A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table.

x –4 –1 0 1 5 8 12
g(x) 0 3 1 2 0 –3 0


If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)? (5 points)
As x→–∞, g(x)→∞ and as x→∞, g(x)→∞.
As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞.
As x→–∞, g(x)→ –∞ and as x→∞, g(x)→∞.
As x→–∞, g(x)→∞ and as x→∞, g(x)→–∞.

Therefore , the solution of this is  the required system of equation is,

y=-x+6 and y=x+10.

A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.

Here,

(0,6) and the blue line pass through them (-2,8). You may figure out the equation for the blue line as,

=> y-6/x-0 =  8-6 /-2-0

=>y-6/x = 2/-2

=> y-6=-1(x)

y=-x+6

(-2, 8) and the red line pass through them (-3,7). The red line's equation can be calculated as,

y-8/x- (-2) = 8-7 /-2-(-3)

y-8 /x+2 = 1

y-8=x+2

y = x + 10

Thus, the required system of equations is,

y=-x+6 and y=x+10.

Therefore , the solution of this is  the required system of equations is,

y=-x+6 and y=x+10.

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Answer:

(2,-2)

Step-by-step explanation:

The answer is the intercept point of both lines, so we need to find the point when both the line touches, with out graphing we can see by the table that point (2, -2) intercepts with the line on the graph.

hope this helps :)

Answer:

--------------------------

From the table we see each y-coordinate is the negative of the corresponding x-coordinate. It gives us the second line:

The first line is given y = 1/2x - 3, equate both to get:

Then the value of y:

The solution is (2, - 2).

The money invested in a  account with 3% interest is $3000 and the money invested in a  account with 6% interest is $6000.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, Susan invested a total of $9000 in two account.

One account pays 3% interest and the other account pays 6% interest.

Let the money invested in a  account with 3% interest be x.

Then, the money invested in a  account with 6% interest be 9000-x.

The total return from both accounts was $450.

Here, (x×3×1)/100 + ((9000-x)×6×1)/100 =450

3x+54000-6x=45000

54000-3x=45000

3x=9000

x=$3000

So, 9000-x=$6000

Therefore, the money invested in a  account with 3% interest is $3000 and the money invested in a  account with 6% interest is $6000.

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Answer:

D

Step-by-step explanation:

first simplify everything

2/9v + 1/3v - 5/9

A and B is wrong because it is - 5/9 not + 5/9

C is wrong because it is -1/3v not 1/3, it is supposed to be - 5/9

You can solve this problem without much solving

hope this helps :)

Answer: x = -5, y = 4

Step-by-step explanation:

Align the two equations according to their terms:

[tex]\left \{ {{-3x-3y = 3} \atop {3x+6y = 9}} \right.[/tex]

Add the two equations. Because -3x and 3x equals zero, they can be eliminated from the equation. This results in:

[tex]3y = 12\\y = 4[/tex]

Plug in y = 4 into the first equation:

[tex]-3x - 3(4) = 3\\[/tex]

Solve for x:

[tex]-3x-12 = 3\\-3x = 15\\x = -5[/tex]

Check by plugging in both x and y:

[tex]-3(-5) - 3(4) = 3\\15 - 12 = 3\\3 = 3[/tex]

So, x = -5 and y = 4

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x).

[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]

from the graphs n f (x) and g( x) are 1 and 5 .

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Answer:

-sqrt(2)/2 , the last option of your document.

Step-by-step explanation:

sin(7pi/4) = -sin(7pi/4 - pi)

                = -sin(7pi/4 - 4pi/4)

                 = - sin(3pi/4)

sin(3pi/4) is a special angle , which is sqrt(2)/2

Hence, sin(7pi/4) = -sin(3pi/4)

                             = -sqrt(2)/2

Answer:

-sqrt(2)/2

Step-by-step explanation:

did the test

Answer: 0.155

Step-by-step explanation:

To find the probability of a certain event occurring in a Poisson distribution, we can use the formula:

P(k) = (μ^k * e^(-μ)) / k!

Where:

Plugging in the given values, we get:

P(5) = (9^5 * e^(-9)) / 5! = 126,441 * 0.000123 = 0.1550

So the probability of the event occurring 5 times is approximately 15.5%.

The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

This inequality can be read as "the cost of x number of stamps plus the cost of the package is less than or equal to Keshia's budget of $10.00."

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Answer:

Step-by-step explanation:

The expression you've provided is a combination of several fractions, but it's not clear how they are supposed to be combined. Without more information, it's impossible to know what the value of the expression is.

It would be helpful if you could provide more context or clarify how you want the fractions to be combined.

I can only tell you how the fraction works in mathematics and how you can evaluate the value of it if you have the complete information.

Yes, the expression; y = x³ is a function because it passes the vertical line test.

Function from a set x to a set y assigns to each element of x exactly one element of y. The set x is called the domain of the function and the set y is called the codomain of the function.

There are 4 types of functions:

On this note, the set containing all possible values of x is called the domain of the function and the set y is called the co-domain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

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The answer is: 55 crayons.

Explanation: He has 6 boxes with 8 crayons in each. 6 times 8 = 48. Plus the seven left from the other box = 48+7= 55 crayons.!!

Answer:

going to have to to get the house ready

In this question, we're looking for the number Malcom used to scale the two numbers. We can see there's a pattern, 9 is 1/6 of 54 and 40 is 1/6 of 240!

(54 divided by 9 is 6 and 240 divided by 40 is 6!)

therefore, the scale factor must be 6

Answer:

Step-by-step explanation:

y= 265

The rate of change of the equation is 25.

The rate at which one quantity changes in relation to another quantity is known as the rate of change function. Simply put, the rate of change is calculated by dividing the amount of change in one item by the corresponding amount of change in another.

Given that the linear equation is y = 25x + 115. The rate of change of the equation is represented by the slope or gradient of the equation of the line.

Here in the equation y = 25x + 115 the rate of change is 25. Which is equivalent to the slope of the line.

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Using the Pythagoras theorem, the value of y is [tex]6\sqrt{7}[/tex], and the value that goes in the green box is 6.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

Mark the intersections as A, B, C, and D.

It is given that BC=12 and CD=9.

The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem. It claims that the altitude is equal to the geometric mean of the two segments.

Apply the geometric mean theorem -

(AC)^2 = BC x CD

(AC)^2 = 12 x 9

(AC)^2 = 108

AC = [tex]\sqrt{108}[/tex]

AC = [tex]6\sqrt{3}[/tex]

Triangle ABC is a right-angled triangle, so apply Pythagoras theorem -

(AB)^2=(BC)^2+(AC)^2

(AB)^2=(12)^2+([tex]6\sqrt{3}[/tex])^2

(AB)^2=144+108

(AB)^2=252

AB=[tex]\sqrt{252}[/tex]

AB=[tex]6\sqrt{7}[/tex]

Therefore, the value of y is obtained as [tex]6\sqrt{7}[/tex].

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On solving the provided question, we can say that - the linear equation

y=mx+b = [tex]y=6.4(82)+1900= > y=524.8+1900= > y=2424.8[/tex]

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y=mx+b

x=gallons of fuel

y=total weight of plane including fuel

m=slope=6.4

b=weight of plane, no fuel....a constant to be calc'd

[tex]y=mx+b\\2245.6=6.4(54)+b\\2245.6=345.6+b\\ b=1900\\ y=6.4x+1900\\ y=6.4x+1900\\ y=6.4(82)+1900\\ y=524.8+1900\\ y=2424.8[/tex]

82gallons fuel is 2424.80 lbs

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Answer:

4

Step-by-step explanation:

The coefficient is 4 because it is the amount placed before a variable. The variable is the x, therefore, the coefficient is the 4, the amount placed before the x.

Hope this helps! :)

The value of x is 10°.

What is a measure of an angle?

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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The value of x is 10°.

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

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Answer: To calculate the sample mean of a distribution, you add up all the values and divide by the number of values in the sample. The sample mean is also known as the average.

The formula for the sample mean is:

X-bar = (X1 + X2 + ... + Xn) / n

To calculate the sample variance of a distribution, you first need to calculate the sample mean. Then, for each value, you subtract the sample mean and square the result. You add up all these squared differences, and divide the sum by the number of values in the sample.

The formula for the sample variance is:

s^2 = ( (X1 - X-bar)^2 + (X2 - X-bar)^2 + ... + (Xn - X-bar)^2 ) / (n - 1)

It would be helpful to have the sample data, however I cannot complete this task without it.

Please provide me with the data.

Step-by-step explanation:

Answer:

wouldn't it be 1/25 black??

Answer:

D+Q = 31

10D + 25Q = 595

10D + 10Q = 310

subtract to get

15Q = 285 Q = 285/15 = 19 quarters D = 31-19 = 12 dimes

Answer: She can multiply the numerator and the denominator by the same number. For example, 30/100 × 2/2

So what you're doing multiplying the numerator & the denominator each by 2. 30 ×2 = 60 and 100 x 2 = 200, ending up with 60/200.

when reduced it would simplify back to 30/100.

You can do the same for each similar. Problem asking for an equivalent. Just multiply both the numerator and denominatorby the same number.

Step-by-step explanation:

The total amount of interest you will have to pay is $21,849.92. As a result, choice A is accurate.

Compound monthly is the term used to describe a loan's interest rate, which is added to the principle each month and charged in installments. For instance, a $1,000 loan with a 12% annual interest rate compounded monthly would become $1,010 after the first month if the interest rate was 1%.

Monthly compounding is calculated by multiplying the principal amount by one plus the interest rate by the number of periods, raised to the power of the number of periods. This quantity is subtracted from the principal amount to determine the interest amount.

Thus;

[tex]Interest = 44,500(1 + 0.1311/100)^{6.5} \\= $21,849.92[/tex]

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now, we're assuming this is some rectangular area, and thus is simply the product of both quantities, let's change all mixed fractions to improper fractions firstly.

[tex]\stackrel{mixed}{12\frac{1}{2}}\implies \cfrac{12\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{25}{2}} ~\hfill \stackrel{mixed}{11\frac{3}{4}} \implies \cfrac{11\cdot 4+3}{4} \implies \stackrel{improper}{\cfrac{47}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{2}\cdot \cfrac{47}{4}\implies \cfrac{1175}{8}\implies 146\frac{7}{8}~ft^2[/tex]

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

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

h(x) = (x+1)²

h(-2) = 1

h(-1) = 0

h(3) = 8

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

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When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

area of the polygon ( triangle ) = 1/2 * b * h

= 1/2 * 4 * 4

= 8 units

so When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)

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Answer: atleast alot

Step-by-step explanation: