Answer:
156
Step-by-step explanation:
You are given the mountain that has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. You are asked to find how many yards will a tourist travel from the base of the mountain to its peak. You can solve this using trigonometric function. More importantly, imagine that the mountain has a 90 - degree vertical height so that when you connect the peak of the mountain down to its base and then connected to the ski, you can form a right triangle.
Use the sine function.
sine β = opposite side / hypotenuse side
the opposite side will be the height of the mountain and the hypotenuse side will be the distance of the ski from the bottom going to the peak of the mountain
sine 40° = 100 yards / hypotenuse side
hypotenuse side = 100 yards / sine 40°
hypotenuse side = 156 yards
In the above figure, AE = 2, CE = 3, and DE = 4. What is the length of BE?
Answer:
its 6 i think
Explanation:
if you have the choices 6, 8, 12, 5.. then 6 is ur answer. why?
well u do CE x DE = AE x BE
(3)(4)= (2)(BE)
12=2x
12÷2= 6
What would be the point of discontinuity in the following function f(x)=x^2+5x+6/x+3
(14 + 13) + 2 = 29 Choose an equivalent addition sentence that shows the associative property of addition. 29 = (14 + 13) + 2 (14 + 13) + 2 = 29 14 + (13 + 2) = 29 14 + 13 + 2 = 29
Final answer:
An equivalent addition sentence showing the associative property of addition in the given example is 14 + (13 + 2) = 29, where the grouping changes but the sum remains the same, rooted in the commutative property of addition.
Explanation:
The question is about the associative property of addition which essentially states that when you add three or more numbers, the way in which you group them doesn't affect the sum. To illustrate with the given example $(14 + 13) + 2 = 29$, an equivalent sentence that demonstrates the associative property would be 14 + (13 + 2) = 29. Here, the grouping has changed, but the resulting sum remains the same. The reason this works is due to the commutative property of addition which tells us that changing the order of the numbers we're adding doesn't change the sum, expressed as A + B = B + A. This universality is showcased by the idea that regardless of 'real-world context' or 'complexity of calculation', the same rules apply.
Compare 9 ⋅ 104 to 3 ⋅ 102.
9 ⋅ 104 is 3 times larger than 3 ⋅ 102.
9 ⋅ 104 is 30 times larger than 3 ⋅ 102.
9 ⋅ 104 is 300 times larger than 3 ⋅ 102.
9 ⋅ 104 is 3,000 times larger than 3 ⋅ 102.
Answer:
9×10⁴ is 300 times greater than 3×10²
Step-by-step explanation:
guy above me's work. thanks to him we get this answer :)
The length of a rectangle is twice its width. if the area of the rectangle is 162 cm2 , find its perimeter.
*WILL GIVE BRAINLIEST* (08.03)Consider the following set of equations:
Equation C: y = 2x + 8
Equation D: y = 2x + 2
Which of the following best describes the solution to the given set of equations?
No solution
One solution
Two solutions
Infinite solutions
Answer:
No solution
Step-by-step explanation:
This is because either way you do it it still doesnt make any sense and doesent line up correctly. THis is high school workand im doing it in 8th grade
Answer:
no solution
Step-by-step explanation:
because it just is
What is the remainder of (x3 - 6x2 - 9x + 3) ÷ (x - 3) A. -25 B. -52 C. -51 D. -17
the correct answer in C. -51 hope this helps you
Which person in the high rise building is closest to the street level?Moira is in her doctor’s office on the fourth floor.Geoffrey is in the elevator between the second and third floors.Sandy is in the laundry room on the –2 basement floor.Hasim is leaving the parking garage and is currently between –1 and –2 levels.
Answer
Hasim is the closest... I just took the test
Choose the correct simplification of (6x4y2z3)(3x4y3z5).
18x16y6z15
18x8y5z8
9x8y5z8
9x16y6z15
Answer:
18 x 8y 5z 8 witch is answer choice B
Step-by-step explanation:
the minute hand of a clock is 9.5cm long, How far does the tip of the hand travel in one day?
Maureen is taking an antibiotic. The table below shows the amount of antibiotic f(t), in mg, that was present in her body after time t:
t (hours) 1 2 3 4 5
f(t) (mg) 150 90 54 32.4 19.4
Ken was administered 200 mg of the same antibiotic. The amount of antibiotic f(t) in his body after time t is shown by the equation below:
f(t) = 200(0.976)t
Which statement best describes the rate at which Maureen's and Ken's bodies eliminated the antibiotic?
Maureen's body eliminated the antibiotic faster than Ken's body.
Maureen's body eliminated the antibiotic at the same rate as Ken's body.
Maureen's body eliminated the antibiotic at half of the rate at which Ken's body eliminated the antibiotic.
Maureen's body eliminated the antibiotic at one-fourth of the rate at which Ken's body eliminated the antibiotic.
Answer:
(A)Maureen's body eliminated the antibiotic faster than Kens body
Step-by-step explanation:
We already have the table for Maureen, so lets figure out the table for Ken. We've been given the formula 200(0.976)^t.
we already know our starting point is 0, 200
first we substitute 1 into t, which would look like this 200(0.976)^1
So we would solve the power of 0.976 to the power of 1, which is just 0.976. so now we do 200 x 0.976 which results in 195.2. on the chart, the point would be (1, 195.2). now lets solve for the rest doing the same steps.
(2, 1905.5)
(3, 181.4)
(4, 135.5)
(5, 01.9)
State two reasons why including the p-value is prudent when you are reporting the results of a hypothesis test.
An athlete eats 45g of protein per day while training. How much protein will she eat during 25 days of training?
Tony is four years younger than his brother josh, and two years older than his sister cindy. tony also has a twin brother, evan. all the ages of the children totaled together is 66. how old is tony?
To solve this problem, let us assign the variables. Let us say that:
x = age of Tony = which also the age of his twin brother Evan
x + 4 = age of Josh (since tony is 4 years younger, then josh must be 4 years older)
x – 2 = age of Cindy (since tony is 2 years older, then cindy must be 2 years younger)
There are a total of 4 children, therefore:
x + x + x + 4 + x – 2 = 66
4 x + 2 = 66
4 x = 64
x = 16
Therefore Tony is 16 years old.
To find Tony's age, we can set up an equation using the information given and solve for x. After solving the equation, we find that Tony is 16 years old.
Explanation:To solve this problem, we can assign variables to each person's age. Let's say Tony is x years old. Since Tony is four years younger than Josh, Josh's age can be represented as x + 4. Since Tony is two years older than Cindy, Cindy's age can be represented as x - 2. Since Tony has a twin brother, Evan, we can assign Evan's age as x as well.
According to the information provided, the sum of all their ages is 66, so we can set up the equation: x + (x + 4) + (x - 2) + x = 66. Simplifying the equation, we get 4x + 2 = 66. By subtracting 2 from both sides and dividing by 4, we find that x = 16.
Therefore, Tony is 16 years old.
To the nearest degree what is the measure of each exterior angle of a regular octagon
Answer:
The measure of exterior angle of regular octagon is 45°
Step-by-step explanation:
Given the regular octagon we have to find the measure of exterior angle of regular octagon.
The formula to find the measure of exterior angle of regular octagon is
[tex]\frac{360}{n}[/tex]
where n is number of sides.
Number of sides in octagon=8 sides
Hence, the measure of exterior angle is
[tex]\frac{360}{8}=45^\circ}[/tex]
Solve by taking square roots: x^2 - 40 = 9
Write an inequality for the situation.
all real numbers y that are less than –3 or greater than 18
A) y < –3 or y < 18
B) y < 18 or y > –3
C) –3 < y < 18
D) y < –3 or y > 18
A yogurt with 1 topping is sold for $3.65. Additional toppings can be added for $0.45 cents each. If y represents the total cost and x represents the total number of toppings added, which function rule describes this pattern? A. y=0.45x+3.65 B. y=3.65+0.45(x-1) C.y=3.65+0.45(x+1) D.3.65(x-1)+0.45
since the 3.65 price includes 1 topping when you calculate the cost of the additional toppings it would be x-1
so the equation would be y=3.65 +0.45(x-1)
To make bread dough, a baker mixes flour, eggs, yeast and salt by weight in pounds in the ratio of 11:9:3:2, respectively. how many pounds of yeast are required to make 20 pounds of bread dough?
A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. What price should the business implement to maximize its revenue?
a $75
b $100
c $120
d $90
The linear relationship is c(p) = -4p + b. Then the price that maximizes revenue is $75.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1.
A carpet cleaning business has 100 customers when they charge $125 for cleaning.
Research shows that every $5 reduction in price attracts another 20 customers.
Since a $5 decrease in price increases customers by 20, we can say that we have two options.
(120, 100) and (120, 120) from these we can find the slope or rate of change of customers as a function of price.
[tex]\rm m = \dfrac{20}{-5}\\\\ m = -4[/tex]
Then we have
[tex]\rm c(p ) = -4 p +b[/tex]
Now, we can use (125, 100) to solve for b
100 = -4(125) + b
b = 600
So our number of customers as a function of price is
[tex]\rm c(p) = 600 - 4p[/tex]
Revenue will simply be the number of customers times the price charged per customer will be
[tex]\rm r(p) = 600 p -4p^2[/tex]
We can find a price that creates maximum revenue by finding when the derivative is equal to zero.
[tex]\rm \dfrac{dr}{dp} = 600 - 8p\\\\[/tex]
WE know that for maximum,
[tex]\rm \dfrac{dr}{dp} = 0\\\\0 = 600 - 8p\\\\p = 75[/tex]
So, the price that maximizes revenue is $75.
More about the linear system link is given below.
Solve the system using elimination. y – x = 13 7y + x = 11
help please
Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)
Answer with explanation:
Vertices of ∆ABC are A (2,5), B (4,6) and C (3,1).
Plotting the points on coordinate plane
a.→ [tex]R_{x}[/tex]
We have to find vertices of image , that is ΔA'B'C' when ∆ABC is reflected across x axis.
The Distance from each of the vertices of ∆ABC from X axis will be same as Perpendicular distance from each of vertices of ∆A'B'C' from X axis.
Result is shown in the image 1.
b.→[tex]R_{y}=3[/tex]
We have to find the image of vertices of triangle through line, y=3.
The Distance from each of the vertices of ∆ABC from line,y=3 will be same as Perpendicular distance from each of vertices of ∆A'B'C' from line, y=3.
Result is shown in the image 2.
c. →T(-2,5)
Translation of vertices of triangle ABC by 2 units left and 5 units up.
[tex]A(2,5)_{-2,5} \rightarrow (2-2,5+5)\rightarrow (0,10)\\\\B(4,6)_{-2,5} \rightarrow (4-2,6+5)\rightarrow (2,11),\\\\C(3,1)_{-2,5} \rightarrow (3-2,1+5)\rightarrow (1,6)[/tex]
d.→T(3,-6)
Translation of vertices of triangle ABC by 3 units right and 6 units left.
[tex]A(2,5)_{3,-6} \rightarrow (2+3,5-6)\rightarrow (5,-1)\\\\B(4,6)_{3,-6} \rightarrow (4+3,6-6)\rightarrow (7,0),\\\\C(3,1)_{3,-6} \rightarrow (3+3,1-6)\rightarrow (6,-5)[/tex]
e.→Rotation by 90° with respect to Origin
When rotated in clockwise direction ,vertices of ΔABC changes by the rule ,that is (x,y)→(y,-x) and in anticlockwise direction ,(x,y)→(-y,x).
In clockwise direction
A(2,5)→A"(5,-2)
B(4,6)→B"(6,-4)
C(3,1)→C"(1,-3)
In Anti clockwise direction
A(2,5)→A'(-5,2)
B(4,6)→B'(-6,4)
C(3,1)→C'(-1,3)
Image is depicted below.
The sum of two numbers is 47 and the difference is 25 . what are the numbers?
The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to the power of x. The straight line f of x joins ordered pairs 4, 1 and 2, negative 3 and is extended on both sides. The straight line p of x joins the ordered pairs 0, 2 and 1, negative 5 and is extended on both sides. Courtesy of Texas Instruments Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
Part A: Intersection at [tex]\((-13/4, -83/4)\)[/tex].
Part B: Two solutions for [tex]\( f(x) \): (0, -11) and (5, 14).[/tex]
Part C: Solve [tex]\( p(x) = g(x) \)[/tex] graphically for the Point of intersection
Part A: Solution to the Pair of Equations (p(x) and f(x)):
The solution to the pair of equations represented by [tex]\( p(x) \) and \( f(x) \)[/tex]is the point of intersection. From the information provided, it seems that the intersection point is [tex]\((-13/4, -83/4)\).[/tex]
Part B: Two Solutions for [tex]\( f(x) \)[/tex]:
1. [tex]\( (0, -11) \)[/tex]
2. [tex]\( (5, 14) \)[/tex]
Part C: Solution to [tex]\( p(x) = g(x) \)[/tex]:
To find the solution to [tex]\( p(x) = g(x) \), set \( p(x) = 7x + 2 \)[/tex] equal to [tex]\( g(x) = 1 + 1.5^x \). Solve for \( x \)[/tex] to determine the point of intersection between [tex]\( p(x) \) and \( g(x) \)[/tex]. The solution to this equation provides the [tex]\( x \)[/tex] coordinate, and substituting it into either [tex]\( p(x) \) or \( g(x) \)[/tex] gives the [tex]\( y \)[/tex] coordinate. The justification lies in the graphical intersection of the functions.
Note: It's essential to examine the graph for precise details, as visual inspection can help confirm the solutions.
For such more questions on point of intersection
https://brainly.com/question/29185601
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What are the possible values of x in x2 + 3x + 3 = 0?
Which law would you use to simplify the expression (p/q)^3
Answer:
B. Power of quotient.
Step-by-step explanation:
We have been given an expression [tex](\frac{p}{q} )^3[/tex] and we are asked to choose the correct rule to simplify our given expression.
Since our given expression is a fraction raised to 3rd power. Power of a quotient rule states when a quotient is raised to an exponent, then the exponent is distributed to both numerator and denominator of the quotient.
Using power of a quotient rule, we will get,
[tex](\frac{p}{q} )^3=\frac{p^3}{q^3}[/tex]
Therefore, we can simplify our given expression using power of a quotient and option B is the correct choice.
The power of quotients is the law that would be used to simplify the expression.
What is the power of quotients?This is a mathematical rule that states that the power of a quotient is the same thing as the quotient that is gotten.
Given that the numerator p and the denominator q are raised to to the power expressed in the question separately.
The division is calculated after this has done
Read more on the power of quotient here:
https://brainly.com/question/2141690
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
what way do you shade in
Answer:
x < = -1/2 or -0.5
Step-by-step explanation:
that's the answer
What is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? y − 5 = −3(x + 2) y − 5 = 3(x + 2) y − 11 = −3(x − 2) y − 11 = −3(x + 2)
Hello : let A(0,5) B(-2,11)
the slope is : (YB - YA)/(XB -XA)
(11-5)/(-2-0) = 6/(-2)
the slope is : -3
Answer: [tex]y-11=-3(x+2)[/tex]
Step-by-step explanation:
Given points : (0, 5) and (−2, 11)
Slope of the line passing through given points .
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-5}{-2-0}=\frac{6}{-2}=-3[/tex]
Thus, slope of line passing through given points m=-3
We know that the equation of a line passing through points [tex](x_0,y_0)[/tex] with slope 'm' is [tex](y-y_0)=m(x-x_0)[/tex]
Thus, equation of a line passing through (−2, 11) with slope m=-3 will be
[tex](y-11)=(-3)(x-(-2))\\\Rightarrow\ y-11=-3(x+2)[/tex]
Hence, the equation of line is [tex]y-11=-3(x+2)[/tex]
The legs of a right triangle have lengths of 3 and 4. What is the length, to the nearest tenth, of the altitude to the hypotenuse?
2, -4, 8, -16, . . . find the next two numbers in the pattern and describe the pattern.