The area of the given figure is, 123ft² .So option c is correct
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
The given figure can be assumed as a trapezoid with the two parallel sides being the bottom side (20.5 feet) and the top side (from the perpendicular to the right vertex to the perpendicular to the left vertex
= 18.4 + 2.1
= 20.5 feet
The height of the trapezoid is given as 6 feet.
The formula for the area of a trapezoid is:
Area = (sum of the parallel sides) * height / 2
So, in this case, the area of the trapezoid would be:
Area = (20.5 + 20.5) x 6 / 2
= 41 x 3
= 123 square feet
Therefore, the answer is 123 square feet.
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What number should go in the space?
Multiplying by 0.65 is the same as decreasing by _____%.
pls show simple working out
Answer:
0.65*10=6.5
10*0.35=3.5
10-3.5=6.5
So, it is decreasing by 35%
Step-by-step explanation:
if a slope intercept what is the equation of the line having a slope of 2 and passing through the point (6,24)
The equation of the line of given slope and point is y = 2x + 12. The solution has been obtained by using the slope-intercept form.
What is slope-intercept form?
The graph of the equation y = mx + b is the line with m as its slope and b as its y-intercept. The slope-intercept form of the linear equation is used when the values of m and b are real integers.
We are given the slope as 2 and which is passing through the point (6,24).
We need to first find the y-intercept using y = mx + b
⇒y = mx + b
⇒24 = 2(6) + b
⇒24 = 12 + b
⇒b = 12
The equation in the slope-intercept form is
y = mx + b
This gives equation as y = 2x + 12.
Hence, the equation of the line of given slope and point is y = 2x + 12.
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Level I Y.15 Surface area of cubes and prisms RFP
What is the surface area?
29 in
Submit
36 in
5 in
square inches
The surface area of rectangular prism above is 2738 in².
Rectangular prismAt the picture above is a rectangular prism with the sides 29 in, 36 in and 5 in.
The question is want to know The are
The surface area of a rectangular prism is given by this formula:
A = 2 (lh +wh + lw )
Substitute the sides of the shapes to the formula
A = 2 (lh +wh + lw )
A= 2( 36.5 + 29.5 + 36.29)
A= 2(180+145+1044)
A= 2(1369)
A=2738 in²
Therefore the surface area is 2738 in².
A right-angle prism is a three-dimensional shape with six faces, where all faces of the prism (top, bottom, and sides) are rectangular and all pairs of opposing faces are congruent. Like all three-dimensional shapes, right-angled prisms have a volume and a surface area. A right angle prism is also called a cuboid
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Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
Answer:
A: No solution
B: Unique Solution: (0, 0)
Step-by-step explanation:
System A:In System A, you may notice that in both equations the two equations have variables with the same coefficient, and this is ideal for the elimination method of solving the equation. We want to add the equations in a way that cancels out variables. So let's multiply the top equation by negative one: [tex]-1(2x+3y)=-(9)\implies -2x-3y=-9[/tex]
Now from here we want to add the two equations:
[tex]\ \ -2x-3y=9\\+2x+3y=4\\0+0=13[/tex]
And the statement provided is clearly not true, 0 is never equal to 13, meaning the systems of equation has no solution, which occurs when you have two parallel lines.
System B:In this case, we can easily solve this using substitution, since y is equal to 7x that means we can substitute in 7x for y in the second equation:
[tex]y=x\implies 7x=x[/tex]
And from here we subtract x from both sides, and divide by 6 giving us:
[tex]x=0[/tex]
And now we can take this value and plug it into either equation to solve for our y value, and it's most convenient to plug it into the y = x equation... since there's nothing to solve, we just get:
y = 0
So x = 0, and y = 0, meaning there is a unique solution of (0, 0)
If a ticket price is lowered by $3.00 for all tickets, how does this demonstrate the income effect
Answer:
the income affect is changed drastically as now for every person they loose $3.00
so sorry if I'm wrongcan someone help me please
here is the picture
135 and 59 are the values of fog(5) and gof(5) respectively.
Composite functionsComposite functions are also known as function of a function. Given the functions below;
f(x) = x^2 + 6x
g(x) = x + 4
For fog(5)
fog(5) = f(g(5))
f(g(x)) = f(x +4)
f(g(x)) = (x+4)^2 + 6(x+4)
f(g(5)) = (9)^2 + 6(9)
f(g(5)) = 81. + 54 = 135
For gof(5))
g(f(x)) = g(x^2 + 6x)
g(f(x)) = x^2 + 6x + 4
g(f(5)) = 5^2 + 6(5) + 4
g(f(5)) = 59
Hence the value of the composite values fog(5) and gof(5) area 135 and 59
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Z-scores measure an observation's standing relative to the ____ of the given data set.
Answer: X and Y values
Step-by-step explanation:
graph the quadrilateral with vertices w(-2,-1) x(-1,3) y (3,3) z(3,-3) and its imagine after rotation 180º about the origin
The image quadrilateral is identical to the original quadrilateral but has been mirrored across the x- and y-axes.
The coordinates W(-2, 1), X(-1, 3), Y(3, 3), and Z(3, 3) can be plotted to form the quadrilateral's graph as follows:
code is as follows:
|
| Y(3,3)
|
|
------Z(3,-3)
------
|
|
|
| X(-1,3)
|
|
|
W(-2,-1)
We may use the following transformation on each vertex to determine the image of this quadrilateral following a 180-degree rotation of the origin:
(x, y) -> (-x, -y) (-x, -y)
As a result, the picture quadrilateral's new vertices are:
W' = (-(-2), -(-1)) = (2, 1) (2, 1)\sX' = (-(-1), -(3)) = (1, -3) (1, -3)\sY' = (-3, -3) = (-3, -3) (-3, -3)\sZ' = (-3, 3) = (3, -3) (3, -3) (3, -3)
To create a quadrilateral image, we can plot these points on the same coordinate plane:
code
|
| Y'(3,-3)
|
|
------
Z'(3,-3)
------
|
|
|
| X'(1,-3)
|
|
|
W'(2,1)
It should be noted that the image quadrilateral is identical to the original quadrilateral but has been mirrored across the x- and y-axes.
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A hockey player passes a puck to his teammate by bouncing it off a wall. The angles formed when the puck hits the wall and bounces off are congruent. Some of the distances are shown.
What is the distance, x, from Player 1 to the wall?
Enter your answer, as a decimal, in the box. Round your answer to the nearest hundredth.
The answer is 10.67 ft. The distance, x, from Player 1 to wall is 10.67 ft.
Given, Two different triangles for player 1 and player 2.
Both triangles have right angle and same angle where they are connected. So other angle is also same. All angles are same so they are similar triangles. smaller triangle is similar to larger triangle.
The distance x in the figure is required.
The required distance is x = 10.65 ft
The given triangles ABC and CDE are similar by Angle.
∠B = ∠D = 90°
∠ACB =∠ECD
The ratio of the sides is:
[tex]\frac{BC}{CD} = \frac{12}{9} = \frac{4}{3}[/tex]
So,
[tex]\frac{AB}{ED} =\frac{4}{3}[/tex]
x/8 = 4/3
x = 4/3 * 8
x = 10.65 ft
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Here is a prism made with 27 cubes that Renata covered with stickers.
You can pull her prism apart using the draggable point.
Fill in the table with the number of cubes in this prism that have 0, 1, 2, and 3 stickers.
The number of cubes in the prism with stickers 0 - 1, 1 - 6, 2 - 12, and 3 - 8.
What is a cube?Cubic form is defined as the shape of a cube. Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped.
According to the prism, the cube at the center has no stickers.
Stickers on 0 side = 1
The face of the prism contains cube that would have stickers on one side. The center cubes on each face will have stickers on one side:
Stickers on 1 side = 6
The edges of the prism will have cubes at the center that contain stickers on both sides:
Stickers on 2 side = 4 (3) = 12
Every vertices on the prism will have sticker on three sides.
Sticker on three side = 8
Hence, the number of cubes in the prism with stickers 0 - 1, 1 - 6, 2 - 12, and 3 - 8.
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The correct question is:
Which of the following are among the most commonly used metrics for comparing the performance of different companies?
Return on assets
Return on equity
Return on invested capital
ROA, ROE, and ROIC are important metrics for comparing the performance of different companies and can provide valuable insights into a company's financial health and competitiveness.
Return on assets (ROA), return on equity (ROE), and return on invested capital (ROIC) are among the most commonly used metrics for comparing the performance of different companies. These metrics are widely used by investors, analysts, and other stakeholders to evaluate a company's financial performance and to compare it with other companies in the same industry.
Return on assets (ROA) is a measure of a company's efficiency in using its assets to generate profits. It is calculated by dividing the company's net income by its total assets. A higher ROA indicates that a company is generating more profits from its assets, while a lower ROA suggests that the company is not using its assets as efficiently.
Return on equity (ROE) is a measure of how much profit a company generates in relation to the equity invested by its shareholders. It is calculated by dividing the company's net income by its total equity. A higher ROE indicates that a company is generating more profits for its shareholders and is a sign of a well-managed company.
Return on invested capital (ROIC) is a measure of how much profit a company generates in relation to the capital it has invested in its business. It is calculated by dividing the company's net income by its invested capital. A higher ROIC indicates that a company is generating more profits from its invested capital, while a lower ROIC suggests that the company is not using its capital as effectively.
In summary, ROA, ROE, and ROIC are important metrics for comparing the performance of different companies and can provide valuable insights into a company's financial health and competitiveness.
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The table and graph below display data from the Fresh 4 Less farm stand in Austin, Texas. The number of customers and total sales in dollars for several months are displayed. Data downloaded on 2/19/2020 from https://data.world/cityofaustin/cfer-vyii.
Farm Stand Data
Number of Customers 216 254 316 397
Total Sales $1900 $1995 $2606 $3482
When answering the questions below, maintain exactly four decimal places in your intermediate computations. In these problems, intermediate computations refers to your average growth rate calculations.
Use interpolation or extrapolation (whichever is appropriate) to predict the total sales when the farm stand has 280 customers. Round your answer to the nearest whole number. $
Use interpolation or extrapolation (whichever is appropriate) to predict the total sales when the farm stand has 410 customers. Round your answer to the nearest whole number. $
The total sales when the farm stands have 410 customers will be $4326.
How to calculate the average growth rate?To predict the total sales when the farm stand has 280 customers, we need to interpolate between the data points for 254 and 316 customers. First, we can calculate the average growth rate between these two data points:
Average growth rate = (ln(2606) - ln(1995)) / (ln(316) - ln(254)) = 0.3763
Using this average growth rate, we can predict the sales for 280 customers as follows:
ln(y) - ln(1995) = 0.3763 x (ln(280) - ln(254))
ln(y) = 7.5835
[tex]y = e^{7.5} = 1961.36[/tex]
Rounding to the nearest whole number, we predict that the total sales when the farm stands have 280 customers will be $1961.
To predict the total sales when the farm stands have 410 customers, we need to extrapolate beyond the data points. We can use the same average growth rate calculated above to make this prediction:
ln(y) - ln(2606) = 0.3763 x (ln(410) - ln(316))
ln(y) = 8.4256
[tex]y = e^{8.4256}[/tex] = 4326.46
Rounding to the nearest whole number, we predict that the total sales when the farm stands have 410 customers will be $4326.
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Jordan took out a loan for 14 months and was charged simple interest at an annual rate of 5.75%. If the amount of the loan was $850, what is the amount of interest she had to pay?
Answer:
$57.02
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
P = $850r = 5.75% = 0.0575t = 14 months = 14/12 yearsSubstitute the values into the simple interest formula and solve for I:
[tex]\implies I=850 \cdot 0.0575 \cdot \dfrac{14}{12}[/tex]
[tex]\implies I=57.0208333...[/tex]
Therefore, the amount of interest is $57.02 (nearest cent).
In a school long jump competition, A placed seventh, while B placed sixth. C, ranked above A and B, ranked above and below some friends. D does worse than E and ranks penultimate. How many of people participated in the contest?
However, we can't determine the exact number of participants with this information alone.
What's the Participated trying to say?an individual who engages in or becomes engaged in a specific action. Examples. Over three thousand people will be competing in the games, a worldwide athletic event. She has contributed significantly to the conversation.
Let's use logic to determine the possible rankings of the participants:
A placed seventh, so at least 6 people ranked higher than A.
B placed sixth, so at least 5 people ranked higher than B.
C ranked above A and B, so C must have ranked at least fifth. This means there are at least four people who ranked higher than C.
D does worse than E and ranks penultimate, which means D ranked second to last. Therefore, there must be at least two people who ranked worse than D. Also, E must have ranked higher than D, so there is at least one person who ranked higher than D.
Putting this information together, we know that there are at least 6 + 5 + 4 + 2 + 1 = 18 people who participated in the contest.
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Find the length of the third side. If necessary, round to the nearest tenth. 8 12
The length of the third side is 14.4 units.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We find the third side of a triangle by using Pythagoras theorem.
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
8²+12²=x²
64+144=x²
208=x²
Take square root on both sides
x=14.4
Hence, the length of the third side is 14.4 units.
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What is your monthly take-home pay 615.29 if your take-home pay is every Monday? Round intermediate calculations and the final answer to the nearest cent; use 365 days in a year.
My monthly take-home pay would be $2461.16.
My yearly take-home pay would be $29533.92.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
If my take-home pay every Monday is $615.29 then my monthly take-home pay would be,
= (4×615.29).
= $2461.16 (as we have 4 Mondays in a month).
Now, My take-home pay for a year would be,
= (4×12×615.29). (as we have 4 Mondays in a month and 12 months in a
year) = $29533.92
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Spiral Review (1.0A.C.6) 2. Show how to make a ten to solve 13 - 7. Write the number sentence. Step I 11 19 - ooo = So, 13 - 7 = Step 2
The value of (13 - 7) is 6 and it can be determined by using the method of making a group of 10 in which arithmetic operations and rearrangement of the given expression is performed.
What is arithmetic operations?The term arithmetic stems from the Greek noun arithmos, which means "number," with pauses in Latin, Anglo-French, and Middle English along the route. Even the most elementary math contains a large vocabulary. The study of numbers and their operations, which are relevant to all other fields of mathematics, are part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.
Given that, expression: 13 - 7
The steps to determine the value of (13 - 7) by making a group of 10 are as follows:
Step 1 - Breakup 13 into the tens and the ones:
= (10 + 3) - 7
Step 2 - Breakup 7 into the tens and the ones:
= (10 + 3) - (10 - 3)
Step 3 - Rewrite the above expression:
= (10 - 10) + (3 + 3)
Step 4 - Subtraction of 10 by 10:
= (3 + 3)
Step 5 - Addition of 3 by 3:
= 6
So, the value of (13 - 7) is 6 and it can be determined by using the method of making a group of 10.
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The complete question is as follows:
Find absolute value integer or simplified fraction!!
Answer:
1/7
Step-by-step explanation:
Absolute value is the distance from zero. 7 and -1/7 and their distance from zero is not the same, but the distance from zero with the numbers -1/7 and 1/7 are the same. The absolute value, the distance from zero, is both 1/7.
which of the following functions grows fastest? group of answer choices n log n n log n n / log n n - log n n log n
In the following option n log n seems to grow the fastest amongst all according to the size of inputs.
In computer science and mathematics, the running time or complexity of an algorithm is often measured in terms of the size of the input, usually denoted by n. The notation O(f(n)) is used to describe the upper bound on the running time of an algorithm, where f(n) is a function of n.
In the context of comparing growth rates of functions, we usually only consider the highest-degree term of the function. For example, we would say that f(n) = n^2 + n grows as O(n^2), because n^2 grows much faster than n and dominates the running time as n grows larger.
Now, let's consider the functions n, n / log n, n - log n, n log n, and n^2. As n grows, each of these functions grows at a different rate.
1. n grows linearly with n, so it takes more time as the size of the input grows.
2. n / log n grows faster than n, but slower than n log n. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n / log n grows faster.
3. n - log n grows slower than n and n / log n, because log n grows much slower than n, so as n grows larger, n - log n becomes closer to n.
4. n log n grows faster than n, n / log n, and n - log n, but slower than n^2. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n log n grows faster.
5.n^2 grows much faster than n, n / log n, n - log n, and n log n, so as n grows larger, n^2 becomes much larger than any of these functions.
So, of the options given, n log n grows the fastest, meaning that an algorithm that takes time proportional to n log n will become slower faster as the size of the input grows than an algorithm that takes time proportional to n, n / log n, or n - log n.
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One angle of a right triangle measures 80°. What is the measure of the other acute angle? please help i dont understand, ty!!
Answer:
10 degrees
Step-by-step explanation:
Triangle Interior Angles:In a triangle, the interior angles of a triangle (the angles in the inside) will always add up to 180 degrees.
We're given that the triangle is a right triangle which immediately gives us one angle, of 90 degrees, since that's a right angle. We're also given another angle of 80, and adding up these two angles plus the last angle, should give us 180.
Let's represent the unknown angle as "A", giving us the equation: [tex]90 + 80+ A= 180[/tex]
Now from here we can combine the 90 and 80 to get:
[tex]170+A=180[/tex]
Now from here we subtract 170 from both sides (to maintain equality and get rid of the 170):
[tex]170-170+A=180-170[/tex]
We simplify 170-170 to 0, which we don't need to put in the equation as 0 + A is just A. We also simplify 180 - 170 to 10:
[tex]A=10[/tex]
So the other acute angle is 10 degrees.
Work out the equation of the line which has a gradient of -2 and passes through the point (1,7).
The equation of line is y = -2x + 9
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 1 , 7 )
The slope of the line is m = -2
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 7 = -2 ( x - 1 )
y - 7 = -2x + 2
Adding 7 on both sides of the equation , we get
y = -2x + 9
Hence , the equation of line is y = -2x + 9
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5 Answer:
You are selling tickets for a high school basketball game. Student
tickets cost $3 and general admission tickets cost $5. You sell 350
tickets and collect $1,450. How many general admission tickets did
you sell?
6 Answer:
Use the substitution method to solve the linear system given. Express
the answer as an ordered pair of the form (x,y)
x + y = 5
2x + y = 6
7 Answer:
A music store is selling compact discs for $11.50 and $7.50. You buy
12 discs and spend a total of $110. How many compact discs that cost
$11.50 did you buy?
8 Answer:
Solve the system of equations and express the answer as an ordered
pair of the form (x,y) or write NO SOLUTION if applicable:
x + 2y = 5
2x - 2y = 4
9 Answer:
Solve the system of equations and express the answer as an ordered
pair of the form (x,y) or write NO SOLUTION if applicable:
x + y = 1
x + y = 3
Answer:
1. 200
2.(1,4)
3. 5
4. (3,1)
5. NO SOLUTION
Step-by-step explanation:
Mauro has $500 to invest in one of two accounts for 3 years.
Account 1 earns 1.2% interest compounded monthly.
Account 2 earns 1.3% interest compounded semiannually.
Which account has a higher return, and how much?
Answer: Account 1 earns a higher return over 3 years, with a total of $515.64.
To calculate the return of Account 1:
$500 * (1 + 0.012/12)^(12*3) = $515.64
To calculate the return of Account 2:
$500 * (1 + 0.013/2)^(2*3) = $515.16
Therefore, Account 1 earns a higher return of $515.64 compared to Account 2's return of $515.16.
Step-by-step explanation:
Someone please help me ASAP!!! Find an equation for the sine graph
Answer:
Step-by-step explanation:
This graph goes up to 2 and down to -2, which tells us that the amplitude of the waves is 2. In the equation for the parent graph, y = sinx, we will throw the 2 out front which is where the amplitude goes in sin and cos curves:
y = 2sinx
For a family dinner, Kiko can make one serving of pasta salad by combining
5
1
2
parts pasta,
2
2
3
parts tomato, and
1
3
4
parts cucumber. If she plans to make
6
servings of pasta salad for the family dinner, how much of each ingredient will Kiko need?
She will need [DROPDOWN 1] parts pasta, [DROPDOWN 2] parts tomato, and [DROPDOWN 3] parts cucumber to make
6
servings of salad.
The equations for the amount of ingredients is
The amount of pasta = 33 parts pasta
The amount of tomato = 16 parts tomato
The amount of cucumber = 10.5 parts cucumber
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of pasta , tomato and cucumber required to make 6 servings be represented as P , T and C respectively
Now , the equation will be
The amount of pasta for 1 servings = 5 1/2
The amount of pasta for 6 servings P = 6 x ( 5 1/2 )
On simplifying the equation , we get
The amount of pasta for 6 servings P = 33 parts pasta
And ,
The amount of tomato for 1 servings = 2 2/3
The amount of tomato for 6 servings T = 6 x ( 2 2/3 )
On simplifying the equation , we get
The amount of tomato for 6 servings T = 16 parts tomato
And ,
The amount of cucumber for 1 servings = 1 3/4
The amount of cucumber for 6 servings C = 6 x ( 1 3/4 )
On simplifying the equation , we get
The amount of cucumber for 6 servings C = 10.5 parts cucumber
Hence , the equations are solved
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100 POINTS PLEASE HELP WILL MARK BRAINLIEST
Answer:
B
Step-by-step explanation:
The entry "cash 700000" is listed as a credit in the T account because it represents an increase in the cash balance of the account. In accounting, credits are used to record increases in asset accounts, such as cash. When cash is received, it is recorded as a credit to the cash account, which increases the balance of the account. Therefore, in this case, the entry "cash 700000" is a credit entry because it represents an increase in the cash balance.
3x ^ -1 - x ^ -3 * (y + 2)
Steve invests $2,807 in a 401k account with a fixed annual interest rate that is compounded continuously. After 13 years, the account balance reaches $9,044.13. What is the interest rate of the account?
The interest rate of the account that Steve invested in after the given number of years would be = 16%
How to calculate the interest rate of the given account?The total amount of money invested (p) = $2,807
The time of investment= 13 years
The interest generated at the end of the given years = 9,044.13-2807 = $6,237.13
Therefore the rate = ?
The formula for simple interest:
= P×T×R/100
6,237.13= 2,807× 14 ×r/100
Make r the subject of formula;
r= 6,237.14×100/2807×14
r = 623714/39298
r= 15.87139294
r= 16%
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Find each function value, if possible. (If an answer is undefined, enter UNDEFINED
g(t) = 5t² - 3t+ 6
(a) g(2)
(b) g(-1)
(c) g(t + 2)
Answer:
see below
Step-by-step explanation:
g(t) = 5t² - 3t+ 6
g(2) = 5*4 - 3*2 + 6 =20
g(-1) = 5*1 -3* (-1) +6 =5+3+6 = 14
g(t+2) = 5(t+2)² - 3(t+2) + 6
= 5*(t²+4t+4) - 3t -6+6
= 5t²+20t+20-3t
= 5t²+17t+20
Determine the equation of the linear function that generates the following table of values.
the equation of the Linear function will be f(x) = -19x + 14.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given a data set of a linear function
The slope-intercept form of the equation of a line
y=mx+b,
where m is the slope
b is the y-intercept (the value of y, at x = 0)
since, slope = (y - y')/(x -x')
In our case,
Slope = (128 -90)/ (-6 + 4)
Slope = 38/-2
Slope = -19
And b = 14 (Given)
Thus,
The equation of Line:
y = -19x + 14
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