
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i need help on geometry, an explanation on the answer would be helpful, thanks.
The following are the correct measures for the angles and arc length:
m∠DFA = 58°
m∠COB = 114°
m∠EOB = 122°
arc CE = 124°.
How to evaluate for the measures of the angles and arcm∠CED = [360 - 2(124)]/2 {angles at a point}
m∠CED = 56°
m∠A = [360 - 2(114)]/2 {angles at a point}
m∠A = 66°
m∠F = 180 - (56 + 66) {sum of interior angles of a triangle}
m∠F = 58°
The lines touching the circle at point C, B, and E respectively are tangents, hence the radii are perpendicular to each lines so;
angles m∠OCA, m∠OBA, m∠OBF, and m∠OEF are all equal to 90°
m∠COB = 360° - (90 + 90 + 66)° {sum of interior angles of a quadrilateral}
m∠COB = 114°
m∠EOB = 360° - (90 + 90 + 58)° {sum of interior angles of a quadrilateral}
m∠EOB = 122°
m∠CDE = 180° - arcCE
56° = 180° - arcCE
arcCE = 180° - 56°
arc CE = 124°.
Therefore, the correct measures of the angles and arc length are:
m∠DFA = 58°
m∠COB = 114°
m∠EOB = 122°
arc CE = 124°
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5(x-y)+4=7 what is the value of x-y
Step-by-step explanation:
We can solve for x-y by isolating the term on one side of the equation and simplifying:
5(x-y) + 4 = 7
5(x-y) = 7 - 4
5(x-y) = 3
Next, we can divide both sides by 5:
x - y = 3/5
Therefore, the value of x-y is 3/5.
What is the volume of a spherical boulder is 10 ft in diameter and weighs almost 6 tons?
The volume of the spherical boulder is approximately 71.21 cubic feet.
To find the volume of a spherical boulder, we can use the formula for the volume of a sphere:
V = (4/3)πr³
where V is the volume and r is the radius of the sphere.
We are given that the diameter of the boulder is 10 feet, so the radius is half of that, or:
r = 10/2 = 5 feet
We are also given that the boulder weighs almost 6 tons. To convert this weight to pounds, we can multiply by 2000 (since 1 ton is equal to 2000 pounds):
6 tons * 2000 pounds/ton = 12,000 pounds
The weight of the boulder is related to its volume through its density. The density of a boulder will depend on its composition, but we can make an estimate based on common rock types. For example, granite has a density of about 2.7 grams per cubic centimeter, or 2.7 metric tons per cubic meter (since 1 metric ton is equal to 1000 kilograms). A boulder made of granite would therefore weigh about 2.7 times its volume in cubic meters.
Assuming the boulder is made of granite, we can find its volume by setting its weight equal to its volume times its density:
12,000 pounds = V * 2.7 metric tons/m³
To convert pounds to metric tons, we can divide by 2204.62 (since 1 metric ton is equal to 2204.62 pounds):
12,000 pounds / 2204.62 pounds/metric ton = 5.44 metric tons
Substituting this into the equation above, we get:
5.44 metric tons = V * 2.7 metric tons/m³
Dividing both sides by 2.7, we get:
V = 5.44 metric tons / 2.7 metric tons/m³ = 2.0148 m³
To convert this volume to cubic feet, we can use the conversion factor 1 cubic meter = 35.3147 cubic feet:
V = 2.0148 m³ * 35.3147 ft³/m³ = 71.21 ft³
Therefore, the volume of the spherical boulder is approximately 71.21 cubic feet.
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Find the distance between the two points rounding to the nearest tenth (if necessary). (-6 and -1) and (-9 and -6)
Step-by-step explanation:
Use the distance formula ( a modified Pyhtagorean theorem)
d^2 = (x1-x2)^2 + ( y1-y2)^2
d^2 = ( -6 - -9)^2 + ( -1 - -6)^2
d^2 = ( 3^2) + ( 5^2)
d^2 = 34
d = sqrt (34 ) =~ 5.8 units
Click the icon to view the table. a. Find the probability of getting exactly 1 girl in 8 births. _________ (Type an integer or a decimal. Do not round.) b. Find the probability of getting 1 or fewer girls in 8 births. _________ (Type an integer or a decimal. Do not round.) c. Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part (a) or part (b)? A. Since getting 0 girls is an even lower number of girls than getting 1 girl, the result from part (b) is the relevant probability. B. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability. C. Since the probability of getting 1 girl is the result from part (a), this is the relevant probability. D. Since the probability of getting 0 girls is less likely than getting 1 girl, the result from part (a) is the relevant probability. d. Is 1 a significantly low number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event. A. Yes, since the appropriate probability is greater than 0.05, it is a significantly low number. B. No, since the appropriate probability is greater than 0.05, it is not a significantly low number. C. No, since the appropriate probability is less than 0.05, it is not a significantly low number. D. Yes, since the appropriate probability is less than 0.05, it is a significantly low number.
a. The probability of getting exactly 1 girl in 8 births is given as follows: 0.0313 = 3.13%.
b. The probability of getting 1 or fewer girls in 8 births is given as follows: 0.0352 = 3.52%.
c. The relevant probability for significantly low is given as follows: B. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability.
d. The correct option regarding whether the probability is significantly low is: D. Yes, since the appropriate probability is less than 0.05, it is a significantly low number.
What is the binomial distribution formula?The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The mass probability formula is given as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single independent trial of the experiment.The relevant probabilities for this problem are given as follows:
P(X = 0) = 0.5^8 = 0.0039.P(X = 1) = 8 x 0.5^8 = 0.0313.Hence the probability of 1 or fewer, used to verify if the event is significantly low, is:
P(X <= 1) = P(X = 0) + P(X = 1)
P(X <= 1) = 0.0352.
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he j and k in the jk-ff (and jk-latch) are very much like the s and r in the sr-ff (and sr-latch), respectively. the j acts like the s and the k acts like the r. the only difference for these devices in 3701 is which of the following? group of answer choices j
The only difference for these devices in 3701 is that the jk-FF (or jk-latch) has an additional control input, which is the clock (CK). The CK input is used to enable and disable the device so that the inputs, j and k, do not always affect the output (Q) of the device.
The SR-FF (or SR-latch) has two inputs, S and R, which directly affect the output, Q. When S=1, the output is set to 1, and when R=1, the output is reset to 0.
On the other hand, the jk-FF (or jk-latch) has three inputs, J, K and CK. When CK is 0, the device is disabled and the outputs remain the same. When CK is 1, the J and K inputs can be used to either set (J=1, K=0) or reset (J=0, K=1) the output, Q.
In summary, the j and k in the jk-FF (or jk-latch) are similar to the s and r in the SR-FF (or SR-latch).
So, the only difference is the addition of a clock (CK) input in the jk-FF (or jk-latch). This clock (CK) input enables and disables the device, which allows the inputs, j and k, to affect the output (Q) of the device.
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Suppose demand d for a company's product at cost x is predicted by the function d(x) = 0. 36x2 + 810, and that the price p that the company can charge for the product is given by p(x) = x + 14. Find the company's revenue function
The revenue for a company's product is the amount of money the company earns from selling the product. R(x) = 0.36x^3 + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.
R(x) = 0.36x^3 + 824x
The revenue for a company's product is the amount of money the company earns from selling the product. To find the revenue function for a company, we can use the demand and price functions given. The demand function tells us how much of the product customers are willing to buy at a certain cost, while the price function tells us how much the company can charge for the product. R(x) = 0.36x^3 + 824x + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.
At x = 10,
R(10) = 0.36(10^3) + 824(10) + 824
R(10) = 3600 + 8240 + 824
R(10) = 17,664
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A curve has the equation y= x² + ax + b, where a and b are numbers. The turning point of the curve is (5, 4). Work out the values of a and b.
The values of a and b are -10 and 29, respectively of the curve.
What do you mean by turning point of a quadratic curve ?
The turning point of a quadratic curve is the point at which the curve changes direction from going up to going down, or vice versa. It is also known as the vertex of the parabola. The x-coordinate of the turning point is given by -b/2a, and the y-coordinate is the value of the function at that point.
Finding the values of a and b :
Given that the turning point of the curve is (5,4), we can write the following equations:
[tex]4 = 5^2 + 5a + b[/tex] (since the turning point lies on the curve)
[tex]0 = 2(5) + a[/tex] (since the derivative of the curve at the turning point is 0)
Simplifying the second equation gives us:
[tex]a = -10[/tex]
Substituting this value of a in the first equation, we get:
[tex]4 = 5^2 - 50 + b[/tex]
[tex]b = 29[/tex]
Therefore, the values of a and b are -10 and 29, respectively.
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A square on the coordinate plane has vertices at (−5, 5), (5, 5), (5, −5), and (−5, −5). A dilation of the square has vertices at (−10, 10), (10, 10), (10, −10), and (−10, −10). Find the scale factor and the perimeter of each square
the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.
To find the scale factor of the dilation, we can compare the corresponding side lengths of the two squares. The distance between the points (-5,5) and (5,5) is 10 units, which is also the length of the side of the original square. The distance between the points (-10,10) and (10,10) is 20 units, which is the length of the side of the dilated square. Therefore, the scale factor is:
Scale factor = Length of dilated square side / Length of original square side = 20 / 10 = 2
This means that the dilated square is twice as large as the original square.
To find the perimeter of the original square, we can add up the length of each side. Each side of the square has a length of 10 units, so the perimeter is:
Perimeter of original square = 4 × length of one side = 4 × 10 = 40 units
To find the perimeter of the dilated square, we can use the same method. Each side of the dilated square has a length of 20 units, so the perimeter is:
Perimeter of dilated square = 4 × length of one side = 4 × 20 = 80 units
Therefore, the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.
Dilation is a transformation that changes the size of an object but leaves its shape unchanged. In this case, the dilation of the square resulted in a larger square that was similar to the original square, meaning that the corresponding angles in the two squares were equal. The scale factor of the dilation determined the ratio of the side lengths of the two squares, and the perimeter of each square was proportional to its side length. Dilations are used in geometry to create similar figures and to scale up or down an object in size.
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A hose for a sprinkler system lies along one diagonal of a square garden. the exact length of the hose is25\sqrt{2} feet. what is the perimeter of the garden?
The perimeter of the square garden is 100 feet.
To find the perimeter of the square garden, first we need to determine the length of one side of the square. The given
information states that the hose, which lies along one diagonal of the garden, has a length of 25√2 feet.
Recall that the diagonal of a square divides it into two congruent right triangles, with the diagonal being the
hypotenuse.
Use the Pythagorean theorem to find the side length of the square. Let 'a' represent the side length of the square.
Then, we have:
a² + a² = (25√2)²
Simplify the equation:
2a² = 625 × 2
Divide both sides by 2:
a² = 625
Find the square root of both sides:
a = 25
Now that we know the side length of the square garden is 25 feet, we can calculate the perimeter.
The perimeter of a square is given by the formula:
Perimeter = 4 × side length
Substitute the side length:
Perimeter = 4 × 25
Calculate the perimeter:
Perimeter = 100
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Use synthetic division to write (6x+5)/(x+7) in the form quotient +( remainder )/( divisor ).
[tex](6x+5)/(x+7)\\[/tex] can be represented as in the form quotient [tex]+( remainder )/( divisor )[/tex] as [tex]6 + 47/(x+7)[/tex] using division.
The methods below show how to use synthetic division to write (6x+5)/(x+7) in the form quotient +(remainder)/(divisor):
The divisor, x+7, should be written in the following format: (a, b, c,... 0), where the final term is 0 and the other terms are the polynomial coefficients in descending order of degree. The divisor is already present in this form in this instance.Using the same format as the divisor and a 0 coefficient for any missing terms, write the dividend, 6x+5, in the same format. The dividend can therefore be expressed as (6, 5).Reduce the dividend's first period, which is six years.Multiply the first coefficient of the dividend by the amount that was just brought down, and then place the answer under the second coefficient of the payout. So, we multiply 7 by 6 to obtain 42, which we then place in the payout under the number 5.To determine the new dividend coefficient value, add the two coefficients from the previous step. Because of this, 5 + 42 = 47.Repeat steps 4 and 5 as necessary to process all of the dividend's terms. The leftover is the last coefficient in the dividend, and together with the other coefficients, it makes up the quotient. In this instance, the remainder is 47 and the quotient is 6.So, (6x+5)/(x+7) is the divisor x+7 divided by the quotient 6 plus the remainder 47. Hence, we can write:
(6x+5)/(x+7) = 6 + 47/(x+7)
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Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. f(x) = 6x3 + 7x2 + x + 5 The number of variations in sign in f(x) is 3 x. Therefore, the number of positive real zeros of f is either 3 or 0x. The number of variations in sign in f(-x) is 3 . Therefore, the number of negative real zeros of f is either 3 or 0x Need Help? Read It Watch It Talk to a Tutor Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. f(x) = 7x3 - 8x2 - 5x - 4 The number of variations in sign in f(x) is 1 Therefore, the number of positive real zeros of f is 0 The number of variations in sign in f(-x) is 2 . Therefore, the number of negative real zeros of f is either 2 or 0 Need Help? Read It Watch It Talk to a Tutor
The number of negative real zeros of f is either 3 or 0.
Using Descartes's Rule of Signs, the possible numbers of positive and negative zeros of the function f(x) = 6x3 + 7x2 + x + 5 can be determined. The number of variations in sign in f(x) is 3. This means that the number of positive real zeros of f is either 3 or 0. The number of variations in sign in f(-x) is 3. This means that the number of negative real zeros of f is either 3 or 0.
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what is 4% of 1 million people?
Answer:
40000
Step-by-step explanation:
To find 4 percent of a number, multiply the number by 0.04. In this instance, 0.04 x 1000000 = 40000. Therefore, 4 percent of 1000000 is equal to 40000.
Do what the picture says and right answer gets brainilest!!!
Answer:
Below
Step-by-step explanation:
See image attached
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Answer:
Please Mark as Brainliest
Step-by-step explanation:
Based on the information provided, the three true statements about Josiah's solution are:
"300 = x." - This statement is true because Josiah predicted that there were 300 rock songs on his MP3 player.
"He did not multiply the numerator and denominator by the correct number to equal 1,500." - This statement is true because in his proportion, Josiah multiplied the numerator and denominator by 30, which is not a multiple of 1,500.
"He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500." - This statement is true because to set up a proportion with 1,500 as the denominator, Josiah should have multiplied the numerator and denominator by a multiple of 1,500. In this case, 75 is a multiple of 1,500, so multiplying by 75 would have been the correct approach.
The table below represents the number of NFL teams that won or lost their first game of the season. What is the probability that a team selected won their first game, given the team is from the AFC?
The prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.
What is Prοbability?Prοbability is a measure οf the likelihοοd οf an event οccurring, expressed as a number between 0 and 1. A prοbability οf 0 means the event is impοssible, and a prοbability οf 1 means the event is certain.
Out οf the tοtal number οf teams that wοn their first game, 12 are frοm the AFC and 6 are frοm the NFC. Out οf the tοtal number οf teams that lοst their first game, 4 are frοm the AFC and 10 are frοm the NFC.
Therefοre, the tοtal number οf AFC teams is 12 + 4 = 16, and the tοtal number οf NFC teams is 6 + 10 = 16.
If we randοmly select a team that wοn their first game, the prοbability that the team is frοm the AFC is:
P(AFC) = number οf AFC teams / tοtal number οf teams
= 16 / (16 + 16)
= 1/2
The prοbability that the team selected wοn their first game and is frοm the AFC is:
P(wοn first game AND AFC) = number οf AFC teams that wοn first game / tοtal number οf teams that wοn first game
= 12 / (12 + 6)
= 12/18
= 2/3
Therefοre, the prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.
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The original price of a laptop was £200.
The price of the laptop was reduced by 10% in sale.
A) work out 10% of the original price of the laptop.
B)work out the sale price of the laptop.
Answer:
A) £20
B) £180
Step-by-step explanation:
The original price is £200. The price was reduced by 10% so the sale price is 90% of the original price.
A) Price Reduction = 200 * 0.1 = £20
B) Sale Price = Original Price - Price Reduction = 200 - 20 = £180
Original Price * Percent Paid = 200 * 0.9 = £180
Which expression is equivalent to (4xexponent2yexponent3)exponent2?
Please refer to the photo attached
Answer:
Below
Step-by-step explanation:
You will need to multiply the exponents in the parens by 2 and square 4 so it is 16
16 x^(2*2) y^(3*2) = 16 x^4 y^6
In circle F with
�
∠
�
�
�
=
54
m∠EFG=54 and
�
�
=
19
EF=19 units, find the length of arc EG. Round to the nearest hundredth.
Answer:
forgot how to do this
Step-by-step explanation:
150√374 283727273737272727272
Giving Brainliest!!!
Answer:294
Step-by-step explanation:
Answer:
[tex]294m^2[/tex]
Step-by-step explanation:
Volume of a cube is side x side x side or [tex]s^3[/tex]
now we find the value of one side
[tex]s^3 = 343m^3\\s = \sqrt[3]{343m^3} \\s = 7m\\[/tex]
Now we have a side value we can find the surface area of this cube which is
Surface area = [tex]6 * s^2[/tex]
= [tex]6 * (7m)^2[/tex]
= [tex]6 * 49m^2[/tex]
= [tex]294 m^2[/tex]
Hope this helps!
Brainliest and a like is much appreciated!
What is the perimeter of the figure with vertices D(-4, 5), E(-4, -6) and F(3, -6)?
The perimeter of the figure with vertices D(-4, 5), E(-4, -6) and F(3, -6) is given as follows:
31.04 units.
How to calculate the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The vertices of the polygon in this problem are given as follows:
D(-4, 5), E(-4, -6) and F(3, -6).
Hence the side lengths are given as follows:
DE = 11 units -> x constant, subtract y.DF = sqrt((-4 - 3)² + (5 - (-6))²) = 13.04 units.EF = 7 units, y constant, subtract x.Hence the perimeter of the polygon is given as follows:
11 + 13.04 + 7 = 31.04 units.
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What is the total amount due on 20000 which has been invested for five years at 10% annual interest?
Therefore , the solution of the given problem of amount comes out to be 30000 is the new amount.
What is an amount?aggregate attempting to determine the length of time needed, overall amount or quantity. The amount in front of you or being thought about is very active. the final outcome, its significance, or its meaning. three accountings: principal, interest, and the third. Word versions include amounts, amounting, and amounted. supple word How much something is, how often you possess
Here,
The straightforward interest formula can be used to determine the total amount owing on $20,000 that has been invested for five years at 10% annual interest:
=> Sum total = Principal + Interest
where Principal represents the amount invested initially and Interest represents the interest collected over the course of five years.
Since the interest gained annually is 10% of the principal, the total interest earned over the course of five years is as follows:
=> Interest is calculated as follows:
=> Interest = P*R*T
=> Interest = 20000 * 0.10 * 5
=> Interest = 10000
Total amount = 20000 +10000 = 30000
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AB=A, B, equals
Round your answer to the nearest hundredth. A right triangle A B C. Angle A C B is a right angle. Angle B A C is forty degrees. Side A C is five. Side A B is unknown
The length of side AB in the right triangle ABC is approximately 3.21 units.
To find the length of side AB in the right triangle ABC, we can use trigonometric ratios.
Given:
Angle BAC = 40 degrees
Side AC = 5 units
Let's use the trigonometric ratio for the sine of angle BAC:
sin(BAC) = opposite/hypotenuse
sin(40°) = AB/AC
Rearranging the equation to solve for AB, we have:
AB = AC * sin(BAC)
Substituting the given values, we get:
AB = 5 * sin(40°)
Using a calculator to evaluate sin(40°), we find:
AB = 5 * 0.6428
≈ 3.21
Therefore, the length of side AB in the right triangle ABC is approximately 3.21 units.
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Select the correct statement about the function represented by the table.
X
1
2
3
4
5
y
6
24
96
384
1536
A. It is an exponential function because the y-values increase by an
equal factor over equal intervals of x-values.
B. It is a linear function because the y-values increase by an equal
difference over equal intervals of x-values.
C. It is a linear function because the difference between each and
y value is constant.
D. It is an exponential function because the factor between each x- and y-value is constant
The true statement about the function is (a) It is an exponential function because the y-values increase by an equal factor over equal intervals of x-values
How to determine the true statement about the functionFrom the question, we have the following parameters that can be used in our computation:
The table of values
In this table, each y-value is obtained by multiplying the previous y-value by 4.
This means that the function has a constant ratio or factor between each x- and y-value.
Such a pattern is typical of exponential functions, where equal intervals of x-values produce increasing or decreasing ratios of y-values.
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Consider the equation z^16=(−1−i). Find the value of z which satisfies this equation and which has the second smallest positive argument θ, 0<θ<2π. Express your answer as z=re^iθ where r=______and theta=_________.
Consider the equation z^13=(−1+sqrt3i). Find the value of z which satisfies this equation and which has the second smallest positive argument θ,0<θ<2π. Express your answer as z=re^iθ where r=_________ and theta=__________
I have found the r values of both, I just need help finding theta. Show work so I can practice, please!
After considering and calculating, the modulus of z is r = [tex]2^{1/32}[/tex] and the argument of z is θ = 5π/32.
To solve this equation, we can first express −1−i in polar form as:
−1−i = √2cis(3π/4)
where cis(θ) = cos(θ) + i sin(θ) is the polar form of a complex number.
Now, we can express z in polar form as:
z = r cis(θ)
where r is the modulus of z and θ is its argument. Substituting this into the equation z¹⁶ = √2cis(3π/4), we get:
r¹⁶ cis(16θ) = √2cis(3π/4)
Taking the modulus of both sides, we get:
r¹⁶ = √2
Taking the argument of both sides, we get:
16θ = 3π/4 + 2kπ or 16θ = -3π/4 + 2kπ
where k is an integer. Solving for θ in the range 0 < θ < 2π, we find that the second smallest positive solution is:
θ = (3π/4 + 2π)/16 = 5π/32
Therefore, the value of z is:
z = r cis(θ) = [tex]\sqrt{2}^{1/16}[/tex] cis(5π/32)
We can simplify this as:
z = [tex]2^{1/32}[/tex]cis(5π/32)
So, the modulus of z is:
r = [tex]2^{1/32}[/tex]
And the argument of z is:
θ = 5π/32
Therefore, the answer is:
z = [tex]2^{1/32}[/tex] cis(5π/32)
So, the modulus of z is r = [tex]2^{1/32}[/tex] and the argument of z is θ = 5π/32.
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What point on the number line is one fourth of the way from the point 0 to the point −3? −0.25 −0.5 −0.75 −1
Answer: 0.75
Step-by-step explanation: Hope this helps :D
Answer: -0.75
Step-by-step explanation:
1/4th of the way to point 0,-3 from 0
-3/4=-0.75, therefore, the answer is C, -0.75.
(4^2)+6×(5^2)−(3^3)÷(3^2)=
Answer: (16)➕6✖(25)➖(9)