Find the least common multiple of each pair of polynomials.
9(x+2)(2 x-1) and 3(x+2)

The given series is an arithmetic series and its sum is equal to 24

The summation notation is used to express long summation in a series into a single formula.

The given series is:

[tex]\sum\limits^8_{n=1} {\frac{2}{3}n }[/tex]

Expand the series:

[tex]\sum\limits^8_{n=1} {n }=\frac{2}{3}\sum\limits^8_{n=1} {n }[/tex]

= 2/3 ( 1 + 2 + 3 + .... + 8)

The term inside the bracket is an arithmetic series with:

a(1) = 1

d = a(2) - a(1) = 1

The sum of the first n terms of an arithmetic series is given by:

S(n) = n/2 (2.a(1) + (n -1) . d)

Substitute n = 8, a(1) = 1, and d = 1 into the formula

S(8) = 8/2 (2 + (8-1) . 1)

S(8) = 4 . 9 = 36

Hence,

[tex]\frac{2}{3}\sum\limits^8_{n=1} {n } = \frac{2}{3}\times36=24[/tex]

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A function which models P(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited is: D) P(t) = 310(1.01)^t.

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = eˣ

Generally speaking, a mathematical model for any quantity (pollen grains) that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + 0.01r)^t

Where:

Substituting the given parameters into the formula, we have;

P(t) = 300(1 + 0.01r)^t

P(t) = 310(1.01)^t

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Complete Question:

Keith modeled the growth over several hundred years of a tree population by estimating the number of the trees’ pollen grains per square centimeter that were deposited each year within layers of a lake’s sediment. He estimated there were 310 pollen grains per square centimeter the first year the grains were deposited, with a 1% annual increase in the number of grains per square centimeter thereafter. Which of the following functions models P(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited?

A) P(t) = 310^t

B) p(t) = 310^{1.01t}

C) P(t) = 310(0.99)^t

D) P(t) = 310(1.01)^t

Each assertion is backed up by property. This same transitive property of equality supports this.

If x, y, and z are really the three quantities, as well as x is connected with y by some rule, and y is connected to z by the same rule, we can say x is connected to z using the same rule.

x=5

b=5

x=b.

That transitive property that equality justifies this.

because :

Transitive Property of Equality  show  If a = b and b = c, then a = c.

so in the given statement the   x=5  and b=5  so x=b.

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The required domain of the function is x = -2, and the required range of is -2 ≤ y <1. And also it is not function.

Given that,
The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case. The domain and the range of the relation and determine whether the relation is a function is to be determined.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

Here, From the graph, the value is only defined at x = -2, Thus, its domain is x = -2 And also the at x = -2 the vertical line is from -2 to 0.99 Thus, its range is -2 ≤ y <1.

Since the curve has a number of pre-images more than one at a single value of x thus it is not a function.

Thus, the required domain of the function is x = -2, and the required range of is -2 ≤ y <1. And also it is not function.

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Answer:

(- 8) × (- 2/3) = 16/3 = 5 1/3

Hope this helps :)

Angle ∠ABC and angle ∠CDE are supplementary angles. Then the value of the variable x will be 18°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

From the figure, the angle ∠ABC and angle ∠CDE are supplementary angles. Then we have

∠ABC + ∠CDE = 180°

2x + 8x = 180°

10x = 180°

x = 180° / 10

x = 18°

Then the value of the variable x will be 18°.

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Answer:

Question 1:

1. - 4

2. 4

3. - 15

4. 15

Question 2:

1. - 6

2. 6

3. - 6

Hope this helps :)

Answer: It would be 17

It would be 17 because if you take 90 and subtract 39, you would get 51. Then if you take 51 and divided it by 3 you would get 17.

Answer:

x=17

Step-by-step explanation:

3x+39=90

3x=90- 39

3x/3=51/3

x=17

The measure of CFD is 66°.

It should be noted that vertically opposite angles are equal.

Therefore, AFE may be equal to BFD.

In this case, AFE is given as 108° while one of the other angles is given as 42°.

Therefore, the value of CFD will be:

= 102° - 42°

= 66°

The value of CFD is 66°.

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Answer:

16.802

Step-by-step explanation:

I just used a calculator

The vertical translation equation of the given equation is y = 2x-(2/5). (First option)

You can do things with equations of the form y=f(x) that modify the graph in various ways.

Vertical movement means moving up and down the graph of a function. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. The form of the function remains the same, known as moving the chart along the Y axis.

Vertical translation translates each point on the graph by k units vertically and the graph/chart by k units vertically.

The vertical translation equation of y=2x-1 by 3/5 units up is y = 2x-(2/5) as y = f(x)+3/5

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The given statement that A triangle with an angle that measures greater than 90° is a right triangle is a FALSE statement.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

A right-angle triangle is a triangle whose any one interior angle is 90°.

Let's say the remaining angles are x and y degrees.

The sum of all interior angles is 180 degrees.

So,

x + y + 90 = 180

x + y = 90

x = 90 - y ⇒ x ≤ 90°

y = 90 - x ⇒ y ≤ 90°

Hence "The given statement that A triangle with an angle that measures greater than 90° is a right triangle is a FALSE statement".

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The probability tree for each outcome is drawn.

Probability is a mathematical concept concerned with determining the likelihood of occurrence of a given event, which is demonstrated as a range of 1 and 0. A certainty is an event with such a probability of one.

Now, as per the given question;

Kelly's first serve percentage is 40% = 0.4.

Kelly's second serve percentage is 70% which comprises of successful and faulty serve.

The probability that the second serve will be successful is;

= 0.6×0.7

= 0.42

Thus, probability that the second serve will be successful is 0.42.

Now, the probability the second serve will be unsuccessful is;

= 0.6×0.3

= 0.18

Thus, probability that the second serve will be unsuccessful is 0.18.

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The equation of the line y = 4.2x + 7.9 expressed in standard form is 42x - 10y = -79.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Given the equation of a line, multiply both sides by 10 to turn the decimals into integers.

y = 4.2x + 7.9

10y = 10(4.2x + 7.9)

10y = 42x + 79

Rewriting it in standard form ax + by = c,

10y = 42x + 79

42x - 10y = -79

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Answer:

6

Step-by-step explanation:

2/.03 = 66.66...7 times .09 = 6

The number is 66.67. And the 9% of the number 66.67 will be 6.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Let the number be 'x'. Then the equation is given as,

3% of x = 2

0.03 x = 2

x = 2 / 0.03

x = 66.67

Then the 9% of that number is calculated as,

⇒ 9% of 66.67

⇒ 0.09 x 66.67

⇒ 6

The number is 66.67. And the 9% of the number 66.67 will be 6.

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The first second third fourth and fifth term of the sequence

[tex]a_{n}[/tex] = 3n + 2 are 5, 8, 11, 14, 17 and 20 respectively.

According to the given question.

We have formula for finding the terms of the sequence, [tex]a_{n}[/tex]  = 3n + 2 .

Therefore, the first term of the sequence [tex]a_{n}[/tex]  = 3n + 2 is given by

[tex]a_{1}[/tex] = 3(1) + 2 = 5

The second term of the sequence [tex]a_{n}[/tex]  = 3n + 2 is given by

[tex]a_{2}[/tex]  = 3(2) + 2 = 8

The third term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by

[tex]a_{3}[/tex]  = 3(3) + 2 = 11

The fourth term of the sequence [tex]a_{n}[/tex] = 3n + 2 is given by

[tex]a_{4}[/tex] = 3(4) + 2 = 12 + 2 = 14

The fifth term of the sequence [tex]a_{5}[/tex] = 3n + 2 is given by

[tex]a_{5}[/tex]  = 3(5) + 2 = 15 + 2 = 17

The sixth term of the sequence [tex]a_{5}[/tex] = 3n + 2 is given by

[tex]a_{6}[/tex]  = 3(6) + 2 = 18 + 2 = 20

Hence, the first second third fourth and fifth term of the sequence

[tex]a_{n}[/tex] = 3n + 2 are 5, 8, 11, 14, 17 and 20 respectively.

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Applying the segment addition postulate, the value of r is determined as: A. 10.

A perpendicular bisector is a line segment which divides another line segment into two equal parts, that is, the segments formed have equal lengths.

Since point G lies on the perpendicular bisector of segment DM, therefore:

DG = GM

Given the following:

DM = 25

GM = 4r - 28

DG = r + 3

Therefore:

DG + GM = DM [segment addition postulate]

Substitute

r + 3 + 4r - 28 = 25

Combine like terms

5r - 25 = 25

5r = 25 + 25

5r = 50

5r/5 = 50/5

r = 10

Thus, applying the segment addition postulate, the value of r is determined as: A. 10.

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A composite number is one that is greater than one and contains more than 2 factors.

For the given statement;

9 is divisible by 3 can be written as;

9/3  = 3 ; as 3 is the prime number, the statement is regarded as prime statement.

For, 9 is odd.

As, 9 is not a prime but a composite number, the statement is considered as the compound statement.

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Answer: 30

Step-by-step explanation:

this is so easy

Answer:

1for 30 students i would need 90

The values of the function for x = 2.

Part a: y = 7- |x|

The modulus function returns the magnitude and absolute value of a number, regardless of whether it is positive or negative. The modulus function is represented by y = |x| or f(x) = |x|, where f: R ---> R and x ∈ R.

Put x = 2 in the function;

y = 7- |2|

y = 7 - 2

y = 5

Part b: y = x²-1

put x = 2

y = 2²-1

y = 3

Part c: y = √x+14​

Put x = 2

y = √2+14​

y = √16​

Squaring both side;

y = 4

Thus, the values for the function are obtained.

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Answer:

17. Invalid

Step-by-step explanation:

It is invalid because not only the angles matter but also the measurement of the sides, if one side is bigger than the other, it cannot be a square.

The likelihood that a five-card poker hand will contain a flush (five cards of the same suit). = 0.001981

Probability is extremely important in everyday life. Weather forecasting, sports as well as gaming strategies, purchase or sale of insurance, online shopping and online games, blood group determination, and political strategy analysis

A standard deck of cards contain 52 cards. A five - card poker hand select 5 of the 52 cards.

C(52 , 5) = [tex]\frac{52 !}{5 !(52-5) !}[/tex]

              = 52!/(5!47!)

             = 2,598,960

Number of hand contenting a flush:

we need to select 1 of the 4 suits and then select 5 of the 13 cards from this suit.

C(4 , 1) = [tex]\frac{4 !}{1 !(4-1) !}[/tex]

           = 4!/(1!3!)

           = 4

C(13 , 5) = [tex]\frac{13 !}{5 !(13-5) !}[/tex]

             = 13!/(5!8!)

              = 1287

Using the product rule:

4*1287 = 5148

Probability:

5148 of the  2,598,960 hands will contain a flush.

The probability is calculated by dividing the number number favorable outcomes by the total number of possible possibilities.

P = 5148/ 2,598,960

= 33/16660

the likelihood that a five-card poker hand will contain a flush (five cards of the same suit). = 0.001981

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Answer:

Step-by-step explanation:

to find the bottom base you add the two numbers that make it

5+18=23

now put everything in the formula

[tex]\frac{1}{2}*12(12+23)\\[/tex]

parathesis first

12+23=35

[tex]\frac{1}{2} *12*35[/tex]

multiply in order

6*35

210

Step-by-step explanation:

i’m doing my geometry homework with the equation 1/2h(b1+b2) but i can’t figure this one out. please help

1/2h (b1 + b2) is the formula for finding the area of ​​the figure (trapezoid)

1/2 * 12 (18 + 5 + 12)=

6 * 35=

210 units²

Answer:

Hello!

Yes, these ratios are equivalent!

Step-by-step explanation:

Since, when we multiply both the numerator and denominator by the same number then we get an equivalent fraction.

We use multiplication or division. Whatever you do to one number of the ratio. You have to do the same thing to the other using multiplication or division. And you get an equivalent ratio.

Hope this helps!

Answer:

  S = (-1, -2)

Step-by-step explanation:

You want the coordinates of S on QR such that QS : SR = 5 : 2. The end points are Q(-11, -12) and R(3, 2).

The coordinates of the dividing point S are the weighted sum of the end point coordinates of Q and R. The weights are the reverse of the division ratio.

  S = (2Q +5R)/(2+5)

  S = (2(-11, -12) +5(3, 2))/7 = (-22+15, -24 +10)/7 = (-7, -14)/7

  S = (-1, -2)

The equivalent expression is 5^6 • 3^12.

Exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

Given:

(5^2 • 3^4)^3

now, using

So,

(5^2 • 3^4)^3

= (5^2)^3 • (3^4)^3

=5^6 * 3^12

Hence, equivalent expression is 5^6 • 3^12

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The two terms of each arithmetic sequence [tex]a_{10}[/tex] = 17 ,[tex]a_{14}[/tex] =34 are d = 17/4 and a = -21.25.

[tex]a_{10}[/tex] = 17

17 = a +9d.............1

[tex]a_{14}[/tex] =34

34 = a + 13d...........2

equating equation 1 and 2

17 = a +9d

34 = a + 13d

d = 17/4

d = 4.25 ..............3

from equation 3

a = -21.25

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Answer:

6

Step-by-step explanation:

Combine like terms:

8u-8u=0

0+6=6

Hope this helps!

Answer:

Profit = $216

Step-by-step explanation:

To solve this, let's first calculate the amount she spent buying 38 shirts at $7 each:

• total spent = 38 × 7

                    = $266

We are told that she then sold 31 shirts at $16 each. Using this information, let us now calculate the total amount she earnt selling these shirts:

• total earnt = 31 × 16

                    = $496

Next, she returned 7 shirts and paid a $2 charge for each returned shirt. Therefore, the amount she spent on returning was:

• total spent returning = 7 × 2

                                     = $14

Therefore she earned a total of $496 and spent $266 and then $14. We can calculate her profit by subtracting the two expenditures from the earnings:

• Profit = $496 - $266 - $14

           = $216

Hence her profit was $216.

Based on figures, Below are the responses to the query.

A. In light of the foregoing, it is necessary to characterize 100% as a whole even though the percentage will change.

B. In light of the foregoing, the percentages 50%, 25%, and 150% will differ and require different descriptions, such as 1/2, 1/4, and 1, respectively.

C, Another example of a fraction is 8/10, or.8, or 80%, hence the diagrams will be different.

D: The diagrams will typically be off by 1/3 or 3.

E. Depending on the illustration (attached), the correct response will be 10%, 1/10, or.1.

In terms of mathematics, a shape or figure is defined as any type of visual representation of an object, including the outer border, outline, and others.

Be aware that the phrase "kept bound to lie on a plane" refers to a plane form or figure.

Consequently, the solutions to the query are provided below.

A. In light of the foregoing, it is necessary to characterize 100% as a whole even though the percentage will change.

B. In light of the foregoing, the percentages 50%, 25%, and 150% will differ and require different descriptions, such as 1/2, 1/4, and 1, respectively.

C, Another example of a fraction is 8/10, or.8, or 80%, hence the diagrams will be different.

The images are attached below

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