Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?
Answer:
the system of equation that can be used to determine how long it will be before the populations of the two species are equal is :
[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]
Step-by-step explanation:
Given that :
the current population of insect A to be 1.3 million
the current population of insect B to be 2.1 million.
As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
The equation that can be used to determine how long it will be before the populations of the two species are equal is an equation for exponential decay, which can be represented as follows:
[tex]\mathtt{y = pe^{-rt}}[/tex]
where;
P represents the population of each species of insect in millions
t represents the elapsed time in years
r is the rate of decrease
So, we can have:
[tex]\mathtt{p_1 = 1.3 }[/tex] in million and [tex]\mathtt{p_2 = 2.1}[/tex] in million
Also for rate of decrease;
[tex]\mathtt{r_1 = 0.038}[/tex] and [tex]\mathtt{r_2 = 0.046}[/tex]
Therefore;
the exponential decay for Population of insect A can now be:
[tex]\mathtt{P = 1.3 e^{-0.038 \ t}}[/tex]
the exponential decay for Population of insect B can now be:
[tex]\mathtt{P = 2.1 \ e^{-0.046 \ t}}[/tex]
Hence, the system of equation that can be used to determine how long it will be before the populations of the two species are equal is :
[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]
Answer:
A!
Step-by-step explanation:
Plato
Repost because someone answered without actually giving an answer. What is the mode of the data shown in the table? Scores: 5 12 13 18 Frequency: 3 2 5 4 A. 12 B. 51.5 C. 12.5 D. 13
Answer:
Option (D) : 13
Step-by-step explanation:
Mode is the observation which occurred the most number of time.
Therefore, mode = 13
I need help! Answer as fast as you can. Marking brainlyiest
Answer:
A
Step-by-step explanation:
We can break down what each term represents in the equation
60 is the constant. This is the base price that is paid regardless of workers and hours needed
Then there is 12nh. 12 represents the cost per hour for one worker. If the job takes only one hour, then it is 12 dollars per worker. Similarly, if the job only takes one person, then it is 12 dollars for each hour.
The most accurate answer is A
Vladimir builds 3 legged stools and 4 legged tables. Last month he used 72 legs to build 3 more stools than tables. How many stools and how many tables did he build?
Answer:
9 tables
12 stools
Step-by-step explanation:
x= number of tables
x+3= number of stools
4x+3(x+3)=72
4x+3x+9=72
4x+3x=72-9
7x=63
x=9
So he built 9 tables and 12 stools
(9x4=36, 3X12=36, 36+36=72) CHECK
Solve for p.
–
19p–2p+16p+12=
–
18
p=
Answer:
6
BRAINLIEST, PLEASE!
Step-by-step explanation:
-19p - 2p + 16p + 12 = -18
-5p + 12 = -18
-5p = -30
p = 6
Answer:
p = 6
Step-by-step explanation:
Given
- 19p - 2p + 16p + 12 = - 18 ( simplify left side )
- 5p + 12 = - 18 ( subtract 12 from both sides )
- 5p = - 30 ( divide both sides by - 5 )
p = 6
Under his cell phone plan, Christopher pays a flat cost of $52 per month and $5 per
gigabyte. He wants to keep his bill at $75 per month. Which tape diagram could be
used to represent the context if x represents the number of gigabytes of data
Christopher can use while staying within his budget?
According to the given information, the tape diagram shown in option C is correct.
Use the concept of inequality defined as:
An inequality is a mathematical statement that uses the inequality symbol to indicate the relationship between two expressions. Both sides of an inequality sign have different expressions.
Given that,
The cost per month = $52
The cost per gigabyte = $5
He wants to keep his bill at $75 per month.
According to the given information the inequality expression be:
52 + 5x ≤ 75
Since now let x = 3
The LHS be:
52 + 15 = 67 < 75
Therefore,
The correct combination be:
52 + 5 + 5 + 5 < 75
Hence,
The tape diagram shown in option C is correct.
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take a square of arbitary measure assuming its area is one square unit.divide it in to four equal parts and shade one of them.again take one shaded part of that square and shade one fourth of it.repeat the same process continuously and find the sum area of shaded region
Answer:
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.[1][2] The order of the magic square is the number of integers along one side (n), and the constant sum is called the magic constant. If the array includes just the positive integers {\displaystyle 1,2,...,n^{2}}{\displaystyle 1,2,...,n^{2}}, the magic square is said to be normal. Some authors take magic square to mean normal magic square.[3]
The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3
Magic squares that include repeated entries do not fall under this definition and are referred to as trivial. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant we have semimagic squares (sometimes called orthomagic squares).
The mathematical study of magic squares typically deals with its construction, classification, and enumeration. Although completely general methods for producing all the magic squares of all orders do not exist, historically three general techniques have been discovered: by bordering method, by making composite magic squares, and by adding two preliminary squares. There are also more specific strategies like the continuous enumeration method that reproduces specific patterns. Magic squares are generally classified according to their order n as: odd if n is odd, evenly even (also referred to as "doubly even") if n is a multiple of 4, oddly even (also known as "singly even") if n is any other even number. This classification is based on different techniques required to construct odd, evenly even, and oddly even squares. Beside this, depending on further properties, magic squares are also classified as associative magic squares, pandiagonal magic squares, most-perfect magic squares, and so on. More challengingly, attempts have also been made to classify all the magic squares of a given order as transformations of a smaller set of squares. Except for n ≤ 5, the enumeration of higher order magic squares is still an open challenge. The enumeration of most-perfect magic squares of any order was only accomplished in the late 20th century.
Magic squares have a long history, dating back to at least 190 BCE in China. At various times they have acquired occult or mythical significance, and have appeared as symbols in works of art. In modern times they have been generalized a number of ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations.
The sum area of shaded region is [tex]\frac{1}{3}[/tex].
Summation formula for geometric progressionThe formula to find the sum of infinite geometric progression is
[tex]S_{n}=\frac{a_{1}(1-q^{n}) }{1-q} \ \ q \ne 1[/tex]
Given
S = [tex]\frac{1}{4} +\frac{1}{16} +\frac{1}{64} +.........[/tex]
Using geometric progression
S = [tex]\lim_{h \to \infty} [\frac{1}{4} +(\frac{1}{4} )^{2} +(\frac{1}{4} )^{3} +.........+(\frac{1}{4} )^{n}][/tex]
Using summation formula for geometric progression
[tex]S_{n}=\frac{a_{1}(1-q^{n}) }{1-q} \ \ q \ne 1[/tex]
= [tex]\lim_{h \to \infty} \frac{\frac{1}{4} (1-(\frac{1}{4} )^{n} }{1-\frac{1}{4} }[/tex]
= [tex]\lim_{h \to \infty} \frac{\frac{1}{4} (1-\frac{1}{4^{n} }) }{\frac{3}{4} }[/tex]
= [tex]\lim_{h\to \infty} \frac{1}{3}(1-\frac{1}{4^{n} } )[/tex]
[tex]\lim_{h\to \infty} \frac{1}{4^{n} }[/tex] = 0
S = [tex]\frac{1}{3}(1-0) = \frac{1}{3}[/tex]
The sum area of shaded region is [tex]\frac{1}{3}[/tex].
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Suppose
f
(
x
)
=
2
x
2
+
4
x
−
10
. Compute the following:
Answer:-80
Step-by-step explanation:f(x)=2*2+4*-10
Get this correct i will give u brainliest.
Answer:
x = - 2, y = - 8
Step-by-step explanation:
Given the 2 equations
13x - 6y = 22 → (1)
x = y + 6 → (2)
Substitute x = y + 6 into (1)
13(y + 6) - 6y = 22 ← distribute and simplify left side
13y + 78 - 6y = 22
7y + 78 = 22 ( subtract 78 from both sides )
7y = - 56 ( divide both sides by 7 )
y = - 8
Substitute y = - 8 into (2) and evaluate for x
x = - 8 + 6 = - 2
Thus x = - 2, y = - 8
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Edgar has test scores of 87, 92, 90, 84, 88, and 91. What is the lowest grade Edger can get on the next test to have an A average (90 or higher)?
A. 94
B. 96
C. 98
D. 100
Answer:
C. 98
Step-by-step explanation:
If you add all of his previous test scores and go through the list of numbers you get C.98 as the answer. I added all of his test scores plus 98 which equals 630 divided by 7 (because if he got a 98 there would be 7 test scores) you would get 90 or an A average.
=============================================================
Explanation:
Let x be the next test grade. It ranges from 0 to 100, inclusive of both endpoints.
The original set {87,92,90,84,88,91} becomes {87,92,90,84,88,91,x} after adding on that score.
We have 7 scores now. We find the average by adding up those seven scores and dividing by 7.
average = (sum of the scores)/(number of scores)
average = (87+92+90+84+88+91+x)/7
average = (532+x)/7
We want the average to be 90 or higher, so we would then have these steps
[tex]\text{average} \ge 90\\\\\frac{532+x}{7} \ge 90\\\\532+x \ge 90*7\\\\532+x \ge 630\\\\x \ge 630-532\\\\x \ge 98\\\\[/tex]
This means Edgar must score a 98 or higher on the seventh test in order for his overall average to be 90 or higher.
In other words, the lowest test score he can get is a 98.
------------------
Extra info (optional section):
Let's say Edgar gets the highest score possible.
So he gets x = 100
This would mean
average = (87+92+90+84+88+91+x)/7
average = (532+x)/7
average = (532+100)/7
average = 632/7
average = 90.2857 which is approximate
We can see that his overall average would stick to 90 if the teacher is rounding to the nearest whole number.
I need help on this During the spring, Nina Milling assembles bicycles at The Wheeler Dealer. She is paid $12.00 for each bicycle assembled during a regular work week, $14.00 for each bicycle assembled on a Saturday, and $16.00 for each bicycle assembled on a Sunday. What is her total pay for a week in which she assembled the following number of bicycles? Mon. Tues. Wed. Thurs. Fri. Sat. Sun. 4 7 6 10 8 4 5
Answer:
$556
Step-by-step explanation:
4+7+6+10+8=35
35x12=420
4x14=56
5x16=80
420+56+80=556
Answer:
$556.
Step-by-step explanation:
So she is paid $12 dollars for every bicycle assembled on a weekday,
paid $14 dollars for every bicycle assembled on Saturday, and is
paid $16 dollars for every bicycle assembled on Sunday.
She assembled 4 on Monday, 7 on Tuesday, 6 on Wednesday, 10 on Thursday, 8 on Friday, 4 on Saturday, and 5 on Sunday.
In other words, she assembled on total of 4+7+6+10+8=35 bicycles during the weekdays. And she assembled 4 on Saturday and 5 on Sunday.
In other words, her total pay is:
[tex]\$12(35)+\$14(4)+\$16(5)=\$556[/tex]
Plz Help...............I’ll give you 50 pts
1. Essential Question How do you use what you know about absolute value to add integers?
2. Reasoning How can you tell the sign of the sum of a positive and negative integer without doing any calculations?
3. Model with Math How would you use a number line to determine the sum of two negative integers?
Do You Know How?
4. Sarah bought a bike that cost $260. She had a coupon that was worth $55 off the cost of any bike. Use the expression 260 + (-55) to find how much Sarah paid for her bike.
5. A shark is swimming 60 feet below the surface of the ocean. There is a fish that is 25 feet deeper in the water. Use the expression (-60) + (-25) to describe the fish’s location relative to the surface of the ocean.
60 feet
25 feet
6. The high temperature one day was 30°F. Then the temperature dropped 23 degrees during the night. Does the expression 30 + (-23) represent the temperature at night? Explain.
Answer:
1) I know that if the two integers have the same sign: Add their absolute values and give the answer the same sign as the two original integers. Also, I know that If the two integers have different signs: Subtract the lesser absolute value from the greater absolute value.
2) To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.
3) First, draw a number line. Then, find the location of the first integer on the number line. Next, if the second integer is positive, move that many units to the right from the location of the first integer. If the second integer is negative, move that many units to the left from the location of the first integer.
4) 205 dollars
5) The fish’s location relative to the surface of the ocean is -85
6) Honestly, I'm not so sure about this now, but I believe yes.
Step-by-step explanation:
there are a lot of resources, here on this app, that i used to help answer your question. If I helped, it would be nice if you rated this brainliest, give 5 stars, and the 50 points :)
1) I know that if the two integers have the same sign: Add their absolute values and give the answer the same sign as the two original integers. Also, I know that If the two integers have different signs: Subtract the lesser absolute value from the greater absolute value.
2) To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of any integer and its opposite is equal to zero.
3) First, draw a number line. Then, find the location of the first integer on the number line. Next, if the second integer is positive, move that many units to the right from the location of the first integer. If the second integer is negative, move that many units to the left from the location of the first integer.
4) $205
5) The fish’s location relative to the surface of the ocean is -85 or -25 if the fish is 25 feet deeper from surface of ocean
6) Yes if both the temperatures are in Degree Fahrenheit
please click thanks and mark brainliest if you like :)
Math nation section 2
Send the question?
Must click thanks and mark brainliest
Solve for x 3(x+7)-14=22
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]3(x+7)-14=22[/tex]
Step 1: Simplify both sides of the equation.
[tex]3 ( x + 7 ) - 14 = 22\\(3)^(x) + (3) (7) + - 14 = 22[/tex] (Distribute)
[tex]3x + 21 + -14 = 22[/tex]
[tex]( 3x) + (21 + -14 ) = 22[/tex] (Combine Like Terms)
[tex]3x + 7 = 22\\3x + 7 = 22[/tex]
Step 2: Subtract 7 from both sides.
[tex]3x + 7 - 7 = 22 - 7 \\3x = 15[/tex]
Step 3: Divide both sides by 3.
[tex]\frac{3x}{3} = \frac{15}{3} \\x = 5[/tex]
So your answer would be : [tex]\boxed {x = 5}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
m. Proportions
1) Write a proportion for the situation, then solve the
proportion to answer the question.
nation:
a. A 6 foot high fence casts a 7 foot shadow.
Standing beside the fence is a tree that casts a
31.5 foot shadow. How tall is the tree?
Answer:
height of tree is 27 ft
Step-by-step explanation:
The corresponding parts of the problem are in proportion
let h be the height of the tree , then
[tex]\frac{6}{h}[/tex] = [tex]\frac{7}{31.5}[/tex] ( cross- multiply )
7h = 189 ( divide both sides by 7 )
h = 27
Height of tree is 27 feet
PLEASE HELP DO TODAY IN A FRW MINUTESSS
How many minutes will it take a caterpillar to go seven feet if it travels 24 inches per minute? To travel seven feet, it will take the caterpillar a0 minutes.
Answer:
3 and and half minutes--> 7ft
Step-by-step explanation:
If it travels 24 inches aka 2ft per minute
then it has to travel 12 inches aka 1ft in 30secs
SO
3mins and 30secs to travel 7ft
24inches--- 2ft---- per minute
4ft--- 2 mins
6ft---- 3mins
7ft--- 3minutes and 30 seconds
construct a quadrilateral PQRS such that PQ=RS=7.3cm,angle Q=60°,QR=5cm and angle R=135°.
Answer:
is your answer how are you
Solve for g.
-3+5+ 6g = 11 – 3g
g =
Answer:
g = 1
Step-by-step explanation:
-3 + 5 + 6g = 11 - 3g
Move the variables to one side and the numbers to the other:
9g = 9
Simplify:
g = 1
Answer:
g=1
Step-by-step explanation:
-3+5=2
2+6g=8
11-3g=8
makes sense that g will have to be 1
Deshaun bought 6 bags of sugar for his restaurant. Each bag weighed 6.9 kilograms. How many kilograms of sugar did he buy total?
Answer:
41.4 kgs
Step-by-step explanation:
Take the number of bags times the weight of each bag
6 * 6.9
41.4 kgs
Answer:
41.4 kilograms of sugar
Step-by-step explanation:
its 41.4 kilograms of sugar because you take the 6 bags and multiply that by the 6.9
Simplify the expression using trigonometric identities: sec (–θ) – cos θ.
Answer:
Step-by-step explanation:
Let's break this down. The secant of a negative angle is the same as the secant of the positive angle. This is because secant is the inverse of cosine, and cosine is an even function. f(-x) = f(x) if the function is even, and f(-x) = -f(x) if the function is odd. Sine is odd and has symmetry about the origin; cosine is even and has y-axis symmetry.
Therefore, sec(-θ) = sec(θ) and we have then
sec(θ) - cos(θ). Since secant is the inverse of cosine, we can write:
[tex]\frac{1}{cos\theta}-cos\theta[/tex] and finding a common denominator:
[tex]\frac{1-cos^2\theta}{cos\theta}[/tex] and using a trig identity:
[tex]\frac{sin^2\theta}{cos\theta}[/tex] and simplify that down a bit by breaking it up:
[tex]\frac{sin\theta}{cos\theta}*sin\theta[/tex] finally boils down to
tanθ · sinθ, the last choice there.
What's the circumference of a
circle with a diameter of 22 inches?
Use 3.14 for n.
C = [?] inches
Enter the number that belongs in the green
box. Do not round your ans er.
Hint: C = tid
Answer:
69.08 inches
Step-by-step explanation:
Circumference = diameter x pi. In this case, diameter x 3.14.
diameter = 22
22 x 3.14 = 69.08 inches
Brainiest please!
Is the expression \left(5 \times 2\right)^x(5×2)
x
always equal to the expression 10^x10
x
? Explain your answer.
9514 1404 393
Answer:
yes
Step-by-step explanation:
The expression (5·2)^x is evaluated by evaluating the expression in parentheses first. When you do that, you get 10^x.
(5·2)^x ≡ 10^x
3.) Find the measure of the missing angle X:
Xº
120°
70°
Answer:
x=50
Step-by-step explanation:
Let's look at the red angle. if a flat line makes the angle 180, and the outer angle is 120, subtract 120 from 180. This will give you 60. Now every angle of a triangle added together will give you the sum of 180. So you already have 60 and 70, which make 130 all together. Subract 130 from 180 - (180-130) - and you'll get the result of 50.
The solution is : the measure of the missing angle X is x=50.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
from the given diagram, we get,
Let's look at the red angle.
if a flat line makes the angle 180, and the outer angle is 120,
subtract 120 from 180.
This will give you 60.
Now every angle of a triangle added together will give you the sum of 180.
So you already have 60 and 70,
which make 130 all together.
Subtract 130 from 180
i.e. (180-130) = 50
and we get the result of 50.
Hence, The solution is : the measure of the missing angle X is x=50.
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it’s a 425 mile drive from San Jose to Los Angeles.
it’s about 320 mile Drive from San Jose to Santa Barbara.
write an equation showing that the distance traveled on the first day plus the distance traveled on the second is equal to 425 miles
Answer:
The answer is below
Step-by-step explanation:
The distance traveled the first day = Distance from San Jose to Santa Barbara = 320 mile.
The distance traveled the second day = Distance from Santa Barbara to Los Angeles.
But From San Jose to Los Angeles = 425 mile. Therefore:
Distance From San Jose to Los Angeles = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles
425 = 320 + Distance from Santa Barbara to Los Angeles.
Distance from Santa Barbara to Los Angeles = 425 - 320 = 105 mile
The distance traveled the second day = Distance from Santa Barbara to Los Angeles = 105 miles
The distance traveled the first day + The distance traveled the second day = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles = 320 + 105 = 425 miles
The distance traveled the first day + The distance traveled the second day = 425 miles
The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made 16of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank? Hint: You do not divide the volume of the main show tank by 6.
Answer:
see below
Step-by-step explanation:
If the original dimensions of the tank are x, y, and z, the mock dimensions will be 1/6x, 1/6y and 1/6z. The volume of the original tank is x * y * z = xyz whereas the volume of the mock-up tank is 1/6x * 1/6y * 1/6z = 1/216 * xyz. Therefore, we know that the volume of the mock-up tank is 1/216 th of the original tank.
The puppy needs to catch a train that is moving at 8 km/h. She is 100m away and running at 10 km/h. How far will the train have traveled before the puppy is able to jump on?
Answer:
400 meters
0 meters if the puppy can jump really really far ha ha ....
P = 10000x - 100
T = 8000x
10000x - 100 = 8000x
2000x = 100
x = 1/20 hr
60/20 = 3 minutes
Step-by-step explanation:
The price of a stock decreased by 60 cents one week, decreased 10 cents the next week, and decreased another 20 cents the following week. What is the average change in the price of the stock over the three weeks? need to know right now ASAP!! –270 cents per week –90 cents per week –87 cents per week –30 cents per week
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------------
It decreased by 30 cents per week.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The average rate of change is calculated as:
the ratio of the sum of the change in the three weeks divided by the number of weeks. (The number of weeks being 3)
Rate of change = [tex]\frac{-60 -10 -20}{3}[/tex].
(-60 + -10 + -20 = -90). So, to simplify it:
[tex]\frac{-90}{3}[/tex] = -30
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Incase you are confused:
Since the average rate of change is negative, this means that the stock price has decreased.
Please please please help
Answer:
m = 4
Step-by-step explanation:
9/6=6/m
9m = 36
m = 4
What is the relationship between the area of ABCD and the area of EFGH? Quadrilateral ABCD with side measures 18 for AB, 24 for BC; quadrilateral EFGH with side measures 6 for EF, x for FG The ratio of the area of ABCD to the area of EFGH is 1:9. The ratio of the area of ABCD to the area of EFGH is 3:1. The ratio of the area of ABCD to the area of EFGH is 1:3. The ratio of the area of ABCD to the area of EFGH is 9:1.
Answer:
The ratio of the area of ABCD to the area of EFGH is 9:1.
Step-by-step explanation:
Let us assume that the shapes are rectangles and they are similar. If the two shapes are similar then their sides are in the same proportion. Therefore the ratio of the sides are in the same proportion.
[tex]\frac{AB}{BC}=\frac{EF}{FG}\\ \\\frac{18}{24}=\frac{6}{x}\\\\18x=24*6\\ \\x=\frac{24*6}{18}=8[/tex]
The area of ABCD = AB × BC = 18 × 24 = 432
The area of EFGH = EF × FG = 6 × 8 = 48
The ratio of the area of ABCD to the area of EFGH = Area of ABCD / Area of EFGH = 432 / 48 = 9/1 = 9 : 1
Help please, would be much appreciated