A company that produces cell phones has a cost function of C = 8x^2 - 171x + 7802, where C is the cost in dollars and x is the number of cell phones produced (in thousands). How many units of cell phone (in thousands) minimizes the cost function?
Answers
To minimize the cost function C = 8x^2 - 171x + 7802, we need to find the value of x (number of cell phones produced in thousands) that results in the lowest cost C.
To do this, we will find the vertex of the parabola represented by the cost function.
1. Find the x-coordinate of the vertex using the formula x = -b / 2a, where a and b are the coefficients of the quadratic function (a = 8 and b = -171):
x = -(-171) / (2 * 8)
x = 171 / 16
x = 10.6875
2. Since the number of cell phones produced cannot be a fraction, we will consider the two closest integer values, 10 and 11.
3. Calculate the cost for each of these values:
C(10) = 8(10)^2 - 171(10) + 7802
C(10) = 800 - 1710 + 7802
C(10) = 6892
C(11) = 8(11)^2 - 171(11) + 7802
C(11) = 968 - 1881 + 7802
C(11) = 6889
Comparing the costs, C(11) = 6889 is the lower cost, so producing 11,000 cell phones (x = 11) minimizes the cost function.
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Related Questions
Compute the effective annual rate of interest at which $ 2,000
will grow to $ 3,000 in seven years if compounded quarterly Express
the final answer as a % rounded to 2 decimal places .
Answers
The formula for calculating the effective annual rate of interest with quarterly compounding is:
(1 + r/4)^4 - 1 = A/P
where r is the quarterly interest rate, A is the final amount, and P is the principal.
In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.
So we have:
(1 + r/4)^4 - 1 = 3000/2000
(1 + r/4)^4 = 1.5
1 + r/4 = (1.5)^(1/4)
r/4 = (1.5)^(1/4) - 1
r = 4[(1.5)^(1/4) - 1]
To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:
effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%
Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.
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calcular la altura del sol sobre el horizonte (medida en ángulo) si un edificio de 24 metros de altura proyecta una sobra de 30 metro
Answers
Usando propiedades de triangulos rectangulos veremos que el angulo de elevación es 38.65°
¿Como encontrar el angulo de elevacion del sol?
El ángulo de elevación del sol sera el angulo que esta en el vertice derecho del triangulo rectangulo en la imagen.
Sabemos que:
tan(a) = (cateto opuesto)/(cateto adjacente).
En este caso:
cateto opuesto = 24m
cateto adjacente = 30m
Entonces:
tan(a) = 24m/30m = 0.8
Aplicando la funcion inversa, obtenemos:
a = Atan(0.8) = 38.65°
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can you explain each step please for i can write it on a paper along with you
Answers
The two groups are given one is those who are studied and other is those who are not studied.
Studied - 88,100,94,79,92,100,95,83,89,99,100,91,89,95,100,93,96,84.
Arrange in order.
79, 83, 84, 88, 89, 89, 91, 92, 93, 94, 95, 95, 96, 99, 100, 100, 100, 100
The mean of this group is
\(\frac{88+100+94+79+92+100+95+83+89+99+100+91+89+95+100+93+96+84}{18}\)\(\frac{1667}{18}=92.6\)The mean is 92.6.
The median of this group is
Use the median formula for even
\(m=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}^{}}{2}\)Substitute the value of n =18
\(m=\frac{(\frac{18}{2})^{th}+(\frac{18}{2}+1)^{th}^{}}{2}=\frac{9^{th}+10^{th}^{}}{2}\)\(m=\frac{93+94}{2}=93.5\)The median is 93.5.
The mode of this group is 100 as it is appears 3 times .
The another group is not studied group.
Not studied - 82,72,45,91,58,83,65,87,90,77,73,89.
Arrange in order-
45, 58, 65, 72, 73, 77, 82, 83, 87, 89, 90, 91
The mean is determined as
\(\frac{82+72+45+91+58+83+65+87+90+77+73+89}{12}=\frac{912}{12}=76\)The median is determined as
\(m=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}}{2}\)Substitute n=12.
\(m=\frac{(\frac{12}{2})^{th}+(\frac{12}{2}+1)^{th}^{}}{2}=\frac{6^{th}+7^{th}}{2}=\frac{77+82}{2}=79.5\)There is no mode.
So, from the all the data given.
The mean of the group that studied is over 15 percent points higher than the mean of the group that did not studied.
\(92.61-76=16.61\)The median of the group that did not studied is less than 80.
In general , those students that studied scored much higher than those students that did not study.
The correct options are a , c and e.
The louvre Pyramid has a square base with sides that are 35 meters long. The slant height of each triangular face of the pyramid is 27. 84 meters. What is the lateral area of the louvre Pyramid. What is the surface area of the louvre Pyramid
Answers
the lateral area of the Louvre Pyramid is 1960.8 square meters, and the surface area is 3185.8 square meters.
ToTo calculate the lateral area of the Louvre Pyramid, we need to find the sum of the areas of all the triangular faces. Since the Louvre Pyramid has a square base, it has four identical triangular faces.
The area of a triangle can be calculated using the formula: 0.5 * base * height.
In this case, the base of each triangular face is equal to the length of one side of the square base, which is 35 meters. The height, or slant height, is given as 27.84 meters.
So, the lateral area of the Louvre Pyramid is:
Lateral Area = 4 * (0.5 * 35 * 27.84) = 1960.8 square meters.
To calculate the surface area of the Louvre Pyramid, we need to consider both the lateral area and the base area. The base area is simply the area of the square base, which is 35 meters * 35 meters = 1225 square meters.
Surface Area = Lateral Area + Base Area = 1960.8 square meters + 1225 square meters = 3185.8 square meters.
Therefore, the lateral area of the Louvre Pyramid is 1960.8 square meters, and the surface area is 3185.8 square meters.
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Determine la fuerza de atracción gravitatoria que existe entre la luna y la Tierra (ML= 7,34 x 1022 kg; MT = 5,98 x 1024 kg) si hay una distancia de separación desde el centro de la Luna hasta el centro de la Tierra de 3,84 x 108 m.
Answers
Answer:
La fuerza de atracción gravitatoria que existe entre la Luna y la Tierra es 1.9865*10²⁰ N.
Step-by-step explanation:
La ley universal de la gravitación describe la interacción gravitacional entre diferentes cuerpos con masa. Esta ley establece que "La fuerza con la que dos objetos se atraen es proporcional al producto de sus masas e inversamente proporcional al cuadrado de la distancia que los separa". En otras palabras, la fuerza con la que dos cuerpos de masas diferentes se atraen solo depende del valor de sus masas y del cuadrado de la distancia que los separa.
La fórmula fundamental de la Ley de Gravitación Universal es:
\(F=G*\frac{m1*m2}{r^{2} }\)
En donde:
F es la fuerza de atracción entre dos masas G es la constante de gravitación universal, cuyo valor es 6.673484.10⁻¹¹ \(\frac{N*m^{2} }{kg^{2} }\)m1 es la masa de uno de los cuerpos m2 es la masa de otro de los cuerpos r la distancia que los separa.En este caso:
ML=m1= 7.34*10²² kgMT=m2= 5.98*10²⁴ kgr=3.84*10⁸ mReemplazando:
\(F=6.673484*10^{-11} \frac{N*m^{2} }{kg^{2} }*\frac{7.34*10^{22}kg *5.98*10^{24}kg }{(3.84*10^{8} m)^{2} }\)
Resolviendo obtienes:
F= 1.9865*10²⁰ N
La fuerza de atracción gravitatoria que existe entre la Luna y la Tierra es 1.9865*10²⁰ N.
(after 3.1) Assume T: R^m → R^n is a linear transformation. (a) Suppose there is a nonzero vector xERm such that T(x) = 0. Is it possible that T is one-to-one? Give an example, or explain why it's not possible. (b) Suppose there is a nonzero vector xe Rm such that T(x) = 0. Is it possible that T is onto? Give an example, or explain why it's not possible. (c) Suppose that u and v are linearly dependent vectors in Rm. Show that T(u) and T(v) are also linearly dependent. (d) Suppose that u and v are linearly independent vectors in R™ Is it guaranteed that Tu) and Tv) are also linearly independent? If yes, explain why. If no, give an example where this is not the case.
Answers
Tu) and Tv) are not linearly independent in this case.
(a) If there is a nonzero vector xERm such that T(x) = 0, then T is not one-to-one. This is because there exists a nonzero vector x and a nonzero vector y such that T(x) = T(y) = 0, and thus T is not injective. For example, consider the transformation T: R^2 -> R^2 defined by T(x,y) = (0,0). This transformation maps every vector in R^2 to the zero vector, and thus there exist nonzero vectors that map to the same output.
(b) If there is a nonzero vector xERm such that T(x) = 0, then T cannot be onto. This is because there exists a vector in the range of T (i.e., a vector yERn) that is not mapped to by any vector in the domain of T. For example, consider the transformation T: R^2 -> R^3 defined by T(x,y) = (x,y,0). This transformation maps every vector in R^2 to a vector in the xy-plane of R^3, and thus there does not exist any vector in the z-axis of R^3 that is in the range of T.
(c) If u and v are linearly dependent vectors in R^m, then there exist scalars a and b (not both zero) such that au + bv = 0. Applying T to both sides of this equation yields T(au + bv) = 0, which implies that aT(u) + bT(v) = 0. Thus, T(u) and T(v) are linearly dependent.
(d) If u and v are linearly independent vectors in R^m, then Tu) and Tv) are not guaranteed to be linearly independent. For example, consider the transformation T: R^2 -> R^2 defined by T(x,y) = (x+y, x+y). The vectors (1,0) and (0,1) are linearly independent, but T(1,0) = T(0,1) = (1,1), which are linearly dependent. Therefore, Tu) and Tv) are not linearly independent in this case.
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simplify the following expression 2(x+16)+3(2x+5)
Answers
Answer:
8x+47
Step-by-step explanation:
First, distribute. Then, solve! Done! ^_^
Hope I helped, have an awesome day! :D
-8 is a term.
Yes
No
Answers
Answer:
yes
Step-by-step explanation:
If the monthly cost for 14 HCF is $48.70, what is the monthly cost for 10 HCF?
Answers
Answer:
$34.78
Step-by-step explanation:
first, we need to find the value of 1 HCF, so we divide $48.70 by 14, giving us the result of 3.47857143. (rounding that turns out to be 3.48.
next, we need to multiply the cost of 1 HCF by 10, so 3.48 * 10 = 34.78
find the matrix a' for t relative to the basis b'. t: r2 → r2, t(x, y) = (−8x y, 8x − y), b' = {(1, −1), (−1, 5)}
Answers
The matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).
\(\textbf{To find the matrix of } t \textbf{ relative to the basis } b', \textbf{we have to follow some steps. The steps are described below:}\)
First, we have to find the images of basis vectors under the transformation \(t\). \(t(-1,1) = (-9,7)\) and \(t(1,-5) = (-37,43)\).
Represent the image vectors of the basis in the standard basis. We use these vectors as columns in the matrix of \(t\) in the basis \(b'\).
\((-9,7) = -9(1,0) + 7(0,1) = (-9,7) = -9(-1,1) + 7(1,-5)\)
\((-37,43) = -37(1,0) + 43(0,1) = (-37,43) = -37(-1,1) + 43(1,-5)\)
Hence, we can write the following equation: \(A[x]_{b'} = [x]_S\)
Where \(A[x]_{b'}\) is the main answer in the form of a matrix, and \([x]_S\) is the coordinate of \([x]_{b'}\) with respect to the standard basis.
Now, we will write the equations with the coordinates of the basis vectors of \(b'\).
\(A[1,0] = [-9, -37]\) and \(A[0,1] = [7, 43]\)
Now we will write the matrix of \(A\) as follows:
\(A = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\)
Thus, the matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).
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G(Q) = 5 + 3Q + 202 - Q2 C2(Q) = 3 + 4Q + 2 1. Find the MC function for both C1(Q) AND C2(Q). 2. Find AVC function for both Ci(Q) AND C2(Q). 3. Find AFC function for both C1(Q) AND C2(Q). 4. Find AC function for both Ci(Q) AND C2(Q). 5. Find ATC function for both Ci(Q) AND C2(Q).
Answers
For C1(Q) = 3 - 2Q.
For C2(Q) = 4.
2. The AVC function
For C1(Q) = 5/Q + 3 + 20/Q - Q.
For C2(Q) = 3/Q + 4 + 2/Q.
3. The AFC function
For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)
For C2(Q) = 0.
4. To find the AC function
For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5.To find the ATC function
For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)
For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
Find the ATC functions for C1(Q) and C2(Q) given the provided cost functions?
1. To find the MC function, we take the derivative of the cost functions with respect to Q.
For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.
For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.
2. To find the AVC function, we divide the cost functions by Q.
For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.
For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.
3. To find the AFC function, we subtract the AVC function from the ATC function.
For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)
= 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.
4. To find the AC function, we add the AVC function to the AFC function.
For
C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5. To find the ATC function, we divide the AC function by Q.
For
C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q
= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).
For
C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q
= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
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Draw rectangle ABCD. Then draw a diagonal line connecting points B and D. If triangle BCD is a right isosceles triangle, what do you know about rectangle ABCD?
Answers
Rectangle ABCD has sides AB equal in length to AD, and sides BC equal in length to CD. The diagonals of the rectangle form two congruent right isosceles triangles, BCD and ABD, with right angles at points B and D, respectively.
In rectangle ABCD with diagonal BD connecting points B and D, we are given that triangle BCD is a right isosceles triangle. This information allows us to make certain conclusions about the properties of rectangle ABCD.
Since triangle BCD is a right isosceles triangle, angle BCD is a right angle (90 degrees) by definition. This means that angle B in the rectangle is also a right angle, which confirms that ABCD is a rectangle as all four angles are 90 degrees. Additionally, in a right isosceles triangle, the two legs (BC and CD) are equal in length. This implies that the length of side BC is equal to the length of side CD in the rectangle.
The diagonal BD of rectangle ABCD also forms another right isosceles triangle, ABD. By symmetry, triangle ABD shares similar properties with triangle BCD. This means that the two legs (AB and AD) are equal in length, so the length of side AB is equal to the length of side AD.
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Calculate the lower confidence limit (LCL) and upper confidence limit (UCL) of the mean for each of the following. bar x= 160, n = 436, sigma = 30, and alpha = 0.01 bar x = 70, n = 323, sigma = 4, and alpha = 0.05 LCL =
Answers
LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.
To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:
LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))
where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).
First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01
1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.
2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39
First Scenario Result:
LCL = 158.61
UCL = 161.39
Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05
1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.
2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35
Second Scenario Result:
LCL = 69.65
UCL = 70.35
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Find the recursive and explicit formula for the sequence 0,4.5,9,13.5,18
Answers
Answer:
Recursive
An=an-1+4.5
Explicit
An=0+4.5(n-1)
Step-by-step explanation:
Absolute value equation with solution -3
Answers
Answer:
m=-3/5
Step-by-step explanation:
Using the following returns, calculate the average returns, the variances, and the standard of deviations for X and Y.
Returns
Year X Z
1 21% 24%
2 -16 -3
3 9 26
4 18 -13
5 4 30
Answers
The variance is calculated as the average of the squared deviations from the average return. The standard deviation is the square root of the variance. For X, the standard deviation is √(130.24%) = 36.07%. For Y, the standard deviation is √(388.48%) = 62.35%.
First, calculate the average returns by summing up the returns for each year and dividing by the total number of years. For X, the average return is
(21% - 16% + 9% + 18% + 4%) / 5 = 7.2%.
For Y, the average return is
(24% - 3% + 26% - 13% + 30%) / 5 = 12.8%.
Next, calculate the variances. For X, subtract the average return from each year's return, square the result, and calculate the average of these squared deviations. The variance for X is
(6.2^2 + (-23.2)^2 + 1.8^2 + 10.8^2 + (-3.2)^2) / 5 = 130.24%.
Similarly, for Y, the variance is
(11.2^2 + (-15.8)^2 + 13.2^2 + (-25.8)^2 + 17.2^2) / 5 = 388.48%.
Finally, calculate the standard deviations by taking the square root of the variances. For X, the standard deviation is √(130.24%) = 36.07%. For Y, the standard deviation is √(388.48%) = 62.35%.
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is an acute triangle sometimes, always or never equilateral? if the answer is always or never explain how you know.
Answers
An acute triangle is never equilateral. The reason is that in an acute triangle, all three angles are less than 90 degrees. An equilateral triangle has three equal angles, each measuring 60 degrees. Since all angles of an acute triangle are less than 90 degrees, none of them can be equal to 60 degrees, which is necessary to form an equilateral triangle.
As a result, an acute triangle cannot be equilateral. An acute triangle is a triangle in which all three angles are acute, meaning that each angle is less than 90 degrees. On the other hand, an equilateral triangle is a triangle with three sides of equal length and three equal angles. Since all angles of an acute triangle are less than 90 degrees, none of them can be equal to 60 degrees, which is necessary to form an equilateral triangle.
Therefore, an acute triangle cannot be equilateral. In conclusion, an acute triangle can never be equilateral, because an equilateral triangle requires all three angles to measure 60 degrees, while all three angles of an acute triangle are less than 90 degrees.
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Look at the following rules for two number patterns. Both patterns start with 40.
the patterns are
Pattern P: "Subtract 2"
Pattern Q: "Subtract 4"
the answers are: Excluding the first term, a term in Pattern P is always 2 greater than its corresponding term in Pattern Q.
Excluding the first term, a term in Pattern Q is always 4 greater than its corresponding term in Pattern P.
Starting with 0, the difference in the corresponding terms in the two patterns decreases by 4.
Starting with 0, the difference in the corresponding terms in the two patterns increases by 2.
Answers
Pattern P:
40, 38, 36, 34, 32, 30, …
Pattern Q:
40, 36, 32, 28, 24, 20, …
(absolute) Differences in corresponding terms:
0, 2, 4, 6, 8, 10, …
and these differences agree with the last statement.
a lot of 50 electrical components numbered 1 to 50 is drawn at random, one by one, and is divided among five customers. (a) suppose that it is known that components 3, 18, 12, 26, and 46 are defective. what is the probability that each customer will receive one defective component? (b) what is the probability that one customer will have drawn five defective components? (c) what is the probability that two customers will receive two defective components each, two none, and the other one?
Answers
The probability of getting one defective component per customer is very low, less than 1/14,254. The probability of getting five defective components to a single customer is also low, 1/14,254. And the probability of getting two defective components to two different customers and the rest of the customers getting none is 10/14,254.
(a) The probability that each customer will receive one defective component is the probability that the five defective components will be drawn in a specific order, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order. So the probability is (5!)/(5049484746) = 1/14,254.
(b) The probability that one customer will have drawn five defective components is the probability that all five defective components will be drawn in a row, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a row. So the probability is (1!)/(5049484746) = 1/14,254,
(c) The probability that two customers will receive two defective components each, two none, and the other one, is the probability that the five defective components will be drawn in a specific order and then divided among the five customers in a specific way, divided by the total number of ways the 50 components can be drawn. The number of ways to divide the defective components among the customers is 5!/(2!2!1!) = 10. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order, so the probability is (105!)/(50494847*46) = 10/14,254.
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Knowing your personal strengths and weaknesses will help to keep your goal a. within your skills and abilities c. both of these b. within its timeline d. none of these please select the best answer from the choices provided a b c d
Answers
The correct choice is within your skills and abilities.
Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.
It will also result in no or less time wasted in doing what you are less capable of.
Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.
Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.
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Answer:
Step-by-step explanation:
a you just had to say a
Solve the system of linear equations by elimination.
12x−7y=−2
8x+11y=30
Answers
Answer:
x=1
y=2
Step-by-step explanation:
Find the DISTANCE between (-4,5) and (3,-9) to the nearest TENTH.
Answers
Answer:
The answer is 15.7.
Step-by-step explanation:
El triángulo ABC es equilátero y L, M y N son los puntos medios de BC, AB y CA respectivamente. Si MN = 3, ¿cuál es el valor de ML?
Answers
The value of ML = 3, using the mid-point theorem of triangles.
According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."
In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.
Thus, by the midpoint theorem, we can say that:
MN || BC, and MN = (1/2)BC,ML || AC, and ML = (1/2)AC, andNL || AB, and NL = (1/2)AB.Assuming AB = BC = AC = x units, we get:
MN = (1/2)BC = x/2,ML = (1/2)AC = x/2, andNL = (1/2)AB = x/2.
Thus, the triangle LMN is an equilateral triangle.
Thus, MN = ML = NL.
Given MN = 3, we can write the value of ML = 3.
Thus, the value of ML = 3, using the mid-point theorem of triangles.
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The given question is in Spanish. The question in English is:
"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"
Given the graph below, what is the y-intercept(s)? Give your answer(s) as an ordered pair.
Answers
Answer:
(0, 4)
General Formulas and Concepts:
Algebra I
The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis.Step-by-step explanation:
According to the graph, the line passes the y-axis at y = 4. Therefore, our y-intercept is (0, 4).
2*2*2*2*2*2*2*2*2*2
Answers
Answer:
=2×2×2×2×2×2×2×2×2×2
=1024
there are ten 2 so the answer is 1024
Step-by-step explanation:
Answer:
1024
Step-by-step explanation:
What is the total rainfall in a three-day period if it rains 3 1/2 inches the first day, 3/8 inches the second day, and 2 2/3 inches on the third day
Answers
The total rainfall in the three-day period is 157/24 inches, which is approximately 6.54 inches when rounded to two decimal places.
To find the total rainfall over a three-day period, you need to add up the rainfall amounts for each day.
First day: 3 1/2 inches
Second day: 3/8 inches
Third day: 2 2/3 inches
To add these fractions and mixed numbers, let's convert them to a common denominator. In this case, we'll use 8.
First day: 3 1/2 inches = 7/2 inches
Second day: 3/8 inches
Third day: 2/3 inches = 8/3 inches
Now, we can add the rainfall amounts:
7/2 + 3/8 + 8/3
To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple of 2, 8, and 3 is 24. Let's convert each fraction to have a denominator of 24:
(7/2) (12/12) = 84/24
(3/8) (3/3) = 9/24
(8/3) (8/8) = 64/24
Now, we can add the fractions:
84/24 + 9/24 + 64/24 = 157/24
Therefore, the total rainfall in the three-day period is 157/24 inches, which is approximately 6.54 inches when rounded to two decimal places.
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two and three fourths times three and one half
Answers
Answer:
9 5/8
Step-by-step explanation:
if this is correct can u mark me as brainliest
Answer:
9 and 5/8
Step-by-step explanation:
2 3/4 = 11/4
3 1/2 = 7/2
11/4 x 7/2 = 77/8 = 9 and 5/8
7(x+3)=-2(x-5)
Help pls? I need a tutor
Answers
Answer:
x = -11/9
Step-by-step explanation:
First, let's distribute (get rid of parenthesis):
7x + 21 = -2x + 10
Then, let's combine like terms:
7x + 2x = 10 - 21
Then, simplify:
9x = -11
Finally, divide 9 on both sides:
x = -11/9
And we're done!
If I can read 10 pages in 50 minutes, how many pages will I read in an hour and a half
Answers
Answer:
18 pages
Step-by-step explanation:
that means you can read 2 pages in 10 minutes.
an hour and a half is 90 minutes.
90 is 9 times more than 10.
so we do 2 * 9 = 18 pages
Find an equation of the tangent line to the graph of f(x)=e*, where x = 3.1. The equation of the tangent line is (Type an equation. Type your answer in slope-intercept form.
Answers
The equation of the tangent line is: y = 22.1975x - 68.3074
The given function is f(x) = e^x. To find the tangent line of this function, we will first find its derivative:
f'(x) = e^x
Now, the slope of the tangent line at x = 3.1 is f'(3.1) = e^3.1 ≈ 22.1975. We can use the point-slope form of the equation of a line, where the slope is f'(3.1) and the point is (3.1, f(3.1)):y - f(3.1) = f'(3.1) (x - 3.1)
We can plug in the values of f(3.1) and f'(3.1):y - e^3.1 = 22.1975 (x - 3.1). Finally, we can simplify this equation to slope-intercept form:y = 22.1975x - 68.3074
To find the equation of the tangent line to the graph of the function f(x) = e^x at x = 3.1, we first need to find the derivative of the function. This will give us the slope of the tangent line at any point on the graph of the function. The derivative of the function is f'(x) = e^x. We want to find the slope of the tangent line at x = 3.1, so we need to evaluate f'(x) at x = 3.1. f'(3.1) = e^3.1 ≈ 22.1975. This is the slope of the tangent line at x = 3.1.
Now we can use the point-slope form of the equation of a line to find the equation of the tangent line. The point-slope form of the equation of a line is y - y1 = m(x - x1)where m is the slope of the line and (x1, y1) is a point on the line. We can use the point (3.1, f(3.1)) as the point on the line since we know x = 3.1 is on the line, and we can use f(3.1) to find y1. f(3.1) = e^3.1 ≈ 22.1975. Now we have:y - 22.1975 = 22.1975(x - 3.1)This is the point-slope form of the equation of the tangent line. We can simplify this equation to slope-intercept form, which is:y = 22.1975x - 68.3074This is the equation of the tangent line to the graph of f(x) = e^x at x = 3.1.
Therefore, the equation of the tangent line is:y = 22.1975x - 68.3074
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