The table shows the world birth rates y number of births ler thousands people) in r years since 1960
Identify an equation that models the birth rate as a function of the number years since 1960
Answers
An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35. Thus, option 3 is correct.
What do you mean by equation?It represents a relationship between variables and constants and is used to describe the behavior of a function or system. Equations can be linear or nonlinear and can have one or multiple variables. They can be used to solve real-world problems, such as finding the slope of a line, calculating distances, or determining the minimum or maximum value of a function. Equations are also used in advanced mathematical disciplines, such as calculus, algebra, and geometry.
When x = 0, y-intercept = 35.4 ≈ 35
And when x increases, the value of y decreases, so slope is negative
From the given options
There is only two negative slope equation but only one with y-intercept = 35. i.e.
y = -0.3x + 35
Thus, An equation that models the birth rate as a function of the number years since 1960 is y = -0.3x + 35.
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Related Questions
Find the eigenvalues and eigenvectors of matrix A = 5 4
1 2
Answers
The matrix A eigenvalues and eigenvectors are as follows:
Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]
Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]
Using the equation (A - λI)v = 0, where is an eigenvalue of A, I am the 2x2 identity matrix, and v is the associated eigenvector, we can determine the eigenvalues and eigenvectors of the matrix A = [[5, 4], [1, 2]].
First, we calculate the (A - λI) matrix's determinant:
det(A - λI) = |5-λ 4| = (5-λ)(2-λ) - 4 = λ^2 - 7λ + 6
|1 2-λ|
We obtain the characteristic equation by setting the determinant to zero:
λ^2 - 7λ + 6 = 0
We obtain two eigenvalues after solving for λ :
λ = 1 and λ = 6
Next, For each eigenvalue, we identify the appropriate eigenvectors:
For λ = 1, We solve the system of linear equations represented by the equation(A - λI)v = 0:
4v1 + 4v2 = 0
v1 + v2 = 0
The second equation is evidently as straightforward as v1 = -v2. When we enter this into the initial equation, we get:
4v2 - 4v2 = 0
Thus, the eigenvector for λ = 1 is v = [1, -1].
For λ = 6, We solve the system of linear equations represented by the equation(A - λI)v = 0:
-v1 + 4v2 = 0
-v1 + 4v2 = 0
v1 - 4v2 = 0
It is evident that the first equation is just v1 = 4v2. When we enter this into the second equation, we get:
4v2 - 4v2 = 0
Thus, the eigenvector for λ = 6 is v = [4, 1].
Therefore, The matrix A eigenvalues and eigenvectors are as follows:
Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]
Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]
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Need ASAP. Questions are in the pictures attached! ty
Answers
The required rate of change of f(x) from x = -6 to x = 3 is f'(x) = 7.
What is the rate of change?Rate of change is defined as the change in value with rest to another value is called rate of change.
Here,
Given that,
f(x) = x² + 4x -15
Now, put x = -3
f(-3) = 9 - 12 - 15
f(-3) = -18
Now put x = 6
f(6)= 36 + 24 - 15
f(6) = 45
Since we know that, the rate of change of function is given as,
f'(x) = f'(a) - f'(b) / a -b
f'(x) =f'(6) - f'(-3) / a - b
f'(x) = 45 - (-18) / 6 -(-3)
f'(x) = 63 / 9
f'(x) = 7
Thus, the required rate of change of f(x) from x = -6 to x = 3 is f'(x) = 7.
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An ore car of mass 4,800 kg rolls downhill on tracks from a mine. At the end of the tracks, 13. 9 m lower in elevation, is a spring with k = 410,000 n/m. How much is the spring compressed in stopping the ore car? ignore friction.
Answers
The spring compressed in stopping the ore car is 4.4719 m.
For answer this we will apply the rule of the conservation of energy,
The conservation of energy principle states that in a closed system, the energy of interacting objects or particles remains constant. Kinetic energy, sometimes known as the energy of motion, was the first type of energy to be identified. The total of the kinetic energy of the particles before collision and the sum of the kinetic energy of the particles after collision are identical in some particle collisions, known as elastic collisions.
where:
[tex]E_i=E_f[/tex]
First, we will call:
[tex]E_i[/tex]:the automobile is parked
[tex]E_f[/tex]:when the spring is shortened
so:
[tex]E_i=E_f[/tex]
[tex]mgh=\frac{1}{2}kx^2[/tex]
where M is the vehicle's mass, g is gravity, h is height, K is the spring's constant, and X is the compressed spring used to halt the ore car. By substituting values, we obtain:
4800×9.8×13.8=[tex]\frac{1}{2}\times 410000\times x^2[/tex]
calculating x:
x = 4.4719 m
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Part I: Make It Simple
1. Which expression is equivalent to 3 (k kk)? S
A. 9k
B. 3k
C. 3k4
D. 3k³
Answers
Lianisse recorded the number of text messages she sent each day over a period of time. She created the box plot shown to display her data.
Finish completing the five-number summary of Lianisse’s data.
Minimum: 1
First Quartile: _____
Median: _____
Third Quartile: ______
Maximum: ______
Answers
The five number summary is 77.5.
First Quartile: 7.5
Median: 15.5
Third Quartile: 23.5
Maximum: 30
completing the five-number summary of Lianisse’s data:
1, 2, 3, 4, 5, 6, 7, 8,9,10,11, 12, 13,14, 15, 16,17, 18, 19, 20 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.
Minimum = 1
First Quartile = 7 + 8
2
= 15/2
= 7.5
Median = 15+ 16
2
=31/2
=15.5
Third Quartile = 15 + 16
2
= 31/2
= 15.5
Maximum = 30
five - number summary = Minimum number + Lower quartile (Q₁) + median (Q₂) + Upper quartile (Q₃) + maximum number
five - number summary = 1 + 7.5 + 15.5 + 23.5 + 30 = 77.5
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el... The vertices of parallelogram HIJK are H(0, -1), I(2, 3), J(7, -1), K(5, -5). Determine if HIJK is a parallelogram.
Answers
The correct option is, No, because HI and JK do NOT have the same slope and HK and IJ have the same slope
What are the properties of parallelogram ?Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.
Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.
Consecutive angles are supplementary: The consecutive angles of a parallelogram are always supplementary, meaning that they add up to 180 degrees.
Diagonals bisect each other: The diagonals of a parallelogram bisect each other, meaning that they intersect at the midpoint of each other.
The sum of the interior angles is 360 degrees: The sum of the interior angles of a parallelogram is 360 degrees.
No, because HI and JK do NOT have the same slope and HK and IJ have the same slope.
In order for a quadrilateral to be a parallelogram, opposite sides must be parallel, which means they have the same slope.
In this case, HI and JK do not have the same slope, and therefore, the opposite sides are not parallel.
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The complete question:
The vertices of parallelogram HUJK are H(0,-1),(2,3), J(7, -1),K(5,-5). Determine if HIJK is a parallelogram.
No, because HI and JK do NOT have the same slope and HK and IJ have the same slope
Yes, because HI and JK have the same slope and HK and IJ have the same slope
Yes, because the image is tilted
No, because HK and JI have the same slope, but HI and JK do NOT have the same slope
The following angles are given in degrees and fractions of degrees. Rewrite them in degrees, arcminutes, and arcseconds.
A. 24.2 degrees?
B. 1.56 degrees?
C. 0.1 degrees?
D. 0.01 degrees?
Answers
The value is approximately equal to 12.0711°
Degrees-Minutes-SecondsWhile measuring angles, we use various units of measurements such as the degrees or the SI unit radians as per our convenience.
When we use the degree system, we can use the degree-minute-second or the degree decimal system as per our requirement of precision.
The angle in degree - minutes - seconds is 12°4'16"
We know that [tex]\frac{1}{60}[/tex] of a degree is minute and [tex]\frac{1}{60}[/tex] of a minute is a second.
Hence, [tex]\frac{1}{3600}[/tex] of a degree is a second.
Therefore the angle [tex]\theta[/tex] in degrees and decimal fractions of degrees will be:
[tex]\theta[/tex] = [tex]12+\frac{1}{60}[/tex] × 4 + [tex]\frac{1}{3600}[/tex] × 16
= [tex](12+\frac{1}{15}+\frac{1}{225} )[/tex]°
The value is approximately equal to 12.0711°
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The given question is incomplete, complete question is:
The angle 12 degrees 4'16" is given in degrees, arcminutes, and arcseconds. How do you rewrite them in degrees and decimal fractions of degrees?
What is 20% of 350000?
Answers
Answer:
Step-by-step explanation:70000
if f is differentiable at a must f be continuous at aa. No. If f is differetiable at a, then f is not continuous at a. The contrapositive of this statement therefore states, if f is continuous at a, then f is not differentiable at a.b. Yes. If f is differentiable at a, then f is continuous at a. the contrapositive of this statement therefore states, if f is continuous at a, then f is differentiable at a.c. No. If f is continuous at a, it is not necessarily true that the limit that defines f' exists at a.d. Yes. if f continuous at a, it is necessarily true that the limit that defines f' exists at a.
Answers
The statement "If f is differentiable at a, then f is continuous at a" is true, but "If f is continuous at a, then f is differentiable at a" is false.
Differentiability and continuity are two important concepts in calculus. A function is said to be continuous at a point if the values of the function approach a finite limit as the independent variable approaches the same value. In other words, there are no sudden jumps or breaks in the function at that point.
On the other hand, a function is said to be differentiable at a point if the limit of the rate of change of the function exists as the independent variable approaches the same value. This rate of change is called the derivative of the function and it is used to determine the slope of the function at that point.
So, it is true that if a function is differentiable at a point, then it is also continuous at that point. In other words, a continuous function must be differentiable. However, the reverse is not necessarily true. A function can reach a point where it is continuous but not differentiable. For example, the absolute value function is continuous everywhere but it is not differentiable at x = 0.
Therefore, we can say that if f is differentiable at a, then f is continuous at a. But if f is continuous at a, it does not imply that f is differentiable at a.
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Ms. Kelley is hiring teachers for the science department at a new high school. There are 9 biology teachers and 5 chemistry teachers to choose from. How many different ways can Ms. Kelley hire a staff that includes one teacher in each subject?
Answers
The total number of ways is 45.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Ms. Kelley needs to hire one biology teacher and one chemistry teacher for the science department.
The number of ways to choose one biology teacher from a pool of 9
is 9.
The number of ways to choose one chemistry teacher from a pool of 5
is 5.
Now,
According to the multiplication principle of counting.
The total number of ways to hire one teacher from each subject.
= The number of ways to choose one biology teacher x The number of ways to choose one chemistry teacher.
= 9 x 5
= 45
Therefore,
The total number of ways Ms. Kelley can hire a staff that includes one teacher in each subject is 45.
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What is 128 lbs to kg ?
Answers
take 128/2.205 = 58.0598
128 pounds is equal to 58.059 kilograms.
To convert pounds (lbs) to kilograms (kg), you can use the conversion factor that 1 pound is equal to 0.45359237 kilograms.
To convert 128 pounds to kilograms, you can multiply 128 by the conversion factor:
= 128 lbs x 0.45359237 kg/lb
≈ 58.059 kilograms
Therefore, 128 pounds is equal to 58.059 kilograms.
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Which step is incorrect?
Answers
Answer:Step 2
Step-by-step explanation: Bc Im right
1. If the given angle is in standard position, find two positive and two negative coterminal angles.
2. a) Find the angle supplementary theta = 15.90
b) Convert the angle to degrees, minutes, and seconds.
3. a) Convert la to a radian.
b) Convert 1b to a degree
PLEASE HELP THANK YOU
Answers
Answer: its A
Step-by-step explanation: you welcome
How do I convert a string to an int in Matlab?.
Answers
In MATLAB, you can convert a string to an integer using the str2double() or str2num() function. Both functions convert a string to a double-precision floating-point number, but str2num() also supports the conversion of strings to other numeric data types.
Here's an example of how to convert a string to an integer using str2double():
str = '123'; % string to convert to integer
num = str2double(str); % convert the string to a double-precision number
int = int32(num); % convert the double-precision number to a 32-bit integer
In this example, the str variable contains the string '123', which we want to convert to an integer. We first use the str2double() function to convert the string to a double-precision number, which we then convert to a 32-bit integer using the int32() function.
Alternatively, you can use the str2num() function to convert the string directly to an integer:
str = '123'; % string to convert to integer
int = int32(str2num(str)); % convert the string to a 32-bit integer
In this example, we use the str2num() function to convert the string directly to a 32-bit integer, and then assign the result to the int variable.
It is important to note that if the string cannot be converted to a number, both functions will return NaN (Not a Number). Additionally, if the string represents a number that is too large to be represented by an integer, the result will be rounded or truncated.
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Chang 0.7 to fraction with workings
Answers
Answer:
7/10
Step-by-step explanation:
all number converted to decimals are X/1. X is any number.
0.7 is equal to 0.7/1
now fractions cannot contain a decimal number so we can times is by 10 to get 7/10.
Answer: 0.7, I think you multiply, algebraic answer ig
Step-by-step explanation:
I dont seem to understand this problem can anyone help?
Answers
The time it will take to do all the activities at the same time is given as follows:
60 minutes = one hour.
How to obtain the period?Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.
The periods of each event are given as follows:
Scones: 15 minutes.Muffins: 12 minutes.Cookies: 10 minutes.
The least common factor is obtaining factoring these numbers according to their prime factors, as follows:
15 - 12 - 10|2
15 - 6 - 5|2
15 - 3 - 5|3
5 - 1 - 5|5
1 - 1 - 1
Hence:
lcm(15,12,10) = 2² x 3 x 5 = 60 minutes.
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What is 15/16 as a decimal?
Answers
The decimal form of 15/16 is 0.9375.
To convert a fraction to a decimal, you can divide the numerator by the denominator. In this case, 15 divided by 16 equals 0.9375.
Alternatively, you can also use long division to find the decimal form of a fraction.
1. Set up the long division problem with 15 as the dividend and 16 as the divisor.
2. Since 16 does not go into 15, add a decimal point and a zero to the dividend.
3. Divide 16 into 150, which equals 9 with a remainder of 6.
4. Add another zero to the dividend and divide 16 into 60, which equals 3 with a remainder of 12.
5. Add another zero to the dividend and divide 16 into 120, which equals 7 with a remainder of 8.
6. Add another zero to the dividend and divide 16 into 80, which equals 5 with no remainder.
7. The final answer is 0.9375.
So, 15/16 as a decimal is 0.9375.
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it take 5 hours to bake 12 loaves of bread. How long will it take to bake 15 loaves?
Answers
Answer:
= 6.25 hours.
Step-by-step explanation:
If 5 hours = 12 loaves of bread
than ? = 15 loaves of bread.
therefore 15/12 × 5 hours
= 75/12
= 6. 25 hours.
Help me with this please
Answers
nswer:
Step-by-step explanation:
6*[tex]10^{6}[/tex]------100
x-------40
x=6*10^6*4*10/100=24*10^5(social media)
6*[tex]10^{6}[/tex]------100
y-------30
y=6*10^6*3*10/100=18*10^5(music)
6*[tex]10^{6}[/tex]------100
z-------25
z=6*10^6*25/100=15*10^5(games)
6*[tex]10^{6}[/tex]------100
f-------5
f=6*10^6*5/100=3*10^5(video)
Magdalena creates the scale drawing shown of a rectangular field. What is the area, in square meters ( m2 ), of the actual field? pls help…
Answers
The perimeter of the actual field is 91.8 meters.
The area of the actual field is 437.4 square meters.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle = 2(L+W)
Where W is the width of the rectangle and L is the length of the rectangle
The scale of a rectangular field is given in the question, as follows:
1 cm = 4.5 m
So, the dimensions of the actual field, are as:
L = 7.2 × 4.5 = 32.4 m
W = 3 × 4.5 = 13.5 m
The perimeter of the actual field = 2(L+W)
The perimeter of the actual field = 2(32.4 + 13.5) = 2(45.9) = 91.8 m
The area of the actual field = L × W
The area of the actual field = 32.4 × 13.5 = 437.4 m²
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mark bike shop rents bikes for 8+5 per hour. jermaine paid $33 to rent a bike. how many hours did he rent the bike for
Answers
Answer:
He rented the bike for 5 hours.
Step-by-step explanation:
Fixed rate for renting a bike is $8 and rate per hour for renting is $5.
Amount paid by Jermaine is $33.
To find the hourly rent amount that he paid, subtract the fixed rate ($8) from total amount $33.
Rent amount for the bike = 33 - 8
= $ 25
Number of hours rented = 25 ÷ 5
= 5 hours
Which of the following is equal to the fraction below?
Answers
Answer:
Choice B
Step-by-step explanation:
(7/4)^11 = 471.431...
(7^11)/(4^11) = 471.431...
The function f(2)=19400(0.40)* represents the values of a certain type of car x years after it is
purchased. Xavier states that the decay rate of the value of the car is 40%. Which accurately
describes Xavier's statement?
A) Xavier correctly determined the decay rate of the value of the car.
B)Xavier should have subtracted 0.40 from 1 to determine a decay rate of 60%.
C)Xavier should have added 0.40 to 1 to determine a decay rate of 1.40%.
D) Xavier should have divided 1 by 0.40 to determine a decay rate of 1.60%.
Answers
Since Xavier states that the decay rate of the value of the car is 40%, an answer option that accurately describes Xavier's statement is: A) Xavier correctly determined the decay rate of the value of the car.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = a(b)^x
Where:
a represents the base value or y-intercept.x represents time.b represents the rate of change (decay rate).In this scenario, we can logically deduce that values of a certain type of car x years after it is purchased can be modeled by the following exponential function:
f(2) = 19,400(0.40)^2
By comparison, we have:
Decay rate (r) = 0.40, which simply means Xavier correctly determined it.
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Solve the right triangle by completing the table below
Answers
The complete table is,
⇒ B = 41°
⇒ a = 9.525
⇒ b = 8.25
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown in figure.
Now, We have;
Two angles of triangle are,
⇒ A = 49°
⇒ C = 90°
Hence, We can formulate;
⇒ B = 180 - (49 + 90)
⇒ B = 180 - 139
⇒ B = 41°
And, By using Sine rule as;
⇒ sin A / a = sin B / b = sin C / c
Takin two identity as;
⇒ sin A / a = sin C / c
⇒ sin 49° / a = sin 90° / 12.7
⇒ 0.75 / a = 1/12.7
⇒ 0.75 × 12.7 = a
⇒ a = 9.525
⇒ sin B / b = sin C / c
⇒ sin 41° / b = sin 90 / 12.7
⇒ 0.65/b = 1/12.7
⇒ 0.65 × 12.7 = b
⇒ b = 8.25
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Which of the following is true?
√2 is a rational number.
-√16 is an irrational number.
0 is neither a rational number nor an irrational number.
O 1.3 is a rational number but not an integer.
Answers
if I'm Wrong Sorry And Have a Nice Day .
I withdraw £80 from my savings account to go shopping.
• I spend 40% of my money in the bookshop.
• I then spend one third of the money I have left at the supermarket.
• Finally, I spend £8 on stationery.
What fraction of the £80 do I have left?
Give your answer in its simplest form.
Answers
The fraction of the £80 that you have left is 3/10.
The FractionLet's start by calculating how much money you spent at the bookshop.
40% of £80 = 0.4 x £80 = £32
So you spent £32 at the bookshop, and you now have:£80 - £32 = £48
Next, you spent one third of the money you had left at the supermarket.One third of £48 = £16
So you spent £16 at the supermarket, and you now have:£48 - £16 = £32
Finally, you spent £8 on stationery, so you now have:£32 - £8 = £24
Therefore, you have £24 left out of the original £80. To find the fraction of the £80 that you have left, we can express this as a fraction:£24 is the same as 24/80 when expressed as a fraction.
This fraction can be simplified by dividing both the numerator and denominator by 8:24/80 = 3/10
So the fraction of the £80 that you have left is 3/10. This is the simplest form.
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ERROR ANALYSIS Describe and correct the error in finding the difference.
X
(x²+x) - (2x²-3x)
= (x²+x) + (-2²-3r)
= (x^² - 2x²) + (x²-3x)
=-2²-2x
Answers
The error is in the second part of the solution.
What is an expression?The definition of an expression in math is a statement composed of terms and operations. The terms may be constant (numbers), or variables with coefficients. The operations may be addition, subtraction, multiplication, or division.
Given that the difference of two expressions, (x²+x) - (2x²-3x), we need to find the error in the solution given,
= (x²+x) - (2x²-3x)
= (x²+x) + (-2²-3x) [Error here]
= (x² - 2x²) + (x²-3x)
= -2²-2x
The error is in the second step,
(x²+x) + (-2²-3x)
When we multiply - sigh with a - sign, we will get a positive sign,
So, the correct step is =
(x²+x) + (-2²+3x)
The correct solution is =
= (x²+x) - (2x²-3x)
= x²+x-2x²+3x
= -2x²+4x
= 2x(2-x)
Hence, the error is in the second part of the solution.
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What is the length of the missing side of the quadrilateral shown if the perimeter is 5x+3 and 8x-4 and 10x+7
Answers
The length of the missing side of the quadrilateral shown if the perimeter is 5x+3 and sides are 8x-4 and 10x+7 and 3x+6 is -16x+12.
What is Perimeter?This is defined as the total distance around the shape.
The perimeter is the sum of the 4 sides.
Adding , 8x-4 and 10x+7 and 3x+6 , we have:
8x-4 + 10x+7 + 3x+6 = 21x+9
Subtract that from the given perimeter to get the missing side length which is:
5x+3 - 21x+9 = -16x+12
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HELPPPPPPP PLEASEEEEEEEEEE
Algebra
Answers
Answer:
(-1, -5)
Equation form:
x=-1, y=-5
Step-by-step explanation:
Basically, all you have to do is solve for the first variable in one of the equations, then substitute the result into the other one. It's as simple as that.
Hope this helps
The length of the sides of a triangle is 15cm, ycm and (y-2)cm. If the area is less than 80cm2(square).Find the possible values of y
Answers
Answer:
We can use Heron's Formula to calculate the area of a triangle given its three side lengths. The formula is:
A = √(s*(s-a)*(s-b)*(s-c)),
where s = (a + b + c)/2, a, b and c are the three sides of the triangle.
In this case, a = 15, b = y and c = (y-2). Therefore, we can plug these numbers in to get:
80 > √[(y + 7.5) * (y - 7.5) * (y - 2) * (y - 15)]
We can simplify this equation to get:
y^2 - 5y - 80 > 0
This equation can be solved using the quadratic formula, where the solution for y is:
y < 14.09 or y > 10.91
Therefore, the possible values for y are any number between 10.91 and 14.09.