From the entrance, most people will go straight to the roller coaster or straight to the tower. The distance from the entrance to the roller coaster is 461m, and the distance from the entrance to the tower is 707 m. If the paths to these two attractions are separated by a 41o angle, how far apart are the roller coaster and the tower?
Answers
The given situation can be illustrated as follow:
In order to determine the distance x between the roller coaster and the tower. Use the law of cosines, as follow:
[tex]x^2=(461)^2+(707)^2-2(461)(707)\cos 41[/tex]By simplifying the previous expression, you obtain:
[tex]\begin{gathered} x^2=220409.5413 \\ x=\sqrt[]{220409.5413} \\ x\approx469.5 \end{gathered}[/tex]Hence, the distance between the tower and the roller coaester is approximately 469.5m
Related Questions
Select the values that make the inequality m≥7 true.
(Numbers written in order from least to greatest going across.)
Answers
Step-by-step explanation:
every number greater than or equal to 7.
just as the expression says.
are we taking only about integer values ?
so,
7, 8, 9, 10, ... +infinity
if we aim for radical or real values, then starting with 7 everything between these numbers.
the interval definition is
[7, +infinity)
please note the different brackets.
"[" or "]" means the interval end value is included.
"(" or ")" means the interval end value is excluded.
which is the normal thing for infinity, because infinity is only a concept and never a number. so, it cannot be included.
PLEASE HELP!!
An ice cube is freezing in such a way that the side length s, in inches, is s of t equals one half times t plus 4 comma where t is in hours. The surface area of the ice cube is the function A(s) = 6s2.Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points)
Answers
Answer:
A(t) = 3/2t² + 24t + 96
Range = (96, ∞)
Explanation:
The equation for the side length of the cube s is given by
[tex]s(t)=\frac{1}{2}t+4[/tex]Where t is the number of hours. In the same way, the equation for the surface area is:
[tex]A(s)=6s^2[/tex]Then, the surface area as a function of time will be the composite function A(s(t)). So, replacing s by the equation of s(t), we get:
[tex]\begin{gathered} A(s(t))=6s(t)^2 \\ A(s(t))=6(\frac{1}{2}t+4)^2 \\ A(t_{})=6(\frac{1}{4}t^2+2(\frac{1}{2}t)(4)+4^2) \\ A(t)=6(\frac{1}{4}t^2+4t+16) \\ A(t)=6(\frac{1}{4}t^2)+6(4t)+6(16) \\ A(t)=\frac{3}{2}t^2+24t+96 \end{gathered}[/tex]Then, the range is the set of all the possible values that A(t) can take. Since t takes values greater than or equal to 0, the minimum value that A(t) will take is 96 because:
A(0) = 3/2(0)² + 24(0) + 96 = 96
Therefore, the range for the surface area will be (96, ∞)
Estimating which integers are between square roots- please explain the steps!
Answers
Hello there. To solve this question, we want to determine how to find the square root of a value using estimations.
Given a number m, we want to determine an estimation for its square root:
[tex]\sqrt{m[/tex]In this case, we have to find the closest integers to m, considering it is not a perfect square and is positive (greater than zero).
Of course, zero is the trivial case, since every square root is bounded below by zero.
For this, consider the function:
[tex]\lfloor m\rfloor[/tex]It is the floor function and it gives us the nearest integer that is less than or equal to m.
We do the same to fi
Pretty please help!!!If x= -3, which number line shows the value of |x|?
Answers
it is given that
x = -3
now
IxI = I-3I = 3
so
IxI = 3
so the correct answer is option C
Evaluate the following expression.x³ when x = 5
Answers
Given x^3, set x=5 and find the corresponding value, as shown below
[tex]\begin{gathered} x=5 \\ \Rightarrow x^3=5^3=5*5*5=25*5=125 \end{gathered}[/tex]Thus, the answer is 125find X and Y so that the quadrilateral is a parallelogram 5y 5x 25
Answers
x=31
y=5
Explanation
Step 1
if the green angles are equal and the blue angles are equal, then
is is a parallelogram, then
[tex]\begin{gathered} green\text{ angle} \\ 5y=25 \\ \\ y=\frac{25}{5} \\ \\ y=5 \end{gathered}[/tex]Step 2
blue angles
we do not have the value for the last angle, but we know
" the sum of the internal angles of a quadrilateral = 360
replacin
2 green angles +1 blue angle+5x=360
2*5y+5x+5x=360
[tex]\begin{gathered} 10y+10x=360 \\ 10x=360-10y \\ x=36-y \\ \text{replace }y=5 \\ x=36-5 \\ x=31 \end{gathered}[/tex]I hope this helps you
5. Is X-1 a factor of x^5+2x^2-1?No, because f(1) = 2.Yes, because f(1) = 3.No, because f(1) = 0.Yes, because f(1) = 0.
Answers
We want to find if x-1 is a factor of
[tex]f(x)=x^5+2x^2-1[/tex]In order to verify that, we must know the last number of the synthetic division of the polynomial divided by x - 1. If it is zero then it is a factor, and if it is not zero then it is not a factor
If we replace x = 1 in the equation we will find that number:
[tex]\begin{gathered} f(x)=x^5+2x^2-1 \\ f(1)=1^5+2\cdot1^2-1 \\ f(1)=1^{}+2^{}-1 \\ f(1)=2 \end{gathered}[/tex]Then the residual of the polynomial divided by x - 1 is 2, then x - 1 is NOT a factor.
Answer: A No, because f(1) = 2.what's the simplest form to represent the area of a rectangular building that's 2y feet and the length to be 9y-4
Answers
The area of a rectangle is given by the formula:
[tex]A=lw[/tex]Where
A is area
l is length
w is width
We find the expression for the area by multiplying the two "lengths" given:
[tex]\begin{gathered} A=2y(9y-4) \\ A=18y^2-8y \end{gathered}[/tex]The answer is:
[tex]A=18y^2-8y[/tex]train moves at a constant speed of 8 miles every 6 minutes. Fill in the table below to show how far the train travels according to differentmounts of time.Time (minutes)Distance (miles)31560
Answers
we have the following:
speed 8 miles every 6 minutes:
[tex]s=\frac{8}{6}=1.34[/tex]therefore, the speed is 1.34 mi/m, now to complete it would be:
[tex]\begin{gathered} d=s\cdot t \\ d1=1.34\cdot3=4 \\ d2=1.34\cdot15=20 \\ d3=1.34\cdot60=80 \end{gathered}[/tex]therefore, the answer is:
Time (minutes) Distance (miles)
3 4
15 20
60 80
Yuson must complete 30 hours of community Service. She does two hours each day. Write a linear equation to represent the hours she has left after X days.
Answers
Yuson must complete 30 hours of community service.
She does two hours each day.
We are asked to write a linear equation to represent the hours she has left after x days.
We can write the following linear equation
[tex]30-2x=0[/tex]Where 30 represents the total hours of community service that Yuson has to complete.
2 represents the hours she works each day.
x represents the days.
We can also solve this equation to find how many days will it take her to complete the community service.
What is the measure of angle J in the triangle below? *Hint: Law of Sines*
Answers
SOLUTION:
Using the sine rules;
The equations developed;
[tex]\frac{15}{sin102}=\frac{12}{sinJ}[/tex]Making sinJ the subject;
[tex]\begin{gathered} sinJ=\frac{12sin102}{15} \\ sinJ=0.7825 \\ J=51.49^o \end{gathered}[/tex]Thus, the angle is 51.5 degrees.
On a local sports team, 20% of 50 players are left-handed. How many left-handed are on the team?There is/are ____ left-handed player(s) on the team. (Type a whole number.)
Answers
Answer:
10 left-handed players
Explanation:
The total number of players on the team = 50
We are told that 20% of 50 players are left-handed.
Therefore, the number of left-handed players will be:
[tex]\begin{gathered} =20\%\text{ of 50} \\ =\frac{20}{100}\times50 \\ =\frac{20}{2} \\ =10\text{ players} \end{gathered}[/tex]There are 10 left-handed players on the team.
What do the expanded form and a place- value chart tell you about a number such as 25,049?How are they alike and different
Answers
The expanded form of a number is written out in such a way that you would be able to see the math value of individual digits.
The number 25,049 which reads "twenty five thousand and forty nine," can be written in expanded form as follows;
2 x 10000 = 20,000
5 x 1000 = 5,000
0 x 100 = 0
4 x 10 = 40
9 x 1 = 9
So, as you can see the expanded form shows that the digit 2 (for example) in this number has a value of 20,000.
The place value chart groups the number in threes starting from the right to the left. That is, you count three numbers from the end (right hand side) insert a coma, and take the next three set of digits and so on. You can now tell the value of each digit by starting from the left (the begining) to the right (the end). Usually starting with billions, the chart now tells you the value of each digit. So in this question, you can read from left to right and by using the expanded form, you can tell the value of the 2, the 5, and so on till the last digit.
They are alike because the expanded form helps you determine the actual value of each digit without mistake, and the place value also tells you which number carries what value.
They are different because an expanded form gives you details of how each number gets its place value, while the place value chart simply tells you the value of each digit simply by arranging and inserting comas.
write an equation in slope intercept form of the line that is perpendicular to the line Y equals 1/4 x -9 and passes through 1, 1
Answers
For perpendicularity
[tex]\begin{gathered} \text{slope of line 1 =}\frac{-1}{slope\text{ of line 2}}_{} \\ \text{slope of line 1 = m}_1 \\ \text{slope of line 2 =m}_2 \end{gathered}[/tex][tex]\begin{gathered} \text{Hence,} \\ m_1=\frac{-1}{m_2} \end{gathered}[/tex][tex]\begin{gathered} \text{From the question} \\ m_1=\text{ }\frac{1}{4} \end{gathered}[/tex][tex]undefined[/tex]what is 7.950•100? and how to do it?
Answers
This problem uses the symbol •, which is another symbol to denote multiplication. Also, we are multiplying a decimal to 100. When multiplying such number, we move the decimal place to the right by two since we are multiplying the decimal by 100.
For this problem, we have
[tex]7.950\cdot100[/tex]We are multiplying 7.950 by 100. This means that we move the decimal point two times to the right. Hence, 7.950 multiplied by 100 will yield
[tex]7.950\cdot100=795.0[/tex]Answer: 795.0
cosx-sin^2x-1how do I write the expression in factored form as an algebraic expression of a single trigometric function?
Answers
You use the next trigonometric inentities:
[tex]\begin{gathered} \sin ^2x+\cos ^2x=1 \\ \\ \sin ^2x=1-\cos ^2x \end{gathered}[/tex][tex]\begin{gathered} \cos x-\sin ^2x-1 \\ \\ =\cos x-(1-\cos ^2x)-1 \\ =\cos x-1+\cos ^2x-1 \\ =\cos x+\cos ^2x-2 \\ \end{gathered}[/tex]Common factor cosx:
[tex]=\cos x(1+\cos x)-2[/tex]-3v - 14> 3v+16 It’s for my final review and I’m so confused
Answers
The given inequality is
-3v - 14 > 3v + 16,
Add 3v on both side of the inequality
-3v -14 +3v > 3v +16 +3v
-3v +3v -14 > 3v + 3v + 16
0 - 14 > 6v + 16
Subtract 16 from both side of the equation,
-14 - 16 > 6v + 16 - 16
-30 > 6v + 0
Now subtract 6v from both side,
-30- 6v > 6v - 6v
-6v -30 > 0
Add 30 on both side,
-6v -30 + 30 > 30
-6v > 30
Divide both side by 6:
-6v/6 > 30/6
-v > 5
Multiply both side by (-1)
(-1) (-v) < (-1) 5
v < -5
Thus, v < -5
Answer : v < -5
Answer:
v < -5
Step-by-step explanation:
Add 14 to each side
[tex]-3v-14+14 > 3v+16+14[/tex]
Next, you need to simplify these additions by adding non-variable integers
[tex]16 + 14 = 30\\= 3v + 30\\= -3v > 3v + 30[/tex]
Now, subtract each side by 3v, the leading term in this equation.
[tex]-3v-3v > 3v+30-3v[/tex]
Again, we must simplify to get to the next step. This time we are dealing with a negative minus a negative. There on, things get trickier. In short words, a negative minus a positive is going to have a negative result, because both sides are treated as a negative plus a negative. In an equation, -a - b is the same as -a + -b.
[tex]-3v - 3v = -3v + -3v\\= -6v\\3v + -3v = 3v - 3v\\= 0\\= 0 + 30\\= 30\\= -6v > 30[/tex]
Next, we must multiply both sides by -1. The reason we're multiplying by a negative instead of a positive is because we are reversing the inequality.
[tex]= -6v\times -1 < 30\times 1[/tex]
Notice the change from greater than to less than.
IMPORTANT NOTE: A negative times a negative is a positive, a positive times a positive is also a positive. Lastly, a negative times a positive is a negative.
[tex]-6v\times -1 = 6v\\30\times -1 = -30\\= 6v < -30[/tex]
For the next step, we must divide by 6, because 6 can be divided by 6, and -30 can also be divided by 6 fairly.
[tex]\frac{6v}{6} < \frac{-30}{6}\\\frac{6v}{6} = \frac{6\times v}{6}\\Assume\:v=1!\\= \frac{6\times 1}{6}\\= \frac{6}{6}\\= 1\\= v[/tex]
[tex]\frac{-30}{6}\\\\(-a)/b = (-a/b)\\\\=-\frac{30}{6}\\= -5[/tex]
And therefore, v is less than -5.
If you need anything else, let me know!
Hope this helps!
enter each answer as a whole number the ratio of United States gold-medal to Russia gold medal was about _________ to 1 b about _________ %of Australia's total medals were gold.
Answers
the ratio of United States gold-medal to Russia gold medal was about 46/24=23/12 to 1
about %of Australia's total medals were gold.
m = y2-yi=X2-X1Find the slope of the line that passesthrough these two points.(6,4)m = [?](2, -4)-
Answers
The slope between two points (x1,y1) and (x2,y2) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case we have the points (2,-4) and (6,4), then:
[tex]\begin{gathered} m=\frac{4-(-4)}{6-2} \\ m=\frac{4+4}{4} \\ m=\frac{8}{4} \\ m=2 \end{gathered}[/tex]Therefore, the slope is 2
What is the prime factorization of 72?
A. What is the prime factorization of 72?
A.
Answers
Answer:
2 3 ⋅ 3 2
Step-by-step explanation:
Answer:23·32
Step-by-step explanation:72 divided by 32 will give you 23 and 32 multiplied by 23 equals 32
What is the first step to solve this equation: 5m + 10= 7m + 4A: subtract 5m to both sides B: add 5m to both sides C: divide by 5 to both sides D: multiply by 5 to both sides
Answers
We are given the linear equation
[tex]5m+10=7m+4[/tex]If we subtract 5m to both sides we get
[tex]5m+10-5m=7m+4-5m[/tex]Simplifying
[tex]10=2m+4[/tex]which is one step closer to the solution, therefore the answer is A.
15 percent of a certain company's life insurance policy holders are smokers. For each nonsmoker the probability of dying during the year is 0.011. For each smoker the probability of dying during the year is 0.04. Find the probability that a policy holder who died last year was a smoker.
Answers
Percentage of Smoker Policy Holders = 15% / 100% = 0.15
Probability of Smokers Dying = 0.04
Let's substitute the values to the equation, we get,
[tex]\text{ P = (0.15)(0.04) = 0.006}[/tex]The probability that a policy holder who died last year was a smoker = 0.006
Graph the solution to the following inequality on the number line,(x + 6) (x-3) 20
Answers
If you have an equality of the form...
[tex](x+a)\cdot(x-b)\ge0[/tex]The inequality can be writen as...
[tex]a\leq x\leq b[/tex]I'll show you how it looks like on the graph
the graph indicates that x is any value less than or equal to -6 or greater than or equal to 3, which is the red area
[tex]\begin{gathered} x\leq-6 \\ x\ge3 \end{gathered}[/tex]Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given interval.
Answers
Given:
[tex]f(x)=10x^4-4x^2+5x-1;\lbrack-2,0\rbrack[/tex]Using the intermediate value theorem,
[tex]\begin{gathered} f(x)=10x^4-4x^2+5x-1 \\ f(-2)=10(-2)^4-4(-2)^2+5(-2)-1 \\ f(-2)=160-16-10-1=133 \\ \text{and} \\ f(0)=10(0)^4-4(0)^2+5(0)-1=-1 \end{gathered}[/tex]So, we have find value c between [-2,0].
[tex]\begin{gathered} f(x)=0 \\ 10x^4-4x^2+5x-1=0 \\ \Rightarrow x=-1\text{ it satisfies the equation} \\ \text{Also, -1}\in\lbrack-2,0\rbrack \end{gathered}[/tex]It shows that, the above polynomial function has zero in the given interval.
Also, the value of f(-2) = 133
Find the measure of each angle in the diagram.
Answers
Answer:
10y+7x+4+4×-22+3y+11
10y+3y+7x+4x+4-22+11
13y+11x-9
Stats To quality for a police academy, applicants are given a lest of physical Itness. Ihe scores are normallyDistributed with a mean of 64 and a standard deviation of 9. If only the top 20% of the applicants are selected,Find the cutoff score.
Answers
Since we want just the top 20% applicants and the data is normally distributed, we can use a z-score table to check the z-score that gives this percentage.
The z-score table usually shows the percentage for the values below a certain z-score, but since the whole distribution accounts to 100%, we can do the following.
We want a z* such that:
[tex]P(z>z^*)=0.20[/tex]But, to use a value that is in a z-score table, we do the following:
[tex]\begin{gathered} P(zz^*)=1 \\ P(zz^*)=1-0.20=0.80 \end{gathered}[/tex]So, we want a z-score that give a percentage of 80% for the value below it.
Using the z-score table or a z-score calculator, we can see that:
[tex]\begin{gathered} P(zNow that we have the z-score cutoff, we can convert it to the score cutoff by using:[tex]z=\frac{x-\mu}{\sigma}\Longrightarrow x=z\sigma+\mu[/tex]Where z is the z-score we have, μ is the mean and σ is the standard deviation, so:
[tex]\begin{gathered} x=0.8416\cdot9+64 \\ x=7.5744.64 \\ x=71.5744\cong72 \end{gathered}[/tex]so, the cutoff score is approximately 72.
ine TrackerWhat additional piece of information is needed in order to say thatthese two triangles are congruent by AAS postulate?BO BC DEO AB DEO BC EFO AB DF
Answers
Answer
Option B is correct.
AB ≅ DE
Explanation
The key to two triangles being similar according to AAS is that they have two angles and an excluded side in common.
An excluded side does not reside between the two congruent angles.
So, for these two triangles to be congruent according to AAS,
Angle C = Angle F
Angle B = Angle E
And
Side AB ≅ Side DE
Hope this Helps!!!
Which of the following is the graph of the following system of equations? { 2x - 3y>12 {y< -1 x + 5 2
Answers
SOLUTION
The graph of the inequality
[tex]\begin{cases}2x-3y\ge12{} \\ y<-\frac{1}{2}x+5\end{cases}[/tex]is shown below
The darkest part is the required region
Comparing with the options,
the answer is the graph below
find the exact value of cosine Pi / 3 express your answer with a rational denominator
Answers
it is given that,
the expression is
cosine Pi/3
we know that
so,
[tex]\cos \frac{\pi}{3}=\cos \frac{180}{3}=\cos 60=\frac{1}{2}[/tex]thus, the answer is 1/2
GIVING 100 POINTS!!
1.) Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 115.2°.
A) 244.8°
B) 64.8°
C) 25.2°
D) 11.5°
2. Find the sum of the interior angles of a 22-sided polygon.
A) 1,980°
B) 2,160°
C) 3,360°
D) 3,600°
HELP! ME PLS!! TWO QUESTIONS!
Answers
Answer:
Step-by-step explanation:
1. The answer is C because 180-115.2=64.8
2. The answer is D.
Please give me brainliest!
Answer:
1. C
2. D
Step-by-step explanation:
Because