A. F(x) = 100(1. 5)

B. F(x) = 200(1. 45)*

C. F(x) = 100x5 + 200x3 + 100

D. F(x) = 200x3 + 100x2 + 100

The **function** that will approach **positive infinity** the fastest is B

F(x) = 200(1.45). Option D is not the correct answer.Option B:

F(x) = 200(1.45)

This is an exponential function that grows much faster than all the **polynomial **functions. The base of this function is greater than 1.

As we increase the value of x, this function will approach infinity much faster than all the other given functions. Therefore, option B is the correct answer.

To solve the given problem, we need to find the function that approaches positive infinity the fastest.

Let's evaluate all the given functions one by one:Option A: F(x) = 100(1.5)

We know that the **exponential **function grows much faster than a linear function. Thus, the function 100(1.5) is an example of a linear function that has a positive slope. As we increase the value of x, this function will approach **infinity**, but not as fast as the exponential function.

Therefore, option A is not the correct answer.

Option C: F(x) = 100x5 + 200x3 + 100

We know that the polynomial function grows much slower than the exponential function. The degree of this function is 5. As we **increase **the value of x, this function will approach infinity, but not as fast as the exponential function.

Therefore, option C is not the correct answer.

Option D: F(x) = 200x3 + 100x2 + 100

We know that the polynomial function grows much slower than the exponential function. The degree of this function is 3. As we increase the value of x, this function will approach infinity, but not as fast as the exponential function.

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if theta is an angle in standard position and it’s terminal side passes through the point (3, -4) find the exact value of csc theta in simplest radical form

The **exact value** of** tanθ **is -4/3 that is -1.33 in the simplest radical form.

**What is Tanx in terms of sinx and cosx ?**

The value of Tanx can be the** ratio of sinx and cosx **or it can be defined by the ratio of its **opposite side and adjacent side.**

Given,

if theta is an angle in **standard position** and

it’s terminal side passes through the point **(3, -4) **

So, the given point is (3,-4)

By the **definition** we can say that ,

If the terminal side passes through the point **(a,b) **

than** tanθ = b/a . **

so, similarly

** tanθ = -4/ 3 **

Hence, The exact **value** of tanθ is **-4/3** that is -1.33 in the simplest radical form.

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Justin opens a savings account with $8. He saves $4 each week. The table represents his account balance. Decide whether the table represents a linear function or a nonlinear function.

The required **relationship **formed as of the given information is a linear **function**.

**Functions **are the **relationship **between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent **variable**.

Here,

Justin opens a savings account with $8. He saves $4 each week.

Let the x be the number of weeks and y be the number of money saved after x weeks.

According to the question,

y = 8 + 4x

Since the above function is a linear function, so table representing the data followed the above expression shows the linear function

Thus, the required **relationship **formed as of the given information is a **linear function**.

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What is the y-intercept of a line that passes through the points (3, -3.8) and (5, -3)? (1 point)

Enter the solution in the box below.

**Answer:**

**Step-by-step explanation:**

We can solve this by either identifying the equation or by graphing. We'll try both.

**Find the Equation**

The slope of the line can be determined from the Rise/Run of the 2 given points:

Going from ((3,-3.8) to (5,-3):

Rise = (-3 - (-3.8) = 0.8

Run = (5 - 3) = 2

Slope = 0.8/2 or 0.4

The equation for this line is y = 0.4x + b, where b is the y-intercept.

Enter either point to find b:

y = 0.4x + b

-3 = 0.4*(5) + b for point (5,-3)

-3 = 2+b

b = -5

The equation is y = 0.4x - 5

**The y=intercept is -5 (the value of b)**

**Graphing**

See the attached graph. Mark the two points and then draw a straight line between them. The point at which the line crosses the y axis is the y-intercept (0,

The function f(x)=x√ is translated 4 units right to form function g(x).

What is the equation of g(x)?

Enter your answer in the box.

g(x) =

The **equation of g(x),** after the **translation **of [tex]f(x) = \sqrt{x}[/tex] 4 units to the right is given as follows:

[tex]g(x) = \sqrt{x - 4}[/tex]

What is a translation?Among the many transformations that a function or a figure can undergo is a **translation**, along with reflections, rotations and dilation.

In a translation, only the **position **of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are **defined **as follows:

The **parent **function for this problem is given as follows:

[tex]f(x) = \sqrt{x}[/tex]

After the translation** 4 units right,** the function g(x) is defined as follows:

[tex]g(x) = f(x - 4) = \sqrt{x - 4}[/tex]

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What is the best interpretation of P(3) =12

The **best **interpretation of P(3) = 12 is that the** probability** of 3 is 12

**Probability** is simply described as an important branch of mathematics that concerns numerical descriptions of the likelihood of the occurance of an event the proposition of how true it is.

The probability of an **event** is a number that must be between 0 and 1.

Given that;

0 indicates impossibility of theNote that the analysis of events that is being governed by probability is known as statistics.

The types of probability are;

Theoretical ProbabilityExperimental ProbabilityAxiomatic ProbabilityHence, P(3) = 12 is the probability of 3 is 12

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On the second grid, create a graph of y = 3 – 4t for -2 ≤ t ≤ 7 with y on the vertical axis and t on the horizontal axis.

The **graph of** y = 3 - 4x is given above.

The **coordinates** on the graph are:

(-2, 11) and (7, -25).

What are coordinates in a graph?The **coordinates** in a graph indicate the location of a point with respect to the **x-axis **and** y-axis.**

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = 3 - 4t

Where -2 ≤ t ≤ 7

Now,

Find the **coordinates** on the graph.

y = 3 - 4t

For t = -2

y = 3 - 4 x (-2) = 3 + 8 = 11

i.e

(-2, 11)

For t = 7

y = 3 - 4 x 7 = 3 - 28 = -25

i.e

(7, -25)

Thus,

The **coordinates** on the graph are:

(-2, 11) and (7, -25).

The **graph** is given below.

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3

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

The table shows the mode of transportation to school for families with a specific number of children.

Mode of Transportation

Car

Number of

Children

0.284

1-2

63

38

3+

25

49

Total

88

87

A family from the survey is selected at random. Match the probability to each event.

0.662

Bus

0.203

0.249

101

74

175

0.624

P (3+ Children Bus)

Total

P(1-2 Children Car) - P (3+ Children Car)

Reset

P (Car 1-2 Children)

0.563

P (Bus 1-2 Children) - P (Bus 3+ Children)

▸

Next

The **probability** of **number** of 1-2 Children in car and 3 plus children in car is 0.203.

The **possibility** of the result of any **random** **event** is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

The probability of P(1-2 children| car). P (3 plus children| car) is given by:

P = 63/88 × 25/88

P=0.203

The probability of P(Bus| 1-2 children). P (Bus | 3 plus children) is given by:

P = 38/101 × 49/74

P=0.249

The probability of P(Car |1-2 Children) is given by:

P= 63/101

P=0.624

The probability of P(3 plus children | Bus)is given by:

P=49/87

P=0.563

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**Answer: The picture below**

**Step-by-step explanation: Correct on Edmentum, if you give me a low rating than you are mean :(**

In parallelogram MLKJ, find mZMLK

and mZLKJ.

18°

M

K

12°

L

So on solving the provided question, we can say that here in the **quadrilateral**; angle MJL = angle JLK = 60

A quadrilateral is a four-sided **polygon **in geometry that has four edges and four corners. The word is a **derivative **of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here in the quadrilateral

angle MJL = 60

angle MJL = angle JLK = 60

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Given △RST with medians RM⎯⎯⎯⎯⎯⎯ , SL⎯⎯⎯⎯ , and TK⎯⎯⎯⎯⎯ , and centroid J, find the value of x if JT=x(TK) .

The **value** of x is **1/2**, and** JT = 1/2(TK), TK = 2JT.**

**What is the centroid of a triangle?**

A **centroid** of a **triangle** is a point that is the **arithmetic mean** position of all the points of a **triangle**, which is the point where the three **medians** of the **triangle** **intersect**. The medians of a triangle divide the **triangle** into 6 equal **areas**.

We know that:

JT = x(TK),

\where J is the centroid and x is a constant.

Since J is the centroid, it divides the median TK into a ratio of 2:1, which means that TK = 2*JT.

Substituting this into the original equation gives:

JT = x(2*JT)

Solving for JT gives:

JT/JT = 2x

x = 1/2

JT = 1/2(TK),

TK = 2JT

Hence, the **value** of x is **1/2**, and** JT = 1/2(TK), TK = 2JT.**

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write an expression for x fewer than 62

The **expression** for x** fewer than** 62 can be written as 62 - x

An** expression** can be evaluated to a single value by substituting specific values for the **variables** and performing the operations in the correct order. Mathematical expressions can be used to model real-world phenomena, make predictions, and solve problems. Expressions are used in various branches of mathematics such as Algebra, Calculus and Geometry.

**Fewer than** tells us that x is less than 62, the solution is to tell us by what number that it is less than.

Hence 62 - x is the expression for x fewer than 62

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What is the area of triangle if sides are 9cm 12cm and 15cm *?

The **area of triangle** if sides are 9cm 12cm and 15cm is 54 square cm.

In the given question we have to find the **area of triangle** if sides are 9 cm 12 cm and 15 cm.

The entire area bounded by a **triangle's three sides** is referred to as the triangle's area. In essence, it equals half of the base times height, or A = 1/2bh. So, in order to calculate the area of a triangular polygon, we need to know its **base** (b) and height (h).

Area of Triangle = 1/2 bh

**Area of Triangle** = 1/2 9*12

Area of Triangle = 9*6

Area of Triangle = 54 square cm

Hence, the area of triangle if sides are 9cm 12cm and 15cm is 54 square cm.

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Is it possible to have a triangle with the sides 3cm 6cm 7cm?

**Answer:**

yes

**Step-by-step explanation:**

for the sides to form a triangle.

the sum of any 2 sides must be greater than the third.

As a check

3 + 6 = 9 > 7

3 + 7 = 10 > 6

6 + 7 = 13 >3

this meets the condition for a triangle to be made.

Help please!!! Test tomorrow

Therefore the **solution **to the given question equation will shift the graph of the original equation up 2 units in y=2x + 9

equation, a declaration of **equivalence **between two expressions with variable- and/or number-filled **expressions**. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.

Here,

It follows a linear function. y=mx + b

If A is the location where the y-axis intersects, then x = 0 and y = b are the coordinates of A.

In order to move the graph up by 2 units, you must add 2 units to b.

In our case, b was originally equal to 7, so shifting it up makes b become 7+2=9, and the new function is y=2x + 9.

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What point on the number line is three fourths of the way from the point −3 to point 4? 5.25 2.25 −1.25 −2.25

(B) 2.25 is three-fourths of the way between -3 and 4 on the** number line.**

A number line is basically a straight line that illustrates real numbers.

It has all the integers marked out evenly and each point corresponds to a certain real number.

We can usually see numbers from -3 up to 3, but it includes all real numbers and even the ones in between the **integers**.

It's a great tool to help teach basic addition and subtraction, especially when you're dealing with negative numbers.

So, according to the number line, we have to count from -3 to 4.

If we count as 3/4 from -3 to 4.

Then, we will land on 2.25 on the number line.

Therefore, (B) 2.25 is three-fourths of the way between -3 and 4 on the number line.

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**Complete question:**

What point on the number line is three-fourths of the way from point −3 to point 4?

(A) 5.25

(B) 2.25

(C) −1.25

(D) −2.25

Answer:

2.25

Step-by-step explanation:

Abby i going to make tie-dyed T-hirt for her cla to wear on a field trip. Each hirt cot $3. 95 and the dye cot $0. 50 then he bought two boxe of alt to add the mix for $4. 50 each. If he collected $124. 70, how many tie-dyed T-hirt can Abby make?

Abby can make 26 tie-**dyed** T-shirts.

We can start by setting up a **linear** **equation** to represent the total cost of making the tie-dyed T-shirts.

What is a **linear equation**?

First-order equations include linear equations. In the **coordinate** system, linear equations are defined for lines. A linear equation in one variable is one in which there is a **homogeneous** variable of degree 1 (i.e., just one variable).

Multiple **variables** may be present in a linear equation. Linear equations with two variables, for example, are used when a linear equation contains two variables.

Let x be the number of T-shirts Abby makes

The cost for each T-shirt is $3.95 + $0.50 = $4.45

The cost of the two boxes of salt is $4.50 * 2 = $9

So the total cost for x T-shirts is $4.45x + $9

We know that the total cost is 124.70 and we want to find the value of x, so we can set up the equation as:

$4.45x + $9 = 124.70

Solving for x:

$4.45x = 115.70

x = 115.70 / 4.45

x = 26

Therefore, Abby can make 26 tie-**dyed** T-shirts.

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Order these numbers from these two greatest?

7,404, 7.44, 7.2, 7.2041

**Answer:Greatest to Smallest > 7.44, 7.404, 7.2041, 7.2 and Smallest To Largest > 7.2, 7.2041, 7.404, 7.44**

**Step-by-step explanation:**

amanda used a total of 13 gallons of gas while driving her car each hour she was driving she used 3/10 gallons of gas what was the total number of hours she was driving

43 hours

The fraction 10/10 would be equal to one gallon, so just 1. So that would mean 3/10 of a gallon would equal 0.3

Divide 13 by 0.3 and you get 43.3 hours. So you’d just put 43 hours as your answer.

The fraction 10/10 would be equal to one gallon, so just 1. So that would mean 3/10 of a gallon would equal 0.3

Divide 13 by 0.3 and you get 43.3 hours. So you’d just put 43 hours as your answer.

11. A cattle ranch has 1,400 acres of grazing land. The ranch has 140 cows. How many acres of grazing land does the ranch have per cow?

**Step-by-step explanation:**

1400-140 this is answer of this question

How would you classify the polynomial equation with a degree of 2?

A **quadratic **equation with real or complex **coefficients **has two roots.

A **quadratic** equation with real or complex coefficients has two roots. A quadratic equation is any algebraic equation that can be **expressed** in standard form as where x is an unknown value and a, b, and c are known values, with a 0. A second-degree equation is a quadratic equation.This signifies that it has at least one (1) squared **phrase**. 'ax2 + bx + c = 0' is a typical formula for solving quadratic equations, where a, b, and c are constants or numerical coefficients.

Here,

A **quadratic** equation with real or complex coefficients has two **solutions**, known as roots.

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**The answer is:**

**Work/explanation:**

You would classify a polynomial with a degree of 2 based on the number of terms. The degree is second.

So you would say "**this is a second-degree polynomial**".

An example of a second-degree polynomial would be [tex]\bf{y^2+7}[/tex].

Hence, this is the answer.what is the fractional part that make up 7/3?

**Answer:**

1/3

**Step-by-step explanation:**

7/3 = 6/3 + 1/3 = 2 + 1/3 = 2 1/3

The fractional part is 1/3.

In a geometric series, the sum of the first three terms is 14. 25 and the sum of the first four terms is 24. 375. Find the first term and the common ratio.

The** first term** and the **common ratio** in the geometric series are **3 and 3/2**.

A geometric series is described as the sum of the **sequence of numbers**. The **sum** of the nth term of a geometric sequence is expressed as:

**Sₙ = a (r^n – 1) / r – 1**

In this case, if the sum of the** first three terms** is 14.25, it means:

n = 3

S₃ = 14.25

Now, substitute the value into the formula:

Sn = a (r^n – 1) / r – 1

S₃ = a (r^3 – 1) / r – 1

**14.25 = a (r^3 – 1) / r – 1**

And, if the sum of the **first four terms** is 24.375, it means:

n = 4

S₄ = 24.375

Substitute the value into the formula:

Sₙ = a (r^n – 1) / r – 1

S₄ = a (r^4 – 1) / r – 1

**24.375 = a (r^4 – 1) / r – 1**

Then, we now can divide both above equations:

14.25 / 24.375 = r^3 – 1 / r^4 – 1

14.25r^4 – 14.25 = 24.375r^3 – 24.375

14.25r^4 – 24.375r^3 = –24.375 + 14.25

14.25r^4 – 24.375r^3 = –10.125

14.25r^4 – 24.375r^3 + 10.125 = 0

After factorizing we get:

r = 3/2

This is the **common ratio**.

Now, substitute the value of r into the equation

14.25 = a (r^3 – 1) / r – 1

14.25 = a ((3/2)^3 – 1) / (3/2) – 1

14.25 = a (19/8) / 0.5

19a / 8 = 14.25 * 0.5

19a / 8 = 7.125

19a = 57

a = 57 / 19

a = 3

Thus, the **first term is 3**.

Hence, the **first term** in the geometric series is **3** and the **common ratio** is **3/2**.

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Determine whether S is a basis for P3.

S = {4t − t2, 5 + t3, 5 + 3t, −3t2 + 2t3}

No, S is not a** basis** for P³. In order for a set of vectors to be a basis for a vector space, the vectors must be linearly independent and span the space.

In this case, the set of vectors does not span P³ because the highest order of the polynomials in S is t³, which does not span all of P³ which contains **polynomials **of order up to and including t³.

Additionally, the set of vectors is not linearly** independent**. For instance, 4t−t²= 5+3t−2t³, which means that the two vectors are linearly dependent. Therefore, S is not a basis for P³.

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Maon bought 6 loave of bread and 3 package of cheee fir a total of $27. The cot of a package of cheee i $1. 50 more than the cot of a one loaf of bread. What i the combined cot of one loaf of bread and one package of cheee?

The combined **cost **of one loaf of bread and one package of cheese will be $6.5 for the **equation**

What is the solution to the **equation**?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1.50 more than the cost of a loaf of bread.

Let 'x' be the **cost **of the loaf and 'y' be the cost of cheese. Then the equations are given as,

6x + 3y = 27

2x + y = 9 ...1

y = x + 1.5 ...2

From equations 1 and 2, then we have

2x + x + 1.5 = 9

3x = 7.5

x = $2.5

Then the value of the **variable **'y' is calculated as,

y = 2.5 + 1.5

y = $4

The combined cost of one loaf of **bread **and one package of cheese will be given as,

⇒ $4 + $2.5

⇒ $6.5

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The cost of a stereo cable was $14 yesterday. Today, the cost rose to $16 . Find the percentage increase. Round your answer to the nearest tenth of a percent.

It increased 114.3

100 was 14 and what was 16

You need to multiply 100 and 16 then divide to 14

100 was 14 and what was 16

You need to multiply 100 and 16 then divide to 14

If jimmy bought 50 apples and each bag had 10 apples and he gave 2 bags of apples to one of his friends and another 2 bags of apples to another friend and he ate 1 bag how many apples does he have left.

The number of **apples** left with** jimmy** is none(zero).

**Jimmy** bought 50 apples and each bag had 10 **apples** and he gave 2 bags of apples to one of his friends and another 2 bags of apples to another friend and he ate 1 bag.

The number of apples Jimmy have left can be calculated as follows;

He has 5 bags of apples containing 10 apples each. Jimmy gave 2 bags of apples(20 apples) to his friend and gave another 2 bags of apples(20 apples) to his friend.

Finally, he ate 1 bag of apple(10 apples).

Therefore, the number of apples left is none.

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What is 2 ordered pair?

If the given ordered pair [tex](2,3) = (3x-4,3)[/tex] are** equal** , then on simplifying we get that the **value of x **is 2 .

The **Ordered Pair** is given as [tex](2,3) = (3x-4,3)[/tex] , and the ordered pair are equal ,

We know that the two ordered pairs [tex](a_{1} ,b_{1} )[/tex] and [tex](a_{2} ,b_{2} )[/tex] , are said to be **equal if and only if** the elements , [tex]a_{1} =a_{2}[/tex] and [tex]b_{1} =b_{2}[/tex] .

So , By the above definition ,

we get that , [tex]3x-4=2[/tex] ;

adding 4 to both the sides of equation ,

we get ; [tex]3x=6[/tex]

Dividing both sides by 3 ,

we get ;

⇒ [tex]x=\frac{6}{3}[/tex] ;

On simplifying further ,

we have ;

⇒ [tex]x=2[/tex] .

Therefor , the value of x is 2 .

The given question is incomplete , the complete question is

What is the value of x if the 2 ordered pair (2 , 3) = (3x-4 , 3) are equal ?

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what is x < 3 as a solution or not a solution

x < 3 is a **solution **of the inequality x - 3 < 0 and x < 3 is not the solution of the inequality x + 3 < 0.

Linear inequalities are defined as those **expressions **which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Suppose that the inequality is x - 3 < 0.

x - 3 < 0

**Adding **3 on both sides of the equation,

x - 3 + 3 < 0 + 3

x < 3

x< 3 is the solution of the expression x - 3 < 0.

Consider the inequality x + 3 < 0.

x + 3 < 0

**Subtracting **3 from both sides,

x + 3 - 3 < 0 - 3

x < -3

x < 3 is not the solution of the expression x + 3 < 0

Hence the expression with x < 3 as a solution is x - 3 < 0 and not as a solution is x + 3 < 0.

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Find each measure using the information given

if possible can you show the equation break down if some are needed

(please i need help with this)

The value of all the **missing angles** of the **triangle** are;

m∠PRQ = 78°

m∠RPQ = 30°

m∠PQR = 72°

m∠PRS = 39°

m∠RPS = 15°

m∠PQS = 36°

m∠PSR = 126°

What is the incenter of a triangle?The** incenter** of a triangle is the** intersection point** of all the three interior angle bisectors of the triangle.

Now, the **sum of angles** in a triangle is equal to 180 degrees. We are given;

m∠PRQ = (8x - 10)°

m∠RPQ = (4x - 14)°

m∠PQR = (7x - 5)°

Thus;

(8x - 10) + (4x - 14) + (7x - 5) = 180

19x - 29 = 180

19x = 209

x = 209/19

x = 11

Thus;

m∠PRQ = (8(11) - 10)° = 78°

m∠RPQ = (4(11) - 14)° = 30°

m∠PQR = (7(11) - 5)° = 72°

By the definition of **incenter** of a **triangle**, we can say that;

m∠PRS = 78°/2 = 39°

m∠RPS = 30°/2 = 15°

m∠PQS = 72°/2 = 36°

Similarly;

m∠PSR = 180 - (m∠RPS + m∠PRS)

m∠PSR = 180 - 54

m∠PSR = 126°

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What is xÂ² in math?

The 5 is the numerical **coefficient** in the expression 5x. 5x denotes a 5x multiplication of the variable x.

x ax2+bx+c=0, a quadratic** polynomial** in a single variable, is a quadratic equation. a 0. Since this polynomial is of second order, the Fundamental Theorem of Algebra guarantees that there is at least one solution. There are both straightforward and** complex solutions**. A quadratic equation is a quadratic equation. This suggests that it contains at least one word that has to be squared. One of the commonly used answers to quadratic equations is "ax2 + bx + c = 0." where the unknown variable "X" is represented by the numerical coefficients or constants a, b, and c.

given

X is the coefficient term, while an is the variable.

Together, x and a2 are multiplied.

A mathematical problem is solved using an algebraic expression, which combines words and numbers.

For illustration

The 5 is the numerical coefficient in the expression 5x. 5x denotes a 5x multiplication of the variable x.

The variable is therefore a, and the coefficient term is x.

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What is a 1/2 scale factor?

Every coordinate point of the original triangle has its scale factor doubled by one-half if the **scale** factor is one. multiply by half after dilation with a scale factor of two.

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