FIND THE SLOPE FROM THE GRAPH
a.
b.
c.
d.

The sum of the geometric progression with the features stated in the text is given as follows:

S = 2.62 x 10^(43).

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of a finite geometric sequence with n terms is given as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

In this problem, the first term and the common ratio are given as follows:

[tex]a_1 = 2, n = 3[/tex]

Hence the equation is:

[tex]a_n = 2(3)^{n - 1}[/tex]

The nth term is of 1458000, hence the number of terms of the sequence is obtained as follows:

[tex]a_n = 2(3)^{n - 1}[/tex]

[tex]1458000 = 2(3)^{n - 1}[/tex]

[tex]3^{n - 1} = 729000[/tex]

[tex]3^{n - 1} = 3^{90}[/tex]

Then:

n - 1 = 90

n = 91.

Thus the sum of the sequence is given as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

[tex]S_{91} = \frac{2(1 - 3^{91})}{1 - 3}[/tex]

S = 2.62 x 10^(43).

The problem is solvable with an nth term of 1,450,800, not 145,800, as 145,800/2 is not a root of 3.

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The principle investment necessary to obtain a total sum of $400.00 from simple interest at an annual rate of 8% for 8 years is $243.90.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on.

Here,

First, converting R percent to r a decimal

r = R/100 = 8%/100 = 0.08 per year.

Solving our equation:

P = 400 / ( 1 + (0.08 × 8)) = 243.90243902439

P = $243.90

The principal investment required to get a total amount, principal plus interest, of $400.00 from simple interest at a rate of 8% per year for 8 years is $243.90.

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The greatest possible number of total points for each of the top three teams is 24.

Given;

Six teams compete against one another twice in a tournament. A team receives three points for a victory, one point for a tie, and no points for a defeat. The top three clubs ended up with the same total number of points when all the games were completed.

After fully understanding the problem, we immediately know that the three top teams, say team A, team B, and team C, must beat the other three teams D, E, F. Therefore, A, B, and C must each obtain (3 + 3 + 3 ) = 9 points. However, they play against each team twice, for a total of 18 points against D, E, and F. For games between A, B, and C, we have 2 cases. There is an equality of points between A, B, and C in the following cases.

Case (I): A team ties the two other teams. For a tie, we have 1 point, so we have (1 + 1) * 2 = 4 points (they play twice).

Therefore, this case brings a total of 4 + 18 = 22 points.

Case (II): A team beats one team while losing to another. This gives equality, as each team wins once and loses once as well. For a win, we have 3 points, so a team gets 3 * 2 = 6 points if they each win a game and lose a game.

This case brings a total of 18 + 6 = 24 points.

Therefore, we use case (II) since it brings the greater amount of points as 24.

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Answer:  [tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]

=====================================================

Explanation:

The notation (g∘f)(x) is the same as g(f(x))

We'll start with the outer function g(x). Then replace each x with f(x). Afterward plug in f(x) = -3x+5 for the right hand side only.

This is what the steps look like

[tex]g(\text{x})=\text{x}^2+2\text{x}+15\\\\g(f(\text{x}))=(f(\text{x}))^2+2f(\text{x})+15\\\\g(f(\text{x}))=(-3\text{x}+5)^2+2(-3\text{x}+5)+15\\\\g(f(\text{x}))=9\text{x}^2-30\text{x}+25-6\text{x}+10+15\\\\g(f(\text{x}))=9\text{x}^2-36\text{x}+50\\\\[/tex]

Therefore,

[tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]

You can use tools like WolframAlpha, GeoGebra, and Desmos as ways to confirm the answer.

The length of the road in the simplest radial form is 10[tex]\sqrt{29}[/tex].

Here a rectangle of dimensions is 20m by 50m. So the length of 50m and the breadth is 20m

As the road is diagonal of the rectangle.

So we have to find the length of the diagonal of the rectangle.

Formula to find the diagonal of rectangle:

Diagonal = [tex]\sqrt{l^{2} + b^{2} }[/tex]

length (l) = 50m

Breadth(b) = 20m

Diagonal = [tex]\sqrt{50^{2} + 20^{2} }[/tex]

               = [tex]\sqrt{2500 + 400}[/tex]

               = √2900

              = 10√29

Therefore the length of the road is 10√29.

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The correct statement regarding the proportional relationships is given as follows:

Boat A travels at a faster rate than Boat B.

A proportional relationship is a special case of a linear function with intercept zero in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

The function for boat A is:

d = 10.5t.

Hence the rate is:

10.5 miles per hour.

From the graph, the rate for boat B is obtained as follows:

k = 90/10 = 9 miles per hour.

A higher constant means a faster rate, 10.5 is greater than 9, hence boat A travels faster.

The problem is given by the image shown at the end of the answer.

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The expressions that show the distance between P and Q are option (d) |-6| + (-2) and option (e) 6 - 2

From the given number line

The distance between P and Q = 4 units

Now we have to solve each expression

Expression 1

|-6| + |-2| = 6 +2

Add the terms

= 8

Expression 2

|2-(-6)| = | 2 + 6|

= |8|

= 8

Expression 3

|-2| - (-6) = 2 + 6

Add the terms

= 8

Expression 4

|-6| + (-2) = 6 - 2

Subtract the term

= 4

Expression 5

6 - 2 = 4

Hence, the expressions that show the distance between -6 and -2 are option (d) |-6| + (-2) and option (e) 6 - 2

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a. The set in set builder form A = {x : x ∈ N}

b. the set in descriptive form, A = {set of natural numbers}

A set is a collection of well defined items.

Set builder form is a way of enumerating a set by using a set of rules which define its elements.

Descriptive form is a way of enumerating the elements of a set in words.

Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N, we identify each element of the set as x and give it a rule that x is an element of N. That is x ∈ N.

So, in set builder form A = {x : x ∈ N}

Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N.

In descriptive form, we write that A = {set of natural numbers}

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The amount received by Charis on Simple interest in 2 years will be $8.4

What is Simple Interest?

The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest (S.I.).

It's formula is given by S.I. = PRT/100  where P = principle amount

R= rate and T = time.

Main Body:

P= $140

R= 3%

T= 2 years

so S.I. = 140*2*3/100

S.I. = $ 8.4

Hence total amount received by Charis at the end of 2 years will be $8.4

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The number 74.9963 would round down to 70

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  74.9963 to the nearest 10

We can see that the 74.9963 is below 75 so it goes down, and it rounds down to 74.9963 instead of, 74.9 then that would round up to the decimal is higher than 70.

The answer would be 70

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Reflection in geometry means the type of transformation that flips a shape in a mirror line.

What is reflection ?

Reflection is a type of transformation that flips a shape in a mirror line so that each point is the same distance from the mirror line as its reflected point.

Let us suppose that the triangle with one coordinate  [tex](3,-5)[/tex] and the other two are unknown and we do not even want to know them but it would be better if we do know them:-

And we have a graph.

Let us draw a line [tex]y=-2[/tex] on the graph and draw the triangle

Now the coordinates [tex](3,-5)[/tex] are three boxes away from the line [tex]y=-2[/tex], so we plot this coordinate three boxes up from the line [tex]y=-2[/tex] and do the same for other coordinates so [tex](x,y)[/tex] is one box up from the line [tex]y=-2[/tex] so we plot the coordinates one box up from the line [tex]y=-2[/tex]

Hence, the image is located at [tex]G[/tex] is plotted above.

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Thus, it takes 1.5 minutes {30 seconds} for filling a 3-litre bowl

The required increasement of height of tree is 33 centimeters annually

Function of time is defined as the change of abject or expression of variables with time. As the time increases, there is change in shape, height, etc. is called function of time.

we have given an expression of height of tree,

H = 210 + 33t

Where t represent the time and H is height of tree.

So, Changes in the height of the tree with years,

for t = 1 year

⇒ H = 210 + 33×1 = 210 + 33 = 243 centimeters

Thus, the height of tree in increases by 33 centimeters yearly.

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Answer:

y = 8x - 6

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

We know that the y-intercept occurs when x = 0 so from the table, it's b = -6

We can use the slope formula to find the slope:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\ \frac{2-(-6)}{1-0} \\\frac{2+6}{1-0} \\8=m[/tex]

Answer:

The absolute difference is 1050

The relative percentage is 32.3076%

Step-by-step explanation:

We are given

The population of a town increased from 3,250 in 2008 to 4,300 in 2010

In 2008:

In 2010:

Absolute difference:

we know that

absolute difference =

absolute difference =

absolute difference is 1050

Relative increase:

we know that

Relative percentage is

now, we can plug values

=32.3076

So, the relative percentage is 32.3076%

21/8 must be added to the terms to give the result as 6. The answer will be in a fraction.

What is a fraction?

In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. In ordinary English, a fraction refers to the number of parts of a specific size.

Main Body:

Let the term to be added be x.

3+3/8+x =6

on solving this we will get the value of  x= 21/8

Hence the answer of this question is 21/8.

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The equation of a line for y-intercept and the coordinate point is y=3x-1.

Given that, y-intercept is -1 and the line passes through the point (3, 8).

In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

Put, c=-1 and (x, y)=(3, 8) in y = mx+c, we get

8=m(3)-1

⇒ 3m=9

⇒ m=3

Substitute c=-1 and m=3 in y = mx+c, we get

y=3x-1

Therefore, the equation of a line for y-intercept and the coordinate point is y=3x-1.

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Answer:

the answer Is 6 .........

y = x²-2x+1, 2x-y=2 is the system of equations represented by the graph

By examining the graph, you will notice that the straight and the curve meet at (3,4) and (1,0) as indicated. The x values of these points of intersection give the solution of the system. Thus:

We have x = 3 and x = 1

These values can be used to form the equation of the system. Thus:

(x-3)(x-1) = 0         (Clear the parenthesis)

x² -x-3x +3 = 0

x² -4x +3 = 0

Next, we are going to check for the option that gives the x² -4x +3 = 0

Given:  y = x²-2x+1, 2x-y=2

Rewrite 2x-y=2 to be in form y: y =2x-2

We now have  y = x²-2x+1 and  y =2x-2

Equate the two y: x²-2x+1 =2x-2

x²-2x+1 -2x+2 = 0

x²- 4x+ 3 = 0

Since y = x²-2x+1, 2x-y=2 gives the same equation, therefore, the system of equations represented by the graph is y = x²-2x+1, 2x-y=2. So option D is the answer

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Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700

Use the simple interest formula

I = P r t

where I = simple interest

P = principal

r= rate of interest

t= number of years

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

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Answer:

Answer is: 8 2/3 but improper is 26/3

g(x) = (x+2-3) + 4 = (x-1)+4

Answer:

DEFG = (1/2)a^2

Step-by-step explanation:

tells us ∠FDG = 45° and ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90°!

So DFB- (1/2)(DF)(FB)=(1/2)a2

We can conclude that train A is moving faster than train B

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

The distance y (in miles) that train A travels in [x] amount of time is represented by the equality y = 78x. The graph shows the distance that train B travels.

Train A is moving with speed s[A] = 78 miles/hour {As slope of the equation is 78}. The train B will move with speed given by -

s[B] = (132 - 66)/(2 - 1) = 66 miles/hour

Therefore, we can conclude that train A is moving faster than train B

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[In the complete question it is asking to find which train is moving faster]

By taking the product between the mass and the acceleration, we will see that the force is:

F = 640 N

By the second Newton's law, we know that a force can cause motion on a body by accelerating it, such that the force is equal to the product between the mass of the object and the acceleration.

F = m*a

Here we know that:

m = 80kg

a = 8 m/s^2

Replacing that we get:

F = (80 kg)*( 8 m/s^2) = 640 N

Where N is the unit Newton.

1 N = 1 kg*m/s^2

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Answer:

(2,1)

Step-by-step explanation:

The x-value stays the same since we are only moving up/down and the y-value becomes the opposite

(x,y)--> (x,-y)

So the point becomes (2,1)

Answer:

(2,-1) hope this helps you understand

The random variable in given problem is "x" . The possible values of random variable x are 0,1,2 and 3..

All possible values of random variable is numrical in nature.

We have a table to right lists probabilities for the corresponding number of girls in three live births.

from the table we cleary see that the random variable is x which represents the number of girls in three live births.

Random variable is a variable whose value is unknown or a variable which assigns a numerical value to each trials in Sample Space.

Also, we can see in list that the number of girls in three live birth values are 0, 1 ,2 and 3 ( 3 live birth)

So, the possible values of random variable x is 4 i.e., 0, 1, 2 and 3..

From data we get a result that all possible values of random variable and it's probabilities are numrical in nature.

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Answer:

Step 2 is incorrect

Step-by-step explanation:

Step 2 is where you are distributing out -5. Step 2 should be distribution rather than division property of equality.