Answer:
x = 3
Step-by-step explanation:
The triangles are similar, using ratios
x 8
------ = -----------
18 48
We can use cross products to solve
48x = 8*18
48x = 144
Divide each side by 48
48x/48 = 144/48
x =3
What are the solutions to the quadratic equation 4(x + + 2)2 = 36
O x= -11 and x = 7
Ox= -7 and x = 11
O x= -5 and x = 1
Ox= -1 and x = 5
Answer:
x= -1 and 5
hope that helps
The solutions to the quadratic equation \(4(x+2)^2=36\) are x = -5 and x = 1.
Given the following data:
\(4(x+2)^2=36\)How to solve a quadratic equation.In this exercise, you're required to determine the value of x by solving for the factors (roots) of the given quadratic equation.
In Mathematics, the standard form of a quadratic equation is given by;
\(ax^2 + bx + c =0\)
Where:
a = 4.b = 16.c = -20.Dividing both sides by 4, we have:
\(4(x+2)^2=36\\\\(x+2)^2=9\)
Taking the square root of both sides, we have:
\(x+2=\pm3\\\\x=\pm 3-2\)
x = -5 or 1.
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Use the Laplace transform to solve the given initial-value problem. y(t) = = y"" + 2y" - y' - 2y = sin(3t), y(0) = 0, y'(0) = 0, y"(0) = 1
The solution to the initial value problem y(t) = (1/3)sin(3t) + (1/2)(1 - e^(-t)).
Let's denote the Laplace transform of y(t) as Y(s). Taking the Laplace transform of the given differential equation, we get:
s^2Y(s) + 2sY(s) - sY(0) - Y'(0) - 2Y(s) = 3/(s^2 + 9).
Since y(0) = 0, y'(0) = 0, and y''(0) = 1, the above equation simplifies to:
s^2Y(s) + 2sY(s) - 1 = 3/(s^2 + 9).
Rearranging the equation, we have:
Y(s) = (3/(s^2 + 9) + 1)/(s^2 + 2s).
Using partial fraction decomposition, we can express Y(s) as:
Y(s) = (3/(s^2 + 9)) + (1/(s^2 + 2s)).
Taking the inverse Laplace transform of each term, we find the solution y(t) in the time domain:
y(t) = (1/3)sin(3t) + (1/2)(1 - e^(-t)).
Therefore, the solution to the given initial-value problem is y(t) = (1/3)sin(3t) + (1/2)(1 - e^(-t)).
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if a student is chosen at random, what is the probability that the student prefers the zoo or the water park?
Without specific data on the number of students who prefer each option, we cannot calculate the probability.
To determine the probability that a student prefers the zoo or the water park, we need to know the total number of students and the number of students who prefer each option. Without this information, it is not possible to calculate the probability accurately.
To calculate the probability, we would need to divide the number of students who prefer the zoo or the water park by the total number of students. For example, if there are 50 students in total and 30 prefer the zoo and 20 prefer the water park, the probability would be:
P(prefer zoo or water park) = (30 + 20) / 50 = 50 / 50 = 1
However, without specific data on the number of students who prefer each option, we cannot calculate the probability.
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Write the equation of the line in fully simplified slope-intercept form.
Answer:
y=-2/3-2
Step-by-step explanation:
Determine the length of the line segment shown. line segment from negative 5 comma 5 to 3 comma negative 1 6 units 8 units 10 units 36 units
fist gets brainlyist and 35 points please help asap
The length of the line segment with points (-5, 5) (3, -1) is 10 units
How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points (-5, 5) and (3, -1) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-5 - 3)² + (5 - -1)²}
d =√{64 + 36}
d = √100
d = 10 units
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a triangle has an area of 68 ft and a height of 16 ft what is the length of the base
Answer:
8.5
Step-by-step explanation:
First we need to know the formula is BxH/2 for triangles. First we would do 68x2=136. Then we would do 136/16 which would give you 8.5! Hope this helps!
A triangle having area of 68 ft and a height of 16 ft, the length of the base for a triangle is, 8.5 ft
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
Given that,
a triangle has an area of 68 ft
a height of 16 ft
the length of the base = ?
Area of triangle = 1/2×base×height
68 = 1/2×base×16
base = 8.5 ft
Hence, the length of the base is 8.5 ft
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what is it called when you describe the steps that are necessary for finding a solution to a problem in programming?
The process of describing the steps necessary for finding a solution to a problem in programming is commonly referred to as algorithm design.
Algorithm design is an essential aspect of programming, as it allows programmers to devise a systematic approach to problem-solving. When faced with a programming problem, the first step is to analyze and understand the problem requirements thoroughly.
Once the problem is understood, the next step is to design an algorithm that outlines the sequence of steps needed to solve the problem.
In algorithm design, programmers typically consider factors such as efficiency, correctness, and maintainability. They aim to devise algorithms that produce accurate results, optimize resource usage, and are easy to understand and maintain.
The process involves selecting appropriate data structures, determining control flow, and defining the specific operations or computations required at each step.
By describing the steps in an algorithm, programmers can effectively communicate their approach to solving a problem and provide a roadmap for implementing the solution in code.
Well-designed algorithms help streamline the programming process, improve code quality, and facilitate the development of reliable and efficient software systems.
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A helicopter spots two landing pads in opposite directions below the angle of depression to pad A to pad B is 46 and 16 degrees respectively if the straight line distance from the helicopter to pad A is 5 miles , find the distance between the landing pads.
The distance between the landing pads is approximately 12.82 miles.
What is straight line?A straight line is the shortest distance between two points in a two-dimensional space. It is a one-dimensional geometric object that extends infinitely in both directions.
Let's label the distance between the helicopter and Pad A as "x" and the distance between the helicopter and Pad B as "y". Also, let's label the distance between Pad A and Pad B as "d".
We can start by using the tangent function to find the height of the helicopter above Pad A:
tan(46) = h / x
h = x tan(46)
Similarly, we can find the height of the helicopter above Pad B:
tan(16) = h / (x + d)
h = (x + d) tan(16)
Since the helicopter is flying at a constant height, we can equate the two expressions for h and solve for d:
x tan(46) = (x + d) tan(16)
xtan(46) = xtan(16) + dtan(16)
d = x(tan(46) - tan(16)) / tan(16)
Substituting x = 5 miles and the values for the tangent functions, we get:
d = 5 (0.9851 - 0.2760) / 0.2760
d = 5 (0.7091) / 0.2760
d = 12.82 miles
Therefore, the distance between the landing pads is approximately 12.82 miles.
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If x2 + y2 =86 and x y = -16 find the value of (x-y)2
Answer:
(x-y)^2=118
Step-by-step explanation:
Answer:
54 is the value of (x-y)^2
Step-by-step explanation:
Given:
Equation 1: \(x^{2} + y^{2} = 86\)
Equation 2: xy = - 16
Multiply Equation 2 with 2 on both sides: 2xy = -32
Find value of(Equation 3) : \((x-y)^2\)
\((x-y)^2 = x^{2} + y^{2} + 2xy\)
Put the value of equation 1 and equation 2 in equation 3
i.e. \((x-y)^2 = (x^{2} + y^{2}) + (2xy)\)
\((x-y)^2 = (86) + (-32)\)
\((x-y)^2 = 54\)
miles per hour. on her way home, she travels at 12 miles per hour. the total travel time is 2 hours. which equation can be used to find the distance in miles from bree’s house to the library? distance (mi) rate (mph) time (hr) trip to library x 6 mph startfraction x over 6 endfraction trip to home x 12 mph startfraction x over 12 endfraction startfraction x over 6 endfraction startfraction x over 12 endfraction
The equation to calculate the distance will be 12 × 2.
How to compute the equation?From the information given, she travels at 12 miles per hour and the total travel time is 2 hours.
It should be noted that:
Distance = Speed × Time
Therefore,
Distance = 12 × 2
The distance is 24 miles.
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A 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.
Answer:
27.89feet
Step-by-step explanation:
Given the following
Length of the ladder = 32foot = hypotenuse
Angle of elevation = 29.37°
Required
Distance of the building from the base of the ladder (adjacent)
Using the SOH CAH TOA identity
Cos theta = adj/hyp
Cos 29.37° = d/32
d = 32cos29.37°
d = 32(0.8715)
d = 27.89 feet
Hence the required distance is 27.89feet
Answer:
27.89 feet
Step-by-step explanation:
Hope this helps :)
can you hlep me plass pp
Answer:
56 m
Step-by-step explanation:
There is a right triangle formed between the height of the tower and Khaled.
The hypotenuse is the distance from the top of the tower to Khaled's feet
The legs are 33 and height h , then
h² + 33² = 65²
h² + 1089 = 4225 ( subtract 1089 from both sides )
h² = 3136 ( take square root of both sides )
h = \(\sqrt{3136} \) = 56
The height of the tower is 56 m
The table shows three functions and their output values for different values of x. Which equation represents h(x)? h(x) = (f(x))(g(x)) h(x) = f(x) – g(x) h(x) = f(x) + g(x)
The equation that represents h(x) is h(x) = (f(x))(g(x)).
To determine which equation represents h(x), we need to analyze the given table and understand the relationship between the functions f(x), g(x), and h(x).
Since h(x) represents the output values obtained by multiplying f(x) and g(x), we should look for values in the table where h(x) is the product of the corresponding values of f(x) and g(x).
Let's examine the table and compare the values:
x | f(x) | g(x) | h(x)
1 | 3 | 4 | 12
2 | 5 | 2 | 10
3 | 2 | 6 | 12
From the table, we can see that the values in the h(x) column are the products of the corresponding values in the f(x) and g(x) columns. Therefore, the equation that represents h(x) is h(x) = (f(x))(g(x)).
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Answer:
It's B.
Step-by-step explanation:
Edge 2020.
Plz help due tomorrow
how to find sample size with margin of error on ti 84
The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.
To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:
1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.
2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.
Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.
3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.
4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.
5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.
6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.
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measuring length and width can determine if the center section is within specification.
true or false?
Measuring length and width can determine if the center section is within specification. The given statement is insufficient to be determined as true or false as the statement doesn't specify the length and width of what is being measured.
Therefore, we can not provide the required answer without knowing the complete question. Hence, we need further information on the complete statement. In technical terms, specifications are a set of specifications and requirements that a product, materials, service, or system must meet. Specifications are developed to ensure that products, systems, or services are consistent, trustworthy, and meet the needs of the end-user. Therefore, specifications play a crucial role in ensuring the quality and reliability of a particular product or service. It also helps to determine whether a product or service meets the required safety and performance standards or not.
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please help
What is thirty-one thousand nine hundred written in expanded form?
A. 10,000 + 3,000 + 100
B. 30,000 + 1,000 + 900
C. 30,000 + 1,000 + 100
D. 90,000 + 1,000 + 300
Answer:
it's letter B
Step-by-step explanation:
you just sound out the numbers
144000x²+431974x-39=0 find the value of X
Answer:
\(x=0.00009028, x=-2.999909725\)
Step-by-step explanation:
Use the quadratic formula:
\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\)
when \(ax^2+bx+c=0\)
Therefore, for \(144000x^2+431974x-39=0\)
a = 144,000 b = 431,974 and c = -39
Substituting this data into the quadratic formula:
\(x=\dfrac{-431974 \pm \sqrt{431974^2-4(144000)(-39)} }{2(144000)}\)
\(x=0.00009028, x=-2.999909725\)
Y=91 if x is 4 what is y
Answer:
y=91
.........???????
Look at this table.
Hours of
Training
10
20
30
40
50
60
70
Monthly
Pay
1100
1200
1300
1400
1500
1600
1700
According to the table, how many hours of training would you need to have a
monthly pay of $2000?
A. 90
B. 80
C. 100
Answer:
100
Step-by-step explanation:
if the pattern continues it looks like the equation f(x)=10x+1000 so you would need 100 hours to make 2000 dollars
sustituir. 20c + 15r + 75p + 50e
Answer:
8c - 7r + 10p - 20e
Step-by-step explanation:
Subtract (20c + 15r + 75p + 50e) - (12c + 22r + 65p + 70e)
(20c + 15r + 75p + 50e) - (12c + 22r + 65p + 70e)
Open bracket
20c + 15r + 75p + 50e - 12c - 22r - 65p - 70e
Collect like terms
= 20c - 12c + 15r - 22r + 75p - 65p + 50e - 70e
= 8c - 7r + 10p - 20e
what is the answer to x2 = 121.
Answer:
11 if you mean x^2
Step-by-step explanation:
Since we are solving for x, we need to just get x by its self. The only thing we have to do is get rid of the exponent of (^2). to do this, we have to take teh square root of both sides:
The square root of x^2 is x
The square root of 121 is 11
So the asnwer is x = 11
Step-by-step explanation: A common mistake in this problem would be to say that if x² = 121, x must equal 11.
However, you must set the equation equal to 0 first.
So our first step is to subtract 121 from both sides to get x² - 121 = 0.
Next, factor the left side to get (x + 11)(x - 11) = 0
So either x + 11 = 0 or x - 11 = 0.
Solving each equation from here, we find that x = -11 or x = 11.
So our answer is not just 11, it's {11, -11}.
What is the volume of the figure below?
A.180 centimeters cubed
B.540 centimeters cubed
C.380 centimeters cubed
D.360 centimeters cubed
Answer:
a
Step-by-step explanation:
Round the following numbers to the nearest 1000: a) 3426 b) 1897 c) 27506 d) 8809
11/12-?=2/3 How do I get the missing fraction with out reducing?
Step-by-step explanation:
11/12-?=2/3
11/12-2/3=?
11-8/12=?
3/12
=1/4
Answer:
? = 1/4
Step-by-step explanation:
11 / 12 - ? = 2 / 3
move constant at Right hand side and change its sign.- ? = 2/3 - 11/12
subtract the fractions- ? = - 1/4
change the sign of both side of equation? = 1/4
Need help,will give 20 points.Use the rectangle to find the measure of the following angles measure ane BAC=25
1) All angles of a rectangle are right angles, so the measure of angle CBA is 90 degrees.
2) Since all angles of a rectangle are right angles, angle BAD measures 90 degrees. Subtracting the 25 degrees of angle BAW from this, we get that angle CAD has a measure of 65 degrees.
3) Opposite sides of a rectangle are parallel, so by the alternate interior angles theorem, the measure of angle ACD is 25 degrees.
4) Because diagonals of a rectangle are congruent and bisect each other, this means BW=WA. So, since angles opposite equal sides in a triangle (in this case triangle ABW) are equal, the measure of angle ABW is 25 degrees. This means that the measure of angle CBD is 90-25=65 degrees.
5) In triangle AWB, since angles in a triangle add to 180 degrees, angle BWA measures 130 degrees.
6) Once again, since diagonals of a rectangle are congruent and bisect each other, AW=WD. So, the measures of angles WAD and ADW are each 65 degrees. Thus, because angles in a triangle (in this case triangle AWD) add to 180 degrees, the measure of angle AWD is 50 degrees.
Match each expression with its value. −9 7 −2 Undefined h( 3.999 ) h(4) h(4.0001) h(9)
The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.
Let's match each expression with its corresponding value:
Expression: -9
Value: -9
Expression: 7
Value: 7
Expression: -2
Value: -2
Expression: Undefined
Value: Undefined
Expression: h(3.999)
Value: Undefined
Expression: h(4)
Value: 8
Expression: h(4.0001)
Value: Undefined
Expression: h(9)
Value: Undefined
Now let's explain the reasoning behind each value:
The expression -9 represents the number -9, so its value is -9.
Similarly, the expression 7 represents the number 7, so its value is 7.
The expression -2 represents the number -2, so its value is -2.
When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.
For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.
The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.
Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.
Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.
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A laboratory tested n = 110 chicken eggs and found that the mean amount of cholesterol was LaTeX: \bar{x}x ¯ = 92 milligrams with σ = 8 milligrams. Find the margin of error E corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs.
Answer:
The margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is of 1.495 miligrams.
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1-0.95}{2} = 0.025\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).
So it is z with a pvalue of \(1-0.025 = 0.975\), so \(z = 1.96\)
Now, find the margin of error E as such
\(E = z*\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
In this question:
\(\sigma = 8, n = 110\). So
\(E = 1.96\frac{8}{\sqrt{110}} = 1.495\)
The margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is of 1.495 miligrams.
Help :(((((((( plz I beg you to help me ok help
Answer:
first one is A and second one is C
Which values are solutions to the inequality below? Check all that apply.
√x <10
A. 100
B. 25
C. -100
D. 105
E. 36
F. 9
Answer:
The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v
Step-by-step explanation:
its E and A
Answer:
The solutions to the inequality are B, E, and F: 25, 36, and 9.
Step-by-step explanation:
The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:
√x < 10
x < 10^2 = 100
So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:
A. 100 (not a solution)
B. 25 (solution)
C. -100 (not a solution)
D. 105 (not a solution)
E. 36 (solution)
F. 9 (solution)