Answer: the answer is 7
Step-by-step explanation: 42/3=14 14/2=7 hope this helps
The value of the height will be 7 units.
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The volume of a rectangular prism = 42 cubic units
And, The length is 3 units ,the width is 2 units.
Now,
Since, We know that;
⇒ Volume of rectangle = Length x Width x Height
Let height of a rectangular prism = x
Hence, we get;
⇒ Volume of rectangle = Length x Width x Height
⇒ Volume of rectangle = 3 × 2 × x
⇒ 42 = 6x
⇒ x = 42 / 6
⇒ x = 7 units
Thus, The value of the height will be 7 units.
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Which of the following are equivalent to the function y=3cosx + 2?
Check all that apply
Note: The ones I highlighted in blue are the answers I've chosen
Answer:
your choices are correct
Step-by-step explanation:
sin(x +π/2) is a translation of the sine function to the left by π/2 units, which makes it look exactly like the cosine function that you want.
cos(-x) is the same as cos(x), since the cosine function is an even function.
___
sin(x -π/2) will look like -cos(x), not what you want.
The third choice is a reflection across the x-axis of the function you started with. It is not equivalent.
Find the area of the trapezoid. leave your answer in simplest radical form.
Answer:
= 32√3 ft²
Step-by-step explanation:
Area of the trapezoid will be equal to the area of the square and that of the triangle.
Considering the triangle part;
Cos 60 = x/8
x = 8 × sin 60
= 4
Base of the triangle part = 4 ft
Therefore, top of the trapezoid = 6 ft
Height = 8 × sin 60
= 8 × √3/2
= 4 √3
Area of the trapezoid
Area = ((a+b)/2) × h
= ((6 + 10 )/2 )× 4√3
= 16/2 × 4√3
= 32√3 ft²
Answer:
4th option is correct
Step-by-step explanation:
Here in the triangle we have angle = 60
hypotenuse= 8
opposite and adjacent can be solved using trigonometric ratios
cos 60 = [tex]\frac{adjacent}{hupotenuse} \\\frac{adjacent}{8} \\\frac{1}{2}=\frac{adjacent}{8}[/tex]
which gives adjacent = 4 on solving
likewise using sine we can find opposite side to the angle which is height of
trapezium.
sin60[tex]\frac{opposite}{hypotenuse}=\frac{x}{8} \\\frac{\sqrt{3} }{2}=\frac{x}{8}\\x=4\sqrt{3}[/tex]
therefore height =[tex]4\sqrt{3}[/tex] and adjacent = 4 ft
therefore opposite sides of Trapezium are 10 ft and 6 ft
Formula for area of Trapezium =[tex]\frac{1}{2}[/tex](sum of parallel sides)x height
= [tex]\frac{1}{2}[/tex](10+6)x [tex]4\sqrt{3}[/tex]
on solving it ,we get [tex]32\sqrt{3}[/tex]
Pumping stations deliver oil at the rate modeled by the function D, given by d of t equals the quotient of 5 times t and the quantity 1 plus 3 times t with t measure in hours and and D(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 4-hour period from t = 0 to t = 4? Give 3 decimal places.
The pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.
Explanation:To find the amount of oil delivered by the pumping stations during the 4-hour period from t = 0 to t = 4, we need to evaluate the definite integral of the function D(t) over that interval. The function D(t) is given by D(t) = 5t / (1 + 3t). We can find the integral of this function using the substitution method. Let u = 1 + 3t, then du = 3dt. Rearranging this equation, we have dt = du / 3.
Substituting this in the integral, we get:
∫ D(t) dt = ∫ (5t / u) * (1/3) du = (5/3) * ∫ (t / u) du
Integrating the above expression, we get:
∫ D(t) dt = (5/3) * ∫ (t / u) du = (5/3) * ∫ (t / (1 + 3t)) du
To evaluate this integral, we can use the natural logarithm function. We know that ∫ (1/u) du = ln|u| + C, where C is the constant of integration. Substituting back for u, we have:
(5/3) * ∫ (t / (1 + 3t)) du = (5/3) * ∫ (t / u) du = (5/3) * ln|1 + 3t| + C
Now, we can use the definite integral to find the amount of oil delivered during the 4-hour period:
∫04 D(t) dt = (5/3) * ∫04 (t / (1 + 3t)) dt = (5/3) * [ln|1 + 3(4)| - ln|1 + 3(0)|] = (5/3) * [ln|13| - ln|1|] = (5/3) * ln|13| = 8.188
Therefore, the pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.
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20 POINTS
Which equation does the graph below represent?
y = 1/4x
y = 4x
y = -1/4x
y = −4x
Answer:
Step-by-step explanation:
Line passes through (0,0) and (-1,4) .
Slope = -4
Equation of line is : y - 0 = - 4(x - 0)
y = - 4x
True or false (picture provided)
Answer:
True
Step-by-step explanation:
The given inequality is
[tex]5\le x\le 8[/tex]
The boundaries of the inequality are inclusive.
We use the square brackets to indicate closed interval.
[tex]5\le x\le 8[/tex] is therefore written in interval notation as;
[5,8]
The correct choice is true
Classify the following sequence as arithmetic, geometric, neither or both: 2, 6, 18, ...
Arithmetic
Geometric
Neither
Both
Answer:
Geometric
Step-by-step explanation:
Does multiplying the same number with each term give the next term?
If so, then it is Geometric Sequence.
Does adding the same number with each term give the next term?
If so, then it is Arithmetic Sequence.
We see that multiplying by 3 gives us each successive term. 2 times 3 is 6 and 6 times 3 is 18. So it is geometric sequence.
It is NOT arithmetic sequence since we add 4 to 2 to get next number 6, but we have 12 to get next number, which is 18. So not an arithmetic sequence.
Answer is "Geometric"
Which ordered pair is the solution set for the system of equations below? 2x + y = 18 x – y = –6
Answer:
(4,10) is the solution
Step-by-step explanation:
2x + y = 18
x – y = –6
Using elimination
2x + y = 18
x – y = –6
----------------------
3x = 12
Dividing each side by 3
3x/3 = 12/3
x =4
Now we can find y
2x+y = 18
2(4) +y =18
8+y = 18
Subtracting 8 from each side
8-8+y = 18-8
y=10
(4,10) is the solution
The speed limit on a higway is 70 miles per hour/ About how fast is this in miles per minute?
Answer:
1 mile a minute.
Step-by-step explanation:
in each family of function,the____function is the most basic function in the family
A.linear
B.quadratic
C.simple
D.parent
Answer: Your answer is option D. In each family of function,the Parent function is the most basic function in the family
The family function has same highest degree, same shape for graph and consequently.
The correct option is D.
Given:
Identify the function is the most basic function in the family.
Below are the few example of family function.
[tex]y=x^2[/tex]
[tex]y=3x^2[/tex]
The graph for the both the function has same highest degree, same shape for graph and consequently. The parent function is the simplest from a family of function.
Thus, the correct option is D.
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email received a $50 gift card for his birthday.after buying some clothes,he had$16 left on the card.how much did he spend on the clothes?
A. 16-c=50
B. 50-c=16
C. 16c=50
D. c=16+50
The correct equation to find out how much was spent on the clothes is 50 - c = 16. Solving this, we find that c, the cost of the clothes, is $34.
The student initially had a $50 gift card and after purchasing some clothes, they were left with $16 on the card. To find out how much was spent on clothes, we need to subtract the remaining amount on the card from the initial amount. The correct equation to represent this situation is:
B. 50 - c = 16
We can then solve for c, which represents the cost of the clothes:
50 - 16 = c
34 = c
So, the amount spent on clothes is $34.
Please help me out! :)
Line AD is a tangent to circle B at point C and m
What is the measure of
(The answer is 90 but how do you get this answer?)
BCA is 90 degrees, because a tangent line is perpendicular to the raduis line BC.
Final answer:
The measure of angle M is 90 degrees.
Explanation:
The measure of angle M is 90 degrees. To understand why, we can use the fact that a line tangent to a circle is perpendicular to the radius drawn to the point of tangency. In this case, line AD is tangent to circle B at point C, so we can draw line AC, which is the radius of the circle, and find the measure of angle M by finding the complement of the angle formed by lines AD and AC. Since the complement of a 90-degree angle is 90 degrees, the measure of angle M is 90 degrees.
HELP WORTH 99 POINTS IM SO CONFUSED.
A. At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge if the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate area of the larger circle (blue)
B. Find the approximate area of the smaller circle (orange)
C. Find the approximate area of the sidewalk (shaded region between the blue and orange circles.)
Use 3.14 for pi. Show your work!
(use 3.14 pi on all three problems!)
Answer:
Area of Large Circle = 380.13
Area of Small Circle = 254.47
Area of Sidewalk = 125.66
Step-by-step explanation:
The side walk is just subtracting the smaller number from the bigger one.
The area is just Pi*r^2
Answer:
A 379.94 m^2
B 254.34 m^2
C 125.6 m^2
Step-by-step explanation:
A Area of a circle is given by
A = pi r^2
We know the radius is 11
A = pi 11^2
A = 3.14 (121)
A = 379.94 m^2
B The Area of the orange circle
A = pi r^2
The radius is 9 m
A = pi 9^2
A = 3.14 (81)
A = 254.34 m^2
C The Area between the circles is the difference between the large circle and the small circle
Ablue-Aorange
379.94-254.34
125.6 m^2
The weather reporter says that there is a 14% chance that it will rain tomorrow. What is the probability that it will not rain
Since an 100% chance is all possibilities, then it must add up to 100. If we take away that 14 from 100 by subtracting, you just get 86. Therefore, there is an 86% chance that it will not rain tomorrow.
If aₙ = 3(3)ⁿ⁻1 , what is S₃?
Answer:
S3 = 39
Step-by-step explanation:
* an = 3(3)^(n-1) is a geometric sequence
* The general rule of the geometric sequence is:
an = a(r)^(n-1)
Where:
a is the first term
r is the common difference between each consecutive terms
n is the position of the term in the sequence
The rules means:
- a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , ........................
∵ an = 3(3)^(n-1)
∴ a = 3 and r = 3
∴ a1 = 3
∴ a2 = 3(3) = 9
∴ a3 = 3(3)² = 27
* S3 = a1 + a2 + a3
∴ S3 = 3 + 9 + 27 = 39
Note:
We can use the rule of the sum:
Sn = a(1 - r^n)/(1 - r)
S3 = 3(1 - 3³)/1 - 3 = 3(1 - 27)/-2 = 3(-26)/-2 =3(13) = 39
Answer:
The correct answer is S₃ = 39
Step-by-step explanation:
It is given that,
aₙ = 3(3)ⁿ⁻¹
To find a₁
a₁ = 3(3)¹⁻¹ = 3(3)°
= 3 * 1 = 3
To find a₂
a₂ = 3(3)²⁻¹ = 3(3)¹
= 3 * 3 = 9
To find a₃
a₃ = 3(3)³⁻¹ = 3(3)²
= 3 * 9 = 27
To find the value of S₃
S₃ = a₁ + a₂ + a₃
= 3 + 9 + 27 = 39
Therefore the correct answer is S₃ = 39
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 136 lb and a standard deviation of 28.5 lb. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 191 lb. The probability is approximately nothing. (Round to four decimal places as needed.) b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 191 lb. The probability is approximately nothing. (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? A. Part (a) because the seat performance for a sample of pilots is more important. B. Part (b) because the seat performance for a sample of pilots is more important. C. Part (b) because the seat performance for a single pilot is more important. D. Part (a) because the seat performance for a single pilot is more important.
Answer:
A) 0.5564; B) 0.8962; C) Choice D. Part (a) because the seat performance for a single pilot is more important.
Step-by-step explanation:
For part A,
We will find the z score for each value and then subtract the probabilities for each to give us the area between them. We use the z score for an individual value:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Our first X is 130 and our second X is 191. Our mean, μ, is 136 and our standard deviation, σ, is 28.5:
[tex]z=\frac{130-136}{28.5}=\frac{-6}{28.5}\approx -0.21\\\\z=\frac{191-136}{28.5}=\frac{55}{28.5}\approx 1.93[/tex]
Using a z table, we can see that the area under the curve to the left of z = -0.21 is 0.4168; the area under the curve to the left of z = 1.93 is 0.9732. This means the area between them is
0.9732-0.4168 = 0.5564.
For part B,
We will find the z score for each value again and subtract them; however, since we have a sample we will use the z score for the mean of a sample:
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our first X-bar is 130 and our second is 191; our mean is still 136; our standard deviation is still 28.5; and our sample size, n, is 36:
[tex]z=\frac{130-136}{28.5\div \sqrt{36}}=\frac{-6}{28.5\div 6}\approx -1.26\\\\z=\frac{191-136}{28.5\div \sqrt{36}}=\frac{55}{28.5\div 6}\approx 11.58[/tex]
The area under the curve to the left of -1.26 is 0.1038; the area under the curve to the left of 11.58 is 1.00:
1.00-0.1038 = 0.8962
For part C,
We want the probability that each individual pilot will be safe in these seats, so the value in part A is more important.
The probability that a randomly selected pilot's weight is between 130 lb and 191 lb is approximately 0.558 or 55.8%. The probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb is approximately 0.1056 or 10.56%. When redesigning the ejection seat, the probability from part (a) is more relevant.
Explanation:To find the probability that a randomly selected pilot's weight is between 130 lb and 191 lb, we need to calculate the z-scores for both weights and find the area under the curve between those two z-scores. First, we calculate the z-score for 130 lb using the formula z = (x - μ) / σ, where x is the weight of 130 lb, μ is the mean weight of 136 lb, and σ is the standard deviation of 28.5 lb. Solving for z, we get z = (130 - 136) / 28.5 = -0.21. Using a z-table or calculator, we find that the area to the left of -0.21 is approximately 0.415. Next, we calculate the z-score for 191 lb using the same formula, z = (191 - 136) / 28.5 = 1.93. Again using a z-table or calculator, we find that the area to the left of 1.93 is approximately 0.973. To find the area between the z-scores, we subtract the smaller area from the larger area: 0.973 - 0.415 = 0.558. Therefore, the probability that a randomly selected pilot's weight is between 130 lb and 191 lb is approximately 0.558 or 55.8%.
To find the probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb, we need to use the Central Limit Theorem. The sample mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the mean is still 136 lb and the standard deviation is 28.5 lb divided by the square root of 36, which is 4.75 lb. We can now calculate the z-scores for 130 lb and 191 lb using the same formula, z = (x - μ) / σ. The z-score for 130 lb is (130 - 136) / 4.75 = -1.26, and the z-score for 191 lb is (191 - 136) / 4.75 = 11.58. However, since the z-score for 191 lb is beyond the range of the standard normal distribution table, we can approximate it as 4. This means that we need to find the area under the curve to the left of -1.26 and subtract the area to the left of -4. Using a z-table or calculator, we find that the area to the left of -1.26 is approximately 0.1056, and the area to the left of -4 is approximately 0.000032. Subtracting the smaller area from the larger area, we get 0.1056 - 0.000032 = 0.1056. Therefore, the probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb is approximately 0.1056 or 10.56%.
When redesigning the ejection seat, the probability from part (a) is more relevant. This is because part (a) calculates the probability of a single pilot's weight falling within the given range, while part (b) calculates the probability of the mean weight of a sample of pilots falling within the given range. The ejection seat should be designed to accommodate the weight range of individual pilots, rather than the mean weight of a sample of pilots.
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Please help if you can!
the answer is A :)))))))))))))))))
Answer:
I am pretty sure it is Rhombus or a sideway rectangle but since they dont say more than givin I would say Rhombus
Step-by-step explanation:
The cost of fabric (y) is directly proportional to he length is yards (x). If 5 yards of fabric cost $14, which equation models this situation?
Answer:
5x = 14
Step-by-step explanation:
If 5 yards of fabric is $14 you need an equation that would solve how much 1 yard of fabric costs. You can say 5x = 14 or x = 2.8 which means that one yard of fabric (1x or just x) is $2.80.
Answer: [tex]y==\frac{14}{5}x[/tex]
Step-by-step explanation:
By definition, we know that Direct proportion equation has the following form:
[tex]y=kx[/tex]
Where k is the constant of proportionality.
Then, If 5 yards of fabric cost $14, you can calculate k as following:
[tex]14=k(5)\\k=\frac{14}{5}[/tex]
Therefore substituting the value of k into the first equation, you obtain the following equation:
[tex]y==\frac{14}{5}x[/tex]
Factor. 49x^2−36y^2
Enter your answer in the boxes.
[tex]\\Rewrite \ in \ form.\\\\(7x)^2 - (6y)^2\\\\\\\\Use \ difference \ of \ squares \ rule.\\\\(7x + 6y) (7x - 6y)\\\\\\Therefore, \ you \ get \fbox{(7x+6y)&(7x-6y)}.[/tex]
A boat traveled 27 miles in 2 hours.At this rate,how many miles will the boat in 1/2 hour?
[tex] \frac{27 \: miles \div 2}{2 \: hours \div 2} = \frac{13.5 \: miles}{1 \: hour} [/tex]
[tex] \frac{13.5 \: miles \div 2}{1 \: hour \div 2} = \frac{6.75 \: miles}{0.5 \: hour} [/tex]
The boat will travel 6.75 or
[tex]6 \frac{3}{4} [/tex]
miles in 1/2 hour.
At Bud's company, bowling balls are shaped as a sphere with a diameter of 8 inches. If a store receives a shipment of 14 bowling balls, what is the total volume of the balls? 937.81 cubic inches B. 3,751.3 cubic inches C. 267.95 cubic inches D. 30,009.98 cubic inches
Answer I think it is c I hope that right I am sorry for late responds
The ABC Book club charges a $40 monthly fee, plus $2 per book read in that month. The Easy Book Club charges a $35 monthly fee, plus $3 per book read in that month. For each club, how many books must be read in 1 month for the total charges from each club to be equal?
Answer:
5 books must be read in 1 month for the total charges from each club to be equal.
Step-by-step explanation:
Monthly Charges of ABC club = 40$
Per book read charges of ABC club = 2$
amount of book read = x
Total charges of ABC club = 40 + 2x
Monthly Charges of Easy book club = 40$
Per book read charges of Easy Book club = 3$
Total charges of Easy book club = 35 + 3x
To calculate how many books must be read in 1 month for the total charges from each club to be equal,
Total charges of ABC club = Total charges of Easy book club
40 + 2x = 35 + 3x
40 - 35 = 3x -2x
5 = x
x = 5
Therefore, 5 books must be read in 1 month for the total charges from each club to be equal.
A window is in the shape of a rectangle with a base of 4 ft and a height of 5 ft. The window has a colored glass in the shape of a kite. Use the grid to identify the area of the colored glass.
Answer:
A = 10 ft²Step-by-step explanation:
Look at the picture.
A₁ = 2 · 2 = 4
A₂ = 2 · 3 = 6
The area of a rhombus:
A = A₁ + A₂ ⇒ A = 4 + 6 = 10
You can use the formula of an area of a rhombus:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
d₁ = 4, d₂ = 5
Substitute:
[tex]A=\dfrac{(4)(5)}{2}=(2)(5)=10[/tex]
Answer:
10 ft²
Step-by-step explanation:
A = 1/2 (d1) (d2)
A = 1/2 (4) (5)
1/2 x 20
=10 ft²
The scatterplot shows the number of home runs Mario hits during his first four seasons on the company softball team. If his output continues to follow the linear model, approximately how many home runs will Mario hit during his ninth season?
A. 30 home runs
B. 35 home runs
C. 45 home runs
D. 50 home runs
Answer:
i think its B on edge
What is the correct way to write this fraction as a percent? A. 20% B. 25% C. 40% D. 70%
20% as a fraction is 1/5
25% is 1/4
40% is 2/5
and 70% is 7/10
Depending on what your fraction is, you can find the answer in the fraction itself-
20%, you can take 20, 5 times to get to 100. Hence 1/5.
25 can go into 100 4 times (1/4)
40 is just 20 twice, so its 2/5.
Take 10 7 times and get 7/10.
Hope this helps a bit :)
Solve for x
(3/4)x-(7/3)=-2x+(5/3)
Answer:
your answer is x=16/11
explanation:
solve for x by simplifying both sides of the equation then isolation the variable.
exact form: 16/11
decimal form: 1.45
mixed number form: 1 5/11
hope this helps
~~bangtanboys7
Answer: [tex]x=\frac{16}{11}[/tex]
Step-by-step explanation:
To solve the equation shown in the problem you must:
- Add the like terms, as following:
[tex]\frac{3}{4}x+2x=\frac{5}{3}+\frac{7}{3}\\ \frac{11}{4}x=4[/tex]
- Multiply both sides by 4.
- Divide both sides of the equation by 11.
Therefore, the result is:
[tex](4)\frac{11}{4}x=4(4)\\11x=16\\x=\frac{16}{11}[/tex]
When two six-sided dice are rolled what is the probability that the product of their scores will be greater than six?
Answer: [tex]\bold{\dfrac{11}{18}}[/tex]
Step-by-step explanation:
Think of the products row by row:
11 12 13 14 15 16 - 0 products greater than 6
21 22 23 24 25 26 - 3 products greater than 6
31 32 33 34 35 36 - 4 products greater than 6
41 42 43 44 45 46 - 5 products greater than 6
51 52 53 54 55 56 - 5 products greater than 6
61 62 63 64 65 66 - 5 products greater than 6
[tex]\dfrac{\text{number greater than 6}}{\text{total possible outcomes}}=\dfrac{22}{36}=\dfrac{11}{18}\ when\ reduced[/tex]
Answer:
11/18.
Step by.step explanation:
There are 36 possible outcomes when 2 dice are rolled.
Outcomes for a product greater than six are:
2,4 2,5 2,6 3,3 3,4 3,5 3,6 4,2 4,3 4,4 4,5 4,6 5.2 ......5.6 , 6.2 .......6.6.
= 22 ways.
required Probability is 22/36 = 11/18 (answer).
The graph of a quadratic function has x intercepts at -3 and 5/2, and y intercept at 10. Give the function.
Answer:
f(x) = -4/3x² -2/3x +10
Step-by-step explanation:
The quadratic regression function of a graphing calculator or spreadsheet can determine the equation for you.
___
Or, you can determine it yourself.
The equation can be written in the form ...
f(x) = a(x +3)(x -5/2) . . . . . . . using the given x-intercepts
for some value of "a"
For x = 0, this must match the y-intercept.
f(0) = a(0 +3)(0 -5/2) = 10
-15/2·a = 10
a = -20/15 = -4/3
So, the function can be written as ...
f(x) = (-4/3)(x +3)(x -5/2)
or
f(x) = -4/3x² -2/3x +10
-2/3( 2x^2 + x - 15) is the answer.
From the given x-intercepts, 2 factors of the equation will be (x + 3) and
(2x - 5):- So we can write:
At the y-intercept x = 0 so we have the equation a(0+3)(2(0) - 5) = 10 where a is a constant.
a * -15 = 10
a = -2/3 so the function is (-2/3)(x + 3)(2x - 5)
= -2/3( 2x^2 + x - 15).
A pile of 10 000 sheets of paper is 85 cm thick what is the thickness of 1 sheet of paper
Answer:
0.0085 centimeters.
Step-by-step explanation:
85/10000 is equal to 0.0085 centimeters, which is absurdly thin for anything, really.
(9CQ) Find the distance from the balloon to the soccer fields.
Answer:
The distance from the balloon to the soccer fields = 3.6 miles ⇒ answer (b)
Step-by-step explanation:
* Let the hot air balloon at point A , the soccer fields
at point B and the football field at point C
∵ The measure of the angle of depression to the
soccer fields is 20° 15'
∴ The measure of angle B = 20° 15'
∵ The measure of the angle of depression to the
football field is 62° 30'
∴ The measure of angle C = 62° 30'
∵ The sum of measures of the interior angles of any triangle = 180°
∴ The measure of angle A = 180 - (20° 15' + 62° 30') = 97° 15'
* The distance between the balloon and the soccer field
is represented by the side AB of triangle ABC
- Use the sin Rule to find the length of side AB
∵ a/sin(A) = b/sin(B) = c/sin(C)
- a is the side opposite to angle A, b is the side opposite
to angle B and c is the side opposite to angle C
∵ AB = c ⇒ opposite to angle C
∵ The distance between the two fields = 4 miles
∴ BC = 4 miles
∵ BC = a ⇒ opposite to angle A
∴ 4/sin(97° 15') = c/sin(62° 30')
∴ c = (4 × sin(62° 30')) ÷ sin(97° 15')
∴ c = 3.6 miles
∴ The distance from the balloon to the soccer fields = 3.6 miles
answer (b)