Answer:
Helio is 53.2 feet from the kite ⇒ the last answer
Step-by-step explanation:
* Lets change this story problem to a trigonometry problem
- Assume that there is a triangle joining between the
kite, Farimah and Helio
- The name of the triangle is KFH, where K position of the kite,
F position of Farimah and H is the position of Helio
∵ Farimah and Helio are standing 15 feet apart from each other
∴ FH = 15 feet
∵ Farimah is flying the kite on a 57 feet string at an angle
of 68 with the ground
∴ FK = 57 feet
∴ m∠KFH = 68°
∵ We need to know that Helio is how far from the kite
∴ We need to calculate the length of KH
* Now lets find the best way to find the length of KH
using the trigonometry
- We have the length of two sides and the measure of the included
angle between them , then the best way is the cosine Rule
* Lets explain the cosine rule:
- In ΔABC:
∵ a is the length of the side opposite to ∠A ⇒ a is BC
∵ b is the length of the side opposite to ∠B ⇒ b is AC
∵ c is the length of the side opposite to ∠C ⇒ c = AB
∴ a² = b² + c² -2bc × cos(A)
∴ b² = a² + c² -2ac × cos(B)
∴ c² = a² + b² -2ab × cos(C)
* We will use the rule in our problem to find HK
∵ FH is k , HK is f , KF is h
∴ f² = h² + k² - 2hk × cos(F)
∵ h = 57 feet , k = 15 feet , m∠F = 68°
∴ f² = (57)² + (15)² - 2(57)(15) × cos(68) = 2833.4227
∴ f = √2833.4227 = 53.2 feet
* Helio is 53.2 feet from the kite
Can someone pls help me out
Answer:
i think its .b. sorry if im wrong
Step-by-step explanation:
Answer:
A) 5x -4y =1
B) 4x -2y = 8
Using Cramer's Rule of detrminants
a = 5 b = -4 e=1
c = 4 d = -2 f = 8
denominator = 5 * -2 -(4 *-4) = 6
x = 1 * -2 [-(8 *-4)] / denom = 30 / 6 = 5
y = 5 * 8 -(4 * 1) / denom = 36 / 6 = 6
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the red graph?
The answer is:
b. [tex]g(x)=x^{2} +3[/tex]
Why?To find what's the equation of the red graph, first, we need to find a function that intercepts the y-axis at 3 and its vertex is located at (0,3)
We must remember that the constant value in a quadratic equation (c) will tell us where the function intercepts the y-axis, so, we are looking for an equation which has a constant value equal to 3, it discards the options a, c and d, so the correct option would be the option b.
Option b function:
[tex]g(x)=x^{2} +3[/tex]
Where,
[tex]a=1\\b=0\\c=3[/tex]
Let's check if the option b is the correct option:
First, let's find the axis intercepts:
Y-axis intercept
[tex]f(x)=x^{2}+3\\f(0)=0^{2}+3\\y=3[/tex]
X-axis intercept
[tex]0=x^{2}+3\\x=\sqrt{-3}[/tex]
There is no x-axis intercepts since the square roots of negative numbers does not exists in the real numbers.
Finding the vertex coordinates:
The x coordinate of the vertex can be found using the following equation:
[tex]x=-\frac{b}{2a}=-\frac{0}{2*1}=0[/tex]
The x coordinate of the vertex is located at x=0, so to find the y-coordinate we must substitute the x value into the parabola equation, so
[tex]y=x^{2}+3=0^{2}+3=3[/tex]
So, the y coordinate of the vertex is located at y=3
Therefore, the vertex of the function is (0,3)
Hence, the calculated values of the option b match with the given graph.
The correct option is: b. [tex]g(x)=x^{2} +3[/tex]
Have a nice day!
Change the fraction 7/12 to a decimal. Round your answer to the nearest thousandth. A. .583 B. .600 C. 1.700 D. 1.714
Answer:
= 0.583
Step-by-step explanation:
Changing 7/12 as a decimal
we could use long method or convert to percentage
such that;
7/12 × 100 = 700/12
=58.333%
This is equivalent to; 58.333/100
= 0.58333 ; to the nearest thousandth
= 0.583
Answer:
The correct answer is option A. 0.583
Step-by-step explanation:
It is given a fraction 7/12. This fraction is a proper fraction.
proper fraction :- Numerator is less than denominator
We have to convert this fraction into decimal number.
we can convert all proper fractions into decimal.
Convert 7/12 into decimal
7/12 = 0.58333333...
It is a non terminating rec-curing decimal number.
Therefore we can write, 7/12 = 0.583
The correct answer is option A. 0.583
Use the properties of equality to find the value of x in this equation.
4(6x – 9.5) = 46
Answer:
X = 3.5
Step-by-step explanation:
First, we distribute the 4 inside of the parentheses.
4 * 6x = 24x
4 * -9.5 = -38
We now have 24x -38 = 46
Now, we will add 38 to each side to isolate the x.
24x - 38 = 46
+38 +38
We now have 24x = 84
Finally, we will divide each side by 24 to find out what x equals.
24x = 84
— —
24 24
We now have x = 3.5
So, our answer is x = 3.5
I hope I helped!
Let me know if you need anything else!
~ Zoe
Answer:
X = 3.5
Step-by-step explanation:
First, we distribute the 4 inside of the parentheses.
4 * 6x = 24x
4 * -9.5 = -38
We now have 24x -38 = 46
Now, we will add 38 to each side to isolate the x.
24x - 38 = 46
+38 +38
We now have 24x = 84
Finally, we will divide each side by 24 to find out what x equals.
24x = 84
— —
24 24
We now have x = 3.5
So, our answer is x = 3.5
The value of 5 is plotted on the number line below plot another point on the number line that is 10 units away from 5
On a number line, a point that is 10 units away from 5 can be either 15 (if you move right) or -5 (if you move left). Both these points are 10 units away from 5.
Explanation:In mathematics, if the value 5 is plotted on the number line, you can plot another point that is 10 units away from 5 by moving 10 places towards either the right or left on the number line. If you move to the right, 10 places ahead of 5 is 15. So, you can plot a point on 15. On the other hand, if you move to the left, 10 places behind 5 is -5. So, you can plot a point at -5. Either of these points (15 or -5) are 10 units away from 5.
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The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00am and 12:30pm, with a dept of 2.5 m, while high tides occur at 6:15am and 6:45pm, with a depth of 5.5 m. Let t=0 be 12:00 am. Which periodic function, since or cosine would be simpler model for the situation?
A cosine function is simpler to model the situation of the changing tides because it starts at an extremum, aligning with the low tide occurring at t=0 (12:00 am). By calculating the amplitude, midline, and period, we can construct an approximate model for the tidal heights using a cosine function without a phase shift.
The phenomenon of tidal movements can be modeled through periodic functions, such as sine or cosine functions, which are suitable for representing recurring events over time.
In this scenario, since the low tide occurs at t=0 (12:00 am) and reaches the same low tide level at t=12.5 (12:30 pm), a cosine function would be more appropriate as it inherently starts at a maximum or minimum value.
On the other hand, a sine function starts from the middle of its range, making it necessary to introduce a phase shift in the function for accurate modeling of the tides in this case.
A simple cosine model for the tidal heights would look like: Depth(t) = A * cos(B * (t - C)) + D, where A represents the amplitude, B is related to the period of the tide cycle, C is the phase shift (in this model C would be zero), and D adjusts the midline to fit the average between high and low tides.
Considering the given data:
Amplitude (A): (High tide depth - Low tide depth) / 2 = (5.5m - 2.5m) / 2 = 1.5m
Midline (D): (High tide depth + Low tide depth) / 2 = (5.5m + 2.5m) / 2 = 4m
Period (Related to B): Since there are two high and two low tides every 24 hours, the period would be 12 hours. We would then find B by using the formula 2 * pi / period, yielding B = 2 * pi / 12.
So, the model would be approximately Depth(t) = 1.5 * cos((pi / 6) * t) + 4, accurately reflecting the transition from low to high tides and back over a 12-hour cycle.
Answer:
A cosine function would be a simpler model for the situation.
The minimum depth (low tide) occurs at t = 0. A reflection of the cosine curve also has a minimum at t = 0.
A sine model would require a phase shift, while a cosine model does not.
Jimmy is trying to dive down and touch the bottom of the pool. On his first try, he makes it 1/3 of the way to the bottom.
on his second try, he makes it 3/5 of the way to the bottom.
Jimmy's second dive was deeper than his first dive by what fraction of the pool?
Answer:
4 feet or 4/15
Step-by-step explanation:
1. So first you have to multiply the top and bottom number of each fraction by the denominator of the opposite fraction to have the same denominator:
1/3 X 5/5 = 5/15
3/5 X 3/3 = 9/15
2. Then you compare the two fractions and subtract the smaller fraction from the bigger:
9/15 - 5/15 = 4/15
So Jimmy dived 4 feet deeper the second time
Answer:
The answer is 4/15 in fraction and 4 feet in whole number
Step-by-step explanation:
how do you write 5/5 as a percentage
5/5 and then convert this to 100. so, you would multiply it by 20 which would equal 100/100. it’s a whole number, so it’d just be 100%.
What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest hundredth, if necessary. units
Answer:
The perimeter of the trapezoid is [tex]38.25\ units[/tex]
Step-by-step explanation:
we know that
The perimeter of the trapezoid is the sum of its four side lengths
so
In this problem
[tex]P=QR+RS+ST+QT[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]Q(8, 8), R(14, 16), S(20, 16),T(22, 8)[/tex]
step 1
Find the distance QR
[tex]Q(8, 8), R(14, 16)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(16-8)^{2}+(14-8)^{2}}[/tex]
[tex]d=\sqrt{(8)^{2}+(6)^{2}}[/tex]
[tex]d=\sqrt{100}[/tex]
[tex]QR=10\ units[/tex]
step 2
Find the distance RS
[tex]R(14, 16), S(20, 16)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(16-16)^{2}+(20-14)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]RS=6\ units[/tex]
step 3
Find the distance ST
[tex]S(20, 16),T(22, 8)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(8-16)^{2}+(22-20)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{68}[/tex]
[tex]ST=8.25\ units[/tex]
step 4
Find the distance QT
[tex]Q(8, 8),T(22, 8)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(8-8)^{2}+(22-8)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(14)^{2}}[/tex]
[tex]d=\sqrt{196}[/tex]
[tex]QT=14\ units[/tex]
step 5
Find the perimeter
[tex]P=10+6+8.25+14=38.25\ units[/tex]
PLEASE HELP ASAP !! TANGENT RATIO
I will help if u help me pls
QUESTION 1
The tangent ratio is the ratio of the length of the opposite side to the length of the adjacent side.
[tex] \tan(M) = \frac{LN}{NM} [/tex]
[tex] \tan(M) = \frac{8}{6} = \frac{4}{3} [/tex]
QUESTION 2.
We again use the tangent ratio to find angle S.
[tex] \tan(S) = \frac{TU}{SU} [/tex]
[tex]\tan(S) = \frac{0.75}{3.5} [/tex]
[tex]\tan(S) = \frac{3}{14} [/tex]
[tex]S = { \tan}^{ - 1} ( \frac{3}{14} )[/tex]
[tex]S = 12.09 \degree[/tex]
to the nearest hundredth.
QUESTION 3
We can find CE using the tangent ratio.
[tex] \tan(27 \degree) = \frac{18}{CE} [/tex]
[tex]CE = \frac{18}{ \tan(27 \degree) } [/tex]
[tex]CE = 35.3 \degree[/tex]
to the nearest 0.1.
A farmer has a section of a field that measures 4×10^3 feet by 5×10^5 feet planted with carrots. Another section is planted with corn measuring 6×10^4 feet by 3×10^4 feet.
Part A: What is the area of the carrot section? Show work.
Part B: What is the area of the corn section? Show work.
Part C: How much larger is the area of the carrot section than the corn section. Show work.
Answer:
Part A. = 2,000,000,000
Step-by-step explanation:
To find the first measurements solve the equation.
10^3 = 1,000
So now 1,000 multiplied by 4
4 x 1,000 = 4,000
for the second side or measurement solve again.
10^5 = 100,000
5 x 100,000 = 500, 000
with both measurements 4,000 and 500,000 to find area we need to multiply both sides
4,000 x 500,000 = 2,000,000,000
See if you can solve the other one, if you can't I'll help!
Hope this helps!
Please mark as brainliest answer!! THanks!!
what is the quotient of 10 and x as an algebraic expression
Answer:
I believe the answer is 10/x.
Step-by-step explanation:
A quotient is a result obtained by dividing one quantity by another and sence we don't know what x is it will have to just be an algebraic equation like the question says.
Mark brainliest if you can thanks!
The two figures are similar. a). Write the similarity statement. b). Is the image of the dilation a reduction or an enlargement of the original figure? Explain. c) what is the scale factor? Explain
Answer:
Part a) [tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure.(the scale factor is greater than 1)
Part c) The scale factor is [tex]3[/tex]
Step-by-step explanation:
Part a) Write the similarity statement
we know that
If two figures are similar, then the ratio of its corresponding sides is equal so
[tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
substitute the values
[tex]\frac{9}{27}=\frac{12}{36} =\frac{15}{45'}[/tex]
[tex]\frac{1}{3}=\frac{1}{3} =\frac{1}{3'}[/tex] ----> is true
therefore
the figures are similar
Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure. (the scale factor is greater than 1)
Part c) we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z------> the scale factor
x-----> corresponding side of the image
y------> corresponding side of the original figure
so
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=A'B'=27\ units[/tex]
[tex]y=AB=9\ units[/tex]
substitute
[tex]z=\frac{27}{9}=3[/tex]
The scale factor is greater than 1
therefore
Is an enlargement
If f(x)=2(x)^2+5\sqrt((x+2)), complete the following statement
f(0)=
Answer: 5
Step-by-step explanation:
[tex]f(x)=2(x)^2+5\\\\f(0)=2(0)^2+5\\\\.\qquad =0+5\\\\.\qquad =5[/tex]
Find the length of the missing side of the right triangle 5yd 13yd
13^2-5^2=144 find the square root of that which is 12
geometry math problem
Answer:
y=1/6x+3
the slope has to be negative reciprocal and it passes though (6,4)
Machine A can fill a bucket from a pipe in 4 minutes. However, Machine B can empty the bucket in 6 minutes. Starting from empty, if the Machines are going at the same time, how long will it take to fill the tank?
Is it 12mins
Answer:
12 minutes
Step-by-step explanation:
if it fills up in 4 minutes but empties in 6 minutes, that means there's a two minute gap of water sitting - meaning it would multiple attempts to get the bucket filled - taking 12 minutes to be exact - hope this helps!!
Is it 12 minutes good job
Sixteen more than a number is 9. What is the number?
Answer:
-7
Step-by-step explanation:
Its really easy, count backwards 16 from 9 and go into negatives.
Here is the answer counting backwards: 9,8,7,6,5,4,3,2,1,0,-1,-2,-3,-4,-5,-6,-7
Answer: -7
Step-by-step explanation:
If you write out the expression it looks like this, x+16=9. All you have to do is solve for x, which would make the answer -7 because 16 more than -7 is 9.
Mark brainliest please!
A tangent to the curve y=6x-x² cuts the x axis at point P. Find the coordinates of P. Help me calc the coordinates please
We know that the line is tangent at the point (2,8)
The derivative of the function at x=2 is
[tex]f'(x) = 6-2x \implies f'(2) = 6-4=2[/tex]
So, the tangent line passes through the point (2,8) and has slope 2. The equation is
[tex]y-8 = 2(x-2) \iff y = 2x+4[/tex]
This line crosses the x axis where y=0:
[tex]0 = 2x+4 \iff 2x = -4 \iff x = -2[/tex]
The coordinates of point P where the tangent to the curve y=6x-x² cuts the X-axis can be found by finding the x-value when the derivative of the curve is equal to zero. In this case, the x-coordinate of point P is 3, so the coordinates of point P are (3, 0).
Explanation:In this question, we are asked to find the coordinates of point P on the X-axis where a tangent to the curve y=6x-x² cuts the X-axis. The equation of the curve is given as y = 6x - x². A tangent line to the curve intersects it at exactly one point. The equation of this tangent line can be written in slope intercept form y = mx + b. When the tangent line cuts the X-axis, y=0.
The first step is taking the derivative of the curve, which gives us the slope of the tangent line. The derivative of y = 6x - x² is y' = 6 - 2x. This gives us the slope of the tangent line.
The second step is finding the x-coordinate of point P where the tangent line intersects the X-axis. This is where the y-coordinate is zero, or when y = 6x - x² is equal to zero. Solving for x, we get x = 0 or x = 6. However, because the curve y = 6x - x² intersects the X-axis at the x-coordinate of 0 and 6, the x-coordinate of point P must be a different value.
The final step is to solve for the x-coordinate when y' = 0, or when 6 - 2x = 0. Solving this equation gives us x = 3. So, the tangent line will cut the X-axis at point P(3, 0).
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find the measures of angle b
Answer:
142
Step-by-step explanation:
The line underneath the straight angle is a straight line, meaning it is 180 degrees. 180-38= 142
A straight line is 180 degrees.
180-38=142
142 degrees is the answer.
What is the cosine of angle D?
Cos(x)=20/25
X=cos-1(20/25)
=36.86989765
=B
What is the sum of the series?
Answer:
44
Step-by-step explanation:
substitute k = 1, 2, 3, 4 into 2k² - 4 and sum the terms
k = 1 : 2(1)² - 4 = 2 - 4 = - 2
k = 2 : 2(2)² - 4 = 8 - 4 = 4
k = 3 : 2(3)² - 4 = 18 - 4 = 14
k = 4 : 2(4)² - 4 = 32 - 4 = 28
sum = - 2 + 4 + 14 + 28 = 44
Heya!
--------------------
Things to know before we solve:
The "4" at the top means that the the sequence only goes to the 4th term.
k = 1 represents that the sequence starts with the 1st term.
(2k² - 4) represents the rule of the sequence, we can substitute 1, 2, 3, and 4 to solve for the terms of the sequence.
--------------------
Solving for each term:
1st term:
2(1)² - 4
2(1) - 4
2 - 4
-2
2nd term:
2(2)² - 4
2(4) - 4
8 - 4
4
3rd term:
2(3)² - 4
2(9) - 4
18 - 4
14
4th term:
2(4)² - 4
2(16) - 4
32 - 4
28
--------------------
Simplifying:
Write these terms in expanded form:
(-2) + 4 + 14 + 28
Find the sum of the series:
(-2) + 4 + 14 + 28 = 44
--------------------
Answer:
The sum of the series is 44
--------------------
Best of Luck!
What is the length of the segment with endpoints A(1,7) and B(-3, -1)?
Answer:
[tex]d = \sqrt{80} = 8.94[/tex]
Step-by-step explanation:
We can find the distance using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We then substitute (1,7) as [tex](x_1,y_1)[/tex] and (-3,-1) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(-3-1)^2+(-1-7)^2} \\d=\sqrt{(-4)^2+(-8)^2} \\d=\sqrt{16+64}\\d=\sqrt{80}=8.94[/tex]
Answer with Step-by-step explanation:
The length of the line segments with end point (a,b) and (c,d) is:
[tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]
Here, we have to find the length of the segment with endpoints A(1,7) and B(-3, -1)
i.e. (a,b)=(1,7)
and (c,d)=(-3,-1)
Length= [tex]\sqrt{(1+3)^2+(7+1)^2}[/tex]
= [tex]\sqrt{4^2+8^2}[/tex]
= [tex]\sqrt{16+64}[/tex]
= [tex]\sqrt{80}[/tex]
Hence, Length of line segment is:
[tex]\sqrt{80}[/tex] or [tex]4\sqrt{5}[/tex]
Add 9 to me, then multiply by 3. If you subtract 16 and then add 7, you get 27. What number am I?
The number obtained when it is added with 9, multiplied by 3, subtracted by 16 and then added with 7 is 3.
Suppose the number is x
An addition of 9 to x = 9+x
Multiplication of 9+x and 3 = 3(9+x)
According to the question
3(9+x)-16+7 = 27
By solving the above equation we will get x
What is an equation?An equation is a statement that equates to two expressions.
So, 3(9+x) = 36
9+x=12
x=3
So, the number is x=3
Thus, the required number that satisfies the question is 3.
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A triangular window pane has a base of 30 inches and a height of 24 inches what is the area of the window pane
The answer is 360in,hope this help!
Factor completely
x^2 - 3x - 28
Answer:
(x-7) (x+4)
Step-by-step explanation:
x^2 - 3x - 28
What two numbers multiply to -28 and add to -3
-7*4 = -28
-7+4 = -3
(x-7) (x+4)
Answer:
on the top: -28
on the bottom: -3
on the sides: -7 and 4
(x-7)(x+4)
Step-by-step explanation:
Which expression helps you find the length of X of a side of a rectangle that has a diagonal of 15 units and a width of nine units
Answer:
12 units
Step-by-step explanation:
by the pythagorean relation,
x^2 + 9^2 = 15^2
x^2 + 81 = 225
x^2 = 144
x = 12 units
Answer:
x^2 = 15^2 – 9^2
Step-by-step explanation:
Convert 100 km/h to mph. Use 10 miles = 16 kilometers.
Here's how you solve this problem.
1) find how many kilometers equals 1 mile (16/10=1.6).
2) Divide 100 (from 100 km/h) by 1.6 (1.6×100=62.5).
3) solve for mph.
The answer is 62.5mph.
what is the measure of an angle, if three subtracted from twice the supplement and the result is 297 degrees?
Answer:
303
Step-by-step explanation:
I believe this is correct but I need to know the supplement.
One of the hiking trails at a state park is 14/3 miles long. Which mixed number shows the length of the hiking trail? A- 4 2/3 miles B- 4 1/3 miles C- 3 2/3 miles D- 3 1/3 miles
Answer:
A- 4 2/3 miles
Step-by-step explanation:
We are given that one of the hiking trails at a state park is [tex] \frac { 14 } { 3 } [/tex] miles long.
We are to determine whether which of the given answer options shows the length of the hiking trail in mixed number.
Basically, we need to divide 14 by 3 to get: [tex] 4 \frac { 2 } { 3 } [/tex]
So the correct answer option is A. [tex] 4 \frac { 2 } { 3 } [/tex].
Answer:
A- 4 2/3 miles
Step-by-step explanation:
To find the mixed fraction, we divide the numerator with the denominator to get a whole number and a remainder. the remainder becomes the numerator of the proper fraction included in the improper fraction.
14÷3=4 remainder 3.
Therefore our fraction becomes,4 2/3 miles.