Answer:
2. 137°
3. 24.7°
Step-by-step explanation:
Using cosine law:
2. 28² = 12² + 18² - 2(12)(18)cosA
cosA = -79/108
A = 137.0107361°
3. 15² = 19² + 30² - 2(19)(30)cosC
cosC =259/285
C = 24.66381079°
The measure of the angle is:
m∠A = 66.8°
m∠C = 30°
We have,
2.
Using tan trigonometric identities.
tan A = 28/12
Simplify the fraction
tan A = 7/3
Take inverse trigonometry
A = [tex]tan^{-1}(7/3)[/tex]
A = 66.8°
3.
Using sin trigonometric identities.
sin C = 15/30
Simplify the fraction
sin C = 1/2
Take inverse trigonometry
C = [tex]sin^{-1}(1/2)[/tex]
C = [tex]sin^{-1} sin ~30[/tex]
C = 30°
Thus,
The measure of the angle is:
m∠A = 66.8°
m∠C = 30°
Learn more about trigonometric identities here:
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The leaning Tower of Pisa was completed in 1372 and makes 86 degree angle with the ground. The tower is 50 meters tall, measured vertically from the ground to the highest point. If you were to climb to the top then accidentally drop your keys, where would you start looking for them?
How far from the base of the tower would they land?
I made having no luck in figuring this out.
Answer:
The distance where the keys would drop from the base is 3.5m
Step-by-step explanation:
Height of the tower = 50m
Angle it makes to the ground = 86°
To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.
The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.
See attached document for better illustration.
The distance from where the keys drop to the base of the tower can be calculated using SOHCAHTOA
We have to use cosθ = adjacent / hypothenus
θ = 86°
Adjacent = ? = x
Hypothenus = 50m
Cos θ = x / hyp
Cos 86 = x / 50
X = 50 × cos 86
X = 50 × 0.06976
X = 3.488 = 3.5m
The distance where the keys would drop from the base of the tower is approximately 3.5m
Find the value of e/a. Just read the variables and numbers.
(50 points)
Answer:
35
Step-by-step explanation:
What is the slope of the line ?
Answer:
-3
Step-by-step explanation:
mean median and mode of 14, 10, 12, 15, and 13
Answer:
mean= 12.8
median=13
mode=there is no mode
Step-by-step explanation:
mean/average=14+10+12+15+ 13=64/5=12.8
median=10,12,13,14,15=13
mode= is the number that repeats more often. = there is no mode
A box in the shape of a rectangular prism has a length of 3 inches, a width of 2, inches,
and a height of 4 inches. What is the volume of the box?
Answer:
24
Step-by-step explanation:
HELP - WILL MAKE BRAINLIEST IF CORRECT - a chunk of lava flies out of a volcano from a height of 12,447 feet a velocity of 608 feet per second. Find the highest point the lava reaches and how long it takes to reach it using the equation y= -16t^2 + 608t + 12,447.
Answer:
18,223 feet
Step-by-step explanation:
y= -16t^2 + 608t + 12,447.
y = -16(t² - 38t) + 12447
y = -16[t² - 2(t)(19) + 19² - 19²] + 12447
y = -16(t - 19)² - 16(-19²) + 12447
y = -16(t - 19)² + 18223
Vertex: (19, 18223)
Max height is 18,223 at t = 19
The parabolas are:
a = -16
b = 608
c = 12,447
x_v = -b/2a
t_v = -608/2(-16)
t_v = -608/-32
t_v = 19
Plug in t_v = 19 to find y_v
y = -16(19)^2 + 608(19) + 12,447
y = -16(361) + 11,552 + 12,477
y = -5,776 + 11,552 + 12,477
y = 18,253
We have the point (19, 18,253)
The max height is at 18,253 when t = 19
Best of Luck!
EMERGENCY!!!! EXTRA POINTS! I HAVE POSTED THIS QUESTION 5 TIMES AND HAD TO REPORT ALL RESPONSES! I ACTUALLY NEED HELP!
The amusement park in Riverdale charges a $10 entrance fee plus $1 per ride. The amusement park in Esterdamb charges a $5 entrance fee and $2 per ride. For how many rides will the cost be the same for both amusement parks? x= # of rides
Number of rides_____?
Cost_____?
Answer:
the price will be the same for either amusement park
Step-by-step explanation:
10+1(x)=?
5+2(x)=?
ex; x=5
10+1(5)= 5+2(5)=
10+5= 5+10=
15 15
Answer:
5 rides, cost of $15
Step-by-step explanation:
With the information given we have two expressions:
10 + 1x and 5 + 2x
Using these expressions we can create this equation:
10 + 1x = 5 + 2x
Knowing some information we can can simply analyze some information:
The closest number each of these equations could equal is 15,
1(5) is 5 + 10 = 15, and 2(5) is 10 + 5 = 15
15 = 15 this is a true statement, so we know this is answer
Hope this helps! Have a good day!
Somebody know how to do this?
Answer:
x=1
Step-by-step explanation:
55+70=125
sum of angles in a triangle is 180 so
180-125=55
54x+1=55
x=1
what is a=1/4 b if b is the subject?
Answer:
b = 4a
Step-by-step explanation:
Given
a = [tex]\frac{1}{4}[/tex] b
Multiply both sides by 4 to clear the fraction
4a = b
A football coach walks 12 meters westward, then 16 meters eastward,
then 22 meters westward, and finally 6 meters eastward.
For this motion, what is the distance moved?
What is the magnitude and direction of the displacement?
Answer:
Total distance traveled = 56 m
Total displacement is 12 m
Direction of coach is westward
Step-by-step explanation:
It is given that football coach first go 12 meter westward then 16 meter eastward.
So no position of coach in eastward direction = 16 - 12 = 4 m
And then 22 m west westward
Therefore position of coach now is 22-4 = 18 m westward
And finally 6 m eastward
Therefore final position of coach is 18-6= 12 m westward
So displacement of coach is 12 m and direction is westward.
Total distance traveled = 12+16+22+6= 56 m
Answer:
right
Step-by-step explanation:
How many solutions are there to the equation below? 12x+32=12x-7
Answer:
I think it's no solutions
Step-by-step explanation:
12x+32=12×-7
-12 -12
32=-7
no solutions
solve each equation. Round your answers to the nearest ten-thousandth. Please show your work. Part 4A
Answer:
22.
log3(4) + log3(5x^2 + 1) = 2
<=> log3(4 x (5x^2 + 1)) = log3(9)
<=> 20x^2 + 4 = 9
<=> 20x^2 = 5
<=> x^2 = 1/4
<=> x = +/- (1/2)
23.
log8(4x^2 + 1) - log8(2) = log8(5)
<=> log8((4x^2 + 1)/2) = log8(5)
<=> 2x^2 + 1/2 = 5
<=> 2x^2 = 9/2
<=> x^2 = 9/4
<=> x = +- (3/2)
24.
log8(4x^2 - 9) - log8(5) = 1
<=> log8((4x^2 - 9)/5) = log8(8)
<=> (4x^2 - 9)/5 = 8
<=> 4x^2 - 9 = 40
<=> 4x^2 = 49
<=> x^2 = 49/4
<=> x = +/- (7/2)
Hope this helps!
:)
Find the surface area of the prism. Write your answer as a fraction or mixed number.
Answer:
The surface area of the prism is 8/3ft²
Step-by-step explanation:
To calculate the surface area of the prism we have to use the following formula:
a = area
w = side = 2/3 ft
h = height = 2/3 ft
l = length = 2/3 ft
a = 2 * (w * h) + 2 * (w * l) + 2 * (h * l)
we replace the values that we know
v = 2 * (2/3 ft * 2/3 ft) + 2 * (2/3 ft * 2/3 ft) + 2 * (2/3 ft * 2/3 ft)
v = 2 * 4/9ft² + 2 * 4/9ft² + 2 * 4/9ft²
v = 8/9ft² + 8/9ft² + 8/9ft²
v = 24/9ft²
v = 8/3ft²
The surface area of the prism is 8/3ft²
Answer:
2⅔ ft²
Step-by-step explanation:
A cube has 6 square faces
6 × (⅔)²
6 × 4/9
8/3
2⅔
Which point on the number line best represents
V10?
3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0
tohoto
E F G H
F
G
E
H
Answer: The answer is F
Step-by-step explanation:
Can someone tell me if I’m right? I put the 80 under 8
And the rule is 3, if I’m wrong please help me
Answer:
80
4
Step-by-step explanation:
You are correct in placing 80 in the box in the table. If you examine the table and the pattern, you'll see that as the number of marbles increases by 10, the weight of the bags increases by 40.
We can determine the rule by dividing 40 by 10: 40 ÷ 10 = 4.
So, the rule is actually to divide the weight of the bag by 4 to find the number of marbles.
Note that this is likely because each marble is 4 grams.
Answer:
No, the answer is to divide by 4
Step-by-step explanation:
You're so close, but if you look closely 320/3=106.67. However, 320/4=80. And if you look at the other choices, it applies to all of them. 40/4=10 , 80/4=20 , 120/4=30 , and 160/4=40.
Hope this help!!!
Margo can purchase tile at a store for $0.89 per tile and rent a tile saw for $45. At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the cost to be the same at both stores?
Margo must buy ____ tiles for the cost to be the same at both stores.
Answer:
She must buy 90 tiles for the cost to be the same at both stores
Step-by-step explanation:
Let x be the no. of tiles bought for the cost to be the same at both stores
Margo can purchase tile at a store for $0.89 per tile at shop 1
Cost of x tiles =0.89x
She rent a tile saw for $45.
So, total cost at Store 1 = 0.89x+45
At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile.
So, cost of 1 tile = 1.39
Cost of x tiles = 1.39x
ATQ
0.89x+45=1.39x
45=1.39x-0.89x
45=0.5x
[tex]\frac{45}{0.5}=x[/tex]
90=x
Hence She must buy 90 tiles for the cost to be the same at both stores
solve the equation 18=n-18
n=_____
Answer:
36
Step-by-step explanation:
The area of a garden is (x² + 7x + 10)
square yards. Find the dimensions of the
garden if x= 14.
Answer:
The dimensions are approximentaly 17.44.
Step-by-step explanation:
= x2 + 7x + 10
= 196 + 7x + 10
= 196 + 98 + 10
= 294 + 10
= 304 yards squared
The dimensions of the garden if x= 14 will be approximately 17.44.
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = [tex]side^{2}[/tex]
The area of a garden= (x² + 7x + 10)
= 196 + 7(14) + 10
= 196 + 98 + 10
= 294 + 10
The area of a garden= 304 yards squared
The area of a garden = side × side
√ 304 = side
side = 17.44 yards
Thus, the dimensions of the garden if x= 14 will be 17.44 yards.
Learn more about the area;
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Someone is visiting a wildlife center to gather information for their term paper. The center has a circular pin with a diameter of 20 meters. What is the approximate area of the pond?
Answer:
300 meters^2
Step-by-step explanation:
10 meters radius
10^2 x pi is about 100 x 3=300
Jamal and Cleo mow lawns together, Jamal can mow an average lawn in 60 minutes by
himself. Cleo would take 90 minutes for the same job. How long would it take both of
them together to mow one (1) lawn
Georgianna wants to use the linear model associated with the data in the table to make a prediction.
A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 0, 5, 10, 15, 30. The second column is labeled distance (miles) with entries 0, 4, 9, 13, 18.
Which range of time values describes the entire interval over which she would be interpolating?
0 to 5 minutes
0 to 18 minutes
0 to 30 minutes
18 to 30 minutes
Answer:
0 to 30 minutes on edg.
Step-by-step explanation:
Answer:
c on e 2020
Step-by-step explanation:
Simplify.
(-9 - 8i) - (3 + 2i)
Answer:
-12-10i
Step-by-step explanation:
(-9 - 8i) - (3 + 2i)
First, remove parantheses.
-9-8i-3-2i
Combine like terms
-9-3-8i-2i
Solve it!
-12-10i
What is the range for the number of cars, new and used, that were sold from July to December?
Answer:
75
Step-by-step explanation:
87-12= 75
edg2020
Find the surface area of the cylinder with a height of 4 and a radius of 9
Answer:
735.13268 units^2
Step-by-step explanation:
A=2πrh+2πr2=2·π·9·4+2·π·92≈735.13268
PLZ HELP I ONLY HAVE 11 points left and I need help with this question plz :( It's URGENT
Answer:
16 units
Step-by-step explanation:
The y intercept is when the x value is 0
f(0) = 2(0)+8 = 8
The y intercept of f(x) is 8
g(0) = -8
The y intercept of g(x) is -8
The distance between f(0) and g(0)
8 - -8 = 8+8 = 16
***I NEED HELP ASAP***
***Please show all the steps***
***I will mark brainliest***
Answer:
1/3 or 3/9
Step-by-step explanation:
The dart board can be split into 9 1x1 squares. 3 of those squares are in the 10 point zone. So, there is a 3 out of 9 (or 1 out of 3) chance to get 10 points.
I have 8 red Valentine card and 2 pink. How many reds and pinks would I need to add to my collection so that the proportion of pink is 44%?
Answer:
88%
Step-by-step explanation:
Please help me now I will mark you brainliest
Answer:
Out side the circle
Step-by-step explanation:
This is because the center is 0 and if the point 6, square root seven is on the circle that mean that as far as the circle goes on each side.
In a classroom of 20 students, 70% of them have brown eyes. If a teacher picks two students
at random to pass out supplies, what is the probability he chooses two students without brown
eyes?
49
A)
100
B)
91
190
3
C)
38
9
D)
100
Answer:
The probability is 9/100
Step-by-step explanation:
First, we know that 70% of the students are with brown eyes. Since we have a total of 20 students, this corresponds to 70/100 * 20 = 14 students
The number of students without brown eyes is thus 20 -14 = 6 students
Now, the probability of selecting a student without brown eyes is 14/20 = 7/10 while the probability of selecting a student with brown eyes is 6/20 = 3/10
Now the probability of selecting two students without brown eyes mean, the first selected is without brown eyes and also the second selected is without brown eyes.
In probability, once we have the work and, we multiply.
So our answer here is 3/10 * 3/10 = 9/100
What is the slope of the equation y = 3.5x – 17?
Answer:
3.5
Step-by-step explanation:
y = 3.5x – 17
This is in the slope intercept form
y= mx+b where m is the slope and b is the y intercept
The slope is 3.5