Answer:
As for the trig functions (sine, cosine, and tangent), you can use the angle you are interested in, θ, and the lengths of the sides of the triangle based off of angle θ to find an unknown length in the triangle.
sinθ = [tex]\frac{opposite}{hypotenuse}[/tex]
cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex]
tanθ = [tex]\frac{opposite}{adjacent}[/tex]
Essentially, if you know the measure of one of the angles in the triangle (not including 90°, and the measure of at least one side length, you can select the proper trig function that will allow you to find the unknown length, or height, of the flagpole.
Ex:
Let's say you are standing 18 feet away from the base of the flagpole, and you know (somehow) that an imaginary line is formed from the top of the flagpole to your feet (this imaginary, slanted line is our hypotenuse) and that the angle between that imaginary line and ground is 30°.
We will use 30° as our θ. In this situation, the unknown side length (the height of the flagpole) is opposite from this angle we have chosen. So it is our "opposite". We know that the distance between you and the base of the flagpole is 18 feet. Because this is not that slanted, imaginary line we formed before, this is not the hypotenuse. This is a side length that is adjacent to where we are standing, where our angle θ is. So 18 feet is our "adjacent".
The trig function that includes both "opposite" and "adjacent" is the tangent function, or tanθ = [tex]\frac{opposite}{adjacent}[/tex].
We have selected our trig function:
tanθ = [tex]\frac{opposite}{adjacent}[/tex]
Substitute in the known values. θ = 30° adjacent = 18
tan(30°) = [tex]\frac{opposite}{18}[/tex]
Multiply both sides of the equation by 18, to remove 18 from the right side of the equation:
(18)·tan(30°) = [tex]\frac{opposite}{18}[/tex]·18
The 18's cancel because that side becomes [tex]\frac{opposite 18}{18}[/tex] and a number divided by itself is equal to 1. And multiplying the opposite by 1 still equals the opposite.
So we are left with:
(18) · tan(30°) = opposite
At this point, simply input tan(30°) into your calculator (make sure your calculator is in degrees, not radians, by checking MODE), then multiply the result by 18.
This should equal about 10.3 = opposite. This means that 10.3 feet is the height of the flagpole.
A student investigates force and motion. She measures the mass of four wood blocks and places the blocks on a smooth surface. She will push each block with an equal amount of force and measure how far each moves with a ruler. Then, she will place the blocks in order based on how far they move when pushed. Which best predicts her results in order, from the block that moves the farthest to the block that moves the least?
Block Mass (g)
1 45
2 25
3 35
4
Answer:
4, 2, 3, 1
Step-by-step explanation:
Blocks that weigh heavier won't go as far because friction will get to much and the weight and air resistance is bigger on a bigger block, therefore it would slow to a stop further behind te lesser weight ones
I hope you are having a lovely day.
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heres the clearer version
Answer:
The midpoint of FH is (3;1)
Step-by-step explanation:
71
4 cm
10 cm
4
10 cm
4
cm
cm
17 cm
4 cm
Answer:
LOL what's THE QUESTION U HAVE JUST GIVEN THE CENTIMETRES
Use slope-intercept form to write an equation of a line passing through the given point and having the given slope. Express the answer in standard form. P(-4,-9); m= -3/4
Answer:
4y = -3x - 48
Step-by-step explanation:
y - y1 = m(x - x1)
y1 = -9 x1= -4 m = -3/4
y -(-9) = -3/4(x -(-4)
y + 9 = -3/4(x + 4)
y + 9 = -3/4x -12/4
multiply through by 4
4y + 36 = -3x -12
4y = -3x -12-36
4y = -3x -48 in the form y = mx + c
Evaluate the following expression for b = -10.
2 (b - 5) + 4
Answer:
−26 and (−1)×2×13=-26
Step-by-step explanation:
2(−10−5)+4
Subtract 5 from −10 to get −15.
2(−15)+4
Multiply 2 and −15 to get −30.
−30+4
Add −30 and 4 to get −26.
−26
Answer:
-26
Step-by-step explanation:
We substitute b for -10, so 2 ((-10) - 5) + 4
Using PEMDAS, we do the parenthesis first: 2 ((-10) - 5) + 4 = 2 (-15) + 4
Then we multiply: 2 (-15) + 4 = (-30) + 4
And finally, we add: (-30) + 4 = -26
2(a - 4) + 15 = 13
Please help
Answer:
a=3
Step-by-step explanation:
Answer:
a = 3
Step-by-step explanation:
write a function of least degree to model this graph with the final answer in factored form.
Answer 1 maybe
Step-by-step explanati
The ratio of Mollie’s age to Heather’s age is 4:9 Heather is 40 years older than Mollie
How old is Mollie?
Answer:
I believe it would be 90
Step-by-step explanation:
The required age of Mollie's is 32years and age of Heather's is 72years.
Given that,
The ratio of Mollie’s age to Heather’s age is 4:9,
Heather is 40 years older than Mollie.
We have to determine,
How old is Mollie.
According to the question,
The ratio of Mollie’s age to Heather’s age is 4:9,
The age of Mollie's = 4x
And age of Heather's = 9x
Then ,
The age of Mollie is calculated in the following steps.
The difference between the age of both is 40 years
Age of Heather's - Age of Mollie = Difference of their ages
Then,
[tex]= 9x-4x = 40\\\\= 5x = 40\\\\= x = \frac{40}{5} \\\\= x = 8[/tex]
The value of x is 8.
Therefore,
Age of Mollie's = 4x = (4).(8) = 32years
And Age of Heather's = 9x = (9).(8) = 72years
Hence, The required age of Mollie's is 32years and age of Heather's is 72years.
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Write an equation of the line that passes through the pair of points.
(0, – 4), (5, – 4)
Answer:
[tex]y = -4[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (0, -4)[/tex]
[tex](x_2,y_2) = (5, -4)[/tex]
Required
Determine the equation
First, calculate the slope using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-4 - (-4)}{5 -0}[/tex]
[tex]m = \frac{-4 +4}{5}[/tex]
[tex]m = \frac{0}{5}[/tex]
[tex]m = 0[/tex]
The equation is then calculated using:
[tex]y = m(x -x_1) + y_2[/tex]
This gives:
[tex]y = 0(x - 0)-4[/tex]
[tex]y = 0-4[/tex]
[tex]y = -4[/tex]
A rectangle is 3 meters wide and 10
meters long. How long is the diagonal
of the rectangle?
a^2 + b^2 = c^2
A-15.1
B-13
Answer:
Diagonal = 10.44 m
Step-by-step explanation:
(3×3)+(10×10) = 109
Sq rt 109 = 10.44 m
PLSS PLSS HELP ME I REALLY DONT UNDERSTAND THIS
Describe the difference between f(x) = 2 ^ x and f (x) = 0.5 (2) ^ x.
Answer:
compress vertically with factor of 0.5
Step-by-step explanation:
f (x) = 0.5 (2) ˣ : compress vertically from f(x) = 2ˣ by a factor of 0.5
MATH who can do this
Answer/Step-by-step explanation:
Recall the acronym SOHCAHTOA. This is what we would apply as appropriate in each case.
8. θ = 40°
Opp = m
Adj = 20
Thus, apply TOA
Tan (θ) = opp/adj
Plug in the values
Tan (40) = m/20 (equation)
20×Tan(40) = m
m = 16.7820
9. θ = 22°
Hyp = w
Adj = 18
Thus, apply CAH
Cos (θ) = adj/hyp
Plug in the values
Cos 22 = 18/w (equation)
w×cos 22 = 18
w = 18/(cos 22)
w = 19.4136
10. θ = 35°
Hyp = 55
Opp = x
Thus, apply SOH
Sin θ = opp/hyp
Plug in the values
Sin 35 = x/55 (equation)
55×sin 35 = x
x = 31.5467
11. θ = 33°
Hyp = 19
Adj = x
Thus, apply CAH
Cos θ = adj/hyp
Plug in the values
Cos 33 = x/19 (equation)
19×cos 33 = x
x = 15.9347
12. θ = 17°
Opp = 7
Hyp = x
Thus, apply SOH
Sin θ = opp/hyp
Plug in the values
Sin 17 = 7/x (equation)
x×sin 17 = 7
x = 7/(sin 17)
x = 23.9421
13. θ = 40°
Opp = 15
Adj = x
Thus, apply TOA
Tan θ = opp/adj
Plug in the values
Tan 40 = 15/x (equation)
x×Tan 40 = 15
x = 15/(Tan 40)
x = 17.8763
-2(4 - 0) = 12x – 3
How is this solved
Answer: x = − 5 12
Step-by-step explanation: yeetus
Can you help me with the income statement?
Find an explicit formula for the geometric sequence -1,-7,-49,-343,.... Note : the first term should be d(1) . d(n) =
Answer:
dn = -7^n-1Step-by-step explanation:
Given the sequence -1,-7,-49,-343,....
We are to find the nth term of the sequence
dn = ar^n-1
a is the first term = -1
r is the common ration = -7/-1 = -49/-7 = 7
n is the number of terms
Substitute
dn = -1(7)^n-1
dn = -7^n-1
hence the nth term of the sequence is dn = -7^n-1
Whats is the slope of line that is perpendicular to the line y= -9x + 7
Answer: 1/9
Step-by-step explanation:
The slope of this line is -9. The slope of the perpendicular line is the opposite reciprocal. The reciprocal of -9 is -1/9, the opposite of that is 1/9
WHAT ARE
THE common FACTORS of 4 and 8
Hello!
Answer:
4- 8, 12, 16, 20, 24 ect keep adding 4
8- 16, 24, 32, 40, 48 ect keep adding 8
Step-by-step explanation:
both- 16, 24, 40, 48
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1 and 5 are yes and the rest are no
Answer: See explanation
Step-by-step explanation:
67 × 100 = 6700
67 × (10 x 10) Yes
10 × 10 = 100
67 × 100 = 6700
67 × (10 × 10 × 10) No
10 × 10 × 10 = 1000
67 × 1000 = 67000
670 × 10³ No
10³ = 1000
670 × 1000 = 670000
670 No
670 ≠ 6700
6700 Yes
6700 = 6700
67000 No
67000 ≠ 6700
Hope this helped!
Is negative 6 a rational number
Yes, negative 6 a rational number because it can be represented as a fraction of two integers.
A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero.
It is any number that can be written in the form "a/b," where "a" and "b" are integers and "b" is not equal to zero.
The number -6 can be expressed as -6/1.
Here, -6 is the numerator and 1 is the denominator.
Both the numerator and denominator are integers, and the denominator is not zero.
Therefore, -6 can be represented as a fraction of two integers and meets the definition of a rational number.
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if 3*2=12,3*5=24and 15-6=3then 16/2=?
a.4
b.6
c.8
d.12
Answer:
16 divided by 2 equals C which is 8.
Step-by-step explanation:
Dory lives 2.5 miles from school. Jim lives 3.2 kilometers from school. Ely lives 2300 meters from school, and Chris lives 3000 yards from school. Which lists the students from closest to farthest from school? (1 mi = 1.61 km; 1 m = 1.09 yd; 1 km = 1000 m) *
Step-by-step explanation:
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Calculate the value of the error rounded to the nearest whole number for the multiplication of x and y:
Answer:
The answer is "15%".
Step-by-step explanation:
[tex]x = 26 \pm 6\% \\\\ y = 29 \pm 9\%\\\\z=x \times y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Z=(x \pm &x \%)\times (y\pm &y \%)[/tex]
[tex]= 26 \pm 6\% \times 29 \pm 9\%\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Z=xy \pm (&x+ &y)\%[/tex]
[tex]=754 \pm 15\%\\\\[/tex]
[tex]15 \% \ \ error[/tex]
please help me
please pleaseplease please please
I Please please please please please please please please please please please please please please please please
Answer:
Your answer is.....
In every big pieces there will be 3 * 1/3 pieces.
So total 12 of 1/3 pieces
Mark it as brainlist answer . follow me for more answer.
Step-by-step explanation:
can u help me with 3 and 4
Answer:
3)
18:6
66:22
4)
1:4
2:24
Hope this helps! <3
50 points! Is this triangle scalene or isosceles? 1st picture is the question 2md picture is the triangle on a graph
Answer:
scalene is the answer
Step-by-step explanation:
of a triangle) having sides unequal in length.
Answer:
scalene - not a right triangleStep-by-step explanation:
The graphed triangle has 3 different sides and no right angles.
Correct answer is
scalene - not a right triangleIf you are making a cake for a work potluck, and the recipe calls for 2 cups of flour to serve 8 people, how many cups of flour will you need in order to make a large enough cake to serve 30 people?
Answer:-
7.5 cups of flour is required for 30 people
Step-by-step explanation:-
2 cups = 8 people
x cups = 30 people
[ Cross multiply ]
=> 2×30 = x × 8
=> (2 × 30)/8 = x
=> 60/8 = x
=> 7.5 cups = x
Thus, for 30 people 7.5 cups of flour is required.
Hope this helps you.
Please solve needed as soon as possible thank you I really appreciate it
Answer:
143
Step-by-step explanation:
6(3³)-2(3²)+3-4=
6(27)-2(9)-1=
162-18-1=
143
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Answer:
The answer is x=3. Want me to explain?
Answer:
816 is the answer
Step-by-step explanation:
Find the probability.
There are three nickels, four dimes, and five quarters in your pocket. You randomly pick
a coin. It is a nickel or a dime.
Answer:
0.583
Step-by-step explanation:
You have a total of 12 coins in your pockets (3 nickels + 4 dimes + 5 quarters).
There are 7 nickels/dimes (3 + 4), meaning you have a 7/12 chance of picking either a nickel or a dime.
7/12 simplifies to 0.583.
You have a 0.583% chance of picking either a nickel or a dime.