HELP!!!!! 35 POINTS ASAP!!!!!!!!!!!
Tension wires are attached from the top of a festival sign to the ground,
3
meters from the base of the sign. The angle of depression from the top of the sign to the point where one of the tension wires is attached to the ground is
28°
. How tall is the sign? Round to the nearest tenth.
The sign is __________ meters tall
Answer:
1.6 m
Step-by-step explanation:
The side of the sign, the ground, and the wire form a right triangle where the wire is the hypotenuse.
The angle of depression plus the upper interior angle of the triangle add to 90 degrees. That means that the upper acute angle of the triangle measures 90 - 28 = 62 deg.
Call the upper acute angle of the triangle Angle A and the height of the sign h.
tan A = opp/adj
tan 62 = 3/h
h tan 62 = 3
h = 3/tan 62
h = 1.6
Answer: 1.6 m
Answer:
The tall of the sign board is 1.6 m.
Step-by-step explanation:
Let's draw a diagram to represents the given situation.
In the diagram, the base of the festival sign to the ground forms 90°. So it is right triangle.
The angle of depression is 28°. The angle of the upper interior angle = 90° - 28° = 62°.
Now we can use the trigonometric ration "tan = [tex]\frac{Oppsoite}{Adjacent}[/tex]" and the height of the sign board.
Let's take "h" be the height/tall of the sign board.
As you can see in the diagram, the opposite side = 3m
Now plug in the given values in the tan ratio, we get
tan 62° = [tex]\frac{3}{h}[/tex]
The value of tan 62° = 1.88
So, 1.88 = [tex]\frac{3}{h}[/tex]
h = [tex]\frac{3}{1.88}[/tex]
h = 1.595
We are asked to round of the nearest tenths place.
So, h = 1.6 m
Therefore, the tall of the sign board is 1.6 m.
The question asks, "Find the equation of the ellipse with the following properties.
The ellipse with x-intercepts (5, 0) and (-5, 0); y-intercepts (0, 3) and (0, -3)."
I know that the equation for an ellipse is x^2/a^2+ y^2/b^2=1 but I have no idea how to create the equation given x-intercepts and y-intercepts. Please help! Thank you.
Answer:
x^2 / 25 + y^2 / 9 = 1
Step-by-step explanation:
The major axis is along the x axis and the minor axis is on the y axis.
Major axis = 2a = 5--5 =10 so a = 5 and a^2 = 25.
Similarly b^2 = 3^2 = 9.
Answer:
[tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex]
Step-by-step explanation:
Equation of ellipse is of form [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex] where [tex](a,0) , (-a,0)[/tex] are the x-intercepts and [tex](0,b) , (0,-b)[/tex] are the y-intercepts . If [tex]a > b[/tex] then it is a horizontal ellipse and if [tex]a < b[/tex] then it is a vertical ellipse .
For horizontal axis ,
Here, [tex](a,0) , (-a,0)[/tex] are known as the vertices of ellipse and [tex](0,b) , (0,-b)[/tex] are the co-vertices of ellipse .
Horizontal axis is known as the major axis and vertical axis is known as the minor axis .
Here, x-intercepts are [tex](5,0) , (-5,0)[/tex] , take a = 5
y-intercepts are [tex](0,3) , (0,-3)[/tex] , take b = 3
As [tex]a > b[/tex] , it is a horizontal ellipse .
On putting a = 5 and b = 3 , we get equation as
[tex]\frac{x^2}{5^2}+\frac{y^2}{3^2} =1\\ \frac{x^2}{25}+\frac{y^2}{9} =1[/tex]
What is the vertex of the quadratic function f(x)=(x-6)(x+2)?
Answer:
(2, -16).
Step-by-step explanation:
(x - 6)(x + 2)
Convert to vertex form:
Expanding the parentheses we have:
x^2 + 2x - 6x - 12
= x^2 - 4x - 12
Completing the square:
= (x - 2)^2 - 4 - 12
= (x - 2)^2 - 16
So the vertex is (2, -16),
Calculate 6.7 x 108 times 6.1 x 106 by using scientific notation and the product rule.
Express your answer in scientific notation with the proper number of significant figures.
I need help with letters (D) and (E). My model equation from letter (C) is: P = -55/4 t+ 340.
Answer:
(a) The two ordered pairs are (0 , 340) and (4 , 285)
(b) The slope is m = -55/4
The slope means the rate of decreases of the owl population was 55/4
per year (P decreased by 55/4 each year)
(c) The model equation is P = -55/4 t + 340
(d) The owl population in 2022 will be 216
(e) At year 2038 will be no more owl in the park
Step-by-step explanation:
* Lets explain how to solve the problem
- The owl population in 2013 was measured to be 340
- In 2017 the owl population was measured again to be 285
- The owl population is P and the time is t where t measure the numbers
of years since 2013
(a) Let t represented by the x-coordinates of the order pairs and P
represented by the y-coordinates of the order pairs
∵ t is measured since 2013
∴ At 2013 ⇒ t = 0
∵ The population P in 2013 was 340
∴ The first order pair is (0 , 340)
∵ The time from 2013 to 2013 = 2017 - 2013 = 4 years
∴ At 2017 ⇒ t = 4
∵ The population at 2017 is 285
∴ The second order pair is (4 , 285)
* The two ordered pairs are (0 , 340) and (4 , 285)
(b) The slope of any lines whose endpoints are (x1 , y1) and (x2 , y2)
is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∵ (x1 , y1) is (0 , 340) and (x2 , y2) is (4 , 285)
∴ x1 = 0 , x2 = 4 and y1 = 340 , y2 = 285
∴ [tex]m = \frac{285-340}{4-0}=\frac{-55}{4}[/tex]
* The slope is m = -55/4
∵ The slope is negative value
∴ The relation is decreasing
* The slope means the rate of decreases of the owl population was
55/4 per year (P decreased by 55/4 each year)
(c) The linear equation form is y = mx + c, where m is the slope and c is
the value of y when x = 0
∵ The population is P and represented by y
∵ The time is t and represented by t
∴ P = mt + c , c is the initial amount of population
∵ m = -55/4
∵ The initial amount of the population is 340
∴ P = -55/4 t + 340
* The model equation is P = -55/4 t + 340
(d) Lets calculate the time from 2013 to 2022
∵ t = 2022 - 2013 = 9 years
∵ P = -55/4 t + 340
∴ P = -55/4 (9) + 340 = 216.25 ≅ 216
* The owl population in 2022 will be 216
(e) If the model is accurate , then the owl population be be zero after
t years
∵ P = -55/4 t + 340
∵ P = 0
∴ 0 = -55/4 t + 340
- Add 55/4 t to both sides
∴ 55/4 t = 340
- Multiply both sides by 4
∴ 55 t = 1360
- Divide both sides by 55
∴ t = 24.7 ≅ 25 years
- To find the year add 25 years to 2013
∵ 2013 + 25 = 2038
* At year 2038 will be no more owl in the park
Elen deposited $2,500 into a savings account that earns 5% interest per year. Her friend's bank offerS a 6% annual interest rate. How much more money would Ellen's money have earned in one year if she had deposited her money at her friend's bank?
Answer:
Ellen's money would have earned $25 more than her money at her account
Step-by-step explanation:
* Lets explain how to solve the problem
- The simple Interest Equation (Principal + Interest) is:
A = P(1 + rt) , Where
# A = Total amount (principal + interest)
# P = Principal amount
# r = Rate of Interest per year in decimal r = R/100
# t = Time period involved in months or years
* Lets solve the problem
- Ellen deposited $2,500 into a savings account that earns 5% interest
per year
- Her friend's bank offers a 6% annual interest rate
* Lets calculate her money after 1 year in each account
# Her account
∵ P = $2500
∵ r = 5/100 = 0.05
∵ t = 1
∵ A = P(1 + rt)
∴ A = 2500(1 + 0.05 × 1) = 2500 (1.05) = 2625
* Her money would be $2625 in one year
# Her friend's account
∵ P = $2500
∵ r = 6/100 = 0.06
∵ t = 1
∵ A = P(1 + rt)
∴ A = 2500(1 + 0.06 × 1) = 2500 (1.06) = 2650
* Her money would be $2650 in one year
∵ 2650 - 2625 = 25
∴ Ellen's money would have earned $25 more than her money at her
account
A recipe calls for 2/3 of a cup of milk. Zeinab wants to make 1/4 of the original recipe. How many cups of milk does Zeinab need?
Answer:
1/6 of a cup of milk. Or at least that's my answer.
Step-by-step explanation:
Okay, we need to find out 25% of 2/3.
25% of 2/3 is 1/6.
To find out how much milk Zeinab needs for 1/4 of the original recipe, multiply 2/3 of a cup by 1/4. The answer is 1/6 of a cup of milk.
Detailed Explanation:
To find out how much milk Zeinab needs, we need to calculate 1/4 of the original amount of milk. The original recipe requires 2/3 of a cup of milk.
Start with the original amount: 2/3 of a cup of milk.
Multiply this amount by 1/4 to find the reduced quantity:
Multiply the fractions: 2/3 * 1/4
Simplify the result, which is 1/6 of a cup of milk.
So, Zeinab needs 1/6 of a cup of milk to make 1/4 of the original recipe.
Hence 1/6 of a cup of milk is required
I am having trouble with this question, can anyone help? This is for Geometry.
Answer:
by geometry rules
for a triangle
external angle of a triangle is equal to the sum of two internal angle of the triangle ( other than external adjacent angle)
m<1= sum of m<2 and m<3
m<1= m<1+<2
m<1 = 31+72
m<1= 103
hope you are clear now !
Answer:
The correct answer is last option. 103
Step-by-step explanation:
Points to remember
Sum of any two angles of a triangle is equal to the exterior angle of the third angle
To find the measure of <1
It is given that m<2 = 31° and m< 3 = 72°
From the figure we can see that <2 and <3 are two angles of a triangle. And <1 is the exterior angle of third angle of same triangle.
Therefore we can write,
m<2 + m<3 = m<1
m<1 = 31 + 72
= 103°
Therefore the correct answer is last option. 103
Find the mean, median, and mode of the data set. Round to the nearest tenth. 15, 1, 4, 4, 8, 7, 15, 4, 15, 4, 5
Answer:
Median: 4.5
Mode: 4
Mean: 6.7
Step-by-step explanation:
First lets find the median, the number in the middle. To do this we need to put this data set in ascending order
1,4,4,4,4,5,7,8,15,15
The two numbers in the middle are 4 and 5. Now we must add these two numbers together and then divide by 2.
[tex]\frac{4+5}{2} =\frac{9}{2} =4.5[/tex]
Nexte lets find the mode, the number that occurs the most. 4 appears 4 times, which is the greatest amount.
Now lets find the mean. First we need to find the sum of these 10 numbers
[tex]1+4+4+4+4+5+7+8+15+15=67[/tex]
Next we have to divide by the number of data points, which is 10
[tex]\frac{67}{10} =6.7[/tex]
What is the range of the function f(x) = 4x + 9, given the domain D = {4, -2, 0, 2}?
O A. R = {-17, -9, -1, 17)
OB. R= {1, 7, 9, 17)
C. R=17, -1, 9, 17)
OD. R= {-7, 1, 9, 17}
For this case we have that by definition, the domain of a function is given by all the values for which the function is defined.
While the range of the function is the set of all the values that [tex]f (x)[/tex] takes.
We have the following function:
[tex]f (x) = 4x + 9[/tex]
We evaluate in the domain:
[tex]f (-4) = 4 (-4) + 9 = -16 + 9 = -7\\f (-2) = 4 (-2) + 9 = -8 + 9 = 1\\f (0) = 4 (0) + 9 = 0 + 9 = 9\\f (2) = 4 (2) + 9 = 8 + 9 = 17[/tex]
ANswer:
{-7,1,9,17}
1. Hector knows there is a relationship between the number of cars he washes and the time it takes
him to wash those cars. Identify the independent quantity and the dependent quantity in the
problem situation.
Answer:
The independent variable is the time (variable x)
The dependent variable is the number of cars he washes (variable y)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem
The relationship between the number of cars he washes and the time it takes him to wash those cars represent a a proportional variation
Let
y -----> the number of cars he washes
x -----> the time
The linear equation is [tex]y=kx[/tex]
The independent variable is the time x
The dependent variable is the number of cars he washes y
Which of the following sets of triangles are similar according to the Angle-Angle Similarity Postulate?
equilateral triangles
equiangular triangles
both equilateral and equiangular triangles
neither equilateral nor equiangular triangles
Answer: both equilateral and equiangular triangles
Answer:
Yes
Both equilateral and equiangular triangles
Step-by-step explanation:
The AA (Angle-Angle) similarity states that if two pairs of corresponding angles are congruent, then the triangles are similar
In equilateral triangles, all angles are equal.The corresponding sides of two equilateral triangles are congruent thus they will be similar. An Equiangular triangle is also an equilateral triangle because its interior angles are the same and add up to 180°.
Both equilateral and equiangular triangles are similar by the Angle-Angle Similarity Postulate because they each have two congruent angles with any other triangle of the same type.
Explanation:The Angle-Angle (AA) Similarity Postulate states that two triangles are similar if two angles of one triangle are congruent to two angles of the other triangle. Equilateral triangles are similar by AA postulate because all angles in any equilateral triangle measure 60 degrees, thus any two will be congruent with any two angles in another equilateral triangle. Equiangular triangles are also similar by the AA postulate, as all their corresponding angles are equal. Consequently, both equilateral and equiangular triangles are similar according to the AA Similarity Postulate.
Use the information given to identify the a9 term of the geometric sequence: a2 = 3, r = −1
Answer:
-3
Step-by-step explanation:
a₁ = a₂/r = 3/(-1)=-3
a₉ = a₁ · r⁸ = -3 · (-1)⁸ = -3 · 1 = -3
Classify this polynomial 5x^2 +3
Answer:
Degree is 2 so it is a quadratic.
The number of terms is 2 so it is a binomial.
It is a binomial quadratic.
Step-by-step explanation:
Let's find the degree of the polynomial first. I'm going to consider first the degrees of 5x^2 and 3.
The degree of the monomial 5x^2 is 2 because x is the only variable and it's exponent is 2.
The degree of the monomial 3 is 0 because there is no variable.
The degree of 5x^2+3 is therefore 2 because that is the highest degree of the monomials contained with in this polynomial 5x^2+3.
Degree 2 has a special name.
The special name for a degree 2 polynomial is quadratic.
Let's look at the number of terms in 5x^2+3.
Terms are separated by addition and subtraction symbols so there are two terms.
There is a special name for a two-termed polynomial, it is binomial.
So this is the following information I collected on our given polynomial:
Degree is 2 so it is a quadratic.
The number of terms is 2 so it is a binomial.
It is a binomial quadratic.
The system of equations y = –2x + 1 and y = x + 5 is shown on the graph below. Which statement is true about the solution to the system of equations?
A. The x-value is between –1 and –2, and the y-value is between 3 and 4.
B. The x-value is between 3 and 4 , and the y-value is between –1 and –2.
C. The x-value is between 1 and 2, and the y-value is between –3 and –4.
D.The x-value is between –3 and –4, and the y-value is between 1 and 2.
Answer:
the answer is a
Step-by-step explanation:
y = -2x +1
y = x + 5
-2x+1=x+5
-3x = 4
x= -4/3
y = -1 1/3 + 5= 3 2/3
Find the solution x-2y=-26 x-y=-2
Answer:
x = 22 and y = 24Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-2y=-26\\x-y=-2&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x-2y=-26\\-x+y=2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-y=-24\qquad\text{change the signs}\\.\qquad\qquad y=24\\\\\text{Put the value of y to the second equation:}\\\\x-24=-2\qquad\text{add 24 to both sides}\\x=22[/tex]
if squar root of x-5 is 15 what is the value of x
Answer:
x = 230
Step-by-step explanation:
Given
[tex]\sqrt{x-5}[/tex] = 15 ( square both sides )
x - 5 = 15² = 225 ( add 5 to both sides )
x = 230
In the diagram of circle A, what is m?
75°
90°
120°
135°
Answer:
90
Step-by-step explanation:
Alright first step what is the degree measure of LN.
A full rotation is 360 degrees so LN=360-270=90.
So angle M is half the difference of the intercepted arcs:
[tex]\frac{1}{2}(270-90)=\frac{1}{2}(180)=90[/tex]
The measure of the vertex angle from the given geometry figure is 90 degrees
Circle geometryThe given circle is made up of arc and angles. In order to determine the value of <M, we will use the theorem
"The half of the difference between the arc is equal to the angle at the vertex
1/2(270 - (360 - 270)) = <M
<M = 1/2 (270 -90)
<M = 1/2(180)
<M = 90degrees
Hence the measure of the vertex angle from the given geometry figure is 90 degrees
Learn more on geometry here:https://brainly.com/question/19241268
#SPJ5
Complete the recursive formula of the arithmetic sequence -16, -33, -50, -67, ....
The recursive formula for the sequence -16, -33, -50, -67, .... is f(n) = f(n - 1) - 17, f(1) = -16
Finding the recursive formula for the sequence
From the question, we have the following parameters that can be used in our computation:
-16, -33, -50, -67, ....
In the above sequence, we can see that -17 is added to the previous term to get the new term
This means that
First term, a = -16
Common difference, d = -17
The recursive formula for the sequence is then represented as
f(n) = f(n - 1) - 17, f(1) = -16
Why is the answer to this C and not E. Don’t you usually keep the negative number negative? Why is this one not left negative?
Answer:
C
Step-by-step explanation:
Given
x² = 7x - 3 ( subtract 7x - 3 from both sides )
x² - 7x + 3 = 0 ← in standard form
with a = 1, b = - 7, c = 3
Using the quadratic formula to solve for x
x = ( - (- 7) ± [tex]\sqrt{(-7)^2-(4(1)(3)}[/tex] ) / 2
= ( 7 ± [tex]\sqrt{49-12}[/tex] ) / 2
= [tex]\frac{7+/-\sqrt{37} }{2}[/tex] → C
ABC paint company needs to paint the outside of the building shown. They will also need to paint the roof. What is the surface area that needs to be painted?
3,100 ft^2
4,600 ft^2
4,100 ft^2
4,300 ft^2
Answer:
3,100 ft^2
Step-by-step explanation:
Answer:
3,100 ft^2
Step-by-step explanation:
A given data set has a symmetrical shape.
Which statement is true about the data set?
It cannot be determined if the mean is greater than, less than, or equal to the median.
The mean is less than the median.
The mean is greater than the median.
The mean is equal to the median.
Answer:
The mean is equal to the median.
Step-by-step explanation:
Median is the middle value of a given data set. In a symmetric distribution, the data on the left side of the median is equal to the data on the right side of the median. Therefore, the mean of that data is equal to the median of the symmetric distribution.
Answer:
the mean is less than the explanation
Step-by-step explanation:
I just checked
What is the base length of a parrellelogram with an area of 33.75 square meters and a height of 3 meters
Answer:
b = 11.25m
Step-by-step explanation:
The base length of a parrellelogram with an area of 33.75 square meters and a height of 3 meters is 11.25 meters.
Answer:
11.25 m
Step-by-step explanation:
area of parallelogram = base x height
so base = area/height
we substitute the values :
base = 33.75/3
= 11.25
What is the slope shown in the graph (-3,2) (-1,-1)
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{The formula is:}\dfrac{\huge\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}[/tex]
[tex]\huge\text{y}_2\huge\text{ = -1}\\\\\huge\text{y}_1\huge\text{ = 2}[/tex]
[tex]\huge\text{x}_2\huge\text{ = -1}\\\\\huge\text{x}_1\huge\text{ = -3}[/tex]
[tex]\dfrac{-1 -2 }{-1 - (-3)}[/tex]
[tex]\huge\text{-1 - 2 = -3}[/tex]
[tex]\huge\text{-1 - (-3) = 2 }[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: }\dfrac{-3}{2}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
What is the midpoint of the segment shown below?
Answer:
D. (-7/2, 3/2)
Step-by-step explanation:
x = (-6+(-1))/2 = -7/2
y = (-2+5)/2 = 3/2
Answer: D.
[tex](\dfrac{-7}{2},\ \dfrac{3}{2})[/tex]
Step-by-step explanation:
The coordinates of mid point (x,y) of a line joining points [tex](x_1 , y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by :-
[tex]x=\dfrac{x_1+x_2}{2},\ y=\dfrac{y_1+y_2}{2}[/tex]
From the given graph , we can see that the line is joining two points (-6,-2) and (-1,5) .
Then, the mid point of the line is given by :-
[tex]x=\dfrac{-6+(-1)}{2},\ y=\dfrac{-2+5}{2}[/tex]
[tex]x=\dfrac{-6-1}{2},\ y=\dfrac{5-2}{2}[/tex]
[tex]x=\dfrac{-7}{2},\ y=\dfrac{3}{2}[/tex]
Hence, the midpoint of the given segment = [tex](\dfrac{-7}{2},\ \dfrac{3}{2})[/tex]
21,42,126,504 If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose "not geometric.
Answer:
Not geometric
Step-by-step explanation:
In a geometric sequence, each term is multiplied by a common ratio to get the next term.
So if this is a geometric sequence, then dividing each term by the one before it should result in the same common ratio.
42 / 21 = 2
126 / 42 = 3
504 / 126 = 4
The ratios are different. This is not a geometric sequence.
Answer:
Some tips for the future, when trying to find if its arithmetic or geometric sequence we can do this to find the common ratio. Arithmetic; subtraction test Geometric; division test
Ex; 19, 25, 31, 37
Subtract-
37-31= 6
31-25= 6
25-19= 6
6 is the common difference for this arithmetic sequence
Ex; 4, 8, 16, 32
Divide-
32/16= 2
16/8= 2
8/4= 2
The common ratio for the geometric sequence is 2
Step-by-step explanation:
21, 42, 126, 504
504/126= 4
126/42= 3
42/21= 2
This is not a geometric sequence, there is no common ratio.
Please help!!! How do I solve questions 4 and 5?
Answer:
[tex]\large\boxed{4.\ V=\dfrac{33.64\pi x}{3}\approx35.21x}\\\boxed{5.\ V=21\ cm^3}[/tex]
Step-by-step explanation:
4.
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have
[tex]2r=11.6\to r=5.8,\ H=x[/tex]
Substitute:
[tex]V=\dfrac{1}{3}\pi(5.8^2)x=\dfrac{1}{3}\pi(33.64)x=\dfrac{33.64\pi x}{3}[/tex]
[tex]\pi\approx3.14[/tex]
[tex]V\approx\dfrac{(33.64)(3.14)x}{3}\approx35.21x[/tex]
5.
The formula of a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - base area
H - height
In the base we have the square. The formula of an area of a square with side s:
[tex]A=s^2[/tex]
We have
[tex]s=3cm,\ H=7\ cm[/tex]
[tex]B=3^2=9\ cm^2[/tex]
[tex]V=\dfrac{1}{3}(9)(7)=(3)(7)=21\ cm^3[/tex]
Really need help!! With picture
Answer:
In order:
2nd step
1st step
3rd step
4th step
Step-by-step explanation:
The checking part comes last.
Before you can determine the solution, your lines need to be graphed.
To graph your lines, they have to be in a form for you to determine how to graph them.
So the first step here is
"Write each equation in a form that is easy to graph"
The second step is:
To graph them
Third step is:
To see where they cross
The last step:
(Some people don't do it but should is check it).
[tex] \frac{7}{15 \frac{17}{22} \frac{22}{37} \frac{5}{17} [/tex]
greatest to least
first off, is noteworthy that on the denominators, 17 and 37 are prime numbers, so we can't quite factor them, and denominators of 15 and 22, have no common factors so the LCD of all denominators is simply their product, 15*22*37*17.
what we do is, turn all fractions with the same denominator, so they all represent the same division of the whole, and from there we can simply look at which numerator is larger or smaller to sort them.
we'll do so by using the LCD of all denominators, and dividing the LCD by each denominator, our quotient we'll use to multiply the fraction, let's do so
[tex]\bf \cfrac{7}{15} \qquad \cfrac{17}{22}\qquad \cfrac{22}{37} \qquad \cfrac{5}{17}~\hspace{5em} \stackrel{\textit{so the LCD for those denominators is}}{15\cdot 22\cdot 37\cdot 17\implies 207570} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{207570\div 15 ~=~ 13838}{\cfrac{7\cdot 13838}{15\cdot 13838}}\qquad \stackrel{207570\div 22 ~=~ 9435}{\cfrac{17\cdot 9435}{22\cdot 9435}}\qquad \stackrel{207570\div 37 ~=~ 5610}{\cfrac{22\cdot 5610}{37\cdot 5610}}\qquad \stackrel{207570\div 17 ~=~ 12210}{\cfrac{5\cdot 12210}{17\cdot 12210}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{96866}{207570}\qquad \cfrac{160395}{207570}\qquad \cfrac{123420}{207570}\qquad \cfrac{61050}{207570} \\\\\\ \stackrel{\textit{and if we sort them from greatest to least}}{\cfrac{160395}{207570}\qquad \cfrac{123420}{207570}\qquad \cfrac{96866}{207570}\qquad\cfrac{61050}{207570}}[/tex]
quick!!!
The admission fee to a zoo is $1.20 for children and twice as much for
adults. If twice as many adults as children visited the zoo and the total
admission fee collected was $1 944, how many people visited the zoo?
Answer:
324 children, and648 adults.That's 972 people in total.
Step-by-step explanation:
Here's how to solve this problem by setting up an equation with a single unknown.
Let the number of children that visited the zoo be [tex]x[/tex].
There are twice as many adults as children. So the number of adults will be [tex]2x[/tex].
Each child's ticket costs [tex]\$1.20[/tex]. The [tex]x[/tex] children will contribute a total of [tex]1.20 x[/tex] dollars to the total admission fee.
Each adult's ticket costs twice as much as a child's ticket. That's [tex]2\times \$1.20 = \$2.40[/tex]. The [tex]2x[/tex] adults will contribute a total of [tex]2.40\times 2x =4.80x[/tex] dollars to the total admission fee.
However,
[tex]\begin{aligned}&\text{Admission fee from children} \\+&\text{Admission fee from adults} \\ = &\text{Total Admission fee collected}\end{aligned}[/tex].
In other words,
[tex]1.20x + 4.80x = 1944[/tex].
[tex]6x = 1944[/tex].
[tex]\displaystyle x = \frac{1944}{6} = 324[/tex].
In other words, [tex]324[/tex] children visited the zoo. Twice as many adults visited the zoo. That's [tex]2x = 648[/tex] adults. [tex]324 + 648 = 972[/tex] people visited the zoo in total.