Elimination method.

The next in the pattern is ← and the conjecture is a rotation by 90 degrees in the clockwise direction

The pattern is given as:

↑, →, ↓

In the above pattern, we can see that each arrow is rotated 90 degrees in the clockwise direction

When the arrow ↓ is rotated in this direction, we have:

←

Hence, the next in the pattern is ← and the conjecture is a rotation by 90 degrees in the clockwise direction

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The value of n in [tex]^nC_3=120[/tex] is 10 .

It is given that [tex]^nC_3=120[/tex]

Using equation (1) , we get

   [tex]\frac{n!}{3!(n-3)!} =120\\\ \\\frac{n(n-1)(n-2)(n-3)!}{3\times2(n-3)!} =120\\\\\n(n-1)(n-2)=720\\[/tex]            ....(2)

Prime factorization of 720 is given by

  [tex]720=2^4\times3^2\times5\\720=10\times9\times8[/tex]

720 can be written as [tex]10(10-1)(10-2)[/tex]

Putting above value in equation (2) , we get

 [tex]n(n-1)(n-2)=10(10-1)(10-2)[/tex]

On comparing LHS = RHS we get

  n = 10

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The explicit formula of the sequence is Tn = 30 - 20(n - 1)

The recursive formula of the sequence is given as

f(1) = 30, f(n) = 2 • f(n - 1) - 50

The above means that

f(n) = 2 • f(n - 1) - 50

f(1) = 30

Substitute 2 for n

So, we have

f(2) = 2 • f(2 - 1) - 50

Evaluate the difference

So, we have

f(2) = 2 • f(1) - 50

Substitute f(1) = 30 in f(2) = 2 • f(1) - 50

f(2) = 2 • 30 - 50

Evaluate

f(2) = 10

Substitute 3 for n

So, we have

f(3) = 2 • f(3 - 1) - 50

Evaluate the difference

So, we have

f(3) = 2 • f(2) - 50

Substitute f(2) = 10 in f(3) = 2 • f(2) - 50

f(3) = 2 • 10 - 50

Evaluate

f(3) = -30

So, we have the first three terms to be

30, 10, -10

The above represents an arithmetic sequence, where

First term, a = 30

Common difference = -20

The nth term of the sequence is

Tn = a + (n - 1)d

So, we have

Tn = 30 - 20(n - 1)

Hence, the explicit formula of the sequence is Tn = 30 - 20(n - 1)

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Answer:

Step-by-step explanation:

The equation which has exactly one solution is .

The equation which has exactly infinitely many solutions is .

The solution to  (f + g) (x) is Option B: |2x +1| + 1

We are given the functions;

f(x) = |2x +1| + 3

g(x) = -2

Now, we want to solve for  (f + g) (x). From operations of functions, we know that there are different operations which could  include addition, division, multiplication and subtraction. However, in this case;

(f + g) (x) simply means;

(f + g) (x) = f(x) + g(x)

Thus, we have;

(f + g) (x) =  |2x +1| + 3 + (-2)

=  |2x +1| + 3 - 2

=  |2x +1| + 1

Thus, the solution to  (f + g) (x) is Option B: |2x +1| + 1

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Answer:

Freshman      Sophomore     Junior      Senior
      3.5                  3.25             3.0           3.2

Step-by-step explanation:

Average GPA = Total GPA / number of years

Freshman Year (1 year): 3.5 = 3.5

Sophomore Year (2 years) = (3.5 + 3.0) = 6.5/2 = 3.25

Junior Year(3 years) =  (3.5 + 3.0 + 2.5)/3 = 9.0/3 = 3.0

Senior Year(4 years) = (3.5 + 3.0 + 2.5 + 3.8) = 12.8/4 = 3.2

Answer:

-1

Step-by-step explanation:

[tex]2(3x-1) \geq 4x-6 \\ \\ 6x-2 \geq 4x-6 \\ \\ 2x \geq -4 \\ \\ x \geq -2[/tex]

Answer:

-1 is the answer

Step-by-step explanation:

The amount invested in each type of investment should be $17,000 and $18,000, respectively, as this problem is based on simple interest.

Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

based on the facts provided;

Calculating the investment amount:

Since the certificate of deposit is assumed to be x in this instance, the bond should be $35,000 - x.

The formula now should be

($35,000 - x) - x = $1,000

$35,000 - 2x = $1,000

$34,000 = 2x

x = $17,000

So, the bond should be

= $35,000 - $17,000

= $18,000

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Due to modulus there can be two answers, one with greater than equal to and one with less than equal to. So the answer is 11 and -7.

Solve the inequality |x−2|≥9

Inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa.

a) |x−2|≥9 = x-2≥ 9

=> x≥ 9+2

=> x≥ 11

b)  |x−2|≥9 = x-2≥ -9 (when sign the negative the greater than equal to sign changes to less than equal to sign)

= x ≤ -9+2 ≤-7

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Step-by-step explanation:

two people like neither animal

Answer:

13

Step-by-step explanation:

15+75-32-45

90-32-45

58-45

13

Check the picture below, so the ellipse looks more or less like so.

[tex]\textit{ellipse, vertical major axis} \\\\ \cfrac{(x- h)^2}{ b^2}+\cfrac{(y- k)^2}{ a^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=3\\ k=-8\\ a=5 \end{cases}\implies \cfrac{(x-3)^2}{b^2}+\cfrac{(y-(-8))^2}{5^2}=1 \\\\\\ \stackrel{\textit{we also know that}~\hfill }{c=3\hspace{3.5em} 3=\sqrt{5^2 - b^2}} \implies 3^2=5^2-b^2\implies b=\sqrt{5^2-3^2} \implies \boxed{b=4} \\\\\\ \cfrac{(x-3)^2}{4^2}+\cfrac{(y-(-8))^2}{5^2}=1\implies \cfrac{(x-3)^2}{16}+\cfrac{(y+8)^2}{25}=1[/tex]

Answer:

6

Step-by-step explanation:

17 is the total length

11 is part of the length

17-11 =6

The correct answer is x/ 7 = 9. Option D

Algebraic expressions are simply defined as expressions comprising of terms, variables, coefficients, constants and factors.

They are also made up of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc.

It is important to note that quotient represents division.

Example;

The quotient of 1 and 2 is 1/ 2

The quotient of 3 and 4 is 3/ 4

From the information given, we have that;

The quotient of a number and 7 is 9

Let the number be x

We have;

x/ 7 = 9

Thus, the correct answer is x/ 7 = 9. Option D

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If the width of the painting is w, then its length is 2w. Then, since the frame is 2 inches thick on each side of the painting, its width is w+4 and its length is 2w+4. So the area of the rectangle bounded by the frame (which includes both the area of the frame and the area of the painting) is (w+4)(2w+4).

The area of the painting is w×2w=2w2, and the area of the frame is 196 square inches, so the area of the two combined is 2w2+196. However, that is the same area as the other one I described, so we can then equate the two, i.e. (w+4)(2w+4)=2w2+196. You can then solve that equation for w, and hence find all of the relevant dimensions.

The volume of the cylinder is 1809.5 cubic units.

The volume of a cylinder is equal to the product of the area of the circular base and the height of a cylinder. The volume of a cylinder is defined as the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it

V = πr²h

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

Given that a cylinder with a radius of 6 and height of 16.

Here r = 6 and h = 16,

the volume of a cylinder = πr²h

the volume of a cylinder = π(6)²×16

the volume of a cylinder = 1809.5 cubic units

Thus, the volume of the cylinder is 1809.5 cubic units.

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Answer: Yes it looks correct i also did it myself and got the same answer

Step-by-step explanation:

According to the parameters given, the rule again for graph of g after so transformations of a function F(x) = 2x - 1 is  g(x) = -4x + 4.

The graph for the given function defined by the equation;

F(x) = 2x - 1

Initially, the graph of g is a three-unit translation, so we have;

Then comes a vertical stretch by such a factor of two and a reflection in the x axis.

The above means that graph must all be multiplied by 2 and that x values containing x are now considered to be -x.

And an x-axis reflection yields;

Thus, the rule for making the graph of function g(x) is by; g(x) = -4x + 4.

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Hence proved, x*0 = 0.

A statement that is assumed to be true is referred to as a postulate, axiom, or assumption. It is used as the foundation for further deductive reasoning and arguments.

Given many of the typical formulations of the Peano axioms, for example, this is the base case for the definition of multiplication, so it’s an axiom, not a theorem.

x*o = 0

By using an example as rings:

Therefore, By definition of negotiation

= x + (-x)

0 = x · 1 + ( - x) where 1 is the multiplicative identity,

Now,

= x · ( 0 + 1) + ( - x)

Therefore by distributive law,

= x · 0 + x · 1 + (-x)

Where 1 is the multiplicative identity.

By definition of negotiation,

= x · 0  + x + (-x)

= x · 0  + 0

Where 0 is the additive identity.

= x · 0

Therefore, x*0 = 0

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Answer:

  12. BC = 8

  14. JL = 18

Step-by-step explanation:

You want to apply the Segment Addition theorem to two problems.

The segment addition theorem tells you the whole is the sum of the parts. The equation for each problem reflects this fact. When given values are substituted, the answer becomes clear.

  AB +BC = AC

  7 +BC = 15

  BC = 8 . . . . . . . . subtract 7

  JK +KL = JL

  8 +10 = JL = 18

__

Additional comment

It often helps to draw a diagram.

Answer:

1024

Step-by-step explanation:

8^2=8x8=64

4^2=4x4=16

64x16=1024 :)

Answer: 1024

Step-by-step explanation: 8^2 times 4^2=80. When you square a number, you multiply it by itself. So, 8^2 = 8 times 8 which equals 64. 4^2 = 4 times 4 which equals 16. 64 times 16 = 1024.

Using translation concepts, the graph of square CDEF after a rotation 270º counterclockwise around the origin is given at the end of the answer.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The rule for a rotation 270º counterclockwise around the origin is:

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

Hence the vertices of the rotated graph will be given as follows:

The graph with these vertices is given at the end of the answer.

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Answer:

Statements:

1) -2(x-4)=2x+12

2) -2x+8=2x+12

3) -4x+8=12

4) -4x=4

5) x=-1

Reasons:

1) Given

2) Distributive Property

3) Combine like terms/Subtraction Property of Equality (subtract 2x from both sides).

4) Subtraction Property of Equality

5) Division Property of Equality

The horizontal limit of the given function is given as follows:

y = -2/5.

A limit is given by the value of function f(x) as x tends to a value. For a standard function, we just calculate the numeric value of a function.

However, in this problem, an horizontal limit means that x goes to infinity, hence it we replace and calculate the numeric values we would have a fraction of infinity divided by infinity as a result, which is an undetermined limit.

Then, we use the algorithm to solve an infinity limit, in which we consider just the term with the highest exponent of both the numerator and of the denominator.

Hence:

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{2x^3}{-5x^3} = \lim_{x \rightarrow \infty} -\frac{2}{5} = -\frac{2}[5}[/tex]

Because the limit of a constant is the constant, hence the horizontal limit of the given function is given as follows:

y = -2/5.

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48 persons are present at the gathering. There are seven times more adults than children in the world. The number of women is two times that of men. If there are five females (young women) in attendance. The total number of male adults are15

The total number of people are in the party is equal to 48

Let the number of children be x

So, the number of adults in the party is equal to 7 x

x + 7 x =48 ( This is a linear equation)

So, the number of children in the comes to be 6

Number of adults in the party = 6 * 7 = 42

Now let the number of males be y

So total number of females = 2 y

Y+2y = 48 ( This is a linear equation)

Y=16

Therefore, the number of males is 16 and the number of females is 32

The number of children in the party is 6 and the female child is equal to 5

Then, the number of male children =6-5 = 1

So total number of males in the party is equal to 16

Adult males =total number of males - number of male children

=16 - 1 = 15

Hence the total number of male adults =15

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Answer:

22 weeks

Step-by-step explanation:

595+65=660

22x30=660

so he could buy a bicycle and owes his sister the money after 22 weeks

The values of a and b make this equation true/sqrt648 = /sqrt2^a x 3^b will be a = 3 and b = 4.

It should be noted that from the information given, the equation is given as:

✓648 = ✓(2^a × 3^b)

when a = 3

b = 4

This will be illustrated as:

✓648 = ✓(2^a × 3^b)

✓648 = ✓(2³ × 3⁴)

✓648 = ✓(8 × 729)

Therefore, the values of a and b make this equation true? /sqrt648 = /sqrt2^a x 3^b will be a = 3 and b = 4.

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Answer:

10 ≤ x ≤ 19

Step-by-step explanation

The sum of the three lengths is 9 + 12 +x =  21 + x

We know the sum ranges from 31 to 40

So we get the inequality

31 ≤ 21 + x ≤  40

Subtracting 21 from each part of this inequality give

31-21 ≤ x ≤40-21

10 ≤ x ≤ 19

The compound inequality to show the possible lengths of the third side is 10 ≤ x ≤ 19.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now it is given as,

Range of sum of three lengths of a fence = 31 to 40 inches

Length of two sides = 9 and 12 inches

Length of third sides = x inches

So, length of sum of three lengths of a fence = 9 + 12 + x

⇒  length of sum of three lengths of a fence = 21 + x

∵ Range of sum of three lengths of a fence = 31 to 40 inches

31 ≤ length of sum of three lengths of a fence ≤ 40

⇒ 31 ≤ 21 + x ≤ 40

Subtracting 21 we get.

10 ≤ x ≤ 19

Thus, the compound inequality to show the possible lengths of the third side is 10 ≤ x ≤ 19.

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John's speed on each section of the walk are 4 km per hour, 0 km per hour and 1.5 km per hour

On the first section, we have the following points

(x, y) = (0, 0) and (1.5, 6)

The speed is calculated as

Speed = (y2 - y1)/(x2 - x1)

This gives

Speed = (6 - 0)/(1.5 - 0)

Evaluate

Speed = 4

On the second section, we have the following points

(x, y) = (1.5, 6) and (2, 6)

The speed is calculated as

Speed = (y2 - y1)/(x2 - x1)

This gives

Speed = (6 - 6)/(2 - 1.5)

Evaluate

Speed = 0

On the third section, we have the following points

(x, y) = (2, 6) and (6, 0)

The speed is calculated as

Speed = (y2 - y1)/(x2 - x1)

This gives

Speed = (0 - 6)/(6 - 2)

Evaluate

Speed = -1.5

Hence, John's speed on each section of the walk are 4 km per hour, 0 km per hour and 1.5 km per hour

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