The given expressions y =- 3+7x and y= − 3 − 7x are compared with the general form of slope y=mx+c. And the y-intercept of both is found to be -3.
A line's slope, often known as its gradient, is a numerical value that represents the line's steepness and direction. This slope provides the ratio of the rise in y when x rises by a specific amount. Therefore, this may be calculated using the basic formula y=mx+c, where c stands for the y-intercept and m for the slope.
Given the expressions are y = -3+7x and y= -3-7x. Compare these two expressions one by one with the general form of the slope. By comparing the first expression we get, the slope as 7 and the y-intercept as -3. Similarly, comparing the second expression we get, the slope is -7 and the y-intercept is -3.
Therefore, the required answers are -3 and -3.
The complete question is -
What is the y-intercept of y =- 3+7x and y= − 3 − 7x?
To know more about the slope:
https://brainly.com/question/29006583
#SPJ4
A 2.8 cm object is placed 35mm in front of a converging lens. The magnification of the lens is 2.5.
a) What is the distance of the image created?
b) What is the height of the image?
c) Describe the S.A.L.T. of the image.
The image will be formed 23.31 cm along the +x direction of the lens. The height of the image is h{i} = 7 cm.
What is magnification of lens?The magnification produced by a lens is defined as ratio of the height of the image to the height of the object. It is denoted by 'm'.
Given is that a 2.8 cm object is placed 35mm in front of a converging lens. The magnification of the lens is 2.5.
Given is that -
m = h{i}/h{o}
h{i} = 2.8 x 2.5
h{i} = 7 cm
f = {object distance} / {(1 / Magnification) + 1)} × 1000
f = {3.5} / {(1/2.5) + 1} x 1000
f = 2.5 cm
Using the lens formula -
1/d(o) + 1/d(i) = 1/(f)
1/d(i) = 1/2.5 - 1/2.8
1/d(i) = 0.0429
d(i) = 1/0.0429
d(i) = + 23.31 cm
Therefore, the image will be formed 23.31 cm along the +x direction of the lens. The height of the image is h{i} = 7 cm.
To solve more questions on magnification, visit the link below -
https://brainly.com/question/28957672
#SPJ1
Evaluate the expression for x = -8.x = 16, and x = 4.
X ÷ 4
Therefore , the solution of the given problem of expression comes out to be -2,4 and 1.
Expression is who or what?It is important to multiply, divide, add, or delete in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical statement, such as additions, subtraction, multiplication, or division, etc., include numbers, variables, and functions. It is possible to contrast expressions and phrases.
Here,
Given :x = -8.x = 16, and x = 4.
The expression is:
=> X/4
For x =-8
=> -8/4 =-2
For x =16
=> 16/4 =4
For x=4
=>4/4 =1
Therefore , the solution of the given problem of expression comes out to be -2,4 and 1.
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ1
The area of a rectangle is [tex]12x^6y^7[/tex] . If the width of the rectangle is [tex]3x^2z[/tex] , what is the length of the rectangle? A = lw
Answer:
[tex]l = \dfrac{4x^4y^7}{z}[/tex]
Step-by-step explanation:
[tex]A = l\cdot w[/tex]
We can divide both sides of this formula by width to solve for length.
[tex]\dfrac{A}{w} = l[/tex]
Then, we can plug in the given values for width and area.
[tex]\dfrac{12x^6y^7}{3x^2z} = l[/tex]
Finally, we can solve for length by applying the quotient exponent rule.
[tex]\dfrac{x^a}{x^b} = x^{(a-b)}[/tex]
[tex]\dfrac{12x^6y^7}{3x^2z} = l[/tex]
[tex]4\cdot x^{(6-2)} \cdot \dfrac{y^7}{z} = l[/tex]
[tex]l = \dfrac{4x^4y^7}{z}[/tex]
x - 5 (x - 1) = x -(2x - 3)
Answer:
Solve for X by simplifying both sides of the equation, then isolating the variable.
X = 4x − 2
Hope this helps!!
square root of 36 in simplest radical form
Answer: The square root of 36 is expressed by √36, where '√' is the radical symbol and 36 is the radical form.
Step-by-step explanation: √36 is equal to 6, which is a rational number. Since 36 is a perfect square, therefore, it becomes easy for us to find its square root.
Hoped It Helped
The square root of 36 is expressed by √36, where '√' is the radical symbol and 36 is the radical form is 6 .
What is square root ?
Its like abundance (quantity ) of which is called amplitude (quantity) of the particular square .
Give : √36
Now,
Few examples of square root,
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√36 is equal to 6, which is a rational number. Since 36 is a perfect square, therefore, it becomes easy for us to find its square root.
Know more about square root,
https://brainly.com/question/13096390
#SPJ1
Which of the following is not a polynomial ?
a: √3x^2-2√3x+3 ,
b: 3x^3/2-5x^2-1/√2x-1 ,
c: x+1/x ,
d: 5x^2-3x+ √2
The answer is c: x+1/x, which is not a polynomial because it contains a fraction (1/x).
This is not a polynomial because it contains a fraction (1/x). A polynomial is an expression consisting of variables, constants, and exponents. It can be of any degree, but it must not contain any fractions. The other three options (a, b, and d) are all polynomials because they only contain variables, constants, and exponents.
For example, option a: √3x^2-2√3x+3, can be written as 3x2-2x+3, which is the standard form of a polynomial. Similarly, option b: 3x3/2-5x2-1/√2x-1, can be written as 3x2-5x+1, and option d: 5x2-3x+√2, can be written as 5x2-3x+2, which are both in the standard form of a polynomial.
Therefore, the answer is c: x+1/x, which is not a polynomial because it contains a fraction (1/x).
Learn more about polynomial here:
https://brainly.com/question/11536910
#SPJ4
Which of the following is the solution set of the inequality x 4 5x 2/3 7x 3 5?
The solution set of the inequality x 4 5x 2/3 7x 3 5 is x> 7.
To solve this inequality, we need to isolate the x term on one side and all the other terms on the other side. We can do this by subtracting 4 from both sides of the equation, which gives us 5x 2/3 7x 3 - 4 < 0.
Next, we can add 7x 3 to both sides of the equation, giving us 5x 2/3 - 4 + 7x 3 < 7x 3.
Now, since the denominator of the first term is 3, we can multiply both sides of the equation by 3/3. This gives us 5x 2 - 4 3 + 21x 3 < 21x 3.
Next, we can subtract 21x 3 from both sides of the equation, which gives us 5x 2 - 4 3 < 0.
Now, we can divide both sides of the equation by 5, which gives us x 2 - 4/5 < 0.
Finally, we can take the square root of both sides of the equation, which gives us x - 2/√5 < 0.
This means that x > 2/√5 + 2. Since 2/√5 + 2 > 7, the solution of the inequality is x > 7.
Learn more about inequality here:
https://brainly.com/question/30228778
#SPJ4
Mybankaccount pays 4% interest at the end of each year. Suppose that I have $x in my bank account at the start of this year, and that I never add money to the account or take money out of the account. (a) Howmuchwill be in the account at the end this year (after the interest is paid)? (b) Howmuchwill be in the account at the end of next year (again, after the interest)? (c) Find an expression for the amount in the account after N years.
a. The amount in the account at the end this year after the interest is paid will be 1.04x
b. The amount in the account at the end this year after the interest is paid will be 1.08x.
c. The expression for the amount in the account after N years will be x + 0.04xn
How to calculate the interest?From the information, Mybankaccount pays 4% interest at the end of each year. The person had $x in the bank account at the start of this year. The amount in the account at the end this year after the interest is paid will be:
= x + (x × 0.04 × 1)
= x + 0.04x
= 1.04x
The amount in the account at the end of 2 years after the interest is paid will be:
= x + (x × 0.04 × 2)
= x + 0.08x
= 1.08x
The expression for the amount in the account after N years will be:
x + (x × 0.04 × n)
x + 0.04xn
Learn more about interest on:
brainly.com/question/25793394
#SPJ1
7) Write an expression for the following situation: Francine saves money in two separate bank accounts. She deposited $200 in one account and then adds $50 monthly. In her second account she deposited $100 and puts in $75 monthly. Write an expression to show her balance after m months.
Take the example of a $10,000 savings account earning 2% interest annually. Since the interest rate is 0.02, expressed as a decimal, the following formula would be appropriate: Interest equals $10,000 divided by 0.02 times one to equal $200.
How to calculate simple interest in a savings account?By dividing the account value by the interest rate and the length of time the money has been in the account, you can figure out how much simple interest you'll receive in a savings account. A savings account's interest is money you earn, not money you pay, so keep that in mind.Interest = P x R x T is the formula for calculating interest.
P is Principal amount
R is the interest rate
T is the quantity of time periods.
Take the example of a $10,000 savings account earning 2% interest annually. Since the interest rate is 0.02, expressed as a decimal, the following formula would be appropriate:Interest equals $10,000 divided by 0.02 times one to equal $200.The finest savings accounts pay interest rates of more than 2%. However, some accounts provide far lower earnings. The average savings rate across the country is actually 0.33%. The savings calculator on NerdWallet allows you to calculate the amount of interest you could earn using various rates and timeframes.The interest rate would be stated as 0.0015 for a deposit of $10,000 in a bank account that only pays 0.15% interest annually. For this situation, the computation would be:Interest is calculated as $10,000 divided by 0.0015 times one.
Interest equals $15.
In terms of practicality, this method works well for approximating the amount of interest that money in a savings account can earn.The Complete Question is interest rate.
To Learn more About interest rate Refer To:
https://brainly.com/question/25793394
#SPJ1
The expression that shows Francine balance after 'm' months is
First bank : 200 + 50m
Second Bank : 100 + 75m
How to calculate simple interest in a savings account?By dividing the account value by the interest rate and the length of time the money has been in the account, you can figure out how much simple interest you'll receive in a savings account. A savings account's interest is money you earn, not money you pay, so keep that in mind.
Simple interest is calculated based on a loan's principle or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principle sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
Interest = P x R x T is the formula for calculating interest.
P is Principal amount
R is the interest rate
T is the quantity of time periods.
For this situation, the computation would be:
In the first bank she deposited $ 200 initially and $50 every month so
The equation will be 200 + 50*m
'm' is the number of months
In the second bank she deposited $ 100 initially and $70 every month so
The equation will be 100 + 75*m
'm' is the number of months
To learn more about Interest refer to :
https://brainly.com/question/29113313
#SPJ1
6. 0.3k - 4m
k = 20 and m = -2
Please help me and show the work please giving 20 points need in 20mins
The equation evaluates to -2 when k = 20 and m = -2
What is a linear equation in 2 variables?
A linear equation in two variables is an equation that can be written in the form of
ax + by = c
where a, b, and c are constants and x and y are the variables. This equation represents a straight line in a two-dimensional coordinate system where x and y are the coordinates. The values of x and y that satisfy the equation form the set of solutions of the equation.
0.3k - 4m = 0.3(20) - 4(-2) = 6 - 8 = -2
Explanation:
First substitute the given values of k and m into the equation: 0.3k - 4m = 0.3(20) - 4(-2)
Next, simplify the multiplication: 0.3(20) = 6
Now we can simplify the subtraction of a negative number: 4(-2) = 8
So we have: 6 - 8 = -2
As you can see, the equation evaluates to -2 when k = 20 and m = -2
To learn more about linear equation in 2 variables, Visit
https://brainly.com/question/24085666
#SPJ1
A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink
6
Blue
Orange
What statement best compares the theoretical and experimental probability of landing on orange?
O The theoretical probability of landing on orange is
5
the experimental probability is 20%.
O The theoretical probability of landing on orange is L, and the experimental probability is 20%.
O The theoretical probability of landing on orange
and the experimental probability is 30%.
The theoretical probability of landing on orange
and the experimental probability is 50%.
Answer:
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
Step-by-step explanation:
What is AX² in quadratic equation?
AX² is the standard form of a quadratic equation, where A is a coefficient and X is a variable.
In mathematics, a quadratic equation is a polynomial equation of the form ax2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to zero. A quadratic equation can have either one, two, or no real solutions, depending on the value of the discriminant, b2 - 4ac. The discriminant determines the nature of the roots of the equation: if it is positive, the equation has two distinct real solutions; if it is zero, the equation has one repeated real solution; and if it is negative, the equation has two complex conjugate solutions.
The standard form of a quadratic equation is ax2 + bx + c = 0, where a is the coefficient of the x2 term, b is the coefficient of the x term, and c is the constant or free term. AX2 is the standard form of the equation, where A is the coefficient of the x2 term and X is the variable. If the coefficient A is not equal to 1, the equation can be simplified by dividing both sides of the equation by A. Solving a quadratic equation requires the use of the quadratic formula, which is used to find the roots of the equation. The quadratic formula states that the roots of the equation are x = [-b ± √(b2 - 4ac)]/2a.
Learn more about quadratic equation here
https://brainly.com/question/30098550
#SPJ4
You went to Sweet Spot to get ome candy. The cot i $5. 00 per pound. You have a coupon that give you a dicount of $0. 20 off per pound. If you buy $4 pound of candy, what will your total cot be, excluding tax?
The total cost of the candy excluding tax is $19.2
How to find the total cost of the candy excluding taxFrom the question we have that
The cost of the candy per pound is $5.00
And a coupon that gives a discount of $0..20 per pound
hence 4 pounds of candy without discount is
= 4 * 5
= $20
the discount is solved to be
= 4 * 0.2
= 0.8
subtracting the discount
= 20 - 0.8
= $19.2
So the amount to be paid for the candy is $19.2
Learn more about discount per pound at:
https://brainly.com/question/26233980
#SPJ1
Point B is between A and C if A , B , and C are collinear and the equation AB + BC = AC is true, where AB , BC , and AC are the distances between points A and B , B and C , and A and C , respectively.
The statement AB + BC = AC is true according to the segment addition postulate.
What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.
The smaller segments in this problem are given as follows:
AB and BC.
The large segment is given as follows:
AC.
Hence the equation is given as follows:
AB + BC = AC.
More can be learned about the segment addition postulate at https://brainly.com/question/2134445
#SPJ1
Solve for X, Leave in simplest radical form.
In mathematics, a radical is a number or expression that represents the principal value of the square root, cube root, or any other higher-order root of a given number or expression.
What is radical form?In mathematics, radical form refers to the expression of a radical in which the number or variable under the radical sign is a product of factors, and any factor that is a perfect power has been removed and is represented as a power outside the radical sign.The radical symbol (√) is used to indicate that the quantity inside the symbol is a radical. An example of a radical in its simplest form is √9, which is equal to 3, the square root of 9. A radical can also be in "radical form" where the number or variable under the radical sign is a product of factors, and any factor that is a perfect power (such as a square or cube) has been removed and is represented as a power outside the radical sign. For example √(36x^6) = 6x^3.If one angle in a right-angled triangle is 30 degrees, and one side has a length of 16 units, then the length of the side opposite the 30 degree angle can be found using the sine function.sin(30) = opposite/hypotenuse
so, the length of the opposite side = sin(30) * hypotenuse
The hypotenuse is the side opposite the right angle, and has a length of 16 units, so we can substitute this into the equation:
sin(30) = opposite/16
To find the length of the opposite side, we can multiply both sides of the equation by 16:
opposite = (sin(30))*16
opposite = 8
So the length of the other side of the triangle is 8 units.
To learn more about radical form refer to:
https://brainly.com/question/565192
#SPJ1
What is the value of f(0)
Answer:
the absolute value of 0 is just 0
Step-by-step explanation:
Equation with variable on both sides
I need help today and I need it now just today
The solution to the equations are as follows:
x = 0
r = -4
b = -8
n = -3
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
The equation can be solved by find the values of the variables as follows:
Hence,
5.
1 - 3x = 3x + 1
-3x - 3x = 1 - 1
-6x = 0
x = 0
6.
4r + 8 + 5 = -15 - 3r
4r + 13 = -15 -3r
13 + 15 = -3r - 4r
28 = -7r
r = 28 / -7
r = -4
7.
-12 - 4b = 4 - 2b
-12 - 4 = -2b + 4b
-16 = 2b
b = -8
8.
3n - 15 = 7n + n
3n - 7n - n = 15
-5n = 15
n = -3
learn more on equations here: https://brainly.com/question/24999849
#SPJ1
can someone help me pls
Using trigonometric function concepts, it is found that:
The angle is of 45 degrees, or radians.
Since pi radians is 180º, this angle is of 180/4 = 45 degrees.
From the tangent: cot∅ =1
For the cosecant and secant: csc∅=√2 :sec∅=√2.
What is trigonometric function?Trigonometric function, in mathematics, one of six functions (sine [sin], cosine [cos], tangent [tan], cotangent [cot], secant [sec], and cosecant [csc]) that represent ratios of sides of right triangles. These six trigonometric functions in relation to a right triangle are displayed in the figure. They are also known as the circular functions, since their values can be defined as ratios of the x and y coordinates (see coordinate system) of points on a circle of radius 1 that correspond to angles in standard positions. Trigonometry can be easily applied to surveying, engineering, and navigation problems in which one of a right triangle’s acute angles and the length of a side are known and the lengths of the other sides are to be found.To learn more about circular functions refer to:
https://brainly.com/question/25618616
#SPJ1
Please answer I need help
Answer:
The correct answer is A. A trapezoid has only 1 pair of parallel sides, but a parallelogram has 2.
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. A trapezoid is a quadrilateral with one pair of opposite sides that are parallel, known as the bases. The other two sides are called legs.
Both a parallelogram and a trapezoid are quadrilaterals that have four sides, but parallelogram has opposite sides parallel to each other, while trapezoid has only one pair of parallel sides, the bases. Also a parallelogram has opposite angles are equal while a trapezoid doesn't have this property.
Option B and D is incorrect, A parallelogram doesn't need to have 4 right angles, and a trapezoid doesn't need to have 4 right angles as well.
Option C is incorrect as well, A parallelogram has two pairs of parallel sides.
What does the factored form of a quadratic function tell you about the function's graph?
The factored form of the quadratic function is f(x) = a(bx + c) (dx + e)
The term quadratic function is defined as a polynomial function with one or more variables in which the highest exponent of the variable is two and the graph of the quadratic equation is always forms the parabola.
Here we have given that we have to find the the factored form of a quadratic function
As we all know that the general form of the quadratic function is written as,
=> f(x) = ax² + bx + c
While we factorize the general form then it can be expanded like the following,
=> f(x) = a(bx + c) (dx + e)
To know more about function here.
https://brainly.com/question/28193995
#SPJ4
Please reduce each fraction, and give an explanation. Thanks so much!
Answer:
Step-by-step explanation:
The students at Benson Middle School were asked to choose a favorite Friday activity. The table shows the survey results for 200 students.
Favorite Percentage of
Activity Students
Bowling 10%
Movies
30%
Dance
50%
10%
Games
How many students chose movies as a favorite activity?
O A 10
OB. 30
C. 60
D. 100
Answer:c60
Step-by-step explanation:
[tex]\frac{6}{2k-6} =3[/tex]
[tex] \frac{6}{2k - 6} = 3 \\ \\ \longrightarrow \: 6 = 6k - 18 \\ \\\longrightarrow \: 6k = 18 + 6 \\ \\\longrightarrow \: 6k = 24 \\ \\ dividing \: both \: sides \: by \: 6 \: , \\ \\\longrightarrow \: \cancel \frac{6k}{6} = \cancel \frac{24}{6} \\ \\ \longrightarrow \: \boxed{k = 4}[/tex]
hope helpful! :)
how to find the domain and range of a piecewise function
To find the domain and range of a piecewise function, you will need to consider each piece separately and then combine the results. First Identify the domain of each piece, then Identify the range of each piece and Combine the domains and ranges
Identify the domain of each piece: The domain of a piecewise function is the set of all input values (x-values) for which the function is defined. For example, if a piece of the function is defined for x > 2, then the domain for that piece would be all real numbers greater than 2.Identify the range of each piece: The range of a piecewise function is the set of all output values (y-values) that the function can produce. For example, if a piece of the function is defined as y = x^2, then the range for that piece would be all non-negative real numbers.Combine the domains and ranges: Once you have identified the domains and ranges for each piece, you can combine them to find the overall domain and range of the piecewise function. The overall domain is the set of all input values for which any piece of the function is defined, and the overall range is the set of all output values that any piece of the function can produce.Note: Sometimes you may find that domain or range of a certain piece is not mentioned in the function, in that case, you can assume it to be the default domain or range of real numbers.
Learn more about a piecewise function here: https://brainly.com/question/27262465
#SPJ4
10. When travel to visit my mom over Thanksgiving vacation I drive from my home to Grandpa Herman's
which is 16 miles away. That first part of my trip to Grandpa's takes 20 minutes with light traffic. We then leave
his house and travel 2 hours to Ganada and take a travel break. That second part of the trip is 185 miles.
Lastly, we drive the 145 miles from Ganada to my mom's home in Port O'Connor in 1 hour and 15 minutes.
What is our average speed of the trip in mi/min AND mi/hr?
Write the formula:
Fill in the formula:
Answer: _____mi/mins
Answer: _____ mi/hrs
The average speed of the trip will be 1.60 miles/mins and 96.64 miles/hrs.
What is an average?
An average of a list of data is a mathematical expression for the center value of a set of data. It is defined mathematically as the ratio of the total of all the data to the number of units in the list. In statistics, the average of a particular collection of numerical data is also known as the mean.
e.g.
The average of 2, 3, and 4 equals (2+3+4)/3 = 9/3 = 3. As a result, the central value of 2,3, and 4 is 3. Thus, the definition of average is to determine the mean value of a set of data.
Average speed:-
The formula for average speed is found by calculating the ratio of the total distance traveled by the body to the time taken to cover that distance.
average speed = total distance / total time
Now,
As given
Total distance covered = 16+185+145
=346 miles
Total time taken=20 + 120 + 75
=215 minute (3.58 hours)
Average speed=346/215
=1.60 miles/mins
Average speed=346/3.58
=96.64 miles/hrs
To know more about average visit the link
https://brainly.com/question/24057012?referrer=searchResults
#SPJ1
What is the remainder when 2x² − 5x − 1 divided by X − 3?
The remainder when 2x² - 5x - 1 divided by x - 3 is (2x + 1)
Let p(x) represents a polynomial 2x² − 5x − 1 and m(x) represents a polynomial x - 3
i.e., p(x) = 2x² − 5x − 1
and m(x) = x - 3
we need to find the remainder when 2x² − 5x − 1 divided by x − 3
If we divide a polynomial p(x) = 2x² − 5x − 1 by m(x) = x - 3 using polynomial long division method, the result is:
p(x) / m(x)
= ( 2x² - 5x - 1 ) ÷ (x - 3)
= [ ( 2x² - 5x - 1 ) × ( 2x + 1)] + 2
This means, the quotient is ( 2x + 1) and the remainder is 2
(see in attachment)
Learn more about a polynomial here:
brainly.com/question/28936357
#SPJ4
( –5g – 6) – (4g – 1)
Answer:
Simplify the following:
-5 g - 6 - (4 g - 1)
Factor -1 out of -5 g - 6 - (4 g - 1):
-(5 g + 4 g - 1 + 6)
Grouping like terms, 5 g + 6 - 1 + 4 g = (5 g + 4 g) + (6 - 1):
-((5 g + 4 g) + (6 - 1))
5 g + 4 g = 9 g:
-(9 g + (6 - 1))
6 - 1 = 5:
Answer: -(9 g + 5)
Step-by-step explanation:
The population P (in millions) of Italy from 2003 through 2015 can be approximated by the model P = 57.59e0.0051t, where t represents the year, with t = 3 corresponding to 2003. (a) According to the model, is the population of Italy increasing or decreasing? Explain.
It can be concluded that the population of Italy is increasing.
What are functions?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
Given is the population {P} (in millions) of Italy from 2003 through 2015 can be approximated by the model → {P} = 57.59[tex]$e^{0.0051t}[/tex], where {t} represents the year, with {t} = 3 corresponding to 2003.
The exponential function is a mathematical function denoted by : f(x) = eˣ.We have the function -
{P} = 57.599[tex]$e^{0.0051t}[/tex]
For {t} = 1, we can find P(1) as -
P(1) = 57.79 x [tex]$e^{0.0051}[/tex]
P(1) = 57.79 x 1.00511302714
P(1) = 58.1
Now, P(3) > P(1), this means that the population of Italy is increasing.
Therefore, it can be concluded that the population of Italy is increasing.
To solve more questions on algebraic expressions, visit the link below -
brainly.com/question/1041084
#SPJ1
How do you convert vertex form to factored form?
The way to convert the vertex form to factored form is explained below.
The term vertex is defined as a special point of a mathematical object, and is usually a location where two or more lines or edges meet.
Here we have to write down the steps to convert the vertex form to factored form.
The very first steps is to expand the vertex form into standard quadratic form and then use the quadratic root formula to determine the roots.
Here as we all know that factored term is the product of a constant and two linear terms and they are the roots of the function.
So, now we have to use the quadratic formula to convert them into factor form.
To know more about vertex here.
https://brainly.com/question/29030495
#SPJ4
<
Find the volume of the sphere.
22
Either enter an exact answer in terms of " or use
7
units3
for T.
If the radius of sphere is 7 units, the volume of the sphere is 1,437.33 units³
What is volume of a shape?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given that, the value of π = 22/7
The radius of sphere is 7 units
Volume of a sphere = 4/3πr³, where r is the radius of the sphere.
= 4/3 * 22/7 * 7³
= 4/3 * 22/7 * 7 * 7 * 7
= (4 * 22 * 7 * 7 * 7) / (3 * 7)
= 30,184/21
= 1437.3333333333 unit³
So that, the volume of a sphere = 1,437.33 unit³
To learn more about volume of sphere visit:
brainly.com/question/9994313
#SPJ1