Arnold is looking at the building from 300 feet away at an angle of elevation of 22 grades when asked arnold says he’s 4.75 feet tall do you agree or desagree with arnold’s height explain your answer with matemátical support?
Answers
We can conclude that Arnold's height of 4.75 feet by using tangent function is not accurate based on the calculations.
To determine whether Arnold's height is accurate, we can use trigonometry and the given information about the angle of elevation and distance to the building.
Let's start by drawing a diagram to represent the situation. We have a right triangle with the opposite side being Arnold's height (h), the adjacent side being the distance to the building (300 ft), and the angle of elevation being 22 degrees.
Using the tangent function, we can write:
tan(22) = h / 300
Solving for h, we get:
h = 300 * tan(22)
Using a calculator, we find that h is approximately 122.8 feet.
Therefore, we can conclude that Arnold's height of 4.75 feet is not accurate based on the calculations. The height we calculated is over 25 times greater than Arnold's claimed height, which is not possible.
It is important to note that this assumes that Arnold's line of sight is parallel to the ground. If Arnold is on uneven ground, this could affect the calculations. Additionally, it is possible that Arnold may have misspoken about his height or the angle of elevation. However, based on the given information and calculations, we can confidently say that Arnold's claimed height is not accurate.
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Related Questions
if the first 2 cards are both spades, what is the probability that the next 3 cards are also spades? (round your answer to four decimal places.)
Answers
the probability that the next 3 cards are also spades is 0.0156.
There are 13 spades in a deck of 52 cards. The probability of each card being a spade is 13/52 or 0.25. The probability that the next 3 cards are also spades is 0.25 x 0.25 x 0.25 = 0.016. Therefore, the probability that the next 3 cards are also spades is 0.0156.
1. Calculate the probability of one card being a spade: 13/52 or 0.25
2. Calculate the probability of the next 3 cards being spades: 0.25 x 0.25 x 0.25 = 0.016
3. Round the answer to four decimal places: 0.0156
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7. Given that 2x² + 4x + 3 = k where k is a constant, find the range of values for k for which the equation has no real roots. (b) The function f is defined on the set R of real numbers by f(x) →kx² + kx + 1, where k is a member of R. Calculate the range of values of k for which the equation f(x) = 0 hasreal roots. Given that k = -2, solve the equation f(x) = 0. 1/2
Answers
Answer: (a) The equation 2x^2 + 4x + 3 = k has real roots if and only if its discriminant, which is 4^2 - 4(2)(3), is nonnegative. The discriminant is equal to 0, so the equation has real roots if and only if k = 3.
(b) For the equation f(x) = kx^2 + kx + 1 to have real roots, its discriminant, which is 1 - 4k, must be nonnegative. This gives us k >= 1/4. The range of values of k for which the equation has real roots is k >= 1/4.
(c) When k = -2, the equation f(x) = -2x^2 - 2x + 1 = 0. Solving this equation using the quadratic formula, we get x = (-1 ± √(1 + 8))/4. So, the roots are x = (-1 ± √(9))/4 = (-1 ± 3)/4 = 1/2, -2.
does a piecewise function always have an x and y intercept
Answers
Answer:yes
Step-by-step explanation:
but if the y intercept is 0 then it’ll show like: y= 3x which is equal to y=3x plus or minus 0
No, a piecewise function does not always have an x and y intercept.
A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain interval of the main function's domain.
An x-intercept is the point where the function crosses the x-axis, and a y-intercept is the point where the function crosses the y-axis.
It is possible for a piecewise function to not have an x or y intercept if none of the sub-functions cross the x or y axis. For example, the piecewise function f(x) = {2x + 1 for x < 0, -2x + 1 for x > 0} does not have an x or y intercept because neither of the sub-functions cross the x or y axis.
In conclusion, a piecewise function does not always have an x and y intercept. It depends on the sub-functions that make up the piecewise function.
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A student begins to build a model of a downtown bridge in the city where he lives. He
measures some of the angles formed by the sides of the model.
The student says both x and y are 65. Why is he incorrect? Use the drop-down menus t
explain your answer.
Answers
Considering supplementary angles, we have that the measures of x and y are given as follows:
x = 50º.y = 80º.We also have that x and y have different measures, hence the student is incorrect, and x and 40º are complementary.
What are supplementary angles?Supplementary angles are angles whose measures add to 180º.
The three internal angles of a triangle are supplementary, hence we can find x as follows:
90 + 40 + x = 180
130 + x = 180
x = 50º.
Angles x, y and 50º are also supplementary, hence:
x + y + 50 = 180
50 + y + 50 = 180
y = 80º.
The angles with measures x and 40º are complementary, as they add to 90º.
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Answer:
sum up to 130 but not equal
Step-by-step explanation:
Which of the following are solutions to the quadratic equation below?\( {x}^{2} + 8x = 9\)Check all that apply.
![Which of the following are solutions to the quadratic equation below?[tex] {x}^{2} + 8x = 9[/tex]Check](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/JxDnsIDg3BoMiMgwI5sDBo56Xiuol3rn.png)
Answers
Given:
There are given the equation:
\(x^2+8x=9\)
Explanation:
According to the question:
We need to find the solution to the given quadratic.
Then,
To find the solution, we will use the quadratic equation formula.
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)Then,
From the equation:
\(x^2+8x-9=0\)Where,
\(a=1,b=8,c=-9\)Then,
Put all the value into the formula:
\(\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-8\pm\sqrt{(8)^2-4\times1\times(-9)}}{2\times1} \\ x=\frac{-8\pm\sqrt{64+36}}{2} \end{gathered}\)Then,
\(\begin{gathered} x=\frac{-8\pm\sqrt{64+36}}{2} \\ x=\frac{-8\pm\sqrt{100}}{2} \\ x=\frac{-8\pm10}{2} \end{gathered}\)Then,
\(\begin{gathered} x=\frac{-8\pm10}{2} \\ x=-\frac{8+10}{2},\frac{-8-10}{2} \\ x=\frac{2}{2},\frac{-18}{2} \\ x=1,-9 \end{gathered}\)Therefore, the solution of the given quadratic equation:
\(x=1,-9\)Final answer:
Hence, the correct options are B and E.
Evaluate the expression for x = 6.
12 + 2x -
5
O A. 19
O B. 79
O C. 14
O D. 54
Answers
Trevor is making payments on a car that costs 26,555 dollars. He makes 36 equal payments. If he rounds the equal payments up to the nearest whole dollar, about how much will he overpay after 36 months? Explain.
Answers
Answer:
$13 overpayment
Step-by-step explanation:
We can find the amount Trevor should pay each month by dividing the $26,555 by 36 months:
($26,555/(36 months)) = $737.64 per month
Since Trevor decide to round up to the nearest dollar, he will pay $738 each month. That's an overpayment of $0.361 each month.
After 36 months of overpaying by $0.361 each month, Trevor will have overpaid:
($0.36/month)*(36 months) = $13 overpayment
Need help ASAP! will give brainliest!
Answers
Answer:
first one.
Step-by-step explanation:
the slope of the line is the rise over run, in triangle STU this is 3 over 2
in triangle FED this is 6 over 4, which simplifies to 3 over 2
proving that the slope of the line is constant.
we can buy 32 ounces of lemonade for $6.08 How much does it cost per ounce.
Answers
Answer: $0.19
Step-by-step explanation: divide 32 by $6.08
Using complete sentences, describe the error in the steps used to solve the equation. There will be no problems that don’t have an error.
“The error was made when.....”
Answers
Answer:
I believe that the error is that sqrt(-2) should be equal to sqrt(2) * i
Step-by-step explanation:
The rest of the steps all use proper algebraic rules, but the square root of a*b = sqrt(a)*sqrt(b)
Using suitable identity, find the value of 87^3+ 13^3/
87^2 −87 ×13 + 13^2
Answers
The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.
We will first calculate the numerator:
As (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :
\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))
= 100(\(87^2\) - 87 * 13 + \(13^2\))
Now, calculate the denominator:
\(87^2 - 87 * 13 + 13^2\)
As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):
\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)
\(= 74^2\)
So by solving the equation further:
\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)
As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:
\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)
So, the value of the given expression is 100.
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A graphing calculator is recommended. Find the maximum and minimum values of the function. (Round your answers to two decimal places.) y = sin x + sin 2x maximum value minimum value
Answers
The maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.
To find the maximum and minimum values of the function y = sin x + sin 2x, we can first take its derivative with respect to x:
y' = cos x + 2 cos 2x
Then, we can set y' equal to zero and solve for x:
cos x + 2 cos 2x = 0
We can use a graphing calculator to find the solutions to this equation, which are approximately x = 0.285 and x = 2.857. We can then evaluate the original function at these values to find the maximum and minimum values:
y(0.285) ≈ 1.724
y(2.857) ≈ -1.724
Therefore, the maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.
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There are three numbers: 4, 26 and 18. A fourth number creates a group average of 12. What is this fourth number
Answers
The fourth number that will create a group average of 12 for the numbers 4, 26 and 18 is 0.
To solve this problem, you will need to use the formula for calculating the average or arithmetic mean. You can calculate the average of a group of numbers by adding them together and then dividing the sum by the number of numbers in the group.
There are three numbers: 4, 26 and 18. To find the fourth number that will create an average of 12 for the four numbers, we can use the formula for calculating the average. We can write this formula as:
(4 + 26 + 18 + x) / 4 = 12
where x is the fourth number we need to find.
To solve for x, we can multiply both sides of the equation by 4 to eliminate the fraction:
4 + 26 + 18 + x = 48
Then, we can simplify the left side by combining like terms:
48 + x = 48
Finally, we can solve for x by subtracting 48 from both sides of the equation:
x = 0
Therefore, the fourth number is 0.
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What percentage of the area under the normal curve lies to the right of μ + 3σ (use 2 decimal places. )?
Answers
The approximately 0.13% of the area under the normal curve lies to the right of μ + 3σ.
To determine the percentage of the area under the normal curve that lies to the right of μ + 3σ, where μ is the mean and σ is the standard deviation, we can use a standard normal distribution table.
To use a standard normal distribution table, we need to standardize the value μ + 3σ by subtracting the mean and dividing by the standard deviation. This gives us:
(μ + 3σ - μ) / σ = 3
So, we are looking for the area to the right of 3 standard deviations from the mean.
Using a standard normal distribution table, we can find that the area to the right of 3 standard deviations from the mean is approximately 0.0013, or 0.13% (rounded to 2 decimal places). This means that 0.13% of the area under the normal curve lies to the right of μ + 3σ.
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Please help I’m extremely confused!!!! (Worth 40 points)
Answers
Answer:
0.025
Step-by-step explanation:
Answer:
0.029
Step-by-step explanation:
1 milligram is equivalent to 0.001 grams, so 29*0.001=0.029.
Evaluate the expression when c=−4 and y=2
-y+4c
Answers
Answer:
-2 - 16 = -18
Step-by-step explanation:
-y+4c
You take the values for c and y and substitute them in the original equation.
It would then look like:
-(2) + 4(-4)
Solving that would be -2 -16 = -18
Answer:
-18
Step-by-step explanation:
-(2)+4(-4) Plug in the values of y and c.
-2+(-16) Simplify.
-2-16
-18
Hope this helps you out!! Have an amazing day <3
i need this asap so can someone answer
Answers
0.2
0.2y+0.4
I think this should be correct
Two surfaces are called orthogonal at a point of intersection P if their normals are perpendicular atthat point.Show that surfaces with equations F(x; y; z) = 0 and G(x; y; z) = 0 are orthogonal at a point Pwhere gradient of F = not equal to 0 and gradient of G is not equal to 0 if and only ifFxGx + FyGy + FzGz = 0 at P :use the above to show that z^2=x^2+y^2 and x^2+y^2+z^2=r^2 are orthogonal on every point of intersection.
Answers
by using the condition for orthogonality between surfaces and applying it to the given equation \(z^{2}\) = \(x^{2}\) + \(y^{2}\) and \(x^{2}\) + \(y^{2}\) + \(z^{2}\) = \(r^{2}\) are orthogonal at every point of intersection.
Let's consider the surfaces F(x, y, z) = 0 and G(x, y, z) = 0, where the gradients of F and G are non-zero at the point of intersection P. To prove that the surfaces are orthogonal at P, we need to show that their dot product, FxGx + FyGy + FzGz, is equal to zero at P.
The dot product of the gradients can be written as FxGx + FyGy + FzGz. If this expression evaluates to zero at P, it implies that the gradients are perpendicular, and therefore the surfaces are orthogonal at P.
Now, let's apply this result to the surfaces \(z^{2}\) = \(x^{2}\) + \(y^{2}\) and \(x^{2}\) + \(y^{2}\) + \(z^{2}\) = \(r^{2}\). Taking the gradients of these surfaces, we find that the dot product FxGx + FyGy + FzGz is equal to 2\(z^{2}\) + 2(\(x^{2}\) + \(y^{2}\) + \(z^{2}\)), which simplifies to 3\(z^{2}\) + 2(\(x^{2}\) + \(y^{2}\)).
Since this expression is equal to zero for all points (x, y, z) satisfying the equation of the second surface, \(x^{2}\) + \(y^{2}\) + \(z^{2}\) = \(r^{2}\), we can conclude that the surfaces \(z^{2}\) = \(x^{2}\) + \(y^{2}\) and \(x^{2}\) + \(y^{2}\)+ \(z^{2}\) = \(r^{2}\) are orthogonal at every point of intersection
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Can someone help me out please please
Answers
To answer this question we will use the following property of logarithms:
\(\ln a^b=b\ln a.\)Dividing the given equation by 4 we get:
\(\frac{4*8^x}{4}=\frac{11.48}{4}.\)Simplifying the above result we get:
\(8^x=2.87.\)Applying the natural logarithm we get:
\(\ln8^x=\ln2.87.\)Applying the property of logarithms we get:
\(x\ln8=\ln2.87.\)Therefore:
\(x=\frac{\ln2.87}{\ln8}\approx0.51.\)Answer: Option D.
write an equation for a line with a slope of 2, through (4,-2) in standard form
Answers
Answer:
y = 2x - 10
Step-by-step explanation:
\(y=mx+b\)
\(y=2x+b\)
\(-2=2(4)+b\)
\(-2=8+b\)
\(b=-2-8\)
\(b=10\)
\(y=2x-10\)
Equation:
\(\sf{y = 2x - 10}\)
Explanation:
First, I will write the equation in point slope:
\(\sf{y-y_1=m(x-x_1)}\)
Where:
m = slopePlug in the data:
\(\sf{y-(-2)=2(x-4)}\)
\(\sf{y+2=2(x-4)}\\\sf{y+2=2x-8}\\\sf{y=2x-8-2}\\\sf{y=2x-10}\)
Hence, the answer is y = 2x - 10.
Jamal is a real estate agent who earns a 4.5% commission on her sales. If she sells a home worth $250,000, what is her commission?
A) $10,450
B) $11,250
C) $12,150
D) $12,850
Answers
Answer:
B 11,250
Step-by-step explanation:
Answer:
11,250
Step-by-step explanation:
4. Explain how to show that the line through points A(-2,-5) and B(-1,5) is parallel to the line that represents
the equation y=10x + 12.
Answers
Find the slope of points A and B
(y2 - y1)/ (x2-x1)
(5-(-5))/(-1-(-2)) = (5+5)/(-1+2) = 10/1
The slope of the points is 10
In the equation
y = 10x + 12
Y = mx + b, m indicating slope
The slope of the equation is also 10
Because both slope is 10, the line through the points and the equation is parallel
Consider this system of equations.
p=2n
p-5 = 1. 5n
What value of n makes the system of equations true?
Enter your answer in the box.
Answers
Therefore, the value of n that makes the system of equations true is n = 10.
Given:
p = 2n
p - 5 = 1.5n
Substituting the value of p from the first equation into the second equation, we have:
2n - 5 = 1.5n
Next, we can solve for n by subtracting 1.5n from both sides of the equation:
2n - 1.5n - 5 = 0.5n - 5
Simplifying further:
0.5n - 5 = 0
Adding 5 to both sides of the equation:
0.5n = 5
Dividing both sides by 0.5:
n = 10
Therefore, the value of n that makes the system of equations true is n = 10.
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FIRST TO ANSWER WILL GET BRAINLIEST!
Answers
Answer:
I think your answer would be 12x - 2
If this is wrong then im sorry
Answer:
12x-2
Step-by-step explanation:
5x+1=JK
7x-3=KL
JL= JK + KL
= 5x+1+7x-3
=12x-2
therefore JL = 12x-2
First she need to find her resting heart rate by counting her pulse for one minute immediately after she wakes up for 5 days in a row. she finds her average resting heart rate to be 62 after 5 days and she remembers the last day pulse was 58 and all the others were the same
Answers
Answer: 63 She finds her average resting heart rate to be 62 after 5 days. That means, average of the 5 heart rate pulse=62 If the last day was 58 and all the other days were the same.
Step-by-step explanation
Line f passes through 4, 0) and is parallel to a line that passes through (7, -3) and (-10. -2)
Answers
A straight line can be written in the form of a two variable linear equation.
The equation of line passing through point (4,0) is y = -1 / 17 x + 4.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
Given that,
The line is passing through the point (4,0).
It is parallel to the line passing through (7, -3) and (-10. -2).
The slope of the line passing through (7, -3) and (-10. -2) is
m₁ = (-2-(-3)) / (-10 - 7)
m₁ = - 1 / 17
Since the slope of two lines parallel to each other is equal, the slope of the line passing through point (4,0) is - 1 / 17.
Thus, the equation of line passing through point (4,0) can be written as,
(y - 4) / (x - 0) = - 1 / 17
=> y = -1 / 17 x + 4
Hence, the equation of the given line is y = -1 / 17 x + 4.
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The radius of a baseball is about 9.25 inches. The radius of the Basketball is 9.55 inches. What is the
difference of the volumes between the basketball and baseball?
331.55
2734.89
333.14
364.52
Answers
Answer:
C. 333.14
Step-by-step explanation:
Both the basketball and baseball has got the shape of a sphere. So that;
volume of a sphere = \(\frac{4}{3}\)\(\pi\)\(r^{3}\)
where r is the radius
i. Volume of the baseball = \(\frac{4}{3}\)\(\pi\)\(r^{3}\)
= \(\frac{4}{3}\) x \(\frac{22}{7}\) x \((9.25)^{3}\)
= 3315.5655
volume of the baseball = 3316.57 cube inches
ii. Volume of the basketball = \(\frac{4}{3}\)\(\pi\)\(r^{3}\)
= \(\frac{4}{3}\) x \(\frac{22}{7}\) x \((9.55)^{3}\)
= 3649.8372
Volume of the basketball = 3649.84 cube inches
The required difference = volume of basketball - volume of baseball
= 3649.84 - 3316.57
= 333.27 cube inches
The difference of the volumes of the basketball and baseball is 333.27 cube inches.
how many cubic centimeters are in 2.11 yards^3
Answers
Answer: 2.11 yd³ = 1613210.750364 cm³
Step-by-step explanation:
Answer:
Step-by-step explanation:
To convert cubic yards to cubic centimeters, you can use the following conversion factors:1 yard = 91.44 centimeters
1 cubic yard = (91.44 centimeters) x (91.44 centimeters) x (91.44 centimeters) = 7,645,549.23 cubic centimetersTherefore, to convert 2.11 cubic yards to cubic centimeters, you can multiply it by the conversion factor:2.11 cubic yards x 7,645,549.23 cubic centimeters/cubic yard ≈ 16,120,247.02 cubic centimetersSo, 2.11 yards^3 is approximately equal to 16,120,247.02 cubic centimeters.
Karen's penny bank is 3/4 full. After she removes 280 pennies, it is 1/2 full. How many pennies can Karen's bank hold?
Answers
Hope this helps!
Simplify: (4x4y3)(4x4)
Answers
Answer:
16x⁸y³
Step-by-step explanation:
You want to simplify (4x⁴y³)(4x⁴).
Rules of exponentsThe relevant rule of exponents is ...
(a^b)(a^c) = a^(b+c)
SimplificationThe simplified form is ...
\((4x^4y^3)(4x^4) =(4\cdot4)x^{4+4}y^3=\boxed{16x^8y^3}\)