Given:
A zip line goes from 28 feet to 11 feet in the air. The angle of depression is 85°.
To find:
The length of the zip line where there is no rider.
Solution:
A right-angled triangle can be formed using the given data.
The difference in height between the start and end of the zipline is [tex]28-11=17[/tex]. The angle of the triangle is 85°.
Assume the zip line is x feet long.
The adjacent side of the triangle measures 17 feet, the hypotenuse of the triangle measures x feet, and the angle of the triangle is 85°.
To determine x, we calculate the cos of the given angle.
[tex]cos \theta = \frac{adjacentside}{hypotenuse} .[/tex]
[tex]cos 85 = \frac{17}{x} , x = \frac{17}{cos85}, cos85= 0.0871.[/tex]
[tex]x = \frac{17}{0.0871} = 195.1779.[/tex]
Rounding this off, we get the length of the zip line when there is no rider is 195.18 feet long.
The length of the zip line when there is no rider is 195.18 feet long.
Calculation of the length of the zip line:Here the difference is
= 28 - 11
=17
And, The angle of the triangle is 85°.
Here we Assume the zip line should be x feet long.
Now
The length should be
[tex]cos\ 85 = 17\div x\\\\x = 17\div 0.0871[/tex]
= 195.18
Hence, The length of the zip line when there is no rider is 195.18 feet long.
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A 3-column table with 4 rows. Column 1 has entries Computer repair, sales tax, gratuity, shipping. Column 2 is labeled Store A with entries 1,200 dollars, 6 percent, 15 percent, Free. Column 3 is labeled Store B with entries 1,350 dollars, 7 percent, 15 percent, 2 percent of total price. What is the cost of the repair and sales tax combined at Store B?
Answer:
$1,444.50.
Step-by-step explanation:
To calculate the combined cost of the repair and sales tax at Store B:
Cost of repair at Store B: $1,350
Sales tax rate at Store B: 7%
Now, let's calculate the sales tax:
Sales tax = 1,350 × 7/100 = 1,350 × 0.07 = 94.50
Next, add the sales tax to the repair cost:
Total cost = 1,350 + 94.50 = 1,444.50
Thus, the combined cost of the repair and sales tax at Store B is $1,444.50.
Which option below gives the formula of k(x) = g(x) × h(x)?
k(x) = 2^x + 1
k(x) = x 2^x - 1
k(x) = 2^x - 1
k(x) = x 2^x + 1
Answer:
the answer is the the 3rd one
Final answer:
The correct formula for k(x) = g(x) × h(x), given that g(x) is an odd function and h(x) is an even function, is k(x) = x 2ⁿ - 1.
Explanation:
The student is asking which formula represents k(x) = g(x) × h(x). Given the functions g(x) = x³ - 3x and h(x) = e⁽¹x², and knowing that the product of an odd function and an even function is an odd function, the correct representation of k(x) will also be an odd function.
From the provided options, the correct formula must satisfy the conditions of being an odd function, meaning that k(-x) = -k(x). This property holds only for option two, k(x) = x 2ⁿ - 1, because this is the only option where k(x) changes sign when x is replaced with -x, fulfilling the criteria of an odd function.
Please help! I will mark you as brainliest!
Answer:
8
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
5(x/2 + 3) = 35
Combine like terms
5x/10 + 15 = 35
Subtract both sides by 15
5x/10 = 20
divide both sides by 5
x/2 = 4
multiply by 2
x = 8
What is the overlap of Data Set 1 and Data Set 2?
high
moderate
low
none
Answer:
Low
Step-by-step explanation:
The tick marks of 40 and 50 are the same on both number lines (each data set has one dot shown over both the 40 and 50 mark). However, nothing else is the same or similar on the data sets, so their overlap is low.
Solve the system of linear equations by graphing. Round the solution to the nearest tenth as needed. Y + 2.3 = 0.45x and -2y = 4.2x - 7.8
Answer:
(2.4, -1.2)
Step-by-step explanation:
Start by moving the x and the y to the same side and moving the number across the equal sign in both equations. We should now have y-0.45x=-2.3 and 2y+4.2x=7.8. We can use the elimination method by multiplying the first equation by -2 to get -2y+0.9x=4.6 and 2y+4.2x=7.8. From there, add the two equations together, eliminating y (-2+2=0). We now have 5.1x=12.4; divide both sides by 5.1 to get x=2.4. Then, in any of the two equations, let's use y-0.45x=-2.3, substitute x with 2.4. Now we have y-1.08=-2.3. Add 1.08 to both sides to get y=-1.22; round that to the nearest tenth to get -1.2.
Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers. 10 + 2.5 x less-than-or-equal-to 40 Which best describes the number of bags of balloons she can buy? She can buy from 0 to 12 bags, but no more. She can buy from 0 to 20 bags, but no more. She must buy 12 or more bags. She must buy 20 or more bags.
Answer:
The one that best describes the amount is 10.00 + 2.50 x 3
Step-by-step explanation:
10,00 + 2,50 = 12,50
12,50 x 1 = 12,50
12,50 x 2 = 25,00
12,50 x 3 = 37,50
12,50 x 4 = 50,00
Final result 12.50 x 3
Answer:
A. Just did it on edge. She can buy from 0 to 12 bags, but no more.
PLEASE HELP. 18 points
You design a frame to surround a rectangular photo. The width of the frame is the same on every side as shown. write a polynomial in standard form that represents the combined area of the photo in the frame. find the combined area of the photo in the frame when the width of the frame is 4 inches.
Answer:
A is 4x^2+84x+440 and B=840 square inches
Step-by-step explanation:
A is 4x^2+84x+440 and B=840 square inches
The task for a is to write a polynomial in standard form that represents the combined area of the photo and the frame. First, lets start with the bottom of the picture and frame. On the bottom, you have 2x+ 22 inches. Then the side of the picture and frame is 2x+20 inches. Writing in polynomial form, it would be (2x+22)(2x+20). You would get 4x^2+84x+440 since you are using the FOIL method. Now for part b, we know that the width of the frame(or x) is 4 inches. Now we plug that into the equation. 84x is 84x4. 84x4=336 x^2 is 16. There are four of those as you can see in the equation so 16x4=64
336+64=400 inches Frame= 400 inches
400 inches plus the picture(440 inches) = 840 square inches.
Length of the rectangular photo = 22 inches
Width of the rectangular photo = 20 inches
Since, width of the frame outside the photo = x inches
Therefore, increase in length and width of the photo with frame = (x + x)
= 2x inches
Length of the photo with frame = (22 + 2x) inches
Width of the photo with frame = (20 + 2x) inches
Combined Area of the photo in the frame = Length × Width
= (22 + 2x)(20 + 2x)
= 22(20 + 2x) + 2x(20 + 2x)
= 440 + 44x + 40x + 4x²
= 4x² + 84x + 440
Therefore, polynomial representing the combined area of the photo in the frame will be (4x² + 84x + 440) square inches.
If width of the frame = 4 inches
Combined area of the photo = 4(4)² + 84(4) + 440
= 840 square inches
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|4x−4(x+1)|=4
find x
Answer: x= 5
Step-by-step explanation:
Let's solve your equation step-by-step.
4x+2=2(x+6)
Step 1: Simplify both sides of the equation.
4x+2=2(x+6)
Simplify: (Show steps)
4x+2=2x+12
Step 2: Subtract 2x from both sides.
4x+2−2x=2x+12−2x
2x+2=12
Step 3: Subtract 2 from both sides.
2x+2−2=12−2
2x=10
Step 4: Divide both sides by 2.
2x /2 = 10 /2
x=5
help me examine this stem and leaf plot!
f(x) = 8 - 4x has one solution.
f(x) = x2 - 9 has two solutions.
f(x) = x3+ 3x2 + 5x + 15 has three solutions.
Make a Conjecture:
A polynomial of degree n appears to have
solutions.
DONE
Answer: N
Step-by-step explanation:
A polynomial of degree n appears to have n solutions
Answer:
n
A polynomial of degree n appears to have
n solutions.
Suppose that F(x) = x2 and G(X) = -3x3. Which statement best compares the graph of G(x) with the graph of F(x)?
Answer:
The graph of G(x) is the graph of F(x) flipped over the x-axis and stretched vertically.
Step-by-step explanation:
Anika was shown a reduction of a complex figure.
What can Anika conclude about the scale factor and missing measurements? Select three options.
The scale factor is 0.60.
The scale factor is 0.25.
The length of side A is 8.75 cm.
The length of side A is 21 cm.
Answer:
B, C, AND E
Step-by-step explanation:
The scale factor is, 0.25.
The length of side A is 8.75 cm.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
From the given information length of the preimage is 60 cm and the corresponding image length is 15 cm.
So, The scale factor is,
= (15/60).
= 1/4.
= 0.25.
Therefore, The length of side A is,
= 35×0.25 cm.
= 8.75 cm.
The length of side B is,
= 25×0.25 cm.
= 6.25 cm.
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k(x) = x -2
h(x) = 32 +1
(h + k)(2) =
Find the area of the figure.
A) 30 cm2
B) 36 cm2
C) 42 cm2
D) 48 cm2
Answer:
B
Step-by-step explanation:
The area of the rectangle would be 30 while the area or the triangle is 6
Rectangle
b x h = A
5 x 6 = 30
A = 30
Triangle
1/2 x b x h = A
1/2 x 3 x 4 = A
1/2 x 12 = 6
A = 6
Answer:
b
Step-by-step explanation:
What value is equivalent to -3 x 32 - 8 ÷ 2 + 6? -18 -7 -16 7
Answer:
-94.
Step-by-step explanation:
((0−3×32)−8÷2)+6
((0−96)−8÷2)+6
(-96−8÷2)+6
(-96−4)+6
-100+6
-94
Answer:
-94
Step-by-step explanation:
-3 x 32 - 8 ÷ 2 + 6
-96 - 4 + 6
-96 + 2
-94
1. The y value in y=mx+b would be considered to be the *
a. input
b. output
c. slope
d. y-intercept
2. The m in the equation y=mx+b would be considered the: *
3. Pick all of the correct responses: The b in the equation y=mx+b would be considered the: *
a. y-intercept
b. slope
c. input
d. rise/run
4. You've been given the equation y=-5x+4. Solve for y when x is -2. *
5. You've been given the equation y=3x-3. Solve for y when x is 0. *
a. 0
b. 3
c. 2
d. -3
6. You've been given the equation y=2x-12. Solve for y when x is 4. *
7. You've been given the equation y=6x. Solve for y when x is 2. *
a. 0
b. 6
c. 9
d. 12
8.You've been given the equation y=3x+1. Solve for y when x is 1. *
a. 4
b. 3
c. 2
d. 1
9. You've been given the equation y=-.25x+7. Solve for y when x is 8. *
10. You've been given the equation y=-3x-9. Solve for y when x is -5. *
Answer:
1. Output
2. Slope
3. y-intercept
4. y = 14
5. y = -3
6. y = -4
7. y = 12
8. y = 4
9. y = 5
10. y = 6
Step-by-step explanation:
To solve problems 4-10, plug in the given values and simplify the equations.
4. y = -5(-2) + 4
y = 10 + 4
y = 14
5. y = 3(0) - 3
y = 0 - 3
y = -3
6. y = 2(4) - 12
y = 8 - 12
y = -4
7. y = 6(2)
y = 12
8. y = 3(1) + 1
y = 3 + 1
y = 4
9. y = -0.25(8) + 7
y = -2 + 7
y = 5
10. y = -3(-5) - 9
y = 15 - 9
y = 6
What is the diameter of this circle?
A)
2.5 cm
B)
3.14 cm
C)
5 cm
D)
10 cm
Answer:
D) 10 cmStep-by-step explanation:
The sales at a baseball game vary directly with the number of people attending. If the sales for a game
are $12,000 when 800 people attend, determine how many people attend if the sales for a game are
$15,000.
Answer:
1,000
Step-by-step explanation:
$12,000÷800 =15. x=people attending
$15,000÷x=15. x=1,000
$15,000×1,000=15
Final answer:
Using the concept of direct variation, a constant of variation ($15 per person) was calculated using the provided sales and attendance. This constant was then used to find the attendance for a different sales amount, which was found to be 1000 people for $15,000 in sales.
Explanation:
The question asks us to determine how many people attended a baseball game based on the direct variation between sales and attendance. Since we know that at 800 people the sales are $12,000, we can set up a proportion to solve for the number of people when sales are $15,000.
First, we find the constant of variation (k) by dividing the sales by the number of people for the given data point:
k = Sales / Number of people = $12,000 / 800 = $15 per person
Next, we use this constant to find the number of people when sales are $15,000:
Number of people = Sales / k = $15,000 / $15 per person = 1000 people
Therefore, 1000 people attended the game when the sales were $15,000.
What percent of 105 is 63 (round to the nearest hundredth)
Answer:
60
if you use a calculator then 63÷105×100
Hope this helps!
Plssss help me, I’ll mark y’all brainliest
Answer:
1 ray is intersecting point O
Step-by-step explanation:
A ray can be defined as a part of a line that has a fixed starting point but no end point.
AD and EC both go on forever but OB has one endpoint and goes on forever.
If a road has a grade of 30°, this means that it's angle of elevation is 30°. If you travel 1.5 miles on this road, how much elevation have you gained in feet (5280ft = 1 mile). Round to the nearest foot.
3450ft
3998ft
3960ft
2760ft
The elevation gained after travelling 1.5 miles will be 3960ft.
Step-by-step explanation:
Angle of elevation = 30°
Distance travelled= 1.5 miles
1 mile = 5280 ft.
1.5 miles = 5280 x 1.5
= 7920 ft.
The height from the ground can be calculated by,
sin 30° = height / 7920
1/2 = height / 7920
Height = 7920/2
= 3960 ft.
The elevation gained after travelling 1.5 miles will be 3960ft.
Final answer:
To determine the elevation gain over 1.5 miles on a road with a 30° angle of elevation, the sine function reveals that the elevation gain is 0.5 * 1.5 miles * 5280 feet/mile, which calculates to approximately 3960 feet.
Explanation:
To calculate the elevation gain when traveling 1.5 miles on a road with a 30° angle of elevation, we can use trigonometric functions. Specifically, the sine function is useful, because it relates the angle of a right triangle to the ratio of the opposite side (elevation gain) over the hypotenuse (distance traveled).
The sine of a 30° angle is 1/2, and if the hypotenuse is 1.5 miles, we can find the length of the opposite side by multiplying:
sine(30°) = elevation gain / (1.5 miles)
0.5 = elevation gain / (1.5 miles * 5280 feet/mile)
elevation gain = 0.5 * 1.5 miles * 5280 feet/mile
elevation gain = 0.5 * 1.5 * 5280 feet
elevation gain ≈ 3960 feet
Therefore, you would gain approximately 3960 feet in elevation after traveling 1.5 miles on the road.
HELP ASAP!
Solve by using Elimination.
2x - y = -3
3x + 4y = -32
A. (1, 4)
B. (-1, 1)
C. (-4, -5)
D. (0, 3)
Answer:
c
Step-by-step explanation:
A teacher conducted survey of one of her classes to see where some of her students had eaten over the last month and displayed this data in the table below.
Which students would be in the set (chic-fil-a)?
(Just the first letter of each student’s name is shown in the sets below)
Question 8 options:
{a,b,g,j,k}
{c,d,e,f,h,i}
{A,c,d,f,h,i}
{C,d,e,f,h,j,k}
Answer:
{a,b,g,j,k}
Step-by-step explanation:
Alan
Bethe
Gail
Jen
Kali
The weights of six animals at the zoo is shown in the table below.
weight of Animals
(LBS)
5
24
38
52
66
85
what is the mean absolute deviation? round to the nearest tenth. _____
(don't guess or lie to your answers pls)
Answer:
22.7
Step-by-step explanation:
The required mean absolute deviation is 22.9, rounded to the nearest tenth.
What is Statistic?Statistic is the study of mathematics that deals with relations between comprehensive data.
The mean weight of the animals is 44.3.
To find the mean absolute deviation, we take the absolute value of the difference between each weight and the mean, and then take the average:
= (|5-44.3| + |24-44.3| + |38-44.3| + |52-44.3| + |66-44.3| + |85-44.3|) / 6
= (39.3 + 20.3 + 6.3 + 8.3 + 22.3 + 41.3) / 6
= 137.5 / 6 = 22.9
So the mean absolute deviation is 22.9, rounded to the nearest tenth.
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Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey. Of graduates in the sample, what fraction came from university A?
https://gyazo.com/024c033fb3022b87aee5e6ca3695277b
75 graduates from University A had an income under $20,000.
From the two-way table, we can see that 35 graduates from University A had an income under $20,000. In addition, 40 graduates from University B had an income under $20,000. However, we should not simply add these two numbers together, as some graduates from each university may have been counted twice.
To avoid double counting, we need to look at the total number of graduates who responded to the survey. This number is 35 + 90 + 35 + 37 = 197. Therefore, we know that there were 197 unique graduates who responded to the survey.
Since there were 197 unique graduates and 40 graduates from University B had an income under $20,000, this means that there must have been 197 - 40 = 157 graduates from University A who responded to the survey.
Finally, we can see from the two-way table that 35 graduates from University A had an income under $20,000. Therefore, there were a total of 75 graduates from University A who had an income under $20,000.
Question
Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.
How many graduates from University A had an income under $20,000?
________graduates
A company made a storage container with sheet steel walls. The container was in the shape of a rectangular prism, as shown below. Suppose the total cost of the sheet steel was $8384. How much did the sheet steel cost per square meter?
Answer:
$ 42.78
Step-by-step explanation:
See attachment for the figure
The formula of the lateral area of the rectangular prism is:
LA = perimeter of base × height
Given:
The length of the base 'l' = 9 m
The width of the base 'w'= 5 m
The height of the prism 'h'= 7 m
perimeter of the base can be determined by
Perimeter of base = 2(l + w ) =>2(9 + 5)
Perimeter of base = 28 m
By using the formula of the lateral area
LA = 28 × 7
LA = 196 m²
Required:
sheet steel cost per square meter=?
Given: The total cost of the sheet steel was $8384
LA = 196 m²
By Dividing the cost by the lateral area, we'll know our unit cost
therefore, The unit cost = 8384 ÷ 196
The unit cost =$ 42.78
The sheet steel costed $42.78 per square meter
Tell whether the triangle with the given side lengths is a right triangle.
24,45,52
Answer:no
Step-by-step explanation:a right triangle needs a 90 degrees angle
The temperature in Denver is –7° Fahrenheit (F). Rounded to the nearest tenth, what is the temperature in Celsius (C) using the conversion formula C = (5F - 160)/9?
13.9° C
21.7° C
-21.7° C
-13.9° C
Answer:
england is NOT my city
stop calling it london
Step-by-step explanation:
jake paul is my bf
Answer: the answer is c if im correct
Step-by-step explanation:
Any help? Also please explain how you got the answer
Answer:
C (i think i did it correctly)
Step-by-step explanation:
9 times 12 is 108 -> 108 - 60 = 1 hour and 48 minutes -> 48 plus 4 = 7:52am
Can anyone help me with this?
Look at the attached picture ⤴
Hope it will help u ..