Select the correct answer. Which graph represents the solutions to this equation? x2 + 8x = -20 A. Linear-quadratic system graph shows upward parabola with vertex at (minus 2, 4) and passing through x and y-axis (minus 8, 0), and (0, 0) B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8) C. Linear-quadratic system graph shows upward parabola with vertex at (4, 0) and passing through (1, 4), and (6, 4) D. Linear-quadratic system graph shows a downward parabola with vertex at (0, 8) which intercepts the x-axis at 3 and minus 3 units.
Answers
A graph which represents the solutions to this equation x² + 8x = -20 include the following: B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8).
What are quadratic functions?In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.
Next, we would re-write the given quadratic function in standard form by equating it to zero (0) as follows;
x² + 8x = -20
Adding 20 to both sides of the linear-quadratic equation, we have the following:
x² + 8x + 20 = -20 + 20
x² + 8x + 20 = 0
In this scenario, we would use an online graphing calculator to plot the graph of the given quadratic function and then determine the point of intersection and vertex.
y = x² + 8x + 20
By critically observing the graph of the given quadratic function, we can logically deduce that the solutions and vertex are as follows;
x = -6, y = 8.
x = -2, y = 8.
Vertex = (-4, 4).
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Related Questions
The mighty oak tree outside of Matt's house had to be cut down. He missed the beautiful tree and the shade it provided and wanted to replace it with an oak tree that would grow quickly. The Nuttall Oak (Quercus nuttalli), the fastest-growing oak tree, grows 7 to 8feet per year (we'll assume it grows at a constant rate). At maturity, it can be up to 50 feet tall.
Which of the following equations, where t represents time in years and h represents the height in feet, describe growth that is slower than the Nuttall Oak growth rate?
CHOICES:
A: h=5t
B: h=8.5t
C: h=10t
D: h=50t
Answers
Growth that is slower than the Nuttall Oak growth rate is h=5t.
What is equation?An equation is a mathematical statement that expresses two values as being equal. It is the basic building block of algebra and can be used to solve for unknown values, or to show the relationships between two or more values. Equations use mathematical operators such as addition, subtraction, multiplication, and division, as well as symbols and numbers, to express relationships between values. An equation can be written in the form of an expression, a system of equations, or a single equation. In all cases, an equation requires both sides of the equation to be equal in order to be valid and have a solution.
This equation describes growth that is slower than the Nuttall Oak growth rate because it has a lower rate of growth of 5 feet per year. The Nuttall Oak grows 7 to 8 feet per year, so any equation with a growth rate lower than that would be slower. Choices B, C, and D have higher growth rates than the Nuttall Oak, so they would not be slower than the Nuttall Oak growth rate.
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The minimum hours of daylight occur mid-year with the maximum hours of daylight occuring in December.b.The maximum hours of daylight occur in January. The amount of daylight decreases each month until the minimum is reached in December.c.The minimum hours of daylight occur in December. The amount of daylight decreases each month until the minimum is reached.d.The minimum hours of daylight occur in January and December. The amount of daylight increases each month until it reaches a maximum mid-year.
Answers
The minimum hours of daylight occur in January and December is the correct answer . The amount of daylight increases each month until it reaches a maximum mid-year. Therefore, option D is correct.
The reason behind this is the rotation and revolution of Earth around the sun. The more the sun is towards the North Pole the shorter the day will be. On the equator, daylight will last generally for 12 hours as because sunlight falls directly on the equator
Therefore the shortest duration of daylight occurs in the month of December solstice when the North Pole is at its maximum distance from the Sun .
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Melee has 1/8 of her candy bar left valid has 3/8 of his candy bar left if they put their candy together which fraction of candy bar do they have
Answers
Answer:
4/8
3/8 + 1/8 = 4/8
Triangle ABC is shown below
Answers
Answer:180 degrees
Step-by-step explanation: add the angles
The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys.
Company A: 1/5=5 25/5=5 50/10=5 75/15=5.
These ratios are all equivalent
This relationship is proportional.
company B: 5/1=5 20/5=4 40/10=4 69/15=4.
These ratios are not all equivalent.
This relationship is not proportional.
Is the ratio constant or varying for company B? Explain
Answers
When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.
Find the equivalent ratio by what method?Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you can determine the equivalent ratio. Finding equivalent fractions follows the same procedure.
A ratio formula is what?The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
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x+2y=3x+4 into y=mx+b form
Answers
x + 2y = 3x + 4
2y = 3x + 4 - x
y = (2x + 4)/2
y = x + 2
Answer: y=x+2
Step-by-step explanation:
you subtract x on the left on both sides then you'll have 2y=2x+4 we have to get y by itself so divide it by 2 on both side and when you do that on the right you divide both 2x and 4 by 2 thus giving y=x+2
A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 41 miles north of the transmitter to a second city 42 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter
Answers
On solving the provided question, we can say that the slope's the intersection points are: (20.698, 42.197) and (43.998,16.527), the transmitter is within range between those to points along the line.
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
city - north at (0,65)
city-east at (59,0)
Slope is m=(-65/59)
[tex]B= y - mx = 65 - (-65/59)(0) = 65[/tex]
The equation of the line between the cities is y = (-65/59)x + 65
[tex]x^2 + ( (-65/50)x + 65) )^2 = 47^2[/tex]
the intersection points are:
(20.698, 42.197) and (43.998,16.527)
The transmitter is within range between those to points along the line.
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F(x)=\begin{cases}-2 & \text{ for }\hspace{10px} -6< x <-1\phantom{\frac{1}{1}} \\ -x-3 & \text{ for }\hspace{10px} -1< x <5\phantom{\frac{1}{1}}\end{cases} f(x)={ −2 −x−3 for −6
Answers
f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
We note that x=7 is on 1<x< 9 so we use the second piece. Replace x with 7 and
evaluate to find f(7):
f(7)=2(7)
f(7)=14
so f( 7 ) = 14
f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.
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Andrew buy 8 pound of apple for $12. 0. He want to know and ue the unit rate of the cot per pound. True or Fale: Two pound of apple cot more than $3. 50
Answers
It is false that the cost of two pounds of apple cast is more than $ 3.50.
Finding the cost of a given quantity:Here to find the cost of the given quantity we need to find the cost of 1 unit i.e 1 pound in the given problem so that we can find the cost of given quantities. It is called a unitary method.
Given that
Andrew buy 8 pounds of apples for $ 12.00
Let 'x' be the cost of 1 pound of apples
By the given data,
=> 8x = $ 12
=> x = 12/8
=> x = 1.5
The cost of 1 pound of apples = $ 1.5
Cost of 2 pounds apples = 2 × 1.5 = 3
Therefore,
It is false that the cost of two pounds of apple cast is more than $ 3.50.
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A)
Find the product of
f(x)=x²-x-4 and g(x)=x+4
With process
Answers
f(x)=[tex]x^{2}[/tex]-x-4 + g(x)=x+4 = the product is with process [tex]x^2+7 x+8$$[/tex] . It is the solution of f(x) and g (x) .
What do you meant by product ?[tex]$$f(x)=x^2-x-4, g(x)=x+4: x^2+7 x+8$$$$\begin{aligned}& \text { Find } f \circ g \text { given } f(x)=x^2-x-4, g(x)=x+4 \\& f \circ g=f(g(x)) \\& g(x)=x+4 \\& =f(x+4)\end{aligned}$$$$\begin{aligned}& f(x+4): \quad x^2+7 x+8 \\& =x^2+7 x+8\end{aligned}$$[/tex]
When a number is multiplied by another number, its products can be found. Because 9 x 3 Equals 27, for instance, 27 is a product of 9 and 3. What you get when you multiply two numbers together is their product. As a result, the product of three and four is twelve, followed by five and four, and so on.
A number that is obtained by multiplying two or more other numbers together is referred to in mathematics as a product. For instance, the result of multiplying 2 by 5 is 10 when the two numbers are combined. Byproducts include things like straw from grain harvesting operations, salt from desalination plants, sawdust from sawmills, and manure from feedlot operations.
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After 2+3/2-x+1/3x have been combined using the least common denominator of 6x, what is the numerator?
Answers
On solving the provided question, we can say that In light of this, the lowest common denominator of the equation is (x - 4)(x + 1)(x - 2) (x - 2)
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
equation is given as:
x2 — 3x — 4 = x2 — Ox + 8
x2 — 4x + x — 4 =
x(x — 4) + I(x — 4)
Factor out x - 4
(x + I)(x — 4) = x-2(x-4)
The common factor between the two sides of the equation is x – 4.
In light of this, the lowest common denominator is (x - 4)
(x + 1)(x - 2) (x - 2)
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What does 4 mean in maths?
Answers
The meaning of the 4! ( factorial ) in mathematics is equal to ( 4 × 3 × 2 × 1 ).
As given in the question,
Given expression in mathematics is written as :
4! ( factorial )
In standard form meaning of the n! ( factorial ) is given by multiplication of all the terms in decreasing order till 1.
It is expressed as:
n! = n × ( n - 1 ) × ( n - 2 ) × ( n - 3 ) × ........× 3 × 2 × (n - (n - 1) ).
Apply this formula for 4! ( factorial ) we get,
4! ( factorial )
= 4 × ( 4 - 1 ) × ( 4 - 2 ) ×( 4 - 3)
= 4 × 3 × 2 × 1
= 12
Therefore, the meaning of 4! ( factorial ) in mathematics is given by
4 × 3 × 2 × 1 .
The above question is incomplete , the complete question is :
What does 4! ( factorial ) mean in mathematics?
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The double number line shows that a traffic signal allows traffic through the intersection for 363636 seconds. A double number line with 2 tick marks. The line labeled Time, seconds, reads from left to right: 0, 36. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. A double number line with 2 tick marks. The line labeled Time, seconds, reads from left to right: 0, 36. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. Complete the table to show different percentages of the time the signal allows. Time (\text{s}sstart text, s, end text) Percentage 100\%100%100, percent of 36\,\text{s}36s36, start text, s, end text 25\%25%25, percent of 36\,\text{s}36s36, start text, s, end text 125\%125%125, percent of 36\,\text{s}36s36, start text, s, end text Report a problem
Answers
The percentages for this problem are calculated as follows:
100% of 36 seconds: 36 seconds.25% of 36 seconds: 9 seconds.125% of 36 seconds: 45 seconds.How to obtain the percentages?The percentages in this problem are obtained applying proportions, multiplying the total amount by the decimal equivalent of the percentage.
Hence the amount that represents 100% of 36 seconds is obtained as follows:
1 x 36 = 36 seconds.
(as a percentage of 100% has a decimal equivalent of 1).
The amount that represents 25% of 36 seconds is obtained as follows:
0.25 x 36 = 9 seconds.
(as a percentage of 25% has a decimal equivalent of 1).
The percentage of 125% of 36 students can be obtained combining the two previous expressions as follows:
1.25 x 36 = 1 x 36 + 0.25 x 36 = 36 + 9 = 45 seconds.
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What are the 3 types of translation?
Answers
When the state of an object is changed from one to another it is known as translation in mathematics and they are of three types.
The three types of translation in math are
horizontal translationvertical translationcompression translationWhen the object moves either from left to right or from right to left it is known as vertical translation.
The movement in up or downward direction of the graph is known as horizontal translation.
The domain of the function remains same in both the cases.
A translation in which the size of the object decreases or is compressed is known as the compression translation.
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find the area of a rectangular garden with side length of 4x+11 and 2x+5
find the perimeter of the garden in the problem
Answers
Answer:
just ask your teacher for clarification, then you will actually learn...
What is the result of adding the system of equations 2x y 4 3x y 6?
Answers
The addition of terms [tex]2x+y^4[/tex] and [tex]3x+y^6[/tex] will be [tex]5x+y^4+y^6[/tex]
A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
Simply add the coefficients of each phrase to add polynomials.
You may remove polynomials by subtracting the coefficients.
To add polynomials, just combine any like terms.
Step 1: Arrange each polynomial in decreasing order of degree, starting with the term with the highest degree.
Step 2: Sort the words that are similar. Similar phrases have the same variables and exponents.
So, the addition of terms [tex]2x+y^4[/tex] and [tex]3x+y^6[/tex] will be (2x+3x) (As here both are only the like terms, so they will be added together)
So, the sum will be: [tex]5x+y^4+y^6[/tex]
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The correct question should be:
What is the result of adding the system of equations:
[tex]2x+y^4[/tex] and [tex]3x+y^6[/tex]
25 less than the sum of a number and 5 results in 15 what is the number
Answers
The number is 35.
What is an equation?
An equation is a statement of equality between two expressions. It uses the equal sign (=) to show that the expressions on either side of the sign have the same value.
For example 2x+3=5y-7z, and x+y=5 are examples of equations.
In solving your problem,
25 less than the sum of a number and 5 results in 15, can be written as an equation like this:
let x be the number we want to find.
x + 5 =15+25 (25 less than the sum of x+5)
x + 5 = 40
then
x=40-5
x=35
So the number is 35.
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The following is a stem-and-leaf display representing the amount of gasoline purchased, in gallons (with leaves in tenths of gallons), for a sample of 25 cars that use a particular service station on the New Jersey Turnpike: 9 147 10 02238 11 125566777 12 223489 13 02 (a) Construct an ordered array. (b) Which of these two displays seems to provide more information? Discuss
Answers
The ordered array will be 9.1 9.4 9.7 10.0 10.2 10.2 10.3 10.8 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 12.2 12.2 12.3 12.4 12.8 12.9 13.0 13.2
What is leaf plot?
A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
In this instance, the number on the left of the division stands in for the number in the tens place. The value or values on the right side are the ones that fall between the tens and ones places. The number "9.1" is the equivalent of the word "911," for instance. When a number appears more than once on the right side of a division, that number appears more than once in the tens place. In this case, the three numbers 9.1, 9.4, and 9.7 are represented by the string "9 | 147".
Hence, There is an ordered array when reading the stem and leaf plot from top to bottom:
9.1 9.4 9.7 10.0 10.2 10.2 10.3 10.8 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 12.2 12.2 12.3 12.4 12.8 12.9 13.0 13.2
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help i cant solve it
Answers
Answer:
Step-by-step explanation:
We have,
x = 3y - 3 ---> x - 3y = -3 ------(1)
5x + 4y = 23 -----(2)
Multiplying eq. (1) by 5:
5x - 15y = -15 ------(3)
5x + 4y = 23
Subtracting (1) from (3):
-19y = - 38
y = 2
therefore, x - 6 = -3
x = 3
Solve for x and express the zeros in a + bi form x^2=6x-10
Answers
Solution of the equation is x = 3 ± i that is a complex number where 3 is the real part and i is the imaginary part.
What is quadratic equation?The equation of two-degree polynomial having one variable is called quadratic equation.
The solution of a quadratic equation is either real or complex. We use quadratic equation formula for solution whenever we cannot expand, and factoring a given two-degree polynomial equation.
How to solve the given equation?given equation, x² = 6x -10
x²-6x +10 =0
This equation cannot be expanded so we need to write the formula for quadratic equation to solve it.
we know that standard form of a quadratic equation is given by
ax² + bx +c = 0
where a is the coefficient of x², b is the coefficient of x and c is the constant.
the solution of the equation is given by x = -b ± √ (b² - 4ac) / 2a
Now, the solution for the above equation is x = 6 ± √ (6² - 4×1×10) / 2×1
x = 6 ± √ (36 -40) / 2
x = 6 ± √-4 / 2
as √-4 = √-1 ×2
x = 6 ± 2 √-1 /2
divide both numerator and denominator by 2
x = 3± i as √-1 = i
this is the solution in (a + bi) form a = 3 and b = 1
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The coordinates of 3 of the vertices of a parallelogram are (-3, 4), (-2, 1), and (2, 6). What is the equation for the
line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a
parallelogram are parallel.)
A.
B.
-2
y=-x
5
2
y=-x+5
52.38
C. y=-3x
D. y=-3x+12.
Answers
y = -3x + 12 is the equation for the line containing the side opposite the side containing the first two vertices.
Given coordinates:
(-3,4) ; (-2,1) ; and (2,6)
let us solve for the slope.
Since , parallel sides have the same slope.
m = y2-y1 / x2-x1
m = 1 - 4 / -2-(-3)
m = -3 / 1
m = -3
y = mx + b
Since , (2,6) is a point which passes through the line . Hence , it must satisfy the equation.
Therefore,
6 = -3(2) + b
6 = -6 + b
6 + 6 = b
12 = b
On Substituting , values of m and b in y = mx +b , we get y = -3x +12 which is the required equation of the line.
Hence, y = -3x + 12 is the equation for the line containing the side opposite the side containing the first two vertices.
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How do you do a simple random sample on a calculator?
Answers
Using the calculator there are various methods according to the calculator we used and the approach we follow, Basic answer is to select N and generate random number.
What do you mean by random sampling?Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.
What are samples?A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.
Define the population size (N) and the sample size (n) that you want to obtain.
Use the calculator's random number generator to generate a random number between 1 and N. This will be the first element of your sample.
Repeat step 2 to generate the remaining elements of the sample, making sure that each element is different from the previous ones.
Record the elements of the sample, which are the random numbers that have been generated.
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A 140 meter rope is cut into two pieces. One piece is four time as long as the other. How long is each piece? Solve using substitution or elimination.
Answers
Answer:
28 m, 112 m
Step-by-step explanation:
x = length of short piece
4x = length of long piece
x + 4x = 140
5x = 140
x = 140/5 = 28
4x = 4(28) = 112
You have to pay 25% income tax on all of the money you make. If you made $3000 this month, how much did you have to pay in taxes this month?
Please answer ASAP! :{
You get 20 points! :)
Answers
Answer: 750
Step-by-step explanation:
3000/4= 750
750
Can you help me with this
Answers
Answer:
y = 3/2x - 3
Step-by-step explanation:
first find slope (m):
m = (-3/2 -(-15/2)) / (1 - (-3)) = (12/2) / 4 = 6/4 = 3/2
plug the point (1, -3/2) into the point-slope form (y-y1) = m(x-x1):
y - (-3/2) = 3/2(x-1)
y + 3/2 = 3/2x -3/2
now put it in slope-intercept form y = mx + b:
y = 3/2x -6/2
y = 3/2x - 3
please help im lost ;math 10th grade
Answers
The outer perimeter of the figure will be 62.3 ft.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
The figure is shown in figure.
Now, The total outer perimeter is,
⇒ Outer perimeter of triangle = 12.2 ft + 6 ft
= 18.6 ft
And, Outer perimeter of rectangle = 14 ft + 14 ft
= 28 ft
And, Outer perimeter of semicircle = πr
= 3.14 × 10 / 2
= 3.14 × 5 ft
= 15.70 ft
Thus, The total outer perimeter is = 18.6 ft + 28 ft + 15.70 ft
= 62.3 ft
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A pound of strawberries costs $3.28 and a pound of apples costs $4.63. What is the combined cost of 0.7 pound of strawberries and 1.4 pounds of apples
Answers
The combined cost of 0.7 pound of strawberries and 1.4 pounds of apples is $8.778.
What is called a pound?The Latin word "poundus," which means "weight," is whence its name originates.
Any of the many weight and mass units. especially: a measurement that is commonly used by English-speaking peoples and equals 16 ounces (about 0.454 kilograms) see measurement. the United Kingdom's fundamental monetary unit. known also as the pound sterling.
Given that A pound of strawberries costs $3.28
and a pound of apples costs $4.63
So the combined cost of 0.7 pound of strawberries and 1.4 pounds of apples is
cost = $3.28(0.7) + $1.4(4.63)
cost = $2.296 + $6.482
cost = $8.778
Therefore, the answer is $8.778.
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An operator works a basic fortnight at a basic
rate of $8. 95 and earns $671. 25. Determine the
basic fortnight for the operator.
just the answer pls
Answers
To determine the basic fortnight for the operator, we need to divide the operator's earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
The basic fortnight for an operator is the number of fortnights the operator has worked at their basic rate of pay. In this case, the operator has earned $671.25 at a basic rate of $8.95 per fortnight. To determine the basic fortnight, we need to divide the operator's total earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
So, the operator has worked 75.05 basic fortnights. It means he has been working for 75.05*14=1053 days. This is the number of days the operator has worked at their basic rate of pay. It is important to note that this calculation assumes that the operator has not earned any overtime pay or other bonuses.
$671.25 ÷ $8.95 = 75.05
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Which of the following statements correctly describes the graph? A. The graph represents a nonlinear function with a constant rate of change. B. The graph represents a nonlinear function with an increasing rate of change. C. The graph represents a linear function with a constant rate of change.
Answers
The statement that correctly describes the graph is given as follows:
C. The graph represents a linear function with a constant rate of change.
How to classify the functions as linear or non-linear?A function is classified as linear or non-linear depending on the rate of change of the function.
If the rate of change of the function is constant, that is, when x changes by one amount, y always changes by the same amount, then the function is classified as linear.
Conversely, if the rate of change of the function is different for different intervals, then the function is classified as non-linear.
As the graph presented at the end of the answer shows a linear function with constant slope, it has a constant rate of change, thus it is linear and option c is correct.
Missing InformationThe graph is given by the image presented at the end of the answer.
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A principal of $$4800wa inveted at 6. 25% interet, compounded annually. Let t be the number of year ince the tart of the invetment. Let y be the value of the invetment, in dollar. Write an exponential function howing the relationhip between y and t
Answers
The exponential function showing the relationship between y and t is y = 4800e^(0.0625t).
What is exponential function?An exponential function is a function of the form f(x) = bx, where b is a positive real number and x is a real number. This type of function is commonly used to model the rate of growth or decay of a quantity over time. Exponential functions have the property that their derivatives (slope) are proportional to the value of the function itself. This property makes them useful for modeling phenomena with compound growth or decay, such as populations, interest rates, and radioactive decay.
In this equation, 4800 is the original principal, 0.0625 is the interest rate (6.25%) and t is the number of years since the start of the investment. This equation can be used to calculate the value of the investment after any number of years. For example, if t = 5, then y would equal 6,842.50. This means that after 5 years, the value of the investment would be 6,842.50.
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