Joe strung a 12-yard rope from the bottom of one flagpole to the top of another. Hemeasured the angle of elevation of the rope as 38°. What is the distance between thetwo flagpoles in yards? Round to the nearest tenth.
Answers
the triangle
cos (38º) = adjacent side / hypotenuse
adjacent side = cos(38º) * hypotenuse
adjacent side = cos(38º) * 12- yard
adjacent side = 9.4561
Rounded to the nearest tenth
adjacent side = 9.5
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Answer
the distance between the two flagpoles is 9.5 yards
Related Questions
How many different ways can you arrange 5 people at a table
Answers
The number of ways n people can arrange at table is,
[tex]n![/tex]Determine the number of ways for 5 people arrange at a table (non-circular).
[tex]\begin{gathered} 5!=5\cdot4\cdot3\cdot2\cdot1 \\ =120 \end{gathered}[/tex]Answer: 120
Factor the polynomial F(x) = x^3 − x^2 − 4x + 4 completely. Lesson 5.4.1Part I: Find and list all the possible roots of F(x) (pq) Show your work. Part II: Use the Remainder Theorem to determine at least one of the roots of F(x) from Part I. Show your work.Part III: Find the remaining factors F(x) = x3 − x2 − 4x + 4 completely. Show your work.
Answers
Given
[tex]x^3−x^2−4x+4[/tex]EXPLANATION
Part 1: Since the constant in the given equation is 4,the integer root must be a factor of 4. The possible values are
Answer:
[tex]\pm1,\pm2,\pm4[/tex]Part 2: The remainder theorem says when a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k). In this case for one of the possible values to be a root, it must give a zero result when inserted in the original expression.
Therefore,
[tex]\begin{gathered} when\text{ }x=1 \\ f(1)=1^3-(1)^2-4(1)+4=1-1-4+4=0 \\ when\text{ }x=2 \\ f(2)=2^3-(2)^2-4(2)+8=8-4-8+4=0 \end{gathered}[/tex]Answer: Therefore, 1 and 2 are roots of the polynomial
Part 3:
Let the last factor of the polynomial be ax+b
Therefore,
[tex]\begin{gathered} (x-1)(x-2)(ax+b)=x^3-x^2-4x+4 \\ By\text{ comparison of terms} \\ ax^3=x^3 \\ \therefore a=1 \\ Also \\ 2b=4 \\ b=\frac{4}{2}=2 \end{gathered}[/tex]The factors of the equation are therefore;
Answer: (x-1)(x-2)(x+2)
Giving a test to a group of students, the grades and gender are summarized below If one student was chosen at random, find the probability that the student was male Give your answer as a fraction or decimal.
Answers
we have that
total students=47
total Male=20
therefore
The probability is equal to
P=20/47x - 12 = 0.5 (x - 4)
Answers
The equation to solve is:
[tex]x-12=0.5(x-4)[/tex]We can use the distributive property on the right hand side to simplify.
The distributive property is:
[tex]a(b-c)=ab-ac[/tex]Using the property, we have:
[tex]\begin{gathered} x-12=0.5(x-4) \\ x-12=0.5(x)-0.5(4) \\ x-12=0.5x-2 \end{gathered}[/tex]Now, we can simply do some algebra and solve for x. The steps are shown below:
[tex]\begin{gathered} x-12=0.5x-2 \\ x-0.5x=-2+12 \\ 0.5x=10 \\ x=\frac{10}{0.5} \\ x=20 \end{gathered}[/tex]The answer is:
x = 20Find the surface area of a cylinder with radius 7 and height 5.
Answers
We have, The general formula for the total surface area of a cylinder is:
[tex]\begin{gathered} A=2\pi rh+2\pi r^2 \\ \end{gathered}[/tex]where r = radius and h = height
Therefore:
[tex]\begin{gathered} A=2\pi(7)(5)+2\pi(7)^2 \\ A=2\pi(35)+2\pi(49) \\ A=70\pi+98\pi \\ A=168\pi \\ A=168(3.14)=527.52 \end{gathered}[/tex]Answer: surface area = 527.52
Help with homework please .Part 2. Find the mass of the pyramid in grams.
Answers
Given:
• Side length of base = 18.2 centimeters
,• Height of pyramid = 23.1 centimeters
,• Mass of pyramid = 2.75 kilograms
Let's find the volume of the pyramid.
To find the volume of the pyramid, apply the formula:
[tex]V=a^2\times\frac{h}{3}[/tex]Where:
a is the side length of the base = 18.2 cm
h is the height = 23.1 cm
Input values into the formula and solve for the volume, V.
[tex]\begin{gathered} V=18.2^2\times\frac{23.1}{3} \\ \\ V=331.24\times7.7 \\ \\ V=2550.55cm^3 \end{gathered}[/tex]Therefore, the small solid pyramid has a volume of approximately 2550.55 cubic centimeters.
• Part 2.
Find the mass of the pyramid in grams.
Given the mass = 2.75 kilograms
To find the mass in grams, apply the standard unit of measurement.
Where:
1 kilogram = 1000 grams
Thus, we have:
[tex]2.75kg=2.75\times1000=2750\text{ grams}[/tex]Therefore, the mass in grams is 2750 grams.
• Part 3.
Let's find the density of the pyramid in grams per cubic centimeter.
To find the density, apply the formula:
[tex]density=\frac{mass}{\text{volume}}[/tex]Thus, we have:
[tex]\begin{gathered} density=\frac{2750\text{ }}{2550.55} \\ \\ \text{density}=1.08\text{ g/}cm^3 \end{gathered}[/tex]Therefore, the density is 1.08 grams per cubic centimeter.
ANSWER:
Part 1: 2550.55 cubic centimeters
Part 2: 2750 grams
Part 3: 1.08 grams per cubic centimeter.
4) Find AC A 4 B 3 C 12 d 16
Answers
We can see from the question that these two triangles are similar since the sides have a ratio of 2/1.
The triangle VUB is similar to triangle CAB. The sides of the triangle VUB are half of the triangle CAB (or the sides of triangle CAB double in measure of the triangle VUB). Then, we can have the next proportions:
[tex]\frac{BC}{BV}=\frac{BA}{BU}=\frac{AC}{UV}=2\Rightarrow AC=2\cdot UV\Rightarrow AC=2\cdot6\Rightarrow AC=12[/tex]Therefore, AC is equal to 12 units (option C).
- Determine which point is a solution to the following system of equations: x + y = -4 -2x - 2y = 6 a) (-5,1) b) (0, -3) c) There are infinite solutions. d) There is no solution.
Answers
there is no solution (option D)
Explanation:x + y = -4 ...equation 1
-2x - 2y = 6 ...equation 2
using elimination method:
let's eliminate y. Multiply equation 1 by 2 so the coefficient of y are the same:
2x + 2y = -8 ...equation 1
-2x - 2y = 6 ...equation 2
Add equation 1 and 2:
2x + (-2x) + 2y + (- 2y) = -8 + 6
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
2x - 2x + 2y - 2y = -2
0 + 0 = -2
0 = -2
left side not equal to right side of the equation
When the left hand side of the equation has a different number from the right hand side of the equation, we say there is no solution (option D)
When dividing polynomials if the remainder is zero (no remainder) then the divisor is a factor. Use synthetic division to determine if the first expression is a factor of the second expression:First expression: x- \frac{1}{2} Second expression: 2x^4-x^3+2x-1 If it is a factor then just type the quotient as the answer. If it is not a factor then just type "no". Be sure to type your answer in descending powers of x with now spaces between your terms. Use the "^" key (shift+6) to indicate a power/exponent.Answer:
Answers
Then the quotient is:
2x² + 2
The dot plot below represents the number of goals scored by the girls' soccer team in every game so far this season.
Answers
The median is 1 goals
Explanation:The goals scored are:
0, 0, 1, 1, 1, 1, 3, 3, 4, 5, 5
The median number of goals scored is 1
Kawika is a woodworker, and he carves a block in the shape of a rectangular prism. What is the total surface area of the block
Answers
Surface Area of a Right Traingular Prism is = bh + L(S1 + S2 + h)
from the question given
h = 5,
S1 = 12 = b
S2 = 13
L =10
= bh + L(S1 + S2 + h)
= 12(5) + 10(12 + 13 + 5)
= 60 + 10(30)
=60 + 300
=360
From the shape
The Triangle side Area = 1/2 X B X H
=1/2 X12 X 5 = 30
we have two faces of the triangle = 2x 30 = 60
For the Top side = 10 X 13 = 130
for the base/floor = 12 x 10 = 120
for the back end side = 5 x 10 = 50
Total = 60 + 130 + 120 +50
=360
Domain of f(x)=2/(3x+4)
Answers
Answer:
[tex](-\infty,-\frac{4}{3})\cup(-\frac{4}{3},\infty)[/tex]Explanation:
Given f(x) defined below:
[tex]f\mleft(x\mright)=\frac{2}{3x+4}[/tex]The domain of f(x) is the set of the values of x for which f(x) is defined.
Find the excluded values, the values at which f(x) is undefined. To do this, set the denominator equal to 0 and solve for x.
[tex]\begin{gathered} 3x+4=0 \\ 3x=-4 \\ x=-\frac{4}{3} \end{gathered}[/tex]The excluded value of the domain is -4/3.
Therefore, the domain of f(x) is:
[tex](-\infty,-\frac{4}{3})\cup(-\frac{4}{3},\infty)[/tex]The graph below shows a linear relationship. The points shown have whole-number coordinates. 9 8 7 6 5 -1 1 3 1 2 3 4 5 6 7 8 9 0 1 2 -3 4 5 -6 -7 8 9
Answers
Answer
The linear relationship between y and x is
y = (2x/3) + 2
Explanation
This is a straight line, that we can just solve for the linear relationship by solving the equation of this straight line.
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line.
So, we just need to solve for the slope and the y-intercept.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-3, 0) and (0, 2)
[tex]\text{Slope = }\frac{2-0}{0-(-3)}=\frac{2}{0+3}=\frac{2}{3}[/tex]Then, the y-intercept is where the line crosses the y-axis
c = y-intercept = 2
y = mx + c
y = (2/3)(x) + 2
y = (2x/3) + 2
Hope this Helps!!!
A normally distributed data set has u = 22 and 0 = 1.5. What would be the value of an element of his data setwith a Z-score = 2?
Answers
Ok, we have to find the value according with the following:
z-score=2
Standard desviation (σ)= 1.5
mean (μ)=22
Now, we need clear the value (x) in the following equation:
[tex]z-\text{score}=\frac{(x-\mu)}{\sigma}[/tex][tex](z-\text{score }\cdot\sigma)=x-\mu[/tex][tex](z-score\cdot\sigma)+\mu=x[/tex]Now, replacing the values, we have:
[tex]x=(2\cdot1.5)+22=3+22=25[/tex]So, finally we got that the value of the element is: 25.
Solve for v2(v-8)+3v=-31Simplify your answer as much as possible
Answers
Answer: v = -3
Given:
[tex]2\left(v-8\right)+3v=-31[/tex]-Distribute 2(v-8):
[tex]\begin{gathered} 2\left(v-8\right)+3v=-31 \\ \Rightarrow2v-16+3v=-31 \end{gathered}[/tex]-Combine like terms:
[tex]\begin{gathered} \begin{equation*} 2v-16+3v=-31 \end{equation*} \\ \Rightarrow2v+3v=-31+16 \\ \Rightarrow5v=-15 \end{gathered}[/tex]-Divide both sides by 5:
[tex]\begin{gathered} \begin{equation*} 5v=-15 \end{equation*} \\ \Rightarrow\frac{5v}{5}=\frac{-15}{5} \\ \Rightarrow v=-3 \end{gathered}[/tex]Therefore, v=-3
If you have 100% of something, then you have the _________ amount or ____ .
Answers
If you have 100% of something, then you have the total amount or whole .
Mr. Rodriguez compared test scores with the amount of students over the past two years.Last YearThis YearninTest ScoresTest ScoresWhich summary statistics should be used to compare the two data sets and why?А.The median and the interquartile range because the data sets are normally distributed.B. The median and the interquartile range because the data sets are skewed.C.The mean and the standard deviation because the data sets are normally distributedD. The mean and the standard deviation because the data sets are skewed.
Answers
First we notice that the data is skewed, we know that in this situation it is better to use the median than the mean. Hence:
B. The median and the interquartile range because the data sets are skewed.
Hello, I could really use the help with this question, your help would be very helpful. This help is much appreciated.
Answers
In order to calculate the function that represents the total amount of money she will have in her bank account, we need to multiply the initial amount of money (given by the function h(x)) by the interest rate (given by the function s(x)), so we will have:
[tex]\begin{gathered} \text{Money}=h(x)\cdot s(x) \\ \text{Money}=200\cdot(1.05)^{x-1} \end{gathered}[/tex]Find f'(x).f(x) = x2 - 6x - 4x-2 + 3x-3f'(x) =
Answers
Given the function
[tex]f(x)=x^2-6x-4x^^{-2}+3x^{-3}[/tex]f'(x) is given by
[tex]f^{\prime}(x)=2x-6+8x^{-3}-9x^{-4}[/tex][tex]f^{\prime}(x)=2x-6+8x^{-3}-9x^{-4}[/tex]given ΔNOP ~QRP. enter segments in tye blanks provided that would results in a true equation
Answers
We have that triangles NOP and QRP are similar; therefore, the ratio between their correspondent sides is constant. This is
[tex]\frac{NO}{QR}=\frac{OP}{RP}=\frac{PN}{PQ}[/tex]Therefore, the answers are OP/RP or PN/PQ, any of those is correct.
Give the equation of a circle with a diameter that has endpoints (-6, 0) and (0,0). Question Help: D Video
Answers
Answer:
[tex](x+3)^2+(y)^2=3^2[/tex]Step-by-step explanation:
Given the endpoints of the diameter, then the center of the circle is in the middle of the diameter:
The middle point is given as:
[tex]\text{ Mid point= (}\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Therefore, the center of the circle is located at:
[tex]\begin{gathered} \text{Center}=\text{ (}\frac{-6+0}{2},\frac{0+0}{2}) \\ \text{ Center=(-3, 0)} \end{gathered}[/tex]The circle is represented by the following equation:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (h,k)\text{ center} \end{gathered}[/tex]By substituting (h,k) and (x,y) (one of the given points), we can solve for r, to find the radius:
[tex]\begin{gathered} (0-(-3))^2+(0-0)^2=r^2 \\ 9=r^2 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Then, this circle is represented by the following equation:
[tex](x+3)^2+(y)^2=3^2[/tex]10. Solve the equation y * 2x for x
Answers
we have
y=2x
solve for x
that means
Isolate the variable x
so
step 1
Divide by 2 both sides -----> by division property of equality
[tex]\begin{gathered} \frac{y}{2}=\frac{2x}{2} \\ \\ \frac{y}{2}=x \\ \text{rewrite} \\ x=\frac{y}{2} \end{gathered}[/tex]the answer isx=y/2Solve the system by substitution:y=2 -3x-4y=1
Answers
Given:
The equation is -3x-4y=1.
The value of y is 2.
The objective is to solve the equation.
The equation can be solved by substituting the value of y.
[tex]\begin{gathered} -3x-4y=1 \\ -3x-4(2)=1 \\ -3x-8=1 \\ -3x=1+8 \\ -3x=9 \\ x=\frac{9}{-3} \\ x=-3 \end{gathered}[/tex]Hence, the value of x is -3 and the value of y is 2.
Evaluate each expression if r=2, =-3, and t = 5.17. 2r + 3t18. 4 s – 3r19. rst – st
Answers
Answer
17) Answer = 19
18) Answer = -18
19) Answer = -15
Explanation
We are asked to evalute the expressions if
r = 2, s = -3 and t = 5
17) 2r + 3t
r = 2, t = 5
2r + 3t
= 2(2) + 3(5)
= 4 + 15
= 19
18) 4s - 3r
s = -3, r = 2
4s - 3r
= 4(-3) - 3(2)
= -12 - 6
= -18
19) rst - st
r = 2, s = -3, t = 5
rst - st
= (2)(-3)(5) - (-3)(5)
= -30 - (-15)
= -30 + 15
= -15
Hope this Helps!!!
question below You are taking a 18 question multiple choice test, where each question has 5 possible answers. Identify n and p. Write p as a fraction, n 18 р 1 5 I Find the mean and standard deviation of the binomial random variable. Write your answers as a fraction, expression or decimal with at least 4 decimal places, 3.6 og 1.697 1.6970562748477 What would be an unusually high number of correct questions? I am still struggle how to find this question Give your answer in the box above as a whole number. x or more correct.
Answers
EXPLANATION
Number of questions in the test = 18
Number of possible answers = 5
n represent the number of questions and p represent the possible answers p.
n-----> number of questions
p ----> possible answers
The unusually high number is 8 or more.
what will be the results if the y-intercepts of the line shown is changed to an 8, but the slope remains the same? select one of the option from each set to complete the sentence
Answers
Given that the new line will have the same slope, it will be parallel to the line in the graph.
Given that the new y-intercept is 2 units down respect the y-intercept of the line in the graph, then the new line will be translated 2 units down
One of the fastest computers in the world can work 4.0 x 10^10 operations per second. Which of the following represents this number in standard notation? O A. 4,000,000,000 OB. 0.0000000004 O C. 0.00000000004 OD. 40,000,000,000
Answers
we must multiply 4 times 10^10. It yields,
[tex]\begin{gathered} 4\cdot10^{10}=4\cdot10000000000 \\ 4\cdot10^{10}=40000000000 \end{gathered}[/tex]Hence, the answer is D.
to find y, if m=6, x=3, and b=5. y=mx+b
Answers
Answer:
y = 23
Explanation:
We're asked to write an equation in the form:
[tex]y=mx+b[/tex]Where:
x = 3
m = 6
b = 5
Then:
[tex]y=6\cdot3+5=18+5=23[/tex]Find the perimeter. Simplify your answer.C+6c+6C+2Submit
Answers
The perimeter of a figure is the sum os the length of the sides of the figure. In this case, you have algebraic expressions for the length of the sides, then, sum the given expressions, as follow:
p = (c + 6) + (c + 6) + (c + 7)
cancel out parentheses:
p = c + 6 + c + 6 + c + 7
simplify like terms:
p = c + c + c + 6 + 6 + 7
p = 3c + 19
Hence, the perimeter of the given figure is 3c + 19
Can you please help me please with a b c d and e
Answers
Given the shape of the triangular prism
We will find the relation between the line segments
1) AB and BC intersecting
2) AE and BF are parallel
3) EF and AD are skew
4) plane ABC and plane ABF are intersecting
5) plane AED and plane BFC are parallel