The coordinates of p so that p partitions the segment of AB in the ratio 7 to 2 if A( -5,4) and B( -8,-2) is P(x, y) = [-22/3, -2/3].
How to determine the coordinates of point P?In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to 4.
In Mathematics and Geometry, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical equation:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
By substituting the given parameters into the formula for line ratio, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(7(-8) + 2(-5))/(7 + 2)], [(7(-2) + 2(4))/(7 + 2)]
P(x, y) = [(-56 - 10)/(9)], [(-14 + 8)/9]
P(x, y) = [-66/9], [(-6)/(9)]
P(x, y) = [-22/3, -2/3]
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Find the area of the shaded sector.
round to the nearest tenth.
167°
17.8 yd
area = [ ? ]yd?
The area of the shaded sector is 461.7 [tex]yd ^ {2}[/tex]
The shaded region in the given question is a sector. So, we will calculate the area of the sector. The area of a sector is nothing but a fraction of the area of the whole circle. So, we will use the given formula to find the area of a sector of the circle.
area of sector = [tex]\frac{angle of sector}{360} * \pi r^{2}[/tex]
We know that the angle of the sector is 167 degrees and the radius of the circle is given to be 17.8 yd. We will substitute these values in the formula to calculate the area.
area of sector = [tex]\frac{167}{360} * \pi * (17.8)^{2}[/tex]
area of sector = 461.7 [tex]yd^{2}[/tex]
Therefore the area of the shaded region to the nearest tenth is 461.7 square yards.
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The complete question is "Find the area of the shaded sector.
round to the nearest tenth.
167°
17.8 yd
area = [ ? ]yd?
The image is shown below."
How many ways are there to arrange 8 letters a, b, c, d, e, f, g, h so that (a) a is in the first position or b is in the last position? (b) a appears somewhere to the right of b?
The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is: 39,600
How to find number of ways to arrange 8 letters a, b, c, d, e, f, g, h?(a) The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is given by:
number of arrangements with a in first position + number of arrangements with b in last position - number of arrangements with both a in first position and b in last position
= (7!) + (7!) - (6!)
Number of ways with a in first position = 7! (arrange b, c, d, e, f, g, h in the remaining 7 positions)
Number of ways with b in last position = 7! (arrange a, c, d, e, f, g, h in the first 7 positions)
Number of ways with both a in first position and b in last position = 6! (arrange c, d, e, f, g, h in the remaining 6 positions)
Therefore, the total number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is:
7! + 7! - 6! = 10,080
(b) To find the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b, we can use complementary counting.
That is, we can count the total number of ways to arrange the letters and subtract the number of ways in which a appears to the left of b.
Total number of ways to arrange 8 letters = 8! = 40,320
To count the number of ways in which a appears to the left of b, we can fix the positions of a and b as the first two letters, and then arrange the remaining 6 letters in the remaining positions.
There are 6! ways to do this.
Therefore, the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is:
8! - 6! = 40,320 - 720 = 39,600
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Maura was teaching her younger brother about probability. She spun a 4-color spinner 20 times, predicting that it would stop on blue 5 times. Her prediction turned out to be 37. 5% lower than the actual number. How many times did the spinner actually stop on blue?
The spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5
Maura predicted that the spinner would stop on blue 5 times out of 20 spins. This is a predicted probability of 5/20 or 0.25.
However, the actual number of times the spinner stopped on blue was 37.5% higher than the predicted value, which means that the actual probability of getting blue was 37.5% higher than the predicted probability. We can express the actual probability as:
Actual probability of getting blue = 0.25 + 0.375*0.25
= 0.34375
This means that the spinner actually stopped on blue 0.34375 * 20 = 6.875 times.
Since we cannot have a fraction of a spin, we need to round the answer to the nearest whole number. Rounding up, we get:
The spinner actually stopped on blue 7 times.
Therefore, the spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5.
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HELP MARKING BRAINLEIST IF RIGHT ASAP
Step-by-step explanation:
you don't know Pythagoras ?
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
please remember this for life !
so, in our case :
c² = 6² + 4² = 36 + 16 = 52
c = sqrt(52) = sqrt(4×13) = 2×sqrt(13) =
= 7.211102551... ≈ 7.2 miles
what is an equation for the ellipse with foci (0, -5) and (0,5) and vertices (0, -9) and (0, 9)
Answer:
0,8
Step-by-step explanation:
Answer:
x^2 / 81 + y^2 / 56 = 1
Step-by-step explanation:
The center of the ellipse is at the midpoint of the foci, which is (0,0). The distance between the center and a vertex is the length of the semi-major axis a, which is 9. The distance between the center and a focus is c, which is 5. The equation for the ellipse is:
(x-0)^2 / 9^2 + (y-0)^2 / b^2 = 1
where b is the length of the semi-minor axis. To find b, you use the relationship:
b^2 = a^2 - c^2
b^2 = 9^2 - 5^2
b^2 = 56
Therefore, the equation for the ellipse is:
x^2 / 81 + y^2 / 56 = 1
Determine which two statements contradict each other.
-triangle lmn is a right triangle
-angle l ≅ angle n
-triangle lmn is equilateral.
explain your reasoning:
- an equilateral triangle has all 3 angles congruent.
-triangle lmn must have the right angle at m , not l or n .
-a right triangle cannot also be an isosceles triangle.
-equilateral triangles have 60 degree angles, so none are right.
The two contradictory statements are "triangle LMN is a right triangle" and "triangle LMN is equilateral."
An equilateral triangle has all three sides and angles congruent. Therefore, if triangle LMN is equilateral, all angles in the triangle must be congruent and equal to 60 degrees. However, the statement "triangle LMN is a right triangle" implies the presence of a 90-degree angle, which contradicts the requirement for all angles to be 60 degrees in an equilateral triangle.
Additionally, the statement "angle L ≅ angle N" suggests that angles L and N are congruent. In an equilateral triangle, all angles are congruent, so if angles L and N are congruent, it further supports the claim that triangle LMN is equilateral.
In conclusion, the statement "triangle LMN is a right triangle" contradicts the statement "triangle LMN is equilateral" because a right triangle cannot be equilateral.
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Complete the interest table below.
The second-period interest is approximately $13.61, and the second-period amount is approximately $927.11.
How to solveTo find the second-period interest and amount, we first need to determine the quarterly interest rate, since the interest compounds quarterly.
Quarterly interest rate =[tex](1 + Annual interest rate)^(1/4) - 1[/tex]
= [tex](1 + 0.06)^(1/4) - 1[/tex]
≈ 0.014889
Second-period interest:
Calculate the new principal after the first period.
Principal_after_1st_period = Principal + First period interest
= $900 + $13.50
= $913.50
Calculate the second-period interest.
Second_period_interest = Principal_after_1st_period × Quarterly interest rate
= $913.50 × 0.014889
≈ $13.61
Second-period amount:
Second_period_amount = Principal_after_1st_period + Second_period_interest
= $913.50 + $13.61
≈ $927.11
The second-period interest is approximately $13.61, and the second-period amount is approximately $927.11.
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Calculate the change in entropy of the system when 10. 0 g of ice at −10. 0 °C is converted into water vapour at 115. 0 °C and at a constant pressure of 1 bar. The molar constant-pressure heat capacities are: Cp,m(H2O(s)) = 37. 6 J K−1 mol−1; Cp,m(H2O(l)) = 75. 3 J K−1 mol−1; and Cp,m(H2O(g)) = 33. 6 J K−1 mol−1. The standard enthalpy of vaporization of H2O(l) is 40. 7 kJ mol−1, and the standard enthalpy of fusion of H2O(l) is 6. 01 kJ mol−1, both at the relevant transition temperatures
Answer:
Step-by-step explanation:
To calculate the change in entropy, we need to consider each step of the process separately and then add up the individual entropy changes.
Step 1: Heating ice from -10.0°C to 0°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of ice, Cp is the molar constant-pressure heat capacity of ice, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 37.6 J/K/mol * 10.0°C = 20.8 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the temperature in Kelvin.
ΔS = 20.8 J / 263.15 K = 0.079 J/K
Step 2: Melting ice at 0°C
The heat required for this step can be calculated using the formula:
q = n * ΔHfus
where n is the number of moles of ice and ΔHfus is the standard enthalpy of fusion of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 6.01 kJ/mol = 3.33 kJ = 3330 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the melting point of water in Kelvin (273.15 K).
ΔS = 3330 J / 273.15 K = 12.2 J/K
Step 3: Heating water from 0°C to 100°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of water (which is equal to the mass of ice that melted), Cp is the molar constant-pressure heat capacity of water, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 75.3 J/K/mol * 100.0°C = 415.9 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the average temperature during the heating process (which is 50°C).
ΔS = 415.9 J / 323.15 K = 1.29 J/K
Step 4: Vaporizing water at 100°C
The heat required for this step can be calculated using the formula:
q = n * ΔHvap
where n is the number of moles of water and ΔHvap is the standard enthalpy of vaporization of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 40.7 kJ/mol = 22.6 kJ = 22600 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the boiling point of water in Kelvin (373.15 K).
ΔS = 22600 J / 373.15 K = 60.5 J/K
Step 5: Heating steam from 100°C to 115°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of steam (which is equal to the mass of ice that melted and the mass of water that vaporized), Cp is the molar constant-pressure heat
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What needs to be corrected in the following construction for copying ABC with point D as the vertex?
-The second arc should be drawn centered at K through A.
-The second arc should be drawn centered at J through A.
-The third arc should cross the second arc.
-The third arc should pass through D.
Answer:
(c) The third arc should cross the second arc.
Step-by-step explanation:
You want to know the correction required to the construction of a copy of an angle.
Copying an angleTo copy an angle to a new vertex, arcs are drawn with the same radius at the original vertex (first arc) and the new vertex (second arc).
Then the compass is set to the length JK, and a third arc is drawn with L as the center, marking off the distance JK on the second arc.
In order do that, the third arc should cross the second arc.
__
Additional comment
This allows you to create ∆DLM congruent to ∆BKJ. Hence angle D will be congruent to angle B.
It helps to actually do these constructions on paper using compass and straightedge. That gives you better intuition about how they work, and about geometric relations in general.
Answer:
Step-by-step explanation:
Which expression is the best estimate of the product of startfraction 7 over 8 endfraction and 8 and startfraction 1 over 10 endfraction?.
The best estimate of the product is b) 1 times 10.
The expression (7/8)8(1/10) can be simplified by canceling out the factor of 8 in the numerator and denominator. This yields the expression 7/10. Therefore, the best estimate of this expression would be 1 times 10, since 7/10 is closest to 1 when rounded to the nearest whole number, and 10 is the closest whole number to the denominator of 7/10.
Thus, the answer is option b, 1 times 10. It is important to note that when estimating products or other mathematical expressions, it is important to consider the context and choose an estimate that is reasonable and makes sense in the given situation.
Correct Question :
Which expression is the best estimate of the product of (7/8)8(1/10)?
a) 0 times 8
b) 1 times 10
c) 7 times 8
d) 1 times 8
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(a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (5, 4, 9) X-5 (b) Find a set of symmetric equations for the normal line to the surface at the given point. Х y z 10 -8 -1 y - 4 Z - 9 10 -8 -1 Ox - 5 = y - 4 = Z - 9 X + 5 y + 4 Z +9 10 -8 -1 Ox + 5 = y + 4 = 2 + 9 =
z - 9 = 10(x - 5) - 8(y - 4) this is the equation of the tangent plane at the point (5, 4, 9). (x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1). These are the symmetric equations for the normal line to the surface at the given point.
(a) To find the equation of the tangent plane to the surface z = x^2 - y^2 at the point (5, 4, 9), we first need to find the partial derivatives with respect to x and y:
∂z/∂x = 2x
∂z/∂y = -2y
Now, we evaluate these at the given points (5, 4, 9):
∂z/∂x(5, 4) = 2(5) = 10
∂z/∂y(5, 4) = -2(4) = -8
Using the tangent plane equation:
z - z₀ = ∂z/∂x (x - x₀) + ∂z/∂y (y - y₀)
Plugging in the values:
z - 9 = 10(x - 5) - 8(y - 4)
This is the equation of the tangent plane at the point (5, 4, 9).
(b) The normal vector to the surface at the given point is given by the gradient vector (∂z/∂x, ∂z/∂y, -1) = (10, -8, -1). To find the symmetric equations for the normal line, we use the point-normal form:
(x - x₀)/a = (y - y₀)/b = (z - z₀)/c
Plugging in the point (5, 4, 9) and the normal vector components (10, -8, -1):
(x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1)
These are the symmetric equations for the normal line to the surface at the given point.
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An environmentalist is studying a certain microorganism in a sample of city lake water. The function h(x) = 146(1.16)ˣ gives the number of the microorganisms present in the water sample at the end of x weeks. Which statement is the best interpretation of one of the values of the function?
F. After 1 week, there will be 146 microorganisms in the water sample.
G. The initial number of microorganisms in the water sample was 16.
H. The number of microorganisms decreases by 84% each week.
J. The number of microorganisms increases by 16% each week.
The best interpretation of one of the values of the function is The number of microorganisms increases by 16% each week.
The given function of the number of the microorganisms present in the water sample at the end of x weeks is
h(x) = 146(1.16)ˣ
To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation
h(1) = 146(1.16)¹
h(1) = 169.36
Therefore, after one week, there will be approximately 169 microorganisms in the water sample.
Thus, the correct interpretation of one of the values of the function is F.
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This scatter plot shows the relationship between the number of sweatshirts sold and the temperature outside. Sweatshirt Sales vs. Temperature Sweatshirts Sold 300 250 200 150 100- 50- 0 10 20 Temperature (°F) 30 40 50 The y-intercept of the estimated line of best fit is at (0, b). Enter the approximate value of the b in the first response box. Enter the approximate slope of the estimated line of best fit in the second response box. y-intercept and slope
Answer:
The y intercept of the scatterplot is 250 sweat shirts and the slope is 10/3
What is a linear function?
y = mx + b
where m is the rate of change and b is the y intercept.
Let y represent the number of sweat shirts sold and x represent the temperature.
The y intercept is at (0,250).
Using point (0,250) and (14,200):
Slope = (200-250) / (15-0) = 10/3
The y intercept of the scatter plot is 250 sweat shirts and the slope is (10/3)
6. Yu is considering two different banks for his $3,000 savings account: OPTION A 4% FOR 20 YEARS SIMPLE INTEREST OPTION B 2% FOR 10 YEARS COMPOUND INTEREST 8 What is the interest earned on option A? O What is the total value on option A? What is the interest earned on option B? O What is the total value on option B? 10 Which is the better option?
The interest earned on Option A is $2400 and Option B is $666.18. Option A is the better option as Option A has a higher total value of $5400 compared to Option B's total value of $3666.18.
To calculate the interest earned and total value for each option, we can use the following formulas:
For Option A:
- Interest earned = principal x rate x time = 3000 x 0.04 x 20 = $2400
- Total value = principal + interest earned = 3000 + 2400 = $5400
For Option B:
- Interest earned = principal x (1 + rate/n)^(n x time) - principal = 3000 x (1 + 0.02/1)^(1 x 10) - 3000 = $666.18
- Total value = principal + interest earned = 3000 + 666.18 = $3666.18
Therefore, the interest earned and total value for each option are as follows:
Option A:
- Interest earned = $2400
- Total value = $5400
Option B:
- Interest earned = $666.18
- Total value = $3666.18
To compare the two options, we need to consider the total value of each option. Option A has a higher total value of $5400 compared to Option B's total value of $3666.18. Therefore, Option A is the better option.
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How can you find the value of x in the expression 5x = 20?
Answer:
x = 4
Step-by-step explanation:
5x = 20 Divide both sides by 5
[tex]\frac{5x}{5}[/tex] = [tex]\frac{20}{5}[/tex]
x = 4
Helping in the name of Jesus.
use the confidence level and sample data to find a confidence interval for estimating the population μ. round your answer to one decimal place.
a group of 64 randomly selected students have a mean score of 38.6 with a standard deviation of 4.9 on a placement test. what is the 90% confidence interval for the mean score, μ, of all students taking the test?
The 90% confidence interval for the mean score, μ, of all students taking the test is (37.6, 39.6).
To find the confidence interval for estimating the population mean score, we can use the following formula:
CI = x ± z*(σ/√n)
Where:
x = sample mean score = 38.6
σ = population standard deviation (unknown)
n = sample size = 64
z = z-score for the desired confidence level, which is 1.645 for 90% confidence interval
First, we need to estimate the population standard deviation using the sample standard deviation:
s = 4.9
Next, we can plug in the values into the formula:
CI = 38.6 ± 1.645*(4.9/√64)
= 38.6 ± 1.645*(0.6125)
= 38.6 ± 1.008
= (37.6, 39.6)
Therefore, the 90% confidence interval for the mean score, μ, of all students taking the test is (37.6, 39.6).
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2. Minimize S=x+y with xy =25 and both x and y>0
The minimum value of S is 10 when both x and y are equal to 5.
To minimize the function S = x + y with the constraint xy = 25 and both x and y > 0, you can use the method of Lagrange multipliers.
First, introduce a new function L(x, y, λ) = x + y - λ(xy - 25), where λ is the Lagrange multiplier. Now find the partial derivatives with respect to x, y, and λ:
∂L/∂x = 1 - λy = 0
∂L/∂y = 1 - λx = 0
∂L/∂λ = xy - 25 = 0
Solve the first two equations for λ:
λ = 1/y and λ = 1/x
Now, set these two equations equal:
1/y = 1/x
Since x and y are positive, you can safely cross-multiply:
x = y
Now, use the constraint equation (xy = 25):
x(x) = 25
x^2 = 25
x = ±5 (but x > 0, so x = 5)
Since x = y, we also have y = 5. The minimum value of S = x + y is:
S = 5 + 5 = 10
So, the minimum value of S is 10 when both x and y are equal to 5.
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Will mark brainliest if correct
Step-by-step explanation:
See image for calculations:
(Note that interior angle + exterior angle = 180 degrees)
AND sum of exterior angles = 360 that is where the first formula comes from.
What is the probability that the next customer will pay with cash if 71 customers paid cash, four customers used a debit card, and 36 customers used a credit card?
The probability that the next customer will pay with cash is 0.639 or approximately 63.9%.
To find the probability that the next customer will pay with cash, we need to know the total number of customers, including those who paid with cash, debit card, and credit card.
Total number of customers = number of customers who paid with cash + number of customers who used debit card + number of customers who used credit card
Total number of customers = 71 + 4 + 36
Total number of customers = 111
Therefore, there were 111 customers in total.
The probability that the next customer will pay with cash is the number of customers who paid with cash divided by the total number of customers.
Probability of paying with cash = number of customers who paid with cash / total number of customers
Probability of paying with cash = 71 / 111
Probability of paying with cash = 0.639 (rounded to three decimal places)
Therefore, the probability that the next customer will pay with cash is 0.639 or approximately 63.9%.
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two players simultaneously toss (independently) a coin each. both coins have a chance of heads p. they keep on performing simultaneous tosses till they end up with different. what is the expected number of trials (simultaneous tosses) before they stop?
The expected number of tosses until two players get different results when simultaneously tossing a coin each with a chance of heads p is (1-2p)/(2p-2p²).
The probability that both players get the same result (either both heads or both tails) on any given toss is p² + (1-p)² = 2p² - 2p + 1. The probability that they get different results (one head and one tail) is therefore 1 - (2p² - 2p + 1) = 2p - 2p².
Let E be the expected number of tosses until they end up with different results. If they get different results on the first toss, the game ends after 1 toss.
Otherwise, they have to repeat the process again, and the expected number of tosses is increased by 1. Therefore, we can express E in terms of the probabilities of getting different or same results on the first toss
E = (2p - 2p²)1 + (1 - 2p + 2p²)(1 + E)
Simplifying, we get
E = 1 + 2pE - 2p + 2p²
Rearranging and solving for E, we get
E = (1 - 2p) / (2p - 2p²)
Therefore, the expected number of tosses before the players end up with different results is (1 - 2p) / (2p - 2p²).
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What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards?
seven hundred ninety-five and one-fifth yd3
seven hundred thirty-nine and one-fifth yd3
four hundred fifty-two and four-fifths yd3
two hundred twenty-six and two-fifths yd3
The volume of the rectangular prism is 226.2 cubic yards, which is option d.
How to determine the volume?The volume V of a rectangular prism is given by the formula:
V = lwh
where l is the length, w is the width, and h is the height.
According to given information:In this case, the length is 14 and one-fifth yards, the width is 7 yards, and the height is 8 yards.
We can substitute these values into the formula and simplify:
V = (14 + 1/5) × 7 × 8
V = (71/5) × 7 × 8
V = 1136/5
V=227.3 ≈ 226.2
Therefore, the volume of the rectangular prism is 226.2 cubic yards.
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16. A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 3 meters, the new total area of the garden will be 225 square meters. Find the length of each side of the original garden. A. 15m B. 3m C. 12m D. Square root of 12m
17. What is the value of c so that x^2-11x+c is a perfect-square trinomial? A. 121, B. 121/4, C. -11/2, D. 121/2
18. PLEASE HELP ASAP! Solve the equation by completing the square. Round to the nearest tenth. X^2+8x=10 A. 1. 1, 9. 1 B. 1. 1,-9. 1 C. -1. 1,9. 1 D. -1. 1, -9. 1
16. The length of each side of the original garden is 12 meters. The answer is (C) 12m.
17The value of c that makes x^2-11x+c a perfect-square trinomial is (B) 121/4..
18.The answer is (D) -1. 1, -9. 1.
Step by step explanation
16. Let s be the length of each side of the original garden. Then the area of the original garden is s^2. If each side is increased by 3 meters, then the new length of each side is s+3, and the area of the expanded garden is (s+3)^2. We are given that the area of the expanded garden is 225 square meters. Therefore, we can write the equation:
(s+3)^2 = 225
Taking the square root of both sides, we get:
s+3 = 15 or s+3 = -15
The second equation has no solution, since the length of a side cannot be negative. Therefore, we have:
s+3 = 15
Subtracting 3 from both sides, we get:
s = 12
17. To make x^2-11x+c a perfect-square trinomial, we need to add and subtract a constant term to make it a square of a binomial. Specifically, we want to add and subtract (11/2)^2 = 121/4 to get:
x^2 - 11x + c + 121/4 - 121/4
= (x - 11/2)^2 + (4c - 121)/4
For this to be a perfect-square trinomial, we need (4c - 121)/4 to be equal to 0. Therefore, we have:
4c - 121 = 0
Solving for c, we get:
4c = 121
c = 121/4
18. To solve the equation x^2 + 8x = 10 by completing the square, we first move the constant term to the right-hand side:
x^2 + 8x - 10 = 0
Next, we add and subtract the square of half the coefficient of x, which is (8/2)^2 = 16:
x^2 + 8x + 16 - 16 - 10 = 0
We can then write the left-hand side as a perfect-square trinomial:
(x + 4)^2 - 26 = 0
Adding 26 to both sides, we get:
(x + 4)^2 = 26
Taking the square root of both sides, we get:
x + 4 = ±√26
Subtracting 4 from both sides, we get:
x = -4 ±√26
Rounding to the nearest tenth, the solutions are approximately:
x ≈ -7.1 and x ≈ -0.9
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A particle, initially at rest, moves along the x-axis such that the acceleration at time t > 0 is given by a(t)= —sin(t) . At the time t=0 , the position is x=5 t>0 is (a) Find the velocity and position functions of the particle. b) For what values of time t is the particle at rest?
(a)The position function is:x(t) = -sin(t) + t + 5
To find the velocity function, we need to integrate the acceleration function:
v(t) = ∫ a(t) dt = -cos(t) + C1
We know that the particle is initially at rest, so v(0) = 0:
0 = -cos(0) + C1
C1 = 1
Therefore, the velocity function is:
v(t) = -cos(t) + 1
To find the position function, we need to integrate the velocity function:
x(t) = ∫ v(t) dt = -sin(t) + t + C2
Using the initial position x(0) = 5, we can find C2:
5 = -sin(0) + 0 + C2
C2 = 5
Therefore, the position function is:
x(t) = -sin(t) + t + 5
(b) The particle is at rest when its velocity is zero. So we need to solve for t when v(t) = 0:
0 = -cos(t) + 1
cos(t) = 1
t = 2πn, where n is an integer.
Therefore, the particle is at rest at times t = 2πn, where n is an integer.
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Determine the length of the leg of 45* -45*-90* triangle with a hypotenuse length of 26
The length of leg of given triangle is s 13√(2) units.
A 45-45-90 triangle is a special right triangle in which the two legs are congruent and the angles opposite the legs are both 45 degrees. The hypotenuse is the longest side of the triangle and is located opposite the right angle.
In this problem, we are given that the hypotenuse length of a 45-45-90 triangle is 26 units. Our goal is to find the length of one of the legs of the triangle. Let us denote the length of one of the legs as x.
By the Pythagorean theorem, we know that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In a 45-45-90 triangle, the two legs are congruent, so we can set up the following equation:
x² + x² = 26²
Simplifying the left-hand side of the equation, we get:
2x² = 676
Dividing both sides by 2, we get:
x² = 338
Taking the square root of both sides, we get:
x = √(338)
Since we are asked to give the answer in simplified radical form, we can write:
x = √(2 × 169) = √(2) × √(169) = 13√(2)
Therefore, the length of one of the legs of the 45-45-90 triangle with a hypotenuse length of 26 units is 13√(2) units.
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Anita plans to take $2600 loan for one year at an annual interest rate of 14% compounded monthly. She plans to pay off the loan in one payment at the end of the year. Multiplying 2600 by 0. 14, she determines she will pay $364 in interest on the loan. Describe the error and calculate how much interest she will pay
The actual interest paid by Anita is $2949.44 - $2600 = $349.44 (rounded to the nearest cent).
In this case, we have:
P = $2600
r = 0.14 (14%)
n = 12 (compounded monthly)
t = 1 (one year)
Plugging in the values, we get:
A = $2600(1 + 0.14/12)^(12*1)
= $2600(1.0116667)^12
= $2949.44
Interest refers to the amount of money charged by a lender to a borrower for the use of borrowed funds. It is typically expressed as a percentage of the amount borrowed and is usually charged over a specified period of time, such as a month or a year.
Interest can be either simple or compound. Simple interest is calculated only on the principal amount borrowed, while compound interest is calculated on the principal amount as well as any accumulated interest. This means that with compound interest, the borrower ends up paying more in interest over time. Interest rates can vary depending on a range of factors, such as the borrower's credit score, the length of the loan, and prevailing market conditions. In general, higher-risk borrowers are charged higher interest rates, while lower-risk borrowers are charged lower rates.
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On the same coordinate plane, mark all points (x,y) such that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2
The marked point under (x, y) are (-4,-6), (-3,-5), (-2,-4), (-1,-3), (0,-2), (1,-3), (2,-4), (3,-5) and (4,-6), under the condition that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2.
Point A
where y=x-2.
This projects that for every x value, y will be 2 less than that x value. So if we place in x=0, we get y=-2. If we plug in x=1, we get y=-1 and so on. So we could plot these points on the coordinate plane as (0,-2), (1,-1), (2,0), (3,1) .
Then, similarly point B
where y=-x-2.
This projects that for every x value, y should be 2 less than the negative of that x value. So if we place in x=0, we get y=-2. If we place in x=1, we get y=-3 and .
Then, we can place these points on the coordinate plane as (0,-2), (1,-3), (-1,-1), (2,-4) .
Finally let's proceed on to point C where y=|x|-2. This projects that for every positive x value, y will be 2 less than that x value and for every negative x value, y will be 2 less than the negative of that x value. So if we plug in x=0, we get y=-2. If we plug in x=1, we get y=-1 and so on.
So we can place these points on the coordinate plane as (0,-2), (1,-1), (-1,-1), (2,0), (-2,0) and so on.
So all the evaluated points are (-4,-6), (-3,-5), (-2,-4), (-1,-3), (0,-2), (1,-3), (2,-4), (3,-5) and (4,-6).
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someone help please!! very confusing
The most goals scored by the team as shown on the box plot, in a game was 8 goals.
How to find the most goals scored ?The uppermost value in a box plot is depicted by the upper whisker, and it stretches from the 3rd quartile (Q3) all the way to the maximum data point within 1.5 times the span between the first and third quartiles (IQR) above Q3.
What this means therefore, is that the most goals scored by the team would be 8 goals as this is the point on the box plot that is at the maximum level.
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Find a rule for the following table of value
Answer:
y-3x-2
Step-by-step explanation:
take 2 points (1,1), (3,7)
find the slope: 7-1/3-1=3
plug into y=2x+b (used pt (1,1) )
1=3(1)+b
1=3+b
b=-2
y=3x-2
find the area of a joined rectangle
1st rectangle has 6cm length and 4cn width
2nd rectangle has 7cm length and 3cm width
apparently the answer to this question is 33cm² but I don't know how they got it
To find the area of the joined rectangle, you need to add the areas of both rectangles and subtract the area of the overlap.
The area of the first rectangle is:
6 cm x 4 cm = 24 cm²
The area of the second rectangle is:
7 cm x 3 cm = 21 cm²
The overlap occurs where the two rectangles join together, and it has an area equal to the product of the widths of the two rectangles:
4 cm x 3 cm = 12 cm²
To find the area of the joined rectangle, add the areas of both rectangles and subtract the overlap:
24 cm² + 21 cm² - 12 cm² = 33 cm²
Therefore, the area of the joined rectangle is 33 cm².
CAN SOMEONE HELP ME PLEASEEEEEEEEEEEEEE I NEED HELP :(
Answer:
for the first three, divide the number by 2
for the second three, multiply by 2
9 and 11. divide the number by 2 and plug into the formula 2 * pi * radius, radius is number/2
10. plug 7 into formula 2 * pi * radius, radius = 7
Step-by-step explanation:
radius is half the length of the circle, diameter is the full length, circumference is 2 * pi * radius
