Answers
Answer:
Height of the cliff = 13.66 m
Step-by-step explanation:
Let the height of the cliff is 'x' m and distance between the base of the cliff and the boat is 'y' m.
From right triangle AOC,
tan 30° = [tex]\frac{\text{Opposite triangle}}{\text{Adjacent side}}[/tex]
[tex]\frac{1}{\sqrt{3}}=\frac{x}{y}[/tex]
y = [tex]x\sqrt{3}[/tex] ------(1)
From right angle triangle BOC,
tan 45° = [tex]\frac{x}{y-10}[/tex]
[tex]1=\frac{x}{y-10}[/tex]
x = y - 10
y = x + 10 -------(2)
From equations (1) and (2),
[tex]x\sqrt{3}=x+10[/tex]
[tex]x(\sqrt{3}-1)=10[/tex]
[tex]x=\frac{10}{\sqrt{3}-1 }[/tex]
x = 13.66 m
Therefore, height of the cliff is 13.66 m.
Related Questions
Zero pint eight x minus eight equals two x plus four
Answers
Identify the eccentricity of the conic section whose equation is given. r = 3/5 - 3cosθ
3/5
1
5/3
3
Answers
Answer:
3/5
Step-by-step explanation:
A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:
[tex]r=\frac{ep}{1 \pm e*cos(\theta)}[/tex]
Given the conic equation [tex]r=\frac{3}{5-3cos(\theta)}[/tex]
We have to make the conic equation to be in the form [tex]r=\frac{ep}{1 \pm e*cos(\theta)}[/tex].
[tex]r=\frac{3}{5-3cos(\theta)}\\\\Multiply\ the\ numerator\ and \ denominator\ by \ 1/5\\r=\frac{3*\frac{1}{5} }{(5-3cos(\theta))*\frac{1}{5}}\\\\r=\frac{3*\frac{1}{5} }{5*\frac{1}{5}-3cos(\theta)*\frac{1}{5}}\\\\r=\frac{\frac{3}{5} }{1-\frac{3}{5}cos(\theta)}[/tex]
Comparing with [tex]r=\frac{ep}{1 \pm e*cos(\theta)}[/tex]. gives:
e = 3/5, p = 1
The eccentricity is 3/5
What categories does 0.972 belong to? Click all that apply. Real Rational Integer Whole Natural
Answers
Answer:
0.972 is a rational real number.
Step-by-step explanation:
A rational number is defined as the number that can be expressed from the result of a fraction.
1/4 = 0.25
An integer number is all those that do not have a decimal part.
(-∞ ..., -3, -2, -1, 0, 1, 2, 3, ... ∞)
Natural numbers are all those positive numbers starting from 0 to infinity.
N = (0, 1, 2, 3, 4, 5, ... ∞)
m44b
4. In little league baseball, the distance of the paths between each pair of consecutive bases is 60 feet
and the paths form right angles. How far does the ball need to travel if it is thrown from home plate
directly to second base?
Answers
Answer:
84.85 feet or 60[tex]\sqrt2[/tex] feet.
Step-by-step explanation:
Given that:
Distance of paths between each pair of consecutive bases is 60 ft.
To find:
Distance that the ball needs to travel if it is thrown directly from home plate to second base?
Solution:
Actually the given problem can be mapped to a right angled triangle in which base and height are given to be equal to 60 ft (because each pair of consecutive bases are 60 ft apart), Plus, they are at right angles to each other.
So, kindly refer to the image attached.
AB and BC are the distance of paths between consecutive bases.
And we have to find AC.
We can use Pythagorean theorem to find out the Hypotenuse of the triangle.
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AC^{2} = AB^{2} + BC^{2} \\\Rightarrow AC^{2} = 60^{2} + 60^{2} \\\Rightarrow AC = \sqrt{2 \times 60^2}\\\Rightarrow AC = \bold{60\sqrt{2}\ ft = 84.85\ ft}[/tex]
x^2 • x^7 simplify and solve
Answers
Answer:
[tex] x^9[/tex]
Step-by-step explanation:
[tex] \huge {x}^{2} . {x}^{7} = {x}^{2 + 7} = {x}^{9} \\ [/tex]
You did some grocery shopping for your mom. She gave you a $10 bill and a list for oranges for $1.50, milk for $2.00, pasta for $3.25, and juice for $1. How much change will you get back?
Answers
Answer:
You would get 2.25 back.
Step-by-step explanation:
1.50 + 2.00 + 3.25 + 1 = 7.75 Dollars
10 - 7.75 = 2.25
please help me on this geometry!! i’ll mark you the brainliest
Answers
Answer:
Median
Step-by-step explanation:
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.
Hope this helps! Please tell me if I did anything wrong, thank you and have a great day!
Please Help Guys! 1) Why is f(x)=(3x+13)2+89 not the vertex form of f(x)=9x2+2x+1? A.The expression has a constant outside of the squared term. B. The expression is not the product of two binomials. C. The variable x has a coefficient. D. Some of the terms are fractions instead of integers. 2) What is the vertex of the parabola with the equation y=(x−2)2+10? A. (−2, −10) B. (2, 10) C. (−2, 10) D. (2, −10) 3) For the given function, identify the x- and y-intercepts if any, the vertex, the axis of symmetry, and the maximum or minimum value. f(x)=−x2+25 A. The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,−25). The vertex is (0,−25). The axis of symmetry is x=0. The minimum value of the function is −25. B. There are no x-intercepts. The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is y=0. The maximum value of the function is 25. C. The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25. D. The x-intercepts are (−25,0) and (25,0). The y-intercept is (0,5). The vertex is (0,5). The axis of symmetry is x=0. The maximum value of the function is 5. 4) A student says that the function f(x)=−x2−9 has the x-intercepts (−3,0) and (3,0). Is the student correct? If not, explain why. A. The student is correct. B. The student is not correct. The equation f(x)=0 has one real solution, so the x-intercept is (9,0). C. The student is not correct. The equation f(x)=0 does not have any real solutions, so the graph has only one x-intercept, (0,0). D. The student is not correct. The equation f(x)=0 does not have any real solutions, so the graph does not have any x-intercepts.
Answers
Answer:
C. The variable x has a coefficient. B. (2, 10) C. The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25. D. The student is not correct. The equation f(x)=0 does not have any real solutions, so the graph does not have any x-intercepts.Step-by-step explanation:
1) Why is f(x)=(3x+1/3)^2+8/9 not the vertex form of f(x)=9x^2+2x+1?
A.The expression has a constant outside of the squared term.
B. The expression is not the product of two binomials.
C. The variable x has a coefficient.
D. Some of the terms are fractions instead of integers.
Vertex form is a(x -h)^2 +k. The coefficient of x inside parentheses is 1. The given form is not vertex form because the leading coefficient has not been removed to outside parentheses.
__
2) What is the vertex of the parabola with the equation y=(x−2)^2+10?
A. (−2, −10)
B. (2, 10)
C. (−2, 10)
D. (2, −10)
Vertex form is a(x -h)^2 +k. Comparing to the given equation, we find the vertex (h, k) = (2, 10).
__
3) For the given function, identify the x- and y-intercepts if any, the vertex, the axis of symmetry, and the maximum or minimum value. f(x)=−x^2+25
A. The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,−25). The vertex is (0,−25). The axis of symmetry is x=0. The minimum value of the function is −25.
B. There are no x-intercepts. The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is y=0. The maximum value of the function is 25.
C. The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25.
D. The x-intercepts are (−25,0) and (25,0). The y-intercept is (0,5). The vertex is (0,5). The axis of symmetry is x=0. The maximum value of the function is 5.
The x-intercepts are the values of x that make y=0. They are (±5, 0). The y-intercept is the value of y when x=0. It is (0, 25).
__
4) A student says that the function f(x)=−x^2−9 has the x-intercepts (−3,0) and (3,0). Is the student correct? If not, explain why.
A. The student is correct.
B. The student is not correct. The equation f(x)=0 has one real solution, so the x-intercept is (9,0).
C. The student is not correct. The equation f(x)=0 does not have any real solutions, so the graph has only one x-intercept, (0,0).
D. The student is not correct. The equation f(x)=0 does not have any real solutions, so the graph does not have any x-intercepts.
The parabola opens downward and has a maximum value of -9, so cannot cross the x-axis. There are no x-intercepts, hence no real solutions.
Multiply the number by 4. Add 10 to the product. Divide this sum by 2. Subtract 5 from the quotient.
The first number is 1 and the result is 2
The second number is 5 and the result is 10
the third number is 9 and the result is 18
the fourth number is 10 and the result is 20
Write a conjecture that relates the result of the process to the original number selected. part a)
Represent the original number as n.
Answer is 2n
part b Represent the original number as n, and use deductive reasoning to prove the conjecture in part (a). Multiply the number by 4.
Help with part b please.
Answers
Answer:
See Explanation
Step-by-step explanation:
Given the illustration in the question
Required:
Use deductive reasoning to prove (a)
From your question, you need only the (b) part and this is done as follows;
Step 1: Represent the number with: n
Step 2: Multiply n by 4: 4n
Step 3: Add 10 to (2) above: 4n + 10
Step 4: Divide (3) above by 2: (4n + 10)/2 = 4n/2 + 10/2 = 2n + 5
Step 5: Subtract 5 from (4): 2n + 5 - 5 = n
Hence, the end result is proved to be 2n
Test this with any of the given illustration in (a) part, your answer will always be 2n
A = (b*h) / 2 or A = :½ b*h. or A = 0.5*b*h
Answers
Answer:
jklfhgugt
Step-by-step explanation:
A function is defined by f(x) = 5(2-x). What is f(-1)?
o 5
o 5
O 15
O 53
Answers
Answer:
the answer is 15
Step-by-step explanation:
f(x)=5(2-x)
f(-1)=5(2-(-1))
f(-1)=5(2+1)
f(-1)=5(3)
f(-1)=15
Write the following absolute value function as a
piecewise function.
f(x) = 3x – 6
Answers
Answer:+c
Step-by-step explanation:
Cuánto es 100 más que 25????????
Answers
Answer:
la respuesta es 25
Step-by-step explanation:
para calcular este tanto ciento, sugerimos usar esta formula:
%/100 = parte/total
realizando la multiplicatión en cruz:
25% x 100 = 100 x parte, o
2500 = 100 x parte
ahora es sólo dividir por 100 y obtener la respuesta:
parte = 2500/100 = 25
Solve the compound inequality. Graph the solution.
-2 <= 2x - 4 < 4
A. 0<= x < - 2
B. 1 <= x < 4
C. 1 <= x < 0
D. 3 <= x < 6
Answers
Answer:
1 ≤ x < 4
Step-by-step explanation:
-2≤ 2x - 4 < 4
Add 4 to each side
-2+4 ≤ 2x - 4+4 < 4+4
2 ≤ 2x < 8
Divide each side by 2
2/2 ≤ 2x/2 < 8/2
1 ≤ x < 4
Answer:
a.0<=x<-2
Step-by-step explanation:
In her last four basketball games, Alexi has scored 12, 14, 26, and 40 points. If the pattern continues, how many points will Alexi score in her next game? 64 66 62 60
Answers
Answer:
66
Step-by-step explanation:
12+14=26
26+40=66
Q1) If Q is directly proportional to P and Q = 28 when P = 4, (i) express Q in terms of P, (ii) find the value of Q when P = 5, (iii) calculate the value of P when Q = 42. Q2) If z is directly proportional to x and z = 12 when x = 3, find the value of x when z = 18. Q3) If B is directly proportional to A and B = 3 when A = 18, find the value of B when A = 24. I NEED THE ANSWERS QUICKLY!!!
Answers
Answer:
Q1)i) Q= 7p
ii) Q= 35
iii) P= 6
Q2)x= 3
Q3) B=4
A horizontal line has points A, B, E, F. A line extends up and to the right from B to point C. A line extends horizontally from point C to point D. A line extends slightly to the left and down from point D to point E. Angle A B C is (3 x) degrees and angle D E F is (2 x) degrees. What is the measure of AngleCBE? 36° 72° 108° 144°
Answers
Answer:
The answer is 72 degrees
Step-by-step explanation:
I hope this helps, leave a heart and rating plz!!?:)
The correct option is 72°. The measure of angle CBE is 72° by using the data angle ABC is (3 x) degrees and angle DEF is (2 x) degrees.
To determine the measure of angle CBE, we need to analyze the given information. We are provided with the angles ABC and DEF, where angle ABC is represented by 3x degrees and angle DEF is represented by 2x degrees.
From the description, we can see that angle CBE is formed by the combination of angles ABC and DEF. The angle ABC is adjacent to angle CBE at point B, and the angle DEF is adjacent to angle CBE at point E.
To find the measure of angle CBE, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since angle ABC and angle D E F are adjacent to angle CBE and form a straight line, they are supplementary angles. Therefore, the sum of angle ABC and angle DEF is 180 degrees.
We can set up the equation:
3x + 2x = 180°
Combining like terms, we get:
5x = 180°
To solve for x, we divide both sides of the equation by 5:
x = 36°
Now that we know the value of x, we can find the measure of angle CBE by substituting x into the expression for angle DEF:
2x = 2 * 36 = 72 degrees
Therefore, the measure of angle CBE is 72 degrees.
Learn more about angles here:
https://brainly.com/question/32854046
#SPJ2
Evaluate : 5-3(x-1) when x=7
Answers
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{ - 13}}}}[/tex]Step-by-step explanation:
Given , x = 7
let's find :
[tex] \sf{5 - 3(x - 1)}[/tex]
Plug the value of x
⇒[tex] \sf{5 - 3(7 - 1)}[/tex]
Subtract 1 from 7
⇒[tex] \sf{5 - 3 \times 6}[/tex]
Multiply the numbers
⇒[tex] \sf{5 - 18}[/tex]
Calculate
⇒[tex] \sf{ - 13}[/tex]
Hope I helped!
Best regards!!
The value of 5-3(x-1) when x=7 is -13.
What is Evaluate meaning?
Evaluation is nothing but to solve an algebraic expression means to find the value of an expression by replacing the value of the variable in it.
To evaluate the expression value, we simply substitute the variable from its given value and simplify the expression by using order of operations.
In our case, the given expression is:
5-3(x-1)
Substitute the given number i.e., 7 for the variable in the expression:
5-3(7-1)
Solve the bracket first:
5-3(6)
Now solve the multiplication part:
5 - 18
Finally Subtract 5 from -18, we get:
-13
Hence the final value of the expression is -13 at x=7.
To learn more about Evaluation, refer to the link:
https://brainly.com/question/12837686
#SPJ2
the radius of the circular base of a cone is (3x-2)m. if its slant height is (9x^2 - 6x)m, express the cone’s surface area as factored polynomial in x.
NOTE: SA= πrs+πr^2
Answers
Answer:
SA= 289.56 m^2
Step-by-step explanation:
A parabola intersects the x-axis at x=3 and x=9.
What is the x-coordinate of the parabola's vertex?
Answers
Answer:
6
Step-by-step explanation:
If the graph intersects the x-axis, then there is an x-intercept at that point. So, we know that 3 and 9 are the x-intercepts of the parabola.
Parabolas can only have 0, 1, or 2, x intercepts. The x coordinate of the vertex will be the average of the x coordinates of the x-intercepts, since the vertex will be in the middle of the 2 x intercept points.
Take the average of 3 and 9:
(3 + 9) / 2
12 / 2
= 6
The x coordinate of the vertex is 6.
h(x)=x•2+1 k(x)=x-2
(H+k)(2)
Answers
Is it a true or false? If yes, the answer is false
If u have to solve the answer will be hx=x.2+kx=x-hk2
The segment addition postulate states that if point C is between points A and B, then... ANSWER ASAP
Answers
Answer & Step-by-step explanation:
The Segment Addition Postulate states that AB + BC = AC when C is between A and B.
___________________________________________________I AM ALWAYS HAPPY TO HELP :)The segment addition postulate states that if point C is between points A and B then the segment AB will be equal to the sum of AC and CB.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that the segment addition postulate states that if point C is between points A and B.
The expression for the line segment can be formed mathematically as below:-
AB = AC + CB
From the above equation, it is observed that the sum of the segment AC and CB will be equal to AB.
Therefore, according to the segment addition postulate, segment AB will equal the sum of the segments AC and CB if point C is located between points A and B.
To know more about line segments follow
brainly.com/question/2437195
#SPJ2
which of the following are solutions to the equation below x^2+4x-9=x+1 check all that apply a. 2 b. 4 c. -7 d. -3 e. -5 f. -4
Answers
Answer:
a. and e.
Step-by-step explanation:
Hello, there are two ways to handle this kind of question.
... Either you solve the equation ...
[tex]x^2+4x-9=x+1\\\\x^2+3x-10=0\\\\x^2-2x+5x-10=x(x-2)+5(x-2)=(x+5)(x-2)=0\\\\x= -5 \ \ or \ \ x = 2[/tex]
So the right answers are a. and e.
... Or, you check which answer can be right.
We replace x by 2 and the two expressions are equal.
[tex]2^2+4*2-9=4+8-9=3 \ and \ 2+1=3[/tex]
So this is a. 2
We replace x by 4 and the two expressions are not equal.
[tex]4^2+4*4-9=16+16-9=23 \ and \ 4+1=5[/tex]
So this is not b. 4
We replace x by -7 and the two expressions are not equal.
[tex]7^2-4*7+9=49-28+9=30 \ and \ -7+1=-6[/tex]
So this is not c. -7
We replace x by -3 and the two expressions are not equal.
[tex]3^2-4*3-9=9-12-9=-12 \ and \ -3+1=-2[/tex]
So this is not d. -3
We replace x by -5 and the two expressions are equal.
[tex]5^2-4*5-9=25-20-9=-4 \ and \ -5+1=-4[/tex]
So this is e. -5
We replace x by -4 and the two expressions are not equal.
[tex]4^2-4*4-9=16-16-9=-9 \ and \ -4+1=-3[/tex]
So this is not f. -4
Thank you.
(20pts) Please help! Sometimes, always, or never true. Prove why
Answers
Answer:
Step-by-step explanation:
[tex]LHS = \frac{1}{m^{2}}-\frac{1}{m^{2}+1}\\\\\\=\frac{1*(m^{2}+1)}{m^{2}*(m^{2}+1)}-\frac{1*m^{2}}{(m^{2}+1)*m^{2}}\\\\\\=\frac{m^{2}+1- m^{2}}{(m^{2}+1)*m^{2}}\\\\\\=\frac{1}{(m^{2}+1)m^{2}}=RHS[/tex]
What number do we divide by -2 to get 6?
Answers
-12. 2 negatives always make a positive
Simplify the expression:
10x + -8x + -10x+ -10 + 8x + -6x
Answers
Quilt
Step-by-step explanation:
A gable roof (isosceles triangle-shaped) has a vertical height of 2.1 metres and the ceiling is 10.9 meters from one side to the other. Find the pitch (angle) of the roof.
Answers
Answer:
[tex]\bold{21.07^\circ}[/tex]
Step-by-step explanation:
The given values can be mapped to an isosceles [tex]\triangle ABC[/tex].
Side AB = AC
Vertical height, AD = 2.1 m
The distance between one side to the other side of ceiling = 10.9 m
To find:
Pitch (Angle of the roof ) = ?
i.e. [tex]\angle B[/tex] or [tex]\angle C[/tex] = ? (because it is isosceles triangle, so both will be equal)
Solution:
As [tex]\triangle ABC[/tex] is isosceles, so vertical height will divide the side BC in two equal parts
i.e. [tex]BD = DC = \frac{1}{2} BC[/tex]
[tex]\therefore BD = \frac{10.9}{2} = 5.45 m[/tex]
In [tex]\triangle ABD[/tex], let us use tangent trigonometric property.
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]tanB = \dfrac{AD}{BD}\\\Rightarrow tanB = \dfrac{2.1}{5.45}\\\Rightarrow tanB = 0.385\\\Rightarrow \angle B = tan^{-1}( 0.385)\\\Rightarrow \bold{\angle B = 21.07^\circ}[/tex]
Plz help will mark brainlist
Answers
Answer:
48
Step-by-step explanation:
180 - 90 - 42 = x
x = 48
Answer:
A) 48°
Step-by-step explanation:
Sum of all angles of a triangle = 180
90 + 42 + x = 180
Add like terms
132 +x = 180
Subtract 132 form both sides
x = 180 -132
x = 48°
What are the factors of x2 – 100?
Answers
I’m not sure how to explain it but I needed more characters to submit this as an answer
the product of the zeros of the quadratic polynomial 2x square _3x _5c is 1by2 which of the following is the value of c
Answers
Answer:
c = - [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
The product of the zeros = [tex]\frac{c}{a}[/tex] = [tex]\frac{1}{2}[/tex]
Given
2x² - 3x - 5c
with a = 2 and c = - 5c , then
[tex]\frac{-5c}{2}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
- 10c = 2 ( divide both sides by - 10 )
c = [tex]\frac{2}{-10}[/tex] = - [tex]\frac{1}{5}[/tex]