Answer:
ALL REAL NUMBERS actually
Step-by-step explanation:
Any exponential function like this, is ALWAYS R.
A man 1.5 metres tall standing on top of a mountain 298.5m high observes the angles of depressions of two flying boats D and C to be 28 and 34 degrees respectively. Calculate the distance between the boats.
Pls I need urgent answer plss
Answer:
119.45 meters
Step-by-step explanation:
This question can be solved using one of the three trigonometric ratios. The height mentioned is 298.5 + 1.5 = 300 m and the angle of depression is 28 degrees for Boat D and 34 degrees for Boat C. It can be seen that the required distance is given by x feet, which is the distance between the two boats. This forms two right angled triangle, as it can be seen in the diagram. The perpendicular is given by 300 m, the base is the unknown, and the angles 28 degrees for boat A and 34 degrees for boat B is is given, as shown in the attached diagram. Therefore, the formula to be used is:
tan θ = Perpendicular/Base (For the distance between the mountain and Boat D)
Plugging in the values give:
tan 28 degrees = 300/d.
d = 300/tan 28.
d = 564.22 m (to the nearest hundredth).
tan θ = Perpendicular/Base (For the distance between the mountain and Boat C)
Plugging in the values give:
tan 34 degrees = 300/c.
c = 300/tan 34.
c = 444.77 m (to the nearest hundredth).
The difference between d and c will be x, i.e. that distance between the boats. So 564.22 - 444.77 = 119.45 meters (to the nearest hundredth).
Therefore, the boats are 119.45 meters apart from each other!!!
To calculate the distance between the two boats, we can use the concept of angles of depression and trigonometry. The distance to boat D is calculated using the tangent function with the angle of depression and the height of the observer. The same process is used to find the distance to boat C. The distance between the boats is then the difference between these two distances.
Explanation:To calculate the distance between the two boats, we can use the concept of angles of depression. Let's consider the boat D first. The angle of depression is the angle that the line of sight makes with the horizontal when looking down. In this case, the angle of depression for boat D is 28 degrees. Similarly, the angle of depression for boat C is 34 degrees.
Now, let's use trigonometry to find the distances. We can use the tangent function, which is the opposite side divided by the adjacent side. The opposite side represents the height difference between the observer and the boat, while the adjacent side represents the distance between the observer and the boat.
For boat D, we have:
tan(28 degrees) = opposite/adjacent
opposite = 1.5 m (height of the observer)
adjacent = distance between the observer and boat D
distance between the observer and boat D = 1.5 m / tan(28 degrees)
We can use the same process to find the distance between the observer and boat C:
distance between the observer and boat C = 1.5 m / tan(34 degrees)
Therefore, the distance between the boats is the difference between the distance to boat D and the distance to boat C.
chris runs 2.3 miles every day of the week, except sunday. on sunday he only runs 2 miles. how many miles will he run in 2 weeks?
Answer:
He will run 31.6 miles in two weeks.
Step-by-step explanation:
6 days a week = 2.3 miles
6 days · 2 weeks = 12 days total running 2.3 miles
1 day a week = 2 miles
1 day · 2 weeks = 2 days total running 2 miles
(12 · 2.3) + (2 · 2)
27.6 + 4
31.6 miles
The Chesapeake Bay tides vary between 4 feet and 6 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? Amplitude = 1 foot; period = 12 hours; midline: y = 5 Amplitude = 2 feet; period = 6 hours; midline: y = 1 Amplitude = 2 feet; period = 12 hours; midline: y = 5
Answer:
The correct option is 1.
Step-by-step explanation:
The general cosine function is
[tex]y=A\cos (Bx+C)+D[/tex]
where, A is amplitude, [tex]\frac{2\pi}{B}[/tex] is period, C is phase shift and D is midline.
It is given that the Chesapeake Bay tides vary between 4 feet and 6 feet. it means the minimum value is 4 and maximum value is 6.
Amplitude of the function is
[tex]Amplitude=\frac{Maximum-Minimum}{2}[/tex]
[tex]Amplitude=\frac{6-4}{2}[/tex]
[tex]Amplitude=1[/tex]
Therefore the amplitude of the function is y=5.
Midline of the function is
[tex]Mid line=\frac{Maximum+Minimum}{2}[/tex]
[tex]Mid line=\frac{6+4}{2}=5[/tex]
Therefore the midline of the function is y=5.
It completes a full cycle in 12 hours.
[tex]Period=12[/tex] hours
[tex]\frac{2\pi}{B}=12[/tex]
Period of the function is 12 hours. Therefore the correct option is 1.
Answer:
A. Amplitude = 1 foot; period = 12 hours; midline: y = 5
d) The surface area if Lake Superior is approximately 31,700 square miles. Express
the surface area of the lake in square kilometers to the nearest square kilometer.
Use the fact that 1 kilometer = 0.6214 miles. (5 pt.)
Answer:
51,013.84 kilometers
Step-by-step explanation:
1 kilometer= .6214
So you have to divide 31,700 by .6214
You get 51,013.839 or round it to 51,013.84
Answer:
51,013.839
Step-by-step explanation: you have to convert to kilometers
Need help with number 8 please
Answer:
B
Step-by-step explanation:
5x+2x=7x
4-1=3
The answer is 7x + 3
Simplify 3 (x+2)- x + 8
Answer:
The answer is x = 7
Step-by-step explanation:
3(x+2) - x + 8
Open the bracket
3(x + 2) distribute
3x + 6
3x + 6 - x + 8
combine the like terms
3x - x + 8 + 6
2x + 14
Please mark me as brainliest
First you must distribute the 3 to the numbers inside the parentheses, which would be x and 2...
(3 * x) + (3 * 2) - x + 8
3x + 6 - x + 8
Now you must combine like terms. This means that first numbers with no variables go together. Then the numbers with the same variables must be combined...
no variable combination:
3x + 6 -x + 8
6 + 8 = 14
3x - x + 14
same variable combination:
3x - x + 14
3x - x = 2x
2x + 14
Hope this helped!
~Just a girl in love with Shawn Mendes
HELP PLEASEEEEEEEEEEEEEEEEEEE
Answer:
counterclockwise rotationclockwise rotation90 degrees rotation270 degrees rotationAdd the following polynomials, t
- 3x2 - 2xy + y2
- 4x2 - xy +6y2
x2+ 6xy- y2
Well, it is 3 polynomials so let’s break it down first.
(-3x*2 -2xy +y*2) (-4x*2 -xy + 6y*2)
Let’s add these first. The rule is to drop parentheses and add regularly. Bases stay the same, powers add and coefficients multiply.
Ans: (-7x*4 -3x*2 y*2 + 7y*4)
Now let’s add it with the last one.
The answer is: -6x*6 +3x*3 y*3 -6y*6
The polynomial obtained after adding the following polynomial is 3x +3xy +4y²-3x².
What are Polynomials ?A polynomial can be defined as a mathematical expressions made up of indeterminate and coefficients and involving only addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
It is given in the question to add the polynomials
- 3x - 2xy + y²
- 4x² - xy +6y²
x²+ 6xy- y²
Adding the coefficients of like variables having same coefficients.
3x - 2xy + y² + (- 4x² - xy +6y²) + ( x²+ 6xy- y² )
3x -2xy+y² -4x² - xy +6y² + x²+ 6xy- y²
3x +3xy +4y²-3x²
The polynomial obtained after adding the following polynomial is 3x +3xy +4y²-3x².
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A triangular city lot bounded by three streets has a length of 300 feet on one street, 250 feet on the second, and 420
feet on the third. Find the approximate measure of the largest angle formed by these streets.
Answer:
The approximate measure of the largest angle formed by these streets is [tex]99.2\°[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]c^{2}=a^{2}+b^{2} -2(a)(b)cos(C)[/tex]
In this problem we have
[tex]a=300\ ft[/tex]
[tex]b=250\ ft[/tex]
[tex]c=420\ ft[/tex] ----> is the greater side
substitute and solve for angle C
[tex]420^{2}=300^{2}+250^{2} -2(300)(250)cos(C)[/tex]
[tex]176,400=152,500 -150,000cos(C)[/tex]
[tex]cos(C)=[152,500-176,400]/150,000[/tex]
[tex]cos(C)=-0.1593[/tex]
[tex]C=arccos(-0.1593)=99.2\°[/tex]
17. In 2014, 16,674 earthquakes occurred world wide. Of these,
89.6% were minor tremors with magnitudes of 4.9 or less on
the Richter scale. How many minor earthquakes occurred in
the world in 2014? Round to the nearest whole. (Source: U.S.
Geological Survey National Earthquake Information Center)
Answer:
15836
Step-by-step explanation:
Formula
Minor Earthquakes = (%) * Total Earthquakes.
Givens
Minor Earthquakes = ??
% = 89.6
Total Earthquakes = 17674
Solution
Minor Earthquakes = 89.6 / 100 * 17674
Minor Earthquakes = 1583590.4/100
Minor Earthquakes = 15836
Answer: There are 14940 minor earthquakes occurred in the world in 2014.
Step-by-step explanation:
Since we have given that
Number of earthquakes occurred world wide = 16674
Percentage of minor tremors with magnitude of 4.9 or less = 89.6%
So, Number of minor earthquakes occurred in the world in 2014 is given by
[tex]\dfrac{89.6}{100}\times 16674\\\\=0.896\times 16674\\\\=14939.90[/tex]
Hence, there are 14940 minor earthquakes occurred in the world in 2014.
What is the remainder in the synthetic division problem below?
Answer: 9
Step-by-step explanation:
Answer:
the remainder is 9
Step-by-step explanation:
find the remainder in the synthetic division
1 4 6 -1
Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder
1 4 6 -1
0 4 10
--------------------------------
4 10 9 -> Remainder
So the remainder is 9
The expression 2(1 + w) is used to calculate the perimeter of a rectangle, where I is length and w is width. If the length is ⅔ unit
and the width is ⅓
unit, what is the perimeter of the rectangle in units?
A: ⅔ unit
B: 1 unit
C: 1 ⅔ units
D: 2 units
PLEEEASEEEE HELLLPPPP FASTTTTT!!!!!
Answer: D: 2 units
Step-by-step explanation:
You may have mistaken the formula, as it's 2(l + w), not 1.
If we use this formula, we can say:
2([tex]\frac{2}{3} + \frac{1}{3}[/tex]) = 2(1) = 2
Therefore, the answer is 2 units.
Hope this helps! :^)
A researcher is studying end-times beliefs of Christians by surveying members of his Methodist church.
This study may suffer from what type of bias?
Participation bias
Availability error
Selection bias
No bias
Answer: Participation bias
Step-by-step explanation: He chose to only use his own church instead of using a number of different denominations.
3. Given: Circle Q
<A = 35
Find: m AB
Answer: 110°
Step-by-step explanation:
∠A ≅ ∠B
since ∠A = 35° (given), then ∠B = 35°
Use the Triangle Sum Theorem to find ∠C:
∠A + ∠B + ∠Q = 180°
35° + 35° + ∠Q = 180°
70° + ∠Q = 180°
∠Q = 110°
The central angle (∠AQB) ≅ arc AB
since ∠AQB = 110° (solved above), then arc AB = 110°
Consider the two points A(9.7) and B(5,2).
What is the ratio of the vertical change from A to B to the horizontal change from A to B? In other words, what is the
slope?
What the answer
Answer:
The slope is [tex]m=\frac{5}{4}[/tex] or [tex]m=1.25[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(9,7)\ B(5,2)[/tex]
Substitute the values
[tex]m=\frac{2-7}{5-9}[/tex]
[tex]m=\frac{-5}{-4}[/tex]
[tex]m=\frac{5}{4}=1.25[/tex]
Find the value of two numbers if their sum is 17 and their difference is 1.
Answer:
The values are 9 and 8
Step-by-step explanation:
Let the first number be x
Let the second number be y
The sum of x and y is x+y=17
The difference of x and y is x-y=1
x+y=17 (this is equation 1)
x-y=1 (this is equation 2)
Now we will add equation 1 and equation 2.
x+y = 17
x-y = 1
______
2x =18
x= 18/2
x= 9
Now put the value of x in equation 1.
x+y = 17
9+y = 17
y = 17-9
y = 8
Solution Set ={(x,y)(9,8)}
compute the probability of tossing a six-sided die and getting a 7
Determine if each number is a whole number, integer, or rational
number. Include all sets to which each number belongs.
4. -12.
5. 7/8
Final answer:
The number -12 is both an integer and a rational number, but not a whole number. The number 7/8 is a rational number but neither a whole number nor an integer.
Explanation:
We need to determine if each provided number belongs to the sets of whole numbers, integers, or rational numbers.
-12
-12 is an integer because it is a whole number that can be positive or negative, including zero. Since all integers are also rational numbers (they can be written as a ratio of integers, for example, -12 can be written as -12/1), -12 is also a rational number. However, it is not a whole number because whole numbers are non-negative integers (0, 1, 2, 3,...).
7/8
7/8 is a rational number because it is expressed as the ratio of two integers (7 and 8). It is not an integer nor a whole number because it is not a whole number without a fractional or decimal component.
A city that had 40,000 trees started losing them at a rate of 10 percent per year because of urbanization.
In approximately years, the number of trees in the city reduced to a quarter of the original amount. Hint: Model the situation as P = P0(1 − r)t.
Answer:
t = 13.1576 years
Step-by-step explanation:
The situation can be modeled as
P = Po.(1-r)^t
Where
t is the years transcurred
Po is the initial amount
r is the rate of change
Po = 40000
r = 10% equivalent to 0.1
Now
A quarter of the original amount
(1/4)*Po = Po.(1-r)^t
(1/4) = (0.9)^t
t = 13.1576
Please, see attached picture
Value A rent a car a luxury car at a daily rate of $36.09 plus 5 cents per mile. A business person is allotted $120 for a car rental each day. How many miles can the business person travel on the $120?
Which is the approximate solution for the system of equations 8x - 10y = -23 and 9x + 10y = -16?
Answer:
it's A (-2.3,0.5)
Step-by-step explanation:
doing it
The approximate solution for the system of equations are (- 2.3, 0.5).
We have to given that,
The system of equations are,
8x - 10y = -23
And 9x + 10y = -16
Now, Solve the equation by substitution method as,
8x - 10y = -23 .. (i)
9x + 10y = -16 .. (ii)
From (ii);
10y = - 16 - 9x
Substitute above value in (i);
8x - (- 16 - 9x) = - 23
8x + 16 + 9x = - 23
17x + 16 = - 23
17x = - 23 - 16
17x = - 39
x = - 39/17
x = - 2.3
From (i);
8 × - 2.3 - 10y = - 23
- 18.4 - 10y = - 23
- 18.4 + 23 = 10y
4.6 = 10y
y = 4.6/10
y = 0.46
y = 0.5
Therefore, Solution is, (- 2.3, 0.5)
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What is the answer to this question
cube root of b to the 12 power
[tex]\sqrt[3]{b^{12}}=\sqrt[3]{(b^4)^3}=b^4[/tex]
Can sumone plzhelp..Apply the distributive property to factor out the greatest common factor of all three terms .
9a-18b+21c=
Answer:
3(3a - 6b + 7c )
Step-by-step explanation:
The greatest common factor of 9, 18 and 21 is 3
Factor out 3 from each term
9a - 18b + 21c
= 3(3a - 6b + 7c) ← in factored form
Answer:
3(3a - 6b + 7c)
Step-by-step explanation:
Write each term as a multiplication of its factors. Then see which factors are in common to all terms.
9a - 18b + 21c =
= 3 * 3 * a - 2 * 3 * 3 * b + 3 * 7 * c
The common factors are shown below in bold:
= 3 * 3 * a - 2 * 3 * 3 * b + 3 * 7 * c
The only common factor is 3.
Now use the distributive property to factor out a 3.
= 3(3 * a - 2 * 3 * b + 7 * c)
Now multiply each term in parentheses again.
= 3(3a - 6b + 7c)
A soccer ball kicked from the ground with an initial velocity of 32 ft/s is given by the function
h(t) = -16 + 321. When is the soccer ball moving through the air?
Answer:
In words the answer is between t=0 and t=2.
In interval notation the answer is (0,2)
In inequality notation the answer is 0<t<2
Big note: You should make sure the function I use what you meant.
Step-by-step explanation:
I hope the function is h(t)=-16t^2+32t because that is how I'm going to interpret it.
So if we can find when the ball is on the ground or has hit the ground (this is when h=0) then we can find when it is in the air which is between those 2 numbers.
0=-16t^2+32t
0=-16t(t-2)
So at t=0 and t=2
So the ball is in the air between t=0 and t=2
Interval notation (0,2)
Inequality notation 0<t<2
According to the question:
Make sure the function I use is what you intended, please.I'm going to interpret it as h(t)=-16t^2+32t, so I'm hoping that's the function.The ball is in the air between those two numbers, therefore if we can determine when it is on the ground or has hit the ground (when h=0), we can determine when it is in the air.0 = -16t^2+32t.
0 = -16t(t-2).
So, at t=0 and t=2.
Thus, between t=0 and t=2, the ball is in the air.
Periodic notation (0,2).
Inequality notation 0<t<2.
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find the volume of a trianglular prism that has a triangular base of 14 and and a height of 17 with a prism height of 5 leave your answer in a0 cubic units WILL GIVE BRAINLIEST!
Answer:
Exact Form:
1190/ 3
Decimal Form:
396. 6
Mixed Number Form:
396 2 /3
Step-by-step explanation:
Final answer:
The volume of the triangular prism with a triangle base of 14 units and height of 17 units and a prism height of 5 units is 595 cubic units.
Explanation:
To find the volume of a triangular prism, we need to first find the area of the base triangle and then multiply it by the height of the prism. The formula for the volume of a triangular prism is given by V = (base area) imes (prism height). However, we need to be clear about what the given 14 and 17 represent. Assuming they stand for base and height of the triangle, respectively, the area of the base triangle is A = (1/2) imes base imes height = (1/2) imes 14 imes 17. Multiplying this area by the prism height of 5 units gives us the volume of the prism.
Calculating the base area: A = (1/2) imes 14 imes 17 = 119 square units. The volume is then V = 119 imes 5 = 595 cubic units. Therefore, the volume of the triangular prism is 595 cubic units.
What rotation was applied to triangle DEF to create D’E’F’?
Answer:
90 degree Clockwise Rotation
Step-by-step explanation:
Look at the figure and its points. When you rotate the paper clockwise, you will see that D'E'F is in the same position as DEF.
Answer:
90 degree anti-clockwise rotation
Step-by-step explanation:
if you turn the paper anti-clockwise, u can see that DEF is turned into D'E'F.
You decide to practice your soccer goal-scoring skills by drawing the outline of a soccer goal for players up to 12 years old(21 by 7 feet) on a wall that measure 36 by 9 feet. Unfortunately, you are a soccer rookie so your shots tend to bounce off the wall randomly. The probability that you actually hit the target goal is
Heyyyyyyyyyyyy
12 is to 7 is the answer
Idlkkk
The probability of hitting the soccer goal drawn onto the wall is approximately 45%, given that the soccer shots are completely random.
Explanation:The subject of this question is probability, which is part of mathematics. The scenario describes a soccer training drill where the aim is to hit a goal that has been drawn onto a wall. The goal's dimensions are 21 feet by 7 feet, and the wall's dimensions are 36 feet by 9 feet.
In order to calculate the probability of hitting the target goal, we first need to calculate the area of the goal and the area of the wall. The area of the goal is obtained by multiplying the length by the height (21ft x 7ft = 147ft^2). Similarly, the area of the wall is 36ft x 9ft = 324ft^2.
Now that we have the areas, the probability of hitting the goal can be calculated by dividing the area of the goal by the area of the wall. That is, 147ft^2/324ft^2 = 0.4537, or approximately 0.45 or 45% when converted into a percentage.
Therefore, given that the shots are completely random, there is a 45% probability that the soccer ball will hit the drawn goal on the wall.
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Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x as the independent variable?
Answer:
f(x) = 6x + 9
Step-by-step explanation:
Given
y - 6x - 9 = 0
Express the equation with y as the subject
Add 6x + 9 to both sides
y = 6x + 9
To express in functional notation let y = f(x), hence
f(x) = 6x + 9
Answer:
A. [tex]f(x)=6x+9[/tex]
Step-by-step explanation:
We have been given an equation [tex]y-6x-9=0[/tex]. We are asked to write our given equation in function notation with x as the independent variable.
First of all, we will convert our given equation in slope-intercept form by separating y on one side of equation.
[tex]y-6x-9=0[/tex]
[tex]y-6x+6x-9=0+6x[/tex]
[tex]y-9=6x[/tex]
[tex]y-9+9=6x+9[/tex]
[tex]y=6x+9[/tex]
Now, we will replace [tex]y[/tex] with [tex]f(x)[/tex].
[tex]f(x)=6x+9[/tex]
Therefore, our required function would be [tex]f(x)=6x+9[/tex] and option A is the correct choice.
Write a general formula to describe the variation: x varies directly with y
Answer:
x veries directly to y means that
x=ky. k is solved for which is substituted into the equation.
Final answer:
To describe the situation where x varies directly with y, one uses the equation y = kx, where k is the proportionality constant signifying the ratio between y and x.
Explanation:
The student is asking for a general formula to describe the situation where x varies directly with y. When two quantities vary directly, as one increases, the other increases as well, and the relationship between them can be described by a directly proportional relationship. This can be expressed with the equation y = kx, where k is the proportionality constant. The value of k remains constant within any given relationship, indicating how much y changes in response to a change in x. If y is plotted against x on a graph, you would obtain a straight line that passes through the origin, reflecting the direct proportionality.