Answers
sin 30 = x/43
43 (sin 30) = x
21.5 = x
Hope this helps :)
height of pole = opposite side = (43 m)*sin (30 deg) = 21.5 m.
Related Questions
What is the larger figure?
Answers
.. (248 m^2)*((3875 m^3)/(248 m^3))^(2/3) = 1550 m^2
Match the corresponding function formula with each function when h(x)=3x+2 and g(x)=2^x
1. K(x)=2^x+3x+2
2. K(x)=2^x-3x-2
3. K(x)=(3x)2^-x+2^-x+1
4. K(x)=2^3x+2
5.k(x)=2^x(3x+2)
6. K(x)=3(2^x)+2
————————————
A. K(x)=g(x)+h(x)
B. K(x)=h(x) divided g(x)
C.k(x)=g(x)-h(x)
D.k(x)=g(x)*h(x)
E. K(x)=g(x)•h(x)
F. K(x)=h(x)•g(x)
Answers
[tex]h(x)=3x+2 \\ g(x)=2^x \\\\ 1) 2^x+3x+2=2^x+(3x+2)=g(x)+h(x)\ answer\ A\\\\ 2)2^x-3x-2=2^x-(3x+2)=g(x)-h(x)\ answer\ C\\\\ 3)(3x)2^{-x}+2^{-x+1}=2^{-x}*(3x+2)= \dfrac{3x+2}{2^x} = \dfrac{h(x)}{g(x)}\ answer\ B\\\\ 4) 2^{3x+2}=2^{h(x)}=g(h(x))=(goh)(x)\ answer\ E\\\\ 5) 2^x*(3x+2)=g(x)*h(x)\ answer\ D\\\\ 6) 3*(2^x)+2 =3*g(x)+2=h(g(x))=hog(x)\ answer\ F\\\\ [/tex]
Find the length of the side of an isosceles triangle with perimeter of 12 and maximum area
Answers
A pilot approaching a 3000-meter runway finds that the angles of depression of the ends of the runway are 14° and 20°. How far is the plane from the closer end of the runway? Round to the nearest tenth place.
Answers
Final answer:
To find out how far the plane is from the closer end of the runway, we use the angles of depression and runway length to calculate the distance using trigonometric ratios. The distance is found to be approximately 26153 meters.
Explanation:
To determine the distance from the plane to the closer end of the runway, we use trigonometric ratios based on the angles of depression given. The angles of depression to the ends of the runway are 14° and 20°. Since the problem involves a horizontal surface (runway) and vertical angles (angles of depression), we can create two right triangles. One triangle has an angle of 14° between the plane's line of sight and the horizontal surface, and the other one has a 20° angle.
Let x be the distance from the plane to the point directly above the closer end of the runway and y be the distance from the plane to the point directly above the far end of the runway. We are looking for x, which can be found using the tangent of the 14° angle.
x = runway length / (tan(20°) - tan(14°))
Given the runway length as 3000 meters, we can calculate:
x = 3000 / (tan(20°) - tan(14°))
Crunching the numbers:
x ≈ 3000 / (0.3640 - 0.2493)
x ≈ 3000 / 0.1147
x ≈ 26153 meters (rounded to the nearest tenth)
Therefore, the distance from the plane to the closer end of the runway is approximately 26153 meters.
A group of art students are painting a mural on a wall. the rectangular wall has dimensions of (6x + 7) by (8x + 5) and they are planning the mural to be (x + 4) by (2x + 5). what is the area of the remaining wall after the mural has been painted?
Answers
The area of the remaining wall after the mural has been painted is 46x^2+73x+15. Hence, he correct answer is [tex]\(\boxed{\text{A. }46x^2+73x+15}\)[/tex]
To find the area of the remaining wall after the mural has been painted, we need to find the area of the entire wall and then subtract the area of the mural.
The area of the rectangular wall is given by the product of its dimensions:
[tex]\[ \text{Area of wall} = (6x+7)(8x+5) \][/tex]
Expanding this expression:
[tex]\[ \text{Area of wall} = 48x^2 + 30x + 56x + 35 \][/tex]
[tex]\[ \text{Area of wall} = 48x^2 + 86x + 35 \][/tex]
Now, the area of the mural is given by the product of its dimensions:
[tex]\[ \text{Area of mural} = (x+4)(2x+5) \][/tex]
Expanding this expression:
[tex]\[ \text{Area of mural} = 2x^2 + 5x + 8x + 20 \][/tex]
[tex]\[ \text{Area of mural} = 2x^2 + 13x + 20 \][/tex]
Now, to find the area of the remaining wall, we subtract the area of the mural from the area of the wall:
[tex]\[ \text{Area of remaining wall} = \text{Area of wall} - \text{Area of mural} \][/tex]
[tex]\[ \text{Area of remaining wall} = (48x^2 + 86x + 35) - (2x^2 + 13x + 20) \][/tex]
[tex]\[ \text{Area of remaining wall} = 48x^2 + 86x + 35 - 2x^2 - 13x - 20 \][/tex]
[tex]\[ \text{Area of remaining wall} = 46x^2 + 73x + 15 \][/tex]
So, the correct answer is [tex]\(\boxed{\text{A. }46x^2+73x+15}\)[/tex].
The complete question is:
A group of art students are painting a mural on a wall. The rectangular wall has dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by (2x+5). What is the area of the remaining wall after the mural has been painted?
A. 46x^2+73x+15
B. 48x^2+86x+35
C. 2x^2+13x+20
D. 50x^2+99x+55
What does the ordered pair (4, 120) represent in context of this problem?
Answers
In the triangle below, which is equivalent to sinA?
Answers
Sin(α)=Opposite/Hypotenuse
2. Then, SinA is:
SinA=BC/AC
A is the angle in the vertice "A".
BC is the opposite leg to the the angle A.
AC is the hypotenuse of the triangle.
3. By definition, you have:
Cosα=Adjacent/Hypotenuse
4. Then, CosC is:
CosC=BC/AC
C is the angle at the vertice "C".
BC is the adjacent leg to the angle C.
AC is the hypotenuse.
5. Therefore, the answer is the last option:
The equivalent to SinA is CosC
sin A=BC/AC
and
cos C=BC/AC
therefore
sin A= cos C
the answer is cos C
Read the word problem. Cate has 10 dolls. Shelayna has 3 times as many dolls as Cate. How many more dolls does Shelayna have compared to Cate? What operations are needed to solve this word problem, and in what order should they be used? addition and subtraction, in that order
addition and division, in that order
division and subtraction, in that order
multiplication and subtraction, in that order
Answers
Therefore to find how many dolls Shelayna has we have to first multiply 10 * 3
Thats 30 dolls
Then we have to find how much more Shelayna has compared to Cate, for this we need to find the difference between the number of dolls they both have.
To find differences we have to subtract the number of dolls Cate has from the number of dolls Shelayna has, thats 30 - 10 = 20
Therefore the operations are multiplication and subtraction in order
Answer:
multiplication and subtraction in order
Step-by-step explanation:
An online company sells handmade samurai katana swords. The website costs $ 475 a month to maintain. Each katana costs $ 200 to make, and they sell each katana for $ 755. Create a linear model in the form y = m x + b where x is the number of swords sold per month and y is the net monthly profit. Using this model, find the number of swords that would need to be sold per month to have a monthly profit of $ 4370.,
Answers
define what Skewed Left, and Skewed Right. (Shape of the data)
Answers
A left-skewed distribution has a long left tail. This is also called negatively-skewed distributions. That’s for the reason that there is a long tail in the negative direction on the number line. The average is also to the left of the peak.
A right-skewed distribution has a long right tail, or positive-skew distributions. That’s for the reason that there is a long tail in the positive way on the number line. The average is also to the right of the peak.
What is the slope of the line
Answers
Hope that helps!
(-2, 3) and (2, -3)
slope = difference in y / difference in x
slope = (3 --3) / (-2 -2)
slope = 6 / -4
slope = -3 / 2
Find an explicit formula for the arithmetic sequence 37, 74, 111, 148
Answers
a₂ = 74
d = a₂ - a₁ = 74 - 37 = 37
a(n) = 37 + 37(n-1)
Let us observe the given series 37,74,111,148
Here, the first term (a) = 37
Common difference(d) = 74-37 = 37
Hence, the given series is in Arithmetic progression.
Hence the nth term of the series is given by:
[tex] a_{n}=a+(n-1)d [/tex]
Substituting the values of 'a' and 'd'.
[tex] a_{n}=37+37(n-1) [/tex]
Therefore, it is the required explicit formula.
Of the 50 shapes in a set, 20 of them are squares. In a circle graph, what would be the measure of the central angle for the section that represents squares?
A. 40 degrees
B. 108 degrees
C. 126 degrees
D.144 degrees
Answers
The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below:
Step 1: 3(2x − 4) = 8 + 2x + 6
Step 2: 5x − 7 = 14 + 2x
Step 3: 5x − 2x = 14 + 7
Step 4: 3x = 21
Step 5: x = 7
In which step did the student first make an error and what is the correct step?
Step 2; 6x − 12 = 14 + 2x
Step 2; 6x − 7 = 2(6 + x + 4)
Step 3; 5x − 2x = 14 − 7
Step 3; 5x + 2x = 14 + 7
Answers
Answer:
The student made the error at step 2.
Step-by-step explanation:
The correct step will be:
Step 2; 6x − 12 = 14 + 2x
As 3 will be multiplied with 2x and 4 which will give 6x − 12
Which out of these 2 "graphs" represent a proportional relationship? PLEASE HELP
x f(x)
–1 –2
0 0
1 2
4 8
x f(x)
–2 2
0 4
2 6
3 7
Answers
Please answer. Confusing me. 20 points.
Answers
The value of a textbook is $120 and decreases at a rate of 12% per year. Write a function to model the situation and then find the value of the textbook after 9 years.
Answers
After the first deduction, the book now costs $105.60.
It decreases $14.40 per year.
Do this for 8 more years.
This should give you what you need to form the needed function modeling the situation.
To model the depreciation of a textbook initially worth $120 with a 12% annual decrease, use the function V(t) = 120 x (1 - 0.12)^t. After 9 years, the textbook's value will be approximately $38.24.
The student asks for a function to model the depreciation of a textbook and the value of the textbook after 9 years. The textbook costs $120 initially and depreciates at 12% annually. To model this, we can use an exponential decay function, which is generally of the form V(t) = V_0 imes (1 - r)^t, where V(t) is the value after time t, V_0 is the initial value, r is the rate of decay, and t is time in years.
Plugging in the given values:
V_0 = $120
r = 0.12 (12% as a decimal)
t = 9 years
The function becomes V(t) = 120 imes (1 - 0.12)^t. Now, we find the value of the textbook after 9 years by substituting t with 9:
V(9) = 120 x (1 - 0.12)⁹
Calculate:
V(9) = 120 x (1 - 0.12)⁹
V(9) = 120 x 0.88^9
V(9) =120 x 0.318630...\approx $38.24
Thus, the value of the textbook after 9 years will be approximately $38.24.
Determine the equation of the graph and select the correct answer below.
y = (x + 3)^2 − 2y = (x − 3)^2 − 2y = (x + 3)^2 + 2y = (x − 3)^2 + 2
Answers
x = -3
y = 2
1. y = (x+3)^2-2
= (-3+3) ^2 -2
= 0^2 -2
= -2
Therefore first equation is wrong
2. y = (x-3)^2 -2
= (-3-3)^2 -2
y = 36-2
y = 34
Since y isn’t 34 the second equation is wrong
3. y = (x+3)^2 +2
= (-3+3)^2 +2
= 0^2 +2
= 2
Since y =2 the third equation is correct
Therefore third equation is correct
The triangles are similar. What is the value of x?
Answers
Answer:
The value of x is [tex]16\ units[/tex]
Step-by-step explanation:
we know that
If two figures are similar , then the ratio of its corresponding sides is equal
In this problem
[tex]\frac{x}{4}=\frac{12}{3}=\frac{20}{5}[/tex]
therefore
[tex]\frac{x}{4}=4[/tex]
[tex]x=16\ units[/tex]
Susan bought a 2 kg bag of grapes on the way home she ate 125 g of the grapes how many grams of grapes that she have left
Answers
Christian is 3 times as old as marie. marie is 12 years old. how old is christian
Answers
Answer:
36 years old
Step-by-step explanation:
Which function grows at the fastest rate for increasing values of x?
h(x)=2x
f(x)=4x2+9x
g(x)=18x
Answers
The blue curve (f(x)) may start out below the others, but quickly surpasses them.
Answer:
Option 2. f(x) = 4x² + 9x
Step-by-step explanation:
In this question we have to tell which function grows at the fastest rate for increasing values of x.
1) h(x) = 2x It's a linear function increasing with the value of x.
2). f(x) = 4x²+9x It's a function representing parabola. Moreover the value of the function increases exponentially as the function is in the form of quadratic equation.
3). g(x) = 18x it's again a linear function.
Therefore out of three functions Function 2 will grow at the fastest rate for increasing values of x.
The pair of points is on the graph of an inverse variation. Find the missing value.
(1.6, 6) and (8, y)
0.83
30
0.03
1.2
WILL GIVE BRANLIEST ANSWER! HELP
Answers
6/5 = 1.2
The second point is (8, 1.2), corresponding to the 4th selection.
You are scheduled to receive $38,000 in two years. when you receive it, you will invest it for 10 more years at 6.0 percent per year. how much will you have in 12 years?
Answers
1.
(08.01 MC) Determine all zeros for the function f(x)=(x2−2−8)(x+6)
-48
-8
-6
-4
-2
0
2
4
6
8
48
Answers
Find tan U.
CR=6.3
UC=4.1
RU=7.7
Answers
This value is approximate. Round it however you need to
------------------------------------
Explanation:
RU = 7.7 is the longest side, so it is the hypotenuse. We will not use this as part of the tangent ratio. Recall that tangent is the ratio of the opposite and adjacent sides of the right triangle.
The opposite side of reference angle U is CR = 6.3 since U is nowhere to be found in the letter pair CR. The adjacent side is UC = 4.1 since U is found here.
So,
tan(angle) = opposite/adjacent
tan(U) = CR/UC
tan(U) = 6.3/4.1
tan(U) = 1.53658536585366
This value is approximate. Round it however you need to
You can upgrade lighting at your factory to LED bulbs that cost $6.95 each and last an average of 5 years. It costs $3 in labor to change a bulb. Over a 10-year period, about how much will it cost per year to install LED bulbs in 100 lamps and change the bulbs when they burn out?
Answers
.. $6.95 +$3 = $9.95
100 bulbs and 10 years totals (100*10) = 1000 bulb·years. For the price of $9.95, you purchase 5 bulb·years, so the total cost for 1000 bulb·years is
.. (1000 b·y)*($9.95/(5 b·y)) = $1990
Over a 10-year period, installation and replacement of 200 bulbs in 100 lamps will cost $1990. Then the per-year cost is ...
.. $1990/(10 yr) = $199/yr
Answer: $200.00
Step-by-step explanation:
$6.95+ $3.00= $19.90
$19.90 * 100= $1,990
$1,990 / $9.95 = $200.00
take the orginal cost 6.95 plus the $3 labor which equals 19.90 then you multiply by the number of bulbs 100 which equals 1990 then divide 1990 by the cost of bulbs 9.95 which equals 200!
A full waterbed mattress is 7 ft by 4 ft by 1 ft. If water weighs 62.4 lb/ft3, what is the weight of the water in the mattress to the nearest pound?
How can you determine the amount of water the mattress can hold?
The weight of the water is in pounds per cubic feet. How can you get an answer with a unit of pounds?,
Answers
The water in the mattress weighs approximately 1,747 pounds.To find the weight of water in the mattress, calculate the volume by multiplying the dimensions and then multiply the volume by the weight of water per cubic foot.
To determine the weight of the water in the mattress, follow these steps:
Calculate the volume of the waterbed mattress by multiplying its dimensions:
Volume = 7 ft * 4 ft * 1 ft = 28 ft³
Next, use the given weight of water per cubic foot to find the total weight:
Weight of Water = Volume * Weight per Cubic Foot
Weight of Water = 28 ft³ * 62.4 lb/ft³
Finally, multiply these values:
Weight of Water = 28 * 62.4 = 1,747.2 lb
To the nearest pound, the weight of the water in the mattress is 1,747 pounds.
What is the prime factorization for 147
Answers
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
147 = 3 x 7 x 7
147 = 3 x 7²
-------------------------------------------------------------------------------
Answer: 147 = 3 x 7²
-------------------------------------------------------------------------------
in short, your starting point is 2, and divide it by 2 till you can't anymore.
then 3, if it's divisible by 3, same, till you can't.
then 5, do the same, then 7, then 11 and so on.
we don't use say hmm 4 because 4 is 2*2, and the division by 2 will have shown any factors of 4 anyway, we don't use 6 either, because 2*3 is 6, and the division of 2 and 3, will have shown any factors of 6 if any at all and so on.
now let's do this fellow,
well, is not divisible by 2 certainly, so we skip that one.
1+4+7 = 12, now 12 is divisible by 3, so 147 is therefore also divisible by 3.
[tex]\bf \begin{array}{l|lll} 147&3\\ 49&7\\ 7&7\\ 1 \end{array}\implies 147=3\cdot 7\cdot 7[/tex]
Order the steps to solve the equation
Log(x^2-15)=log(2x) form 1 to 5.
Answers
Answer:
x2 − 15 = 2xx2 − 2x − 15 = 0(x − 5)(x + 3) = 0x − 5 = 0 or x + 3 = 0Potential solutions are −3 and 5Answer:
The answers in order are 2,5,1,4,3
Step-by-step explanation:
Correct on edge