Answer:
24
Step-by-step explanation:
let x be the number of children in the class , then
number of boys = [tex]\frac{1}{4}[/tex] x , so
x = [tex]\frac{1}{4}[/tex] x + 18 ( multiply through by 4 to clear the fraction )
4x = x + 72 ( subtract x from both sides )
3x = 72 ( divide both sides by 3 )
x = 24
There are 24 children in the class
A boat is heading towards a lighthouse, whose beacon-light is 105 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 7^{\circ}
∘
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 21^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.
Answer:
AB ≈ 581.6 ft
Step-by-step explanation:
The triangle from point A to the base of the lighthouse to the light beam can be modeled as a right triangle with the side opposite the angle being given. That means the distance from A to the base of the lighthouse is found from the tangent relation:
Tan = Opposite/Adjacent
tan(7°) = (105 ft)/A
A = (105 ft)/tan(7°)
Using similar reasoning, the distance to B is ...
B = (105 ft)/tan(21°)
Then the distance from A to B is ...
AB = (105 ft)/tan(7°) -(105 ft)/(tan(21°)) = (105 ft)(1/tan(7°) -1/tan(21°))
AB ≈ 581.6 ft
_____
Additional comment
We know that 1/tan(7°) = cot(7°) = tan(83°). This means the relation can be written ...
AB = (105 ft)(tan(83°) -tan(69°))
find the quotient-you must show your thinking to support your answer - 5/4 divided by 1/4
Work Shown:
[tex]-\frac{5}{4} \div \frac{1}{4}\\\\-\frac{5}{4} \times \frac{4}{1}\\\\-\frac{5\times4}{4\times1}\\\\-\frac{5}{1}\\\\-5[/tex]
Whenever you divide fractions, you flip the second fraction and multiply. In this case, the '4's cancel.
A trapezoid has an area of 18 mi.² the bases are 5 miles and 7 miles what is the height of the trapezoid-
Answer:
the answer is H=3 miles
Step-by-step explanation:
Area of Trapezoid = [tex]{(Base1+Base2)/2 }* (Height)[/tex]
we sub the values we have in the formula:
18= ( 5+7)/2 * (H)
H = (2*18)/(5+7)
H = 3 miles
where is H is the Height
I'M BEGGING YOU PLEASE HELP ME!!
5/6 = 10/12
1/2 = 2/3
3/5 = 6/10
Hope this helped.
What is the solution for x in the equation?
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
Answer: x=3
Step-by-step explanation:
First, we combine like terms.
2-x = x-4
Next we move the variables to one side and the numbers to another
2x = 6
We divide by 2.
x = 3
Find the value of x.
Answer:
x = 36°
Step-by-step explanation:
Where a transversal crosses parallel lines, any obtuse angle it creates is supplementary to any acute angle it creates:
3x +2x = 180°
5x = 180° . . . . . . . . . collect terms
x = 180°/5 = 36° . . . . . divide by 5
.
Find the values of x and y
3. In the Diagram, DEFG = WXFG.
E
х
75°
F
60°
question # 3
(15x + ylº
G 3x - 5
0
W
Answer:
x = 5 , y = 15
Step-by-step explanation:
Since the figures are congruent then corresponding sides and angles are congruent , that is
WG = DG ( substitute values )
3x - 5 = 10 ( add 5 to both sides )
3x = 15 ( divide both sides by 3 )
x = 5
and
∠ WGF = ∠ DGF , that is
15x + y = 90 ( substitute x = 5 )
15(5) + y = 90
75 + y = 90 ( subtract 75 from both sides )
y = 15
Suppose that $5500 is placed in an account that pays 2% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.
Х
?
Answer: After 1 year: $5,610
After 2 years: $5,722.20
Step-by-step explanation: Use the formula for periodic compounding interest, which is
A = P(1 + r/n)^(nt), where A is the final amount, P is the initial deposit, r is the interest rate as a decimal, n is the number of times the interest is compounded per year, and t is how many years.
Here, P = 5,500, r = 0.02 (that's 2% as a decimal), n = 1,
t = 1 for the first answer, t = 2 for the second answer (1 year, then for 2 years)
Plug the known values in to solve...
For 1 year...
A = 5,500(1 + 0.02/1)^(1*1)
A = 5,500(1.02)^1
A = 5,610
For 2 years...
A = 5,500(1 + 0.02/1)^(1*2)
A = 5,500(1.02)²
A = 5,722.20
One more I think!
We got this!
How many golf balls can fit into a container that is 14 inches tall and has a radius of 5 inches? Each golf ball has a volume of 2.5 cubic inches.
Answer:
about 440 balls
Step-by-step explanation:
The volume of the container is first calculated
[tex]v=\pi (5)^{2} (14)=1099.6 cu.in[/tex]
It is now divided by the volume of the golf ball
[tex]#balls=\frac{1099.6}{2.5} =439.8[/tex]
Hope this helps
How many buses do you need for 200 people if each bus holds
34 people?
Answer:
6
Step-by-step explanation:
you divide 200 people by 34 people per bus and get 5.88 (6)
Answer: 6 is correct! thax
USACanada
Step-by-step explanation:
Which relationships describe angles 1 and 2?
Select each correct answer.
adjacent angles
complementary angles
vertical angles
supplementary angles
Answer:
supplementary angles
Step-by-step explanation:
they are on the same line, so they sum up to 180°
What is the value of x in the equation one-fifthx – two-thirdsy = 30, when y = 15? 4 8 80 200.
On solving the linear system, for the value of y = 15, the value of x is 200. The correct option is D.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
The linear equation is shown below.
[tex]\rm \dfrac{1}{5}x - \dfrac{2}{3}y = 30[/tex]
The equation can be written as
[tex]\rm 3x - 10y = 450\\[/tex]
For y = 15, the value of x will be.
[tex]\begin{aligned} \rm 3x - 10*15 &= 450\\\\\rm 3x - 150 &= 450 \\\\\rm 3x &= 600\\\\\rm x &= 200\\\end{aligned}[/tex]
The value of x is 200.
Thus, option D is correct.
More about the linear system link is given below.
https://brainly.com/question/20379472
a right triangle has legs measuring 20 in. and 28 in. what is the length of the hypotnuse? round to the nearest tenth.
Let Hypotenuse be x
X² = 20² + 28²
x² = 400 + 784
[tex] \tt x= \sqrt{400 + 784 } [/tex]
[tex] \tt x= \sqrt{1,184} [/tex]
[tex] \tt x= 34.4[/tex]
7. The number of fish, f, in Skipper's Pond at the
beginning of each year can be modeled by the equation
f(x) = 3(2*), where x represents the number of years
after the beginning of the year 2000. For example,
x = 0 represents the beginning of the year 2000, x= 1
represents the beginning of the year 2001, and so forth.
According to the model, how many fish were in
Skipper's Pond at the beginning of the year 2006 ?
A. 96
B. 192
C. 384
D. 1,458
E. 46,656
Using the given exponential model, it is found that the number of fish in Skipper's Pond at the beginning of the year 2006 is given by:
B. 192
What is the exponential model?The exponential model for the number of fish in the Pond in x years after 2000 is given by:
[tex]y(x) = 3(2)^x[/tex]
2006 is 6 years after 2000, hence the amount is of y(6), that is:
[tex]y(6) = 3(2)^6 = 192[/tex]
Hence option B is correct.
More can be learned about exponential functions at https://brainly.com/question/25537936
please please help me please!
Step-by-step explanation:
the number line : a potentially infinite horizontal line.
it shows all numbers, with 0 in the center, eher we are looking at it. the negative numbers go to the left of 0, with -1, -2, -3, ... going from right to left.
the positive numbers go to the right of 0, with 1, 2, 3 going from left to right.
point S = -14
and the distance to a point R (RS) is 10.
now, on such a line we can always go in 2 directions : left and right.
our starting point is S (-14).
going 10 units to the right (positive direction) we get to -4.
as -14 + 10 = -4
going 10 units to the left (negative direction) we get to -24.
as -14 - 10 = -24
so, R can be at -4 or -24.
Kayla and her best friend found some money in a trash can. They split the money evenly, each getting $21.45. How much money did they find
Answer:
$42.90
Step-by-step explanation:
You do 21.45 x 2, or you can add 21.45+ 21.45
This is because it was only two people, Kayla and her best friend.
The graph for Pool A shows the gallons of water filling the pool as a function of time. The graph for Pool B shows the rate of filling the pool as a function of time. Use the drop-down menus to complete the statements below about the two pools.
The graphs of pool A and pool B are illustrations of piece-wise functions
The rate of both pools from t1 to t2, t is 0.
How to determine the rates of the graphsFrom 0 to t1, the rates of the pools are:
Pool A = A/t1
Pool B = B/t1
Where A represents the gallons of water in the pool and B represents the rate at time t1
From t1 to t2, the rate of both pools is 0.
This is so because both intervals are represented by horizontal lines
Read more about piecewise functions at:
https://brainly.com/question/3628123
In the diagram below, AB is parallel to CD. What is the value of x?
72
А
B
D
O 72
O 18
62
108
Answer:
x = 72
Step-by-step explanation:
angles x and 72° are corresponding angles and are congruent , then
x = 72
The value of x is 72 degree.
Option A is correct.
What is Parallel line?The basic qualities listed below make it simple to identify parallel lines.
Parallel lines are defined as straight lines that are always the same distance apart.Parallel lines never intersect, regardless of how far they are extended in either direction.We have the parallel line AB || CD.
As, we know the parallel line have following property
Corresponding Angle are EqualAlternate Interior Angle are EqualAlternate Exterior Angle are EqualNow, from the figure using Corresponding angle
x = 72 degree
Thus, the required angle is 72 degree.
Learn more about Parallel line here:
https://brainly.com/question/16701300
#SPJ7
pls help me!!
find x and y
y= 8
y= x + 1
Answer:
x = 7, y = 8
Step-by-step explanation:
Knowing y = 8, we can substitute into equation and solve:
8 = x + 1
- 1 - 1
7 = x
Y is given, X is solved. Therefore:
x = 7, y = 8
10/15 = x/20 in decimal
1. Observe problem
Restriction: Decimal Form
Least common multiple of 15 and 20 is: 60
Time sixty on both sides
40=3x
x=40/3
Therefore, decimal representation would be 13.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333...
Answer: 13.3 repeating
Step-by-step explanation:
First you cross multiple 10 times 20 to get 200=15x. Then you divide 200 by 15 to get 13.3 repeating
Please can you help I’ll give most Brainly worth 63 points to but also this is my last question and I’m stuck
Answer:
2.726
Step-by-step explanation:
This question has a lot of answers because it doesn't specify a certain w or l.
11.6*9.4=109.04
109.04*.1/4=27.26
x*y=27.26
x*10=27.26
x=2.726
any two numbers could multiply to that number.
I just used 10 and got 2.726
identify the type of function represented by f(x)(1)/(2)*(3)^(x)
I’m stuck on this question please help x
Answer:
a = -3 and b=5
Step-by-step explanation:
Given that 10 can be written as 2*5 or √2*√2*5, and √18 can be written as √(2*9) or √2*√9 or 3√2, you can write the fraction as:
[tex]\frac{5\cdot\sqrt2\cdot\sqrt2-3\sqrt2}{\sqrt2}[/tex]
So getting rid of the √2 factor, you get 5√2 - 3, so a=-3 and b=5
Two airplanes leave the airport. Plane A departs at a 44° angle from the runway, and plane B departs at a 40° angle from the runway. Which plane was farther away from the airport when it was 6 miles from the ground? Round the solutions to the nearest hundredth.
Group of answer choices
Plane A because it was 31.67 miles away
Plane A because it was 22.78 miles away
Plane B because it was 34.23 miles away
Plane B because it was 26.22 miles away
Answer: Answer:
Plane B was farthest away from the airport
Step-by-step explanation:
"This question requires you to visualize the run way as the horizontal distance to be covered, the height from the ground as the height gained by the plane after take of and the distance from the airport as the displacement due to the angle of take off.
In plane A
The take-off angle is 44° and the height gained is 22 ft.
Apply the relationship for sine of an angle;
Sine Ф°= opposite side length÷hypotenuse side length
The opposite side length is the height gained by plane which is 22 ft
The angle is 44° and the distance the plane will be away from the airport after take-off will be represented by the value of hypotenuse
Applying the formula
sin Ф=O/H where O=length of the side opposite to angle 44° and H is the hypotenuse
In plane B
Angle of take-off =40°, height of plane=22miles finding the hypotenuse
Solution
After take-off and reaching a height of 22 ft from the ground, plane A will be 31.67 miles from the airport
After take-off and reaching a height of 22 ft from the ground, plane B will be 34.23 miles away from the airport."
Excerpt from Brainly
find the slope intercept
Answer:
11 is B and 12 is A
Step-by-step explanation:
What is the magnitude (size) of 3.7?
Answer:
A)
Step-by-step explanation:
|3.7| = 3.7
I need help with three and four
Answer:
Step-by-step explanation:
Part 3 :
We simply expand the brackets
(a+b)² = (a+b)(a+b)
(a+b)(a+b) = a²+ab+ab+b² = a²+2ab+b²
This is part 3 done
Part 4:
We simply expand 3 brackets now:
(2x-1)³ = (2x-1)(2x-1)(2x-1)
We do the first 2 brackets first:
(2x-1)(2x-1) = 4x²-2x-2x+1 = 4x²-4x+1
Now we multiply this by the last bracket:
(4x²-4x+1)(2x-1) = 8x³ -4x²-8x² +4x+2x -1 = 8x³-12x²+6x-1
This is part 4 done
Hope this helped and brainliest please
Kiran leaves home at 9.45 am. She drives 135 km to visit a friend. She arrives at her friend’s house at 11.15 am. Work out her average speed in km/h.
Answer:
I believe the answer is 12.1km/per hour
A cone-shaped tent has a diameter of 12 ft and a height of 6 ft. What is the approximate volume of the tent? Use 3. 14 to approximate pi, and express your final answer as a decimal. Enter your answer as a decimal in the box. Ft³.
Answer:
226.08 ft³
Step-by-step explanation:
[tex]\textsf{volume of a cone}=\frac{1}{3}\pi r^2h[/tex]
(where [tex]r[/tex] = radius of the base and [tex]h[/tex] = height)
[tex]\textsf{radius}\ r=\frac{1}{2}\ \textsf{diameter}[/tex]
Given:
diameter = 12ft ⇒ radius = 12 ÷ 2 = 6 ftheight = 6ft[tex]\pi[/tex] ≈ 3.14[tex]\implies \textsf{volume of tent}=\frac{1}{3}\times3.14 \times 6^2 \times 6=226.08 \ \textsf{ft}^3[/tex]