The distance from the person to the base of the cliff is 269.78 meters.
The height of the building from the base of the cliff is 829.37 meters
The situation forms right angle triangle.
The building is constructed on top the cliff that is 300 meters high.
Right angle triangle:Right angle triangle has one of its sides as 90 degrees. Therefore, the sides can be found using trigonometric ratios.
The height of the building from the cliff is 300m. let's find the hypotenuse side of the angle of elevation formed to the cliff.
Using sin rule,
300 / sin (72 - 63) = y / sin (180 - 162)
300 / sin 9 = y / sin 18
300 sin 18 = y sin 9
y = 300 sin 18 / sin 9
y = 92.7050983125 / 0.156
y = 594.230769231
Therefore, how far the person to the base of the cliff can be calculated as follows;
cos 63 = adjacent / hypotenuse
cos 63 = x / 594.2307
x = 594.2307 cos 63
x = 269.775092454
x = 269.78 meters
Therefore, the distance from the person to the base of the cliff is 269.78 meters.
height of the cliff / 269.78 = tan 63
height of cliff = 269.78 tan 63
height of cliff = 529.37493165
height of cliff = 529.37
The height of the building = 300 + 529.37 = 829.37493165 = 829.37 meters
learn more on right triangle here: https://brainly.com/question/14806301
If you multiply a number by 3 and then subtract 5, you will get 40 what is the number
Answer:
Number = 15.
Step-by-step explanation:
Given : If you multiply a number by 3 and then subtract 5, you will get 40.
To find : what is the number.
Solution : We have given if you multiply a number by 3 and then subtract 5, you will get 40.
According to question :
Let the number = x
Multiply is with 3 = 3x
Subtract 5 from it we get 40 .
3x -5 = 40
On adding both sides by 5
3x = 45 .
On dividing both sides by 3
x = 15.
Therefore, Number = 15.
Answer:
15
Step-by-step explanation:
3×y-5=40
3y-5=40
3y=40+5
3y=45
y=45÷3
y=15
I climb half the steps in a staircase. Next, I climb one-third of the remaining steps. Then I climb one-eight of the rest and stop to catch my breath. What is the least possible number of steps in the staircase?
Given parameters:
First sets of staircase = [tex]\frac{1}{2}[/tex]
Next sets = [tex]\frac{1}{3}[/tex]
Third sets = [tex]\frac{1}{8}[/tex]
Unknown:
The least possible number of steps =?
Solution:
The least possible number of steps will be the lowest common multiples of these sets of steps.
We want fractions that will give whole numbers because realistically, one cannot take half a step of a step.
So, the number of steps must be a multiple of denominators of the fractions given.
Denominators are 2 , 3 and 8
Their least common multiple is 24;
This the lowest number by which 2, 3 and 8 can all divide.
So, the least number is 24 steps
The length of a rectangle is 11cm more than the width. Find the dimensions of the
rectangle if the area is 60cm?
width x
lenght : x + 11
area = x * (x+11) = 60 cm²
x² + 11x - 60 = 0
Δ = 11² - 4*1*(-60) = 121 + 240 = 361 = 19²
x' = (-11 - 19) / 2 = not possible
x" = (-11 + 19) / 2 = 4
witdh = 4
lenght = 4+11 = 15
work out the value of angle x
Answer:
x = 45°
Step-by-step explanation:
the triangle has 2 congruent sides and is therefore isosceles with the base angles being congruent, both x
the sum of the 3 angles = 180° , then
x + x + 90° = 180° ( subtract 90° from both sides )
2x = 90° ( divide both sides by 2 )
x = 45°
Carter deposits $200 into a new savings account that pays 6% simple interest annually. Reese deposits $200 into a new savings account that pays 6% interest compounded annually. If both Carter and
Reese leave their $200 deposit in their accounts for 6 years, how much more will Reese's deposit eam in interest than Carters deposit
Explain all steps taken to solve the problem
Answer:
ok bet
Step-by-step explanation:
how would u like me to answer it pls
Please Help! Answer Number 4
Answer:
1485
Step-by-step explanation:
sorry if im wrong
What is the approximate volume of the cylinder
A 324 cm3
B 452.16 cm3
C 734.76 cm3
D 1, 017.36 cm3
Answer:
B 452.16 cm^3
Step-by-step explanation:
the volume of the cylinder is 16π x 9, and if we replace π with 3.14, the answer will be 452.16 cm^3
Step-by-step explanation:
[tex]v = \pi \: r {}^{2} h[/tex]
v = ?
r = 4 cm
h = 9 cm
[tex]v = \frac{22}{7} \times 4 {}^{2} \times 9[/tex]
[tex]v = \frac{22}{7} \times 16 \times 9[/tex]
[tex]v = \frac{3168}{7} [/tex]
[tex]v = 452.57 \: cm {}^{3} [/tex]
if this helped pls give brainliest
- Solve the equation. (1 point)
3(x-7) – x=2x-21
07
0-2
O infinitely many solutions
Ono solution
Answer:
3(x-7) – x=2x-21 ( the equation)
--> infinitely many solutions
Step-by-step explanation:
The solution of the equation is infinitely many solutions, the correct option is C.
What is a linear equation?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
Equation 3(x-7) – x=2x-21
Now,
To solve the equation, we need to simplify both sides and isolate x. We can do this by following these steps:
3(x-7) – x = 2x - 21 Expand the parentheses by multiplying 3 with x and -7:
3x - 21 - x = 2x - 21 Combine like terms on the left side by subtracting x from 3x:
2x - 21 = 2x - 21 Subtract 2x from both sides to eliminate x:
-21 = -21 This equation is always true, regardless of the value of x. This means that the equation has infinitely many solutions. Any value of x will satisfy the equation
Therefore, the answer of the given equation will be infinitely many solutions
Learn more about linear equations;
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Dalton is saving up money to buy a car. He deposits $10 in his savings account the 1st month. Each month after that, he deposits $5 more than the amount he deposited the previous month. Thus, Dalton's deposit is $15 the 2nd month, $20 the 3rd month, and so on. He makes his final deposit of $95 the 18th month . How much money does Dalton have in his account after these 18 deposits ?
2, X2 + x - 3
True or False
Answer:
(True or False) The inequality |x + 1| < 0 has no solution.
Solution
The absolute value of a real expression is either positive or equal to zero. Therefore there is no value of x that makes |x + 1| negative and therefore |x + 1| < 0 is never true and the statement "The inequality |x + 1| < 0 has no solution" is TRUE.
make me brainlieast and follow me..Answer:
false
2,x2+x-3
2
x
2
−
x
−
3
=
0
Factor by grouping.
Tap for more steps...
(
x
+
1
)
(
2
x
−
3
)
=
0
If any individual factor on the left side of the equation is equal to
0
, the entire expression will be equal to
0
.
x
+
1
=
0
2
x
−
3
=
0
Set the first factor equal to
0
and solve.
Tap for more steps...
x
=
−
1
Set the next factor equal to
0
and solve.
Tap for more steps...
x
=
3
2
The final solution is all the values that make
(
x
+
1
)
(
2
x
−
3
)
=
0
true.
x
=
−
1
,
3
2
Step-by-step explanation:
In the diagram above <1=40%.find the measure of <2. <2=[?]%
Answer:
∠ 2 = 40°
Step-by-step explanation:
∠ 1 and ∠ 2 are corresponding angles and congruent, thus
∠ 2 = ∠ 1 = 40°
whats the value of x in the triangle 9 3
Answer:
X = 9.4868
Step-by-step explanation:
Use the pythagorean theorem
a squared plus b squared equals c squared
in this case c equals x
A&b are the side and base length of a right triangle
Will Give Brainliest if you show all the steps. 8x - 6 / 2 = x + 12
Solve for X
Answer:
x=
15
7
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
8x−
6
2
=x+12
8x+−3=x+12
8x−3=x+12
Step 2: Subtract x from both sides.
8x−3−x=x+12−x
7x−3=12
Step 3: Add 3 to both sides.
7x−3+3=12+3
7x=15
Step 4: Divide both sides by 7.
7x
7
=
15
7
x=
15
7
Find the equation of the line passing through the points (4,5) and (-6,15)
Answer:
y = − x + 9
Step-by-step explanation:
Plz Mark brainliest!
Answer:
The answer would be y=-x+9
Step-by-step explanation:
Fill in - and then 9
"Important put in negative symbol without 1 just negative symbol".
Instructions: Find the missing side lengths. Leave your answers as radicals in the simplest form. I need help with finding what a is.
Answer:
a = 17
Step-by-step explanation:
using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{a}{17\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
a × [tex]\sqrt{2}[/tex] = 17[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
a = 17
b = 17 since the legs of an isosceles triangle are congruent
Ingredients for 10 pancakes
Your answer would be ten times the ingredients it would take to make ONE pancake.
What kind of question is this?
Jim had €80 he spent 0.3 of it how much did he spend?
Answer:
€24
Step-by-step explanation:
If he had €80 and spent 0.3 of it, he spent 30% or 30/100 of it.
€80*[tex]\frac{30}{100}[/tex] = €80*[tex]\frac{3}{10}[/tex] = €24.
Please mark as brainliest!
What mixed number is equivalent to 4.01?
Answer:
4 1/100
Step-by-step explanation:
Answer:
4 1/100
Step-by-step explanation:
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are 2 numbers to the right of the decimal point, place the decimal number over 10 ^2 ( 100 ) . Next, add the whole number to the left of the decimal.
PLEASE HELP
14 in.
12 in.
14 in.
Find the area of the figure above.
[?] square inches
Answer:
280 inches
Step-by-step explanation:
The area can be found by looking at each shape individually.
The area of the square can be found my multiplying the length by the width...
14*14 = 196 square inches
The area of the triangle can be found by multiplying the base by the height and dividing by 2...
A = b*h/2 (or some text books say half of the base times the height)
We knot the height of the triangle is 12 inches, and the base is implied as it shares a side with a square which has 4 equal sides of 14 inches. Therefore
A = (14*12)/2 = 84 square inches
We get the total area by combining the two segments...
Area (triangle) + Area (square) = Area (total)
84 + 196 = 280 square inches
What is the Measure of ZADB?
A
(3x + 9)
B
(2x - 4)^
D
с
Answer:
60
Step-by-step explanation:
m(ADB) + m(BDC) = 90°
(3x+9) + (2x -4) = 90°
5x + 5 = 90°
5x = 85
5x/5 = 85/5
x = 17
m(ADB) = 3x + 9
3.17 + 9 = 51 + 9 = 60
Hope this helps ^-^
Answer: 60°
Step-by-step explanation:
Looking at the figure, we know that the angles add up to 90°. We add both equations and solve for x.
3x+9+2x-4=90 [combine like terms]
5x+5=90 [subtract both sides by 5]
5x=85 [divide both sides by 5]
x=17
Now that we know x, we can plug it into ADB to find the angle.
3(17)+9 [multiply]
51+9 [add]
60
Now, we know that ADB is 60°.
im just trynna see if im correct but this is urgentt
Answer:
dont have question
Step-by-step explanation:
Answer:
161.557- so the second one
Step-by-step explanation:
Lydia got her learners permit and helped her parents drive to her grandparent's house and back. It took one hour less time to get there than it did to get back. The average speed on the trip there was 60 km/hour. The average speed on the way back was 40 km/hour. How many hours did the trip there take?
Select the correct response:
2 hours
3 hours
5 hours
4 hours
Using the relation between velocity, distance and time, it is found that the trip took 2 hours.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
On the first part of the trip, a time of t was taken, with an average speed of 60 km/hour, hence:
[tex]60 = \frac{d}{t}[/tex]
d = 60t
On the second part, a time of t + 1 was taken, with an average speed of 40 km/hour, hence:
[tex]40 = \frac{d}{t+1}[/tex]
d = 40(t + 1).
Since the distance is equal for both parts, we can equal the equations and find the time.
60t = 40t + 40
20t = 40
t = 2.
The trip took 2 hours.
More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569
can someone please help me ?
9514 1404 393
Answer:
solution: (-2, 2), (-4, -4)not a solution: (4, -2), (0, 0)Step-by-step explanation:
Plot the given points on the graph. Those that are on the (solid) boundary line or in the shaded area are solutions. Those in the white space are not solutions.
please help me I have tried and I'm so confused i don't know why- (due in 10 minutes)
Answer:
B
C
A
D
E
Step-by-step explanation:
i know this is due in 10 mins so i didnt want to waste time aha
but ill gladly give an explanation later
Answer:
See below.
Step-by-step explanation:
A) a⁴ => Some number to the power of four
B) y - 4 => Four less than an unknown number
C) z / 4 => Quotient of a variable and four
D) 4x => Four times an unknown value
E) b + 4 => Four more than some number
Which quadratic equation has no real roots? Choose exactly two answers that are correct. Question 12 options: –x2 2x – 6 = 0 –2x2 3x 4 = 0 2x2 x – 6 = 0 2x2 – x 3 = 0.
The quadratic equations that have real roots are [tex]-2x^2+3x+4 = 0[/tex] and [tex]2x^2+x-6 = 0[/tex].
What is the discriminant of a quadratic equation?The value of a discriminant of a quadratic equation shows how many roots f(x) have. If the value of the discriminant is greater than 0 then the quadratic equation has real and distinct roots and if the value of the discriminant is equal to 0, then the quadratic equation has real and same roots. In case the value of the discriminant is less than zero then the quadratic equation will have no real roots.
In order to know if the quadratic equation has real roots or not, we need to find the discriminant of the given quadratic equations,
A.) [tex]-x^2+2x -6 = 0[/tex]
Here, a= -1, b=2 and c=-6
[tex]D = b^2 -4ac[/tex]
[tex]D = 4 -24\\D = -20[/tex]
As the value of the discriminant is negative it will not have real roots.
B.) [tex]-2x^2+3x+4 = 0[/tex]
Here, a= -2, b=3 and c=4
[tex]D = b^2 -4ac[/tex]
[tex]D = 9 +32\\D = 41[/tex]
As the value of the discriminant is positive it will have real roots.
C.) [tex]2x^2+x-6 = 0[/tex]
Here, a=2, b=1 and c=-6
[tex]D = b^2 -4ac[/tex]
[tex]D = 1 +48\\D =49[/tex]
As the value of the discriminant is positive it will have real roots.
A.) [tex]2x^2 -x+3 = 0[/tex]
Here, a=2, b=-1 and c=3
[tex]D = b^2 -4ac[/tex]
[tex]D = 1-24\\D = -23[/tex]
As the value of the discriminant is negative it will not have real roots.
Learn more about Discriminant:
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Write a contextual story for the equation 2x+4=24
Answer:
Step-by-step explanation:
2X=24-4 x=20/2 x=10
Answer:
Amy had 4 erasers. Brianna gave her x more erasers which doubled the amount of erasers she had. How many erasers does Amy have in total?
What is the value of y?
Answer:
12
Step-by-step explanation:
it will be 12 because if you see the length were number 12 is it's the same as the other side
How were the Cherokee impacted by European settlement? Why did hostilities
escalate? Pls help!!
Answer:
Cherokees were forced to leave their homes. There are usually peaceful, but this angered them, so naturally, they fought back and that's why the hostilities escalated.
Step-by-step explanation:
[tex]1. \sqrt{12} [/tex]
[tex]2. \sqrt{50} [/tex]
[tex]3. \sqrt{ \frac{49}{81} } [/tex]
Answer:
1. 3.46410162
2. 7.07106781
3. 0.08641975
Two people, Adam and Bianca, are competing to see who can save the most money in one month. Adam starts the month with $3 and then saves an additional $3 each day.
Bianca's savings can be seen in the table below.
Answer:
What is the question?
Step-by-step explanation:
You did not attach a file, and all you posted was a statement, not a question. Please edit the question or I cannot help. Sorry......