Evaluate each expression for x=-2,0,1 , and 4.
3x+1

Answer:

My teacher helped

Step-by-step explanation:

The given sequence is geometric, with common ratio = -1.

Now, Given: -1, 1, -1, 1, ...

Here, a₁ = -1, r = [tex]\frac{1}{-1}=\frac{-1}{1} = \frac{1}{-1} = -1[/tex]

Hence, it is a geometric sequence, with common ratio = -1.

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The domain restrictions that would allow the inverse of f(x) to also be a function are given as follows:

The function is one to one if there are no horizontally aligned points, that is, each value of y is also related to only one value of x. A function will have an inverse in the part of the domain of the function that is one to one.

For this problem, the relation is symmetric at x = -4, hence the domains x <=  -4 and x >= -4 must not intersect for the inverse to be a function, and the restrictions are given by:

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The probability that the marble that you drew was either blue or green is 0.7.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

There are 4 blue ,3 green , 1 yellow and 2 red

In total there are 10 balls.

probability of getting blue or green ball is = 7/10

P (blue or green) = 0.7

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Answer:

Step-by-step explanation:

[tex]−6(x−2)+50\\\\-6x+12+5\\\\\sf{-6x+17}[/tex]

we are done!! ~~

Answer:

-6x + 17

Step-by-step explanation:

We can use algebraic expansion and order of operations to solve for this expression.

[tex] - 6(x - 2) + 5 \\ = - 6x + 12 + 5 \\ = - 6x + 17[/tex]

The answer to your question would be, 171.5

The given series is geometric series. The sum of its first 5 terms is 6248.

To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.

If it is an arithmetic series, then:

   a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric series, then:

   a(n) = a(n-1) . r

where r is the common ratio.

The given series is:

      5000 + 1000 + 200 +. . . .

and the number of terms is 5.

In the given series:

a(1) = 5000

a(2) = 1000

a(3) = 200

Notice that

a(2)/a(1) = 1000/5000 = 0.2

a(3)/a(2) = 200/1000 = 0.2

Since the ratio of consecutive terms are constant, then the given series is a geometric series. Furthermore, its ratio, r = 0.2

Sum formula for the first n term of a geometric series is:

S(n) = a(1) . (1 - rⁿ)/(1 -r)

Substitute n = 5, a(1) = 5000, and r = 0.2

S(5) = 5000 . (1 - (0.2)⁵)/(1 - 0.2)

S(5) = 5000.  (0.99968) / 0.8

       = 6248

Since the number of terms is not much we can also evaluate the sum directly. Write all the terms until n = 5.

a(4) = 200 . (0.2) = 40

a(5) = 40 . (0.2) = 8

Hence, the series is:

5000+1000+200+40+8 = 6248.

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The given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference

What is an arithmetic sequence?

An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.

here the given sequence is 0,1,3,6,10,......is an arithmetic sequence

then the common difference between the consecutive terms is constant

lets check take two consecutive terms as 0 and 1 then the difference is 1

take 1 and 3 then common difference is 3-1 =2

take 3 and 6 then common difference is 6-3 =3

take 6 and 10 then common difference is 10-6=4

.............in the same way we check for other terms also

and found that the common difference is not same

Hence the given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference

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

[tex]\\[/tex]

[tex]33\div x=3\\[/tex]

multiplying both sides by x

[tex]33=3x\\3x=33[/tex]

dividing by 3 both sides

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

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[tex]\textcopyright ELIZA[/tex]

Answer:

x = 11

Step-by-step explanation:

33/x = 3

33 = 3x

x = 33/3

x = 11

Hope it helps!!!

The domain of f is [-5, ∞) because the vertex is the global minimum of a parabola that opens up.

The domain of any polynomial, including quadratics, is (–∞, ∞).

The domain of a parabola is always all real numbers (sometimes written (−∞,∞). The domain is all real numbers because every single number on the x− axis results in a valid output for the function (a quadratic).

When x=−b2a, y=c−b24a. Therefore the maximum or minimum value of the quadratic is c−b24a. Whether it is the maximum or minimum can be determined by examining the sign of a. If a is positive, then the range is y≥c−b24a

Hence, The range here is [-5, ∞), because the vertex is the global minimum of a parabola that opens up, and the global minimum is the lowest value.

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Answer: -8/11

Step-by-step explanation:

apply the formula

x sub 2- x sub 1

over

y sub 2 - y sub 1

yw

The new mean of a distribution of tests would be 175 and the new standard deviation of a distribution of tests would be 10 which is unchanged.

We have been given that in the question:

Mean of data = 80

Standard deviation = 10.

Then,  every score is doubled and 15 is added to each score.

The mean of a distribution is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.

a) Mean of new data

The mean of the data rises by the same amount when a constant value is applied to each observation.

Mean of new score =

μ' = 2μ + 15 = 2(80) + 15 = 175

b) Standard deviation of new data

Every observation has a constant value added to it, therefore the standard deviation stays constant.

The standard deviation of the new score =

σ' = σ = 10

Therefore, the new mean and standard deviation would be 175 and 10 respectively.

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Using basic mathematical operations such as addition and subtraction, the beaker now has 5.2 ml of liquid.

Basic mathematical operations include addition, subtraction, multiplication, and division.

Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.

If a scientist measures 4.62 ml of a chemical into a beaker, then takes out 0.67 ml of the chemical, and finally adds 1.25 ml of water into the beaker, subtracting the amount of chemical taken out from the initial amount of chemical and adding the amount of water, we can solve how much liquid is in the beaker.

4.62 ml - 0.67 ml + 1.25 ml = 5.2 ml

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Answer:

7/8 if you divide you will get your answer

The correct location on the table is:

An equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=7x+2. Where:

a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex] .

b= the constant term that represents the y-intercept.

For the given example: a=7 and b=2.

For solving  linear equations, you should organize variables on one side of the equation and the numbers on the other side. When a number or variables change side, its signal also is changed.

       x= 9*3

       x=27

      Therefore, x≠3

       x=-9+6

       x= -3

      Therefore, x≠3

       x= 5 -2

       x= 3

      Therefore, x=3

       x= 12/5 + 3/5

       x= 15/5

      x=3

      Therefore, x=3

       14x=42

       x=3

      Therefore, x=3

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Answer:

(2A)/(r^2)=pi

Step-by-step explanation:

The goal is to get pi by itself, so you have to move all the other elements over

2A=pir^2

(2A)/(r^2)=pi

The square root of the 15384 by division method is a 124.032.

According to the statement

We have to find that the square root with the division method.

So, For this purpose, we know that the

The long division is the mathematical method for dividing large numbers into smaller groups or parts

And

A generalised version of this method called polynomial long division is also used for dividing polynomials

From the given information:

The number is a 15384.

And then

Firstly in this number by the squaring of the same number and by this method after going down until the remainder is zero.

And after solving the square root of 15384

The answer will become 124.032.

So, The square root of the 15384 by division method is a 124.032.

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Answer:

2

Step-by-step explanation:

Given equations:

[tex]\begin{cases}ab=a-b\\\\\dfrac{a}{b}+\dfrac{b}{a}-ab\end{cases}[/tex]

Rewrite the second equation as a rational expression:

[tex]\begin{aligned}\implies \dfrac{a}{b}+\dfrac{b}{a}-ab & = \dfrac{a}{b} \cdot \dfrac{a}{a}+\dfrac{b}{a} \cdot \dfrac{b}{b}-ab\cdot \dfrac{ab}{ab} \\\\&=\dfrac{a^2}{ab}+\dfrac{b^2}{ab}-\dfrac{(ab)^2}{ab}\\\\&=\dfrac{a^2+b^2-(ab)^2}{ab}\\\\\end{aligned}[/tex]

Substitute the first equation  [tex]ab=a-b[/tex]  into the rational expression:

[tex]\begin{aligned}\implies \dfrac{a^2+b^2-(a-b)^2}{ab}&=\dfrac{a^2+b^2-(a^2-2ab+b^2)}{ab}\\\\&=\dfrac{a^2+b^2-a^2+2ab-b^2}{ab}\\\\&=\dfrac{2ab}{ab}\\\\&=2\end{aligned}[/tex]

Therefore, the possible value of the given expression is 2.

The restrictions on the variables x and y of the equation

(3y-12)/(2y+4) ÷ (6y-24)/(8+4y) be y ≠ 4 and y ≠ -2

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 exists as pursues: Expression: (Math Operator, Number/Variable, Math Operator)

Let the equation be (3y-12)/(2y+4) ÷ (6y-24)/(8+4y)

simplifying the equation, we get

(3y-12)/(2y+4) × (8+4y)/(6y-24)

⇒ (3y-12)/(2y+4) × 2(4+2y)/2(3y-12)

⇒ 2/2 = 1

If y = 4 ⇒ denominator (6 × 4 - 24) = 0 = ∞

Similarly, If y = -2 ⇒ denominator ((2 × -2) + 4) =0 = ∞

So, y ≠ 4, y ≠ -2

How to find restrictions on the variables?

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Answer:

Coefficient(s):9

Variable(s):x,y

Constant(s):-22

Step-by-step explanation:

The second graph shows a set of ordered pairs that represent a function.

Functions are an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

here, we have,

A relation is a function in which every x value will have different y values, this represents "every input will have unique output" part of the definition of the function,

When we observe the graphs (attached), we will notice in graph 1) there are two ordered pairs with same x value and different y values, (2, -1) and (2, -3), which is making them out of the list of being a function,

In graph 2) we have, (-2, 2), (1, 1), (5, 4), (-4, -4), (2, -5) and (4, -3), in this all the order pairs have different x-y values, therefore, this set of ordered pairs that represent a function.

Hence, the second graph shows a set of ordered pairs that represent a function.

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The question do not have graph, so, the question is solved for the graph attached.

Answer:

36÷7.2=5

So this is the answer

Answer:

the answer is 225

Step-by-step explanation:

[tex] \frac{300 \times 25}{100} = 75[/tex]

this is the amount of discount

so remove it from the original price

300 - 75 = 225

which is the price after the 25% discount

hope this helps

C. y = 1/3 x - 9

The slope-intercept form is one way to represent a linear function that is set equal to y.

Simplifying and Solving

To find slope-intercept form from point-slope you should simplify the equation and then solve for y.

Firstly, distribute the 1/3.

Then, subtract the 6 from both sides.

This means that the slope-intercept form is y = 1/3 x - 9.

What Slope-Intercept Form Shows

We use slope-intercept form for 2 main reasons; it shows the slope and the y-intercept of a line (hence the name). The formula of slope-intercept is y = mx + b. In this formula, m is the slope and b is the y-intercept.

So, the slope of the line above is 1/3. The y-intercept of the line is -9.

According to the question, the region is bounded by the curve with the given data as [tex]x = y^{3} , x=1, y=0.[/tex]

To compute the volume of the solid, use the disk method. The given object is rotated along the horizontal axis with the disk cross sectional area and the volume can be written as:

[tex]v=\int\limits^a_b {\pi x^{2} } \, dx[/tex]

As per question, when x = 1 then the value of y is: y = 1

Now, substituting calculated values in the expression:

[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx[/tex]

Substitute the value of the variable 'x':

Therefore, the expression can be written as:

[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx=\int\limits^0_1 {\pi (y^{3}) ^{2} } \, dx=\frac{\pi }{7}=0.448[/tex]

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its stem and leaf just took the test

Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.

In order to help visualize the shape of a distribution, a stem-and-leaf presentation or stem-and-leaf plot is a tool for displaying quantitative data in a graphical manner, comparable to a histogram. They are helpful tools for exploratory data analysis and developed from Arthur Bowley's work in the early 1900s.

This is simply accomplished by creating a draft of the unsorted leaves before arranging them in the final stem-leaf display. On the Undergraduate and graduate levels, you may find a number of examples that have been solved and even obtain expert assistance to learn the subject of stem and leaf plots.

A school is studying Math for Data and Financial Literacy standardized test scores.

Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.

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Answer:

x = 1 if the perimeter is 42

Step-by-step explanation:

Given

s = 4x + 10

when Perimeter = 42, what is x?

Solution

Perimeter = 3s

Perimeter = 3(4x +10)                Remove the brackets

Perimeter = 12x + 30

Let the Perimeter = 42

42 = 12x + 30                              Subtract 30 from both sides

42-30 = 12x + 30-30                   Combine

12 = 12x                                        Divide by 12

12/12 = 12x/12

x = 1

Answer:

Solution

verified

Verified by Toppr

Correct option is C)

Perimeter of window P=2y+3x=16    

⇒y=

2

16−3x

​

  ....(1)

Area A=xy+

4

3

​

​

x

2

=

4

3

​

​

x

2

+x(

2

16−3x

​

)

A=8x+(

4

3

​

​

−

2

3

​

)x

2

dx

dA

​

=8+(

4

3

​

​

−

2

3

​

)2x

For maxima or minima,

dx

dA

​

=0

⇒4−

4

(6−

3

​

)

​

x=0.

∴x=

6−

(3)

​

16

​

=

36−3

16(6+

3

​

)

​

=

33

16(6+1.73)

​

=

33

16(7.73)

​

=

33

123.68

​

⇒x=3.75 nearly.

Now,  

dx

2

d

2

A

​

=2(

4

3

​

​

−

2

3

​

)<0

Hence A is maximum.

By (1),

y=2.375

Step-by-step explanation:

Answer:  [tex]A^{2} + B^{2}[/tex] correct answer.

Step-by-step explanation:

What is Pythagorean Theorem?

Image result for Pythagorean theorem

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation.

                               [tex]A^{2} + B^{2} + C^{2}[/tex]

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.

So, We can write,

Consider the triangle given above:

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

                    [tex]Hypotenuse^{2}[/tex] = [tex]Perpendicular^{2}[/tex] + [tex]Base^{2}[/tex]

                           [tex]C^{2} = A^{2} + B^{2}[/tex]

Hence,

                              [tex]A^{2} + B^{2}[/tex] correct answer.

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Answer:

[tex] 81g^4 [/tex]

Step-by-step explanation:

When you raise a product to a power, raise each factor of the product to the power.

Rule:

[tex] (ab)^n = a^nb^n [/tex]

Our problem:

[tex] (3g)^4 = 3^4g^4 = 81g^4 [/tex]