Using similar side theorem, the value of x is 4 units and the length of BD is 13 units.
What is similar side theoremThe Similar Side Theorem, also known as the Angle Bisector Theorem, states that if a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.
More formally, let ABC be a triangle with angle bisector AD, where D lies on the side BC. Then, the following proportion holds:
BD/DC = AB/AC
where BD and DC are the two segments into which AD divides the side BC, and AB and AC are the other two sides of the triangle.
In this problem, we have to find the value of x
12 / x = 27 / x + 5
27x = 12(x + 5)
27x = 12x + 60
27x - 12x = 60
15x = 60
x = 4
BD = BC + CD
BD = 4 + (4 + 5)
BD = 4 + 9
BD = 13
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for the rectangle, what is the length of side AB
A=(-4,10) B=(2,10) C=(2,2) D=(-4,2)
Answer:
6 units
Step-by-step explanation:
the answer is the image above
Answer:
I've attached the Answer
PLEASE HELP! all u have to do is determine if it is positive or negative!
Answer:
I think it is positive.
Step-by-step explanation:
Iam soory if Iam wrong.
seven people were chosen from a pool of 21 people tested that resulted in an outcome of 33%. this is an example of a ratio. break-even selection furlough retention turnover
It is important to note that the term "break-even," "selection," "furlough," "retention," or "turnover" does not directly apply to this scenario.
The given scenario, where seven people were chosen from a pool of 21 people and resulted in an outcome of 33%, is an example of a ratio.
In this case, the ratio is calculated as the number of chosen individuals (7) divided by the total number of individuals in the pool (21), resulting in a ratio of 7/21 or 1/3. This ratio represents the proportion or percentage of the pool that was selected.
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What is 33% of 171? how did you get it
Answer:
56.43
Step-by-step explanation:
= 33/100×171
=56.43
What is the slope of the line, what does the slope represent? write an equation for emma’s graph x=time and y=distance
Answer:
5/2 or 2.5
Step-by-step explanation:
Slope formula:
(y₂ - y₁) / (x₂ - x₁)
Two points are given:
(2, 5) and (6, 15)
x₁ = 2
y₁ = 5
x₂ = 6
y₂ = 15
Substitute and solve:
(15 - 5) / (6 - 2)
10 / 4
5/2 or 2.5
What is the number in scientific notation of 0.0765
Answer:
7.65x10^-2 should be your answer
Step-by-step explanation:
write an equation in slope intercept form of the line that passes through (2,8) and (-3,6)
The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y=-5/3x-2.
Given that the line passes through the point (-6,8) and has a slope of -5/3.
We are required to find the equation of the line whose description is given.
Equation is basically the relationship between two or more variables that are expressed in equal to form. It may be linear equation, quadratic equation or cubic equation. Slope intercept form in the equation be y=mx+c.
We have been given slope be -5/3.
y=mx+c--------------1
Put m=-5/3 in equation 1.
y=-5/3x+c------------2
Put (-6,8) in equation 2.
8=-5/3 *(-6)+c
8=-5*(-2)+c
8=10+c
c=-2
Use the value of c in equation 2.
y=-5/3x-2
Hence the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y=-5/3x-2.
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hey i need some help with this one.
Answer:
y = -2x - 8
Here's how I got that:
- You first assign the points -
(-8, 8) → x1 = -8, y1 = 8
(1, -10) → x2 = 1, y2 = -10
- Now you plug those points into slope formula and solve-
\(s=\frac{y2-y1}{x2-x1}\)
↓
((-10) - 8)/(1 - (-8))
↓
-18/9
↓
slope = -2
- Now we plug the numbers we got into intercept formula -
b = y1 − s ⋅ x1
↓
8 - (-2) · (-8)
↓
y-intercept = -8
- Put everything together and you get.. -
y = -2x - 8
~That's all folks~
-Siascon
\(\text{Given that,}\\\\(x_1,y_1) = (-8,8) ~ \text{and}~ (x_2,y_2) = (1,-10)\\\\\text{Slope, m}= \dfrac{y_2- y_1}{x_2-x_1} = \dfrac{-10-8}{1+8} = -\dfrac{18}{9} =-2\\\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y = m(x-x_1)+y_1\\\\\implies y = -2(x+8) + 8\\\\\implies y = -2x -16 +8\\\\\implies y = -2x -8\)
Measure and record the length of each side of parallelogram . type the correct answer in each box. use numerals instead of words. do not round your answers.
Measuring and recording the length of each side of a parallelogram means using a measuring tool, such as a ruler or a tape measure, to determine the length of each of the four sides of the parallelogram and then recording that measurement.
The measurement should be noted with the appropriate unit of measurement (inches, centimeters, etc.) and recorded in a way that is easy to understand and reference later.
To measure and record the length of each side of a parallelogram, the following steps can be taken:
Obtain a measuring tape or ruler: measure the length of one side of the parallelogram using the measuring tape or ruler, starting from one corner and extending to the opposite corner.Record the measurement: write down the measurement, noting the unit of measurement (inches, centimeters, etc.).Measure the next side: move to the next side of the parallelogram and repeat the process, measuring the length and recording it.Repeat the process for all four sides: continue to measure and record the length of all four sides of the parallelogram, making sure to note the order in which the measurements were taken, in case it is needed later.Double-check measurements: review the measurements to ensure accuracy and check for any discrepancies that may have occurred during the measurement process.Label and organize measurements: label each measurement with the appropriate side (for example, "side A," "side B," etc.) and organize them in a way that makes them easy to understand and reference in the future.It is important to note that a parallelogram has opposite sides of equal length and opposite angles of equal measure. Therefore, after measuring and recording the length of two sides, you can use this property to measure the other sides without measuring them again.
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The Taylor series about x=0 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x=0 is given by
f(n)(0)=(−1)n+1(n+1)!5n(n−1)2 for n≥2
The graph of f has a horizontal tangent line at , x=0 and f(0)=6
A) Write the third-degree Taylor polynomial for f about x=0.
B) Find the radius of convergence of the Taylor series for f about x=0. Show the work that leads to your answer.
C) Determine whether f has a relative maximum, a relative minimum, or neither at x=0. Justify your answer.
f has a relative maximum at x=0.
A) To write the third-degree Taylor polynomial for f about x=0, we need to find the function and its first three derivatives at x=0.
f(0) = 6 (given)
f'(x) = sum_(n=1)^∞ [f(n)(0)/n!] \(x^{(n-1\))
f'(0) = f(1)(0)/1! = (-1+1!/50)\(\times\)6 = 5.88
f''(x) = sum_(n=2)^∞ [f(n)(0)/n!] \(x^{(n-2)\)
f''(0) = f(2)(0)/2! = (-1+1!/50)\(\times\)6/2 = -0.06
f'''(x) = sum_(n=3)^∞ [f(n)(0)/n!] \(x^{(n-3)\)
f'''(0) = f(3)(0)/3! = (-1+1!/50)\(\times\)6/6 = -0.016
Therefore, the third-degree Taylor polynomial for f about x=0 is:
P3(x) = f(0) + f'(0)x + f''(0)\(x^2\)/2 + f'''(0)\(x^3\)/6
= \(6 + 5.88x - 0.03x^2 - 0.0033x^3\)
B) To find the radius of convergence of the Taylor series for f about x=0, we can use the ratio test:
R = lim_(n→∞) |a_n/a_(n+1)|
= lim_(n→∞) |f^(n)(0)/n!| / |f^(n+1)(0)/(n+1)!|
= lim_(n→∞) |(n+1)/(5(n-1\()^2\))|
= 0
Since the limit of the ratio is zero, the radius of convergence is infinite, which means the Taylor series converges for all x.
C) To determine whether f has a relative maximum, a relative minimum, or neither at x=0, we can use the second derivative test. If f''(0) > 0, then f has a relative minimum at x=0. If f''(0) < 0, then f has a relative maximum at x=0. If f''(0) = 0, then the test is inconclusive.
From part A, we know that f''(0) = -0.06, which is negative. Therefore, f has a relative maximum at x=0.
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i) 43x + 31y = 98
31x + 43y = 50
There are no solutions to the given system of equations.
Hope this helps.
WILL GIVE BRAINLIEST!!
A line has a slope of 1/3 and passes through the point (–9, –3). What is its equation in slope-intercept form?
Answer:
y = \(\frac{1}{3}\) x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = \(\frac{1}{3}\) , then
y = \(\frac{1}{3}\) x + c ← is the partial equation
to find c substitute (- 9, - 3) , that is x = - 9, y = - 3 into the partial equation
- 3 = \(\frac{1}{3}\) (- 9) + c = - 3 + c ( add 3 to both sides )
0 = c
y = \(\frac{1}{3}\) x + 0 , that is
y = \(\frac{1}{3}\) x
because of different units being used for various data series, which fit statistic can be used across different series that are in fact measured in different units?
The fit statistic that can be used across different series that are in fact measured in different units is; MAPE
What statistic can be used?There are different statistics models in this regards such as;
Mean Absolute Error (MAE)
Mean Absolute Scaled Error (MASE)
Accuracy Percent (Accuracy %)
Mean Squared Error (MSE)
Root Mean Squared Error (RMSE)
Mean Absolute Percent Error (MAPE)
Now, we are told that we need the fit statistic that can be used across different series that are in fact measured in different units.
The correct one will be Mean Absolute Percent Error (MAPE) because the average absolute percent difference between the values that are fitted by the model and the observed data values.
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The cost to rent an rv is $150 per day plus $0.35 per mile. what is the maximum distance you can drive the rv in a day if your budget is $200?
Answer:
142.86 miles
Step-by-step explanation:
150 + .35m < 200
150 + .35m -150 < 200-150
.35m < 50
.35m/35 < 50/.35
m < 142.86
The maximum distance I can drive the rv in a day if my budget $200 is, approx. 142 miles
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
The cost to rent an rv is $150 per day + $0.35 per mile
The maximum distance in a day = ?
Budget is $200
So,
The maximum distance in a day ≤ 200
The maximum distance in a day = 150 + 0.35x
Now,
⇒ 150 + 0.35x ≤ 200
⇒ 0.35x ≤ 200 - 150
⇒ x ≤ 142.85
Hence, maximum distance in a day is approx. 142 miles
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Suppose the sample space for a continuous random variable is 0 to 200. If
the area under the density graph for the variable from 0 to 50 is 0.25, then the
area under the density graph from 50 to 200 is 0.75.
OA. True
B. False
A teacher takes her nephew shopping. She tells her nephew that they can spend x dollars knowing
that 16x = 641.6.
What operation does the nephew need to use to find how much money they can spend?
Choose the correct answer below:
A.Addition
B. Division
C. Multiplication
D. Subtraction
Answer:
division
Step-by-step explanation:
division so as to find the value of x
A walkway forms one diagonal of a square playground. The walkway is 30 m long. How long is a side of the playground?
Answer:
21.213 m
Step-by-step explanation:
If the diagonal d = 30 m
then the side a = d÷(√2)
hence a = 30 m ÷ (√2) = 21.213 m
HELP DUE IN A COUPLE HOURS Mrs. Penny bought a rectangular box that is 6 inches long, 10 inches wide, and 4 inches high. She wants to cover it in fabric. The fabric costs $0.25 per square inch. How much money will the fabric cost?
Answer:
dont get cote with the link below
Step-by-step explanation:
https://www.symbolab.com/solver/step-by-step/2x%5E%7B2%7D-7%3D-7
Use the definition of logarithm to fill in the blanks below. (Simplify your answers completely.) (a) log2(64)
Logarithm (a) log2(64) = 6
The definition of a logarithm states that for any base "b" and a positive number "x", if bx = y, then logb(y) = x. In other words, the logarithm tells us the exponent to which the base must be raised to obtain a given number.
In this case, we are asked to find log2(64), which means we need to determine the exponent to which 2 must be raised to obtain 64.
To find this exponent, we can think of 2^6 = 64. This means that log2(64) = 6, since the exponent 6 is required to get 64 as the result when 2 is raised to that power.
Therefore, log2(64) = 6.
Using the definition of logarithm, we can find the exponent needed to obtain a given number when raised to a certain base. In this case, applying the definition of logarithm allows us to determine that log2(64) is equal to 6, indicating that 2 must be raised to the power of 6 to yield 64.
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-10+5=7x-4
how to i explain this step by step
Answer:
5/7 x 4 = 2.8571 in decimal form.
Answer:
x = -1/7
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
& is the order of operation.
First simplify the expression to the left: -10 + 5 = 5 - 10 = -5
-5 = 7x - 4
Next, isolate the variable, x. Do the opposite of PEMDAS. Add 4 to both sides:
-5 (+4) = 7x - 4 (+4)
-5 + 4 = 7x
-1 = 7x
Divide 7 from both sides:
(-1)/7 = (7x)/7
-1/7 = x
x = -1/7
~
01:41:08
Dependent variable C depends on both independent variable A and independent variable B. Which statement is
correct?
Answer:
The correct answer is B. The relationship between independent variable A and dependent variable C, and the relationship between independent variable B and dependent variable C can both be analyzed, but they must be analyzed using separate scatter plots.Apr 30
Step-by-step explanation:
hope you get it right
giving the funtions f(x)=2x-5 and g(x)=3x2=2 perform the indicated operation
Answer:3165
Step-by-step explanation:
City received 3/4 inch of rain on July 31  This represents 3/10 of the total amount of rain this to received in July the equation 3/10r =3/4 can be used to find the amount of rain r in inches  The city received in July how much rain did the city receive in July ?
The amount of rain the city received in July is r = 2.5 inches
Given data ,
City received 3/4 inch of rain on July 31
Now , it represents 3/10 of the total amount of rain this to received in July
So , the equation is represented as A
Now , the value of A is
( 3/10 )r = 3/4
Multiply by 10 on both sides , we get
3r = 30/4
Divide by 3 on both sides , we get
r = 30/12
r = 2.5 inches
Hence , the city received 2.5 inches of rain
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Quadrilateral A has side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 2. What is the perimeter of Quadrilateral B?
Answer:
Look below
Step-by-step explanation:
Ok, you got a Quadrilateral with the side lengths 6, 9, 9, 12
The shortest of B is 2
Find the scale factor of the A to B
6 -> 2
6/2 = 3
Scale factor is 3
Now divide all the sides by scale factor
6/3, 9/3, 9/3, 12/3 = 2, 3, 3, 4
Add them all together to get the perimeter
2+3+3+4 = 12
Perimeter of B is 12
solve for C
7(c-12)=-21
Answer: c=9
Step-by-step explanation:
Which system of equations has no solution?
A 3y = 1 + x
y=-2x + 5
B. 4x - 5y = 3
-3 = 4x - 5y
C. 5x + 4y = 1
4x – 2y = 4
O D. y=-3x + 4
y=-x+1
Answer:
b
Step-by-step explanation:
b
convert the line integral to an ordinary integral with respect to the parameter and evaluate it. ; c is the helix , for question content area bottom part 1 the value of the ordinary integral is 11. (type an exact answer, using radicals as needed.)
To convert a line integral to an ordinary integral with respect to the parameter, we need to parameterize the curve. In this case, the curve is a helix. Let's assume the parameterization of the helix is given by:
x(t) = a * cos(t)
y(t) = a * sin(t)
z(t) = b * t
Here, a represents the radius of the helix, and b represents the vertical distance covered per unit change in t.
To find the ordinary integral, we need to determine the limits of integration for the parameter t. Since the helix does not have any specific limits mentioned in the question, we will assume t ranges from 0 to 2π (one complete revolution).
Now, let's consider the line integral. The line integral of a function F(x, y, z) along the helix can be written as:
∫[c] F(x, y, z) · dr = ∫[0 to 2π] F(x(t), y(t), z(t)) · r'(t) dt
Here, r'(t) represents the derivative of the position vector r(t) = (x(t), y(t), z(t)) with respect to t.
To evaluate the line integral, we need the specific function F(x, y, z) mentioned in the question.
However, if we assume a specific function F(x, y, z), we can substitute the parameterization of the helix and evaluate the line integral using the ordinary integral. Given the answer value of 11, we can solve for the unknowns in the integral using radicals as needed.
In summary, to convert the line integral to an ordinary integral with respect to the parameter and evaluate it, we need to parameterize the curve (helix in this case), determine the limits of integration, and substitute the parameterization into the integral.
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Assuming a level of significance of 0.01, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines
Answer: Yes, there is
Step-by-step explanation:
PLEASE Hurry I NEED my answer today!
Sanjay rides his bike to work 15 kilometers in two days. He works five days per week.
How many weeks will Sanjay need to ride his bike to work in order to ride 150 kilometers?
A. 4 weeks
B. 7.5 weeks
C. 10 weeks
D. 20 weeks
Answer:
4 weeks
Step-by-step explanation:
Well since he rides his bike 15 kilometers every two period, we can assume that he rides his bike 7.5 kilometers a day. So:
\(150=7.5x\)
Where x is the number of days he rides his bike.
\(\frac{150}{7.5}=\frac{7.5x}{7.5}\)
\(20=x\)
So it will take him 20 days to ride his bike 150 kilometers.
Now all we have to do is divide the 20 days by 5 to show how many weeks it took:
\(\frac{20}{5}=4\)
It took him 4 weeks.
Assume the population of human body temperatures has a mean of 98.6 degrees Fahrenheit as is commonly believed. Assume the standard deviation is .62 degrees Fahrenheit. Find the probability that the mean of a sample of 106 randomly selected humans is lower than 98.5 degrees Fahrenheit. Write your answer using a decimal. Be sure to use the appropriate rounding rules.
The probability that the mean of a sample of 106 randomly selected humans is lower than 98.5°F is 4.85%
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Z score is given as:
z = (raw score - mean) ÷ (standard deviation/√sample size)
Given mean of 98.6°F, standard deviation is 0.62°F, sample size = 106
For x < 98.5:
z = (98.5 - 98.6) ÷ (0.62÷√106) = -1.66
P(z < -1.66) = 0.0485
The probability that the mean of a sample of 106 randomly selected humans is lower than 98.5°F is 4.85%
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