A communications tower is supported by two wires, connected at the same point on the ground. One is attached to the tower at D and the long-on at C. The angle AD makes with the ground is 30 ° and the angle between the two wires is 10 °. How much below the top of the tower is the shorter one attached?
Answer:
10.99 m
Step-by-step explanation:
✍️What we are basically asked to solve here is to find the distance between C and D.
To find CD, find the length of BC, and BD. Their difference will give us CD.
Thus, BC - BD = CD.
✍️Finding BC using trigonometric ratio formula:
[tex] \theta = 30 + 10 = 40 [/tex]
Opposite side = BC = ??
Adjacent side = 42 m
Thus:
[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]
Plug in the values
[tex] tan(40) = \frac{BC}{42} [/tex]
Multiply both sides by 42
[tex] tan(40) \times 42 = \frac{BC}{42} \times 42 [/tex]
[tex] 35.24 = BC [/tex]
BC = 35.24 m
✍️Finding BD using trigonometric ratio formula:
[tex] \theta = 30 [/tex]
Opposite side = BD = ??
Adjacent side = 42 m
Thus:
[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]
Plug in the values
[tex] tan(30) = \frac{BD}{42} [/tex]
Multiply both sides by 42
[tex] tan(30) \times 42 = \frac{BD}{42} \times 42 [/tex]
[tex] 24.25 = BD [/tex]
BD = 24.25 m
✍️How much below the top of the tower is the shorter one attached:
Thus,
BC - BD = CD
35.24 m - 24.25 m = 10.99 m
Which ordered pair would form a proportional relationship with the point graphed below?
(10.-20)
(-30, 20)
(-10,5)
(35, -20
y = 12 • 3x for x = –2
Answer:
y=-72
Step-by-step explanation:
3(-2) = -6, y=12 times -6, y= -72
$120 less than half of d dollars
Answer:
[tex]\frac{d}{2} - 120[/tex]
Step-by-step explanation:
You work backwards:
Half of d dollars is d/2. Then you take 120 less than that, which means you are subtracting.
Answer:
1/2d-120
Step-by-step explanation:
Alright.
d=amount of money
1/2d=half of the amount of money
1/2d-120=half of the money minus 120
The measure of the angle is 44 times greater than its supplement.
What is the measure of the supplement?
Answer: The measure of it's supplement is 4°
Step-by-step explanation:
If an angle is 44 times is supplement, then we can represent it by the equation x = 44y where x is the angle and y is it's supplement.
Supplementary angles add up to 180 degrees, meaning that x + y = 180.
x = 44y
x + y = 180
Using both equations substitute the value for x in the first equation, into the second equation and solve for y.
44y + y = 180 Combine like terms on the left side
45y = 180 Divide both sides 45
y = 4
This means the measure of it's supplement is 4 degrees.
Now input 4 into one of the equations for y and solve for x to find the main angle.
x = 44(4)
x = 176
This also means that the angle itself is 176 degrees.
The measure of the supplementary angle is 4°.
It is given that the measure of the angle is 44 times greater than its supplement.
We have to find out the measure of the supplement.
What are supplementary angles ?
Two angles are said to be supplementary angles if the sum of two angles is 180°.
As per the question ;
The measure of the angle is 44 times greater than its supplement.
Let's assume the supplementary angle is x .
So,
The other angle will be 44 × x .
We know that sum of two angles if they are supplementary is 180°.
⇒ x + 44 x = 180 °
⇒ 45 x = 180°
⇒ x = 180 ÷ 45
⇒ x = 4°
And the other angle will be ;
= 44 × 4
= 176°
Thus , the measure of the supplementary angle is 4°.
To learn more about supplementary angles click here ;
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Do you guys know this.
Answer:
0.77
Step-by-step explanation:
You solve the inner first, then move to the outer.
Plug in x = 20 for g(x) = [tex]\frac{2x+2}{x-6}[/tex]. It should give you [tex]\frac{42}{14}[/tex], which simplifies to 3.
You then need to solve f(x) with the given value from g(x), which is 3.
Plug in x = 3 for the equation [tex]\sqrt{0.4x^2-x}[/tex], and you should get [tex]\sqrt{0.6}[/tex].
The answer is roughly 0.77.
Jonathan decides to go to an arcade  Play some games. He sets a limit of $35 that he will spend 
Answer:
Hope it will help you
Step-by-step explanation:
Option BJonathan can buy 33 games.
What is equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Jonathan decides to go to an arcade to play some games. He sets a limit of $35 that he will spend
Let he can buy x games, then the equation will be,
0.75x+10 = 35
0.75x = 25
x = 100/3 ≈ 33
Hence, Jonathan can buy 33 games.
For more references on equation, click;
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What is the measure of angle G? Type only the number:
Answer: 48
Step-by-step explanation:
total of all the degrees of the angles of the triangle is ALWAYS 180
let the measure of angle G be x
180 = 102+30+x
180 = 132+x
x = 48
algebra help quick lol
Answer:
Its the top right one
Step-by-step explanation:
8y-2x=-72 in slope form
Answer:
y=1/4x-9
Step-by-step explanation:
Slope-intercept form is y=mx+b.
8y-2x=-72
Add 2x to both sides
8y=2x-72
Divide both sides by 8.
y=1/4x-9
HTH :)
A square has a side length 9 cm. What is its area? A square has an area of 9 cm2. What is its side length?
Answer:
Area = 81; Side Length = 3
Step-by-step explanation:
The area of a square is the side lenght squared, and 9² is 81.
The side lengh can be found by taking the square root of the area. √9 = 3
What is f(4) for the function f(x)= 6x+7?
Answer:
31
Step-by-step explanation:
f(4) = 6x4 + 7
= 24 + 7
= 31
Sam wrote his bike 2/5 of a mile and walked another 3/4 of a mile how far did he travel?
Answer:
1.15 miles
Step-by-step explanation:
Answer:
24/20
Step-by-step explanation:
Changed denominator to 20 since 4 and 5 both go into 20. Got 8/20 and 15/20. Added and got 24/20. As a mixed number it is 1 1/5/ Hope this helps!
Sarah earns $9 an hour at a Mort’s Pizza Palace, working 20 hours per week. She spends $3 each week for snacks at work, but saves all her other earnings. How many hours must Sarah work to buy a new phone that costs $150?
Answer:
15h
Step-by-step explanation:
Answer:
17 hours
Step-by-step explanation:
she needs 150, she spends 3 and she makes 9 per hour
153/9 = 17
Charlie's art class is 8 hours long. How long is his class in minutes?
Answer:
480 minutes
Step-by-step explanation:
60 minutes = 1 hr
60 x 8 = 480
480 minutes = 8 hrs
How many elements are in this equation:Mg2N3?
Answer:
there are 2 Magnesium and Nitrogen
Step-by-step explanation:
An apple tree can grow about 400 apples. Jake says that 13 apple trees can grow about 6,000 apples. Do you agree? Explain.
Answer: No. Since 13×400=5,200, 13 apple trees can grow about 5,200 apples. Jake's estimate of 6,000 is much higher than 5,200.
Answer:
you answered it
Step-by-step explanation:
you put no blah blah blah
PLEASE HELP ASAP!!
what is the range of the graphed function?
A) {x | -2 < x < 2}
B) {y | -2 < y < 2}
C) {x | x is a real number}
D) {y | y is a real number}
Answer:
Since this graph is continuing, y must be any real number. So, d.
Solve the inequality 2 (x - 2) +8.6 < 14.
Answer:
x<4.7
Step-by-step explanation:
2(x-2)+8.6<14
2x-4+8.6<14
2x=4.6<14
2x<14-4.6
2x<9.4
_____
x<4.7
mom said its my turn to be brainliest answer ;0
also, help me on my math hw maybe ?
Answer: x < 4.7
Step-by-step explanation:
f(x) = 72-12x what is the domain and range
Answer:
The domain is x and the range is f(x)
Step-by-step explanation:
(1 pt)What is the vertex of the graph of
the function f(x) = x2 + 6x + 9?
Answer:
(-3,0)
Step-by-step explanation:
PLEASE HELP I WILL GIVE YOU A BRAINLIEST! During a basketball game, Tom attempted 25 shots and made 9. He says he made 40% of the shots he took. Is Tom correct? Explain your reasoning using complete sentences.
Answer:
Correct I think
Step-by-step explanation:
9 is nearly half of 25. (12.5) Half is equal to 50%. 40 is close to 50 and 9 is close to 12.5. So, he is correct. I think, hope this helps.
Aisha divides 15 meter of ribbon into 2 equal pieces.
What is the length of each piece of ribbon?
Answer: 7.5 meters
Step-by-step explanation:
plz do this ill mark brainly
Answer:
7+(−2) = 7 − 2 = 5
Step-by-step explanation:
Answer:
The Positive number has to be greater than the negative number you are adding with.
Example(s):
-30 + 35 = 5
-65 + 70 = 5
y= p2 + qr write p in terms of y, q and r
Step-by-step explanation:
y=p²+qr
y-qr=p²
p=√y-qr
now, is it fine..
Solve for e
7 = 15 - 2e
e equals....
Answer:
e=4
Step-by-step explanation:
Consider the composite function g(F(x)) = x square root of 6.
If f(x) = 3x2, what is g(x)?
Answer:
g(x) = √(2x)
Step-by-step explanation:
f(x) = 3x^2
g(f(x)) =√6x
g(3x^2) = x√6
g(x) must be √(2x)
because if we substitute x = 3x^2 in this we get
(√2(3x^2))
= √2√3√(x^2)
= √6 x
For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is approximated by the function below. Find the maximum blood pressure and the disage at which it occurs.
B(x)= 395x^2- 2370x^3, 0 <= x <= 0.16
a. The maximum is obtained for a dosage of __________________.
b. The maximum blood pressure obtained is ______________.
Answer:
A) Maximum for dosage is 0.11
B) maximum blood pressure = 1.625
Step-by-step explanation:
We are given the function;
B(x) = 395x² - 2370x³
To find maximum, we will find the derivative of the function and equate to zero.
B'(x) = 790x - 7110x²
Equating to zero gives;
790x - 7110x² = 0
790x = 7110x²
Dividing both sides by x gives;
790 = 7110x
x = 790/7110
x = 0.11
This falls in between the range of 0 <= x <= 0.16 given to us.
Therefore x = 0.11 is a maximum
Plugging this into B(x) = 395x² - 2370x³ gives;
B(0.11) = 395(0.11)² - 2370(0.11)³
B(0.11) = 1.625
Thus;
Maximum dosage is 0.11
maximum blood pressure = 1.625
20. John Navarro is a salesperson in the appliance department at Morris
Appliance, Inc. He is guaranteed a minimum salary of $185 per week, or
5.5 percent of his total sales—whichever is greater. What is his gross pay
for a week in which his total sales were $3,422?
Answer:
$373.21Step-by-step explanation:
Step one:
weekly pay = $185
commission= 5.5% of sales= 0.055
let the sale be x
and his gross pay be represented by y
hence the expression for the total/gross pay is
y=0.055x+185
Step two:
Required is the gross pay y for x=3422
substituting we have
y=0.055*3422+185
y=188.21+185
y=373.21
Hence for a sale of $3,422 made his gross pay is $373.21
12*PLEASE ANSWER FAST!!!!!!!!