An ant stands atop a grassy hill looking at a castle. A horizontal bridge 20 feet long crosses the gap, forming a right angle with the castle wall. The hill slopes down to a moat (water) that is 10 feet wide. The moat has 0 alligators because this is a math problem, not Louisiana. The castle is 38 feet tall, measuring from moat to roof.
a) Draw a sketch showing all the information you have right now.
b) The angle of elevation from the ant to the castle roof is 54.5°. Find the height of the castle above the bridge to the nearest foot (whole number).
c) What is the distance of the vertical drop from the bridge into the moat?
d) Find the angle between the hillside and the underside of the bridge. You may assume that the hill's slope is perfectly straight.
Answers
Answer:
Step-by-step explanation:
Related Questions
Guided Practice
Solve the compound inequality.
3 ≤ w + 2 ≤ 7
A.
5 ≤ w ≤ 9
B.
1 ≤ w ≤ 7
C.
1 ≤ w ≤ 5
Answers
Answer:
C.
1 ≤ w ≤ 5
Step-by-step explanation:
Move all terms not containing
w
from the center section of the inequality.
Inequality Form:
1 ≤ w ≤ 5
Interval Notation:
[ 1 , 5 ]
2. Find the slope from the ordered pairs. (-4, 7).(-6, -4) *
2 1/10
-2 1/1
-1 1/10
11/10
Answers
Answer:
Step-by-step explanation:
slope = m
m = y2-y1 / x2 - x1
m = (-4) - 7 / (-6) - (-4)
m = -11 / (-6) + 4
m = -11 / -2
m = 11/2
:)
If angle 3 is 3x and angle 5 is 2x+30, what are the measures of angle 3 and 5?
Answers
Answer:
23
Step-by-step explanation:
Write
39
100
as a decimal number
Answers
Answer:
0.391.00Step-by-step explanation:
"100% as a decimal is written as 1.00 as decimal notation.""39% = 0.39 in decimal form. Percent means 'per 100'. So, 39% means 39 per 100 or simply 39/100."Herby is a corn farmer in lowa who likes to track the growth of his crops. At various times Herby will go
into the field and document the height of the corn (in cm) and how many weeks it has been since the corn
was planted. He plotted the points below.
He is looking for a function that models his data. Since the trend of the data is increasing and convex, he
found an increasing convex exponential model and an increasing convex quadratic model.
Which of the following functions fits the data better?
Choose 1 answer:
Function A: y = 7.2
B
Function B: y = 1202 – 12x + 18
Ilse the function that you chose to predict the height of the corn 6 weeks after it has been planted. Round
Answers
Answer: B
Step-by-step explanation:
Select each option that represents a proportional between x and y.
(50 points)
If get all correct (Brainliest)
Answers
Answer:
I think that is A and C and F
I don't understand the problem. Can you help me solve it please? I also have an IEP.
Answers
Answer:
12
Step-by-step explanation:
The Pythagorean theorem is
a^2+b^2 = c^2 where a and b are the sides and c is the hypotenuse ( the side opposite the right angle)
a^2 + b^2 = c^2
Substitute the known values
5^2 + b^2 = 13^2
25+b^2 = 169
Subtract 25 from each side
25+b^2-25 =169-25
b^2 = 144
Take the square root of each side
sqrt(b^2) = sqrt(144)
b=12
Answer:
Given:
a = 5c = 13To find:
missing side b
Solution:
Using Pythagorean theorem,
(Hypotenuse² = base² + perpendicular²)
b² = c² - a²
= 13² - 5²
= 169 - 25
= 144
b = √144
= 12
Diragio Lawn Care cuts lawns every week. Each lawn uses 34 of a tank of gas when it is cut (on average). How much gas is used if 10 lawns are cut in one week? Choose two answers that represent the solution.
Answers
Answer:
7.5 tank oil will be used
Step-by-step explanation:
Amount of gas used to cut one lawn (on an average) = 3/4 of a tak
Given ,
In a week , ten such lawns are cut
Hence, Total amount of gas used
= 3/4* 10
= 7.5 tank
What is 20% of 90???
Answers
Answer: 18
Step-by-step explanation:
First we want to turn 20% into a decimal so we can multiply it by 90.
So to do that we divide 20 by 100.
20/100=0.2 so 0.2 is the decimal form of 20%.
Then we multiply 90 by 0.2 to get 18 as our answer.
Answer:
Answer: 20% of 90 is 18.
Let's find 20% of 90.
Explanation
20% of 90 can be written as 20% × 90
= 20/100 × 90
= 18
Thus, 20% of 90 is 18.
Step-by-step explanation:
sorry if i get it wrong
I tried my best
PLEASE HELP with question 2! BRAINLIEST to correct answer!! NO LINKS AS ANSWERS, or you will be REPORTED!!!
Answers
get x = 128 is not a step
Find the circumference of the pizza to the nearest whole number. 7 in
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So the answer is 10”
A triangle has sides with lengths of 5 millimeters, 8 millimeters, and 10 millimeters. Is it a right triangle?
Answers
Answer:
It is not.
Step-by-step explanation:
Using the Pythagorean Theorem, a squared + b squared = c squared, we get 25 + 64 = 100, and this is not true.
Factor out the GCF from the given polynomial. 10^3 + 16^2 - 18x 10^3 + 16^2 - 18x = (Type your answer in factored form.)
Answers
Answer:
2x
Step-by-step explanation:
Given the expression 10x^3 + 16x^2 - 18x, we are to find the GCF
First find the factors
10x^3 = 2 * 5 * x * x^2
16x^2 = 2 * 8 * x * x
18x = 2 * 9 * x
From the factors shown, you will see that 2 and x are the common factors. Hence the GCF of the expression is 2x
please help!!!!!!!!!!!!! due in 5 min!!!!!!!!!!
Answers
Christopher's backyard is in the shape of a trapezoid. The bases of the backyard are 30 and 50 feet long. The area of the backyard is 960 square feet. Write and solve an equation to find the height of Christopher's backyard. =12(1+2)ℎ
Answers
Answer:
24 feet
Step-by-step explanation:
The formula for the height of a trapezoid =
h = 2A/ a + b
A = 960 square feet
a = 30 feet
b = 50 feet
h = 2 × 960/30 + 50
h = 1920/80
h = 24 feet
1. You start a biology experiment with 4,500 cells. The cells are continuously growing and 2 minutes later
there are about 22583 cells. What is the rate of growth per minute?
Answers
Answer:
80.65% per minute
Step-by-step explanation:
For continous growth :
A = Pe^rt
A = amount after time, t
P = initial amount
r = growth rate
22583 = 4500 * e^r*2
22583 = 4500 * e^2r
22583 / 4500 = e^2r
5.0184444 = e^2r
Take the In of both sides
1.61312 = 2r
r = 1.61312 ÷ 2
r = 0.80656
0.80656 * 100% = 80.65%
Please help me with this questionnn
Answers
Answer:
V = 1436.76
Step-by-step explanation:
Formula:
V = 4/3πr³
Given:
r = 7
Work:
V = 4/3πr³
V = 4/3π(7³)
V = 4/3π(343)
V = 1436.76
What does A equal: 3(6a+12)=9
Answers
Answer:
a = -3/2
Step-by-step explanation:
3(6a+12)=9
Divide each side by 3
3/3(6a+12)=9/3
6a+12 = 3
Subtract 12 from each side
6a+12-12 = 3-12
6a = -9
Divide by 6
6a/6 = -9/6
a = -3/2
3(6a+12)=9
distribute
18a+36=9
subtraction P.O.E.
18a=-27
division P.O.E.
a=-1.5
which of the following differential equations have x^2-4y^2=8 as a solution?
a) dy/dx = 4xy
b) dy/dx = 4x/y
c) y dy/dx = x/4
d) dy/dx = -x/4y
Answers
Answer:
B
dy/dx = 4x/y
Sorry if it's wrong!
Find the slope of the line containing the points whose coordinates are (1/,) and (1/,) a. Ab b. A+b/ab c. 1/ab d. A-b/ab
Answers
Answer:
1/ab
Step-by-step explanation:
Complete question
Find the slope of the line containing the points whose coordinates are(a,1/b) and (b,1/a)
Slope is expressed as;
m = y2-y1/x2-x1
Substitute the coordinate values
m = (1/a - 1/b)/b -a
m = (b-a)/ab ÷ b-a
m = (b-a)/ab × 1/b-a
m = b-1/b-a × 1/ab
m = 1 × 1/ab
m = 1/ab
Hence the slope is 1/ab
Can anyone please help?
Answers
Answer:
Step-by-step explanation:
1. 7x/3
2.7x/5
3. 2(1 + 3x)/5x
4. x-8??
5. 5x+9/27x
Not sure if i did this how you wanted it done but i just simplified if its wrong let me know i can try to fix it
bia earns a commission on the sales she makes each month. Within a month, bia earns a 3% commission on the first $3000 she has in sales. she earn less a 4.5% commission on the amount of her sales that are greater then $3000. last month, bia had $5000 in sales. how much money did she earn in commission
Answers
Answer:
225
Step-by-step explanation:
4.5 percent *5000 =
(4.5:100)*5000 =
(4.5*5000):100 =
22500:100 = 225
Solve for x.round to the nearest tenth. 70,6
Answers
Answer:
16.5
Step-by-step explanation:
Tan70°=x/6
x=6tan70°
=16.5
I need to find its surface are help please I am really stuck and need to complete this assignment
Answers
Answer:
114.6
Step-by-step explanation:
Left Side
It's a rectangle.
L = 12 km
w = 5 km
Area = L*W= = 60
Right Side (top)
It too is a rectangle.
L = 10
W = 3
Area = L*W = 30
Triangles
Area = 1/2 * b * h
Area = 1/2 * 12 * 4.1 24.6
Total Area 114.6
two sides of a triangle measure 24 inches and 29 inches. which of the following lenght could represent the third side
(A) 8,8,17
(B) 2,11,12
(C) 20,6,15
(D) 19,34,15
Answers
Step-by-step explanation:
We know that the sum of two sides of a triangle is always greater than the third side . Here , the sum of sides is , 24 + 29 = 53 .
Storage container J has a diameter of 5.25 and a hight of 6.25 centimeters. Which value is closest to the volume of storage container J?
A.51
B.103
C.135
D.540
Answers
Answer:
im not sure
Step-by-step explanation:
Answer:
the answer is 135
Step-by-step explanation:
Calculate the closing price of a bond that has a face value of $1,000 and is closing at 101 7/8% of the face value.
A. $1,001.78
B. $1,000.78
C. $1,018.75
D. $1,000.75
Answers
Answer:
The present value of this bond is simply the sum of these two present values: ... an investment in an 8%, $1,000 par value, 5-year Government of Canada bond. ... D.T-bill yield is calculated as (100-price)/price x (365/term) x 100. ... maturity (per $100 face value) for a bond with a 7.0% coupon, current market price of $107.50 ...
Step-by-step explanation:
The answer is C $1,018.75
Pls HELP I don’t understand :,(
Answers
this is very confusing to me
Answers
Answer
what is?
STEP-BY-STEP-EXPLANATION
Oak Street and Elm Street run parallel to each other. When Main Street
intersects them, it forms interior 24, measuring 35°. What is the measure of
272
Main
Oak
4 (35)
5
6
Elm
O A. 145°
B. 135
C. 35
D. 45°
