Five math questions

2n + 1 will be an odd number.

If the number is divisible by 2 then the number will be an even number. Similarly, the number is not divisible by 2 then the number will be an odd number.

Given

2n+1 is a number where n is a positive integer.

The 2n + 1 is an odd number.

We know that if the integer is multiplied by 2 then it becomes the even number.

So the 2n is an even number.

We know that the sum of an even number and an odd number is an odd number. That is

Even + odd = odd

so 2n + 1 will be an odd number.

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The expression 2n + 1 represents an odd number for any positive integer n.

The expression 2n + 1 represents an odd number for any positive integer n. This can be shown through an algebraic proof.

Let's assume that n is any positive integer. When we multiply 2 by any integer, we always get an even number because an even number multiplied by 2 is always even. Adding 1 to an even number results in an odd number. Therefore, 2n is always an even number, and by adding 1 to it, we get an odd number (2n + 1).

For example, if we take n = 1, then 2n + 1 = 2(1) + 1 = 3, which is an odd number. Similarly, if we take n = 2, then 2n + 1 = 2(2) + 1 = 5, which is also an odd number.

Answer:

1. 35, 32, 29, 26 are in Arithmetic Sequence having common difference - 3.

5. -7, -9, -11, -13 are in Arithmetic Sequence having common difference - 2.

Step-by-step explanation:

1. 35, 32, 29, 26 are in Arithmetic Sequence having common difference - 3.

2. -1. 6, -36, 216 are not in Arithmetic Sequence.

3. -2, -4, -8, -16 are not in Arithmetic Sequence.

4. -1, 1, 4, 8 are not in Arithmetic Sequence.

5. -7, -9, -11, -13 are in Arithmetic Sequence having common difference - 2.

6. 1, -5, 25, -125 are not in Arithmetic Sequence. (Answer)

The 7th term of the geometric sequence described by this explicit formula [tex]a_{n}=7*3^{(n-1)}[/tex] is 5103 ⇒ answer D

Step-by-step explanation:

The explicit formula of nth term in the geometric sequence is

[tex]a_{n}=a(r)^{n-1}[/tex] , where

∵ The explicit formula of a geometric sequence is [tex]a_{n}=7*3^{(n-1)}[/tex]

∵ The explicit formula of nth term in the geometric sequence

   is [tex]a_{n}=a(r)^{n-1}[/tex]

∴ a = 7 and r = 3

∵ We need to find the 7th term

∴ n = 7

- Substitute n by 7 in the formula

∴ [tex]a_{7}=7*3^{(7-1)}[/tex]

∴ [tex]a_{7}=7*3^{(6)}[/tex]

∵ [tex]3^{(6)}=729[/tex]

∴ [tex]a_{7}=7(729)[/tex]

∴ [tex]a_{7}=5103[/tex]

The 7th term of the geometric sequence described by this explicit formula [tex]a_{n}=7*3^{(n-1)}[/tex] is 5103

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The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The number of members in the drama club that are seventh graders is 14.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

5% = 5/100 = 1/20

We have,

Total number of members = 40

Percentage of members who is 7th graders = 35%

The number of 7th graders.

= 35% of 40

= 35/100 x 40

= 35/10 x 4

= 7 x 2

= 14

Thus,

The number of members in the drama club that are seventh graders is 14.

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Answer:

183

Step-by-step explanation:

Add 62 and 59 to get Brians score and then add another 62 to find the combined score.

Their combined score is 183.

To find the combined score of Colin and Brian, we need to add their individual scores.

Given:

- Colin's score: 62

- Brian's score: 59 more than Colin's score

We'll find Brian's score first, then add it to Colin's score to get the combined score.

Brian's score = Colin's score + 59

[tex]\[ \text{Brian's score} = 62 + 59 \][/tex]

[tex]\[ \text{Brian's score} = 121 \][/tex]

Now, to find the combined score:

[tex]\[ \text{Combined score} = \text{Colin's score} + \text{Brian's score} \][/tex]

[tex]\[ \text{Combined score} = 62 + 121 \][/tex]

[tex]\[ \text{Combined score} = 183 \][/tex]

So, their combined score is 183.

Answer:

1st mechanic charges $55 per hour

2nd mechanic charges $50 per hour

Step-by-step explanation:

Suppose rate charged per hour for first meachnic is "x"

rate charged per hour for 2nd mechanic is "y"

So,

1st mechanic 10 hrs, 2nd mechanic 15 hrs, total charge 1300, so we can write:

10x + 15y = 1300

Also, total hourly rate of both is 105, so we can write:

x + y = 105

or

x = 105 - y

We can substitute this into 1st equation and solve for y:

[tex]10x + 15y = 1300\\10(105-y) + 15y = 1300\\1050-10y+15y=1300\\5y=250\\y=50[/tex]

And x is:

x = 105 - y

x = 105 - 50

x = 55

1st mechanic charges $55 per hour

2nd mechanic charges $50 per hour

Answer:

Step-by-step explanation:

y=4x-2

The slope is already given in the question, so we only ned to solve for the y-intercept using  y = mx + b.

4 = 3(1) + b

4 = 3 + b

4 - 3 = 3 + b - 3

1 = b

Now, write the equation in slope-intercept form.

y = 3x + 1

_____

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Answer:

1. Rhombus

2. Square

Step-by-step explanation:

1. A rhombus is a quadrilateral whose four sides all have the same length and opposite sides are parallel.

From the diagram, you can see that [tex]\overline{AB}\parallel \overline{CD},\ \overline{AD}\parallel \overline{BC}[/tex] (given) and all four sides are congruent, thus this shape is a rhombus.

2. A square is a quadrilateral which has four equal sides, four equal angles (90-degree angles) and opposite sides are parallel.

From the diagram, you can see that [tex]\overline{EF}\parallel \overline{GH},\ \overline{EH}\parallel \overline{FG}[/tex] (given), all four sides are congruent, and all four angles are right angles, thus this shape is a square.

Answer: a. 9:5

b: 14:9

Step-by-step explanation:

if there are 14 people in a class given 5 boys, then there are 9 girls. The values needed are boys (5), girls (9), and total students (14). Ratio Girls : Boys is  9 : 5 and Ratio All Students : Girls is 14 : 9

Answer:

9:5

Step-by-step explanation:

if there are 14 people in a class given 5 boys, then there are 9 girls.

The estimated increase in height each year for a boy, according to the model h = 3a + 28.6, is 3 inches.

The equation h = 3a + 28.6 is used to estimate the height h of a boy, in inches, in terms of the boy's age a, in years. The coefficient of a in this linear equation represents the rate of change of height with respect to age. Given that the coefficient is 3, this indicates that the estimated increase in height each year is 3 inches. Therefore, the answer to the question is A) 3.

Answer:

[tex]x>-5.733[/tex]

Step-by-step explanation:

Given : Expression [tex]-1.5x-3.1<5.5[/tex]

To find : Solve the expression ?

Solution :

Step 1 - Write in inequality,

[tex]-1.5x-3.1<5.5[/tex]

Step 2 - Add 3.1 both side,

[tex]-1.5x-3.1+3.1<5.5+3.1[/tex]

[tex]-1.5x<8.6[/tex]

Step 3 - Divide by 1.5 both side,

[tex]-\frac{1.5x}{1.5}<\frac{8.6}{1.5}[/tex]

[tex]-x<5.733[/tex]

Step 4 - Multiply by -1 both side,

[tex]x>-5.733[/tex]

The number is -5.733 and symbol is greater (>).

Answer:

?

Step-by-step explanation:

theres nothing there

To find the number of different arrangements of 3 books from 7, we use permutations, specifically P(7, 3) = 7! / (7-3)! = 210. Thus, there are 210 different arrangements possible.

The student's question involves determining the number of different arrangements of 3 books that can be made from a set of 7 books. In mathematics, this is known as a permutation problem, since the order in which the books are placed matters.

To calculate permutations, we use the formula P(n, k) = n! / (n-k)!, where n is the total number of items to choose from, in this case, 7 books, and k is the number of items to arrange, in this case, 3. Using the formula:

P(7, 3) = 7! / (7-3)! = 7! / 4! = (7 × 6 × 5 × 4!) / 4! = 210.

Therefore, there are 210 different arrangements possible when selecting and arranging 3 books out of 7.

Answer:

The width of the rectangle is  [tex]\frac{1}{14}[/tex] miles

Step-by-step explanation:

Given as for rectangle

The area of rectangle = A = [tex]\frac{3}{4}[/tex] mile²

The Length of rectangle = L = [tex]\frac{21}{2}[/tex] mile

Let The width of rectangle = W miles

Now, From area of rectangle

I.e Area of Rectangle = Length × Width

Or , A = [tex]\frac{21}{2}[/tex] mile  × W mile

Or, [tex]\frac{3}{4}[/tex] mile² = [tex]\frac{21}{2}[/tex] mile  × W mile

or, W = [tex]\frac{\frac{3}{4}}{\frac{21}{2}}[/tex] mile

or, W = [tex]\frac{3\times 2}{4\times 21}[/tex]

∴  W = [tex]\frac{1}{14}[/tex] miles

Hence The width of the rectangle is  [tex]\frac{1}{14}[/tex] miles  Answer

Final answer:

The width of the rectangular piece of land is 0.3 miles.

Explanation:

To find the width of the rectangular piece of land, we need to divide the area of the land by its length.

Area = 3/4 square mile

Length = 2 1/2 miles = 5/2 miles

Width = Area / Length

Width = (3/4) / (5/2) = (3/4) * (2/5) = 6/20 = 0.3 miles

So, the width of the land is 0.3 miles.

There are 55 quarters and 30 dimes in the machine.

Step-by-step explanation:

Total coins = 85

Total amount = $16.75 = 16.75*100 = 1675 cents

1 quarter = 25 cents

1 dime = 10 cents

According to given statement;

x+y=85    Eqn 1

25x+10y=1675   Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=85)\\10x+10y=850\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](25x+10y)-(10x+10y)=1675-850\\25x+10y-10x-10y=825\\15x=825[/tex]

Dividing both sides by 15

[tex]\frac{15x}{15}=\frac{825}{15}\\x=55[/tex]

Putting in Eqn 1;

[tex]55+y=85\\y=85-55\\y=30[/tex]

There are 55 quarters and 30 dimes in the machine.

Keywords: linear equation, subtraction

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Answer:

The correct answer is D. 2x, -4y, and 8.

Step-by-step explanation:

The concept of the terms of an equation is used for the monomials of each member participating in the equation. In Mathematics we distinguish between two types of terms:  

1. The terms in x: when the terms are accompanied by a literal.

2. The independent terms: when the terms are constituted by numerical elements.

Answer:

the slope is 0

Step-by-step explanation:

If 7 = -4, then the line will be horizontal on (-4) going on forever, never moving up or down. Therefore, there will be no slope.

Answer:

x + 1 + 4√(x-3)

Step-by-step explanation:

Given: [tex]$ (\sqrt{x - 3} + 2)^2 $[/tex]

We know that:  (a + b)² = a² + b² + 2ab

Using this formula, we expand the given expression:

⇒ [tex]$ (\sqrt{x - 3} + 2)^2  = (\sqrt{x - 3})^2 + 2.\sqrt{x - 3}. 2 + 2^2 $[/tex]

⇒ [tex]$ x - 3 +4\sqrt{x - 3} + 4 $[/tex]

⇒ [tex]$ (\sqrt{x - 3} + 2)^2 $[/tex] = x + 1 +4√(x - 3).

Answer:

A. f(2k)=0

Step-by-step explanation:

The factor theorem states that a polynomial f(x) has a factor (x−k) if and only if f(k)=0 (i.e. k  is a root).

If (x – 2k) is a factor of f(x), then by the factor theorem f(2k)=0 (i.e. 2k is a root).

Option A is true, f(2k)=0

Option B is false, it should be like in option A, f(2k)=0

Option C is false, because x=2k is a root, not x=-2k

Option D is false, because x-intercept of f(x) is x=2k, not y-intercept.

Answer:

A. f(2k) = 0

Step-by-step explanation:

Answer:

-6/125

Step-by-step explanation:

well first, the decimal is negative so automatically whatever fraction you write is going to be negative

the you look at the decimal:

-0.048

there is a 0 in the tenths place, a 4 in the hundredths place, and an 8 in the thousandths place

so that means, the fraction would be -48/1000

but since it isnt simplified, that what you have to do

both can be divided by 2

which will give you:

-24/500

but those can be divided by 2 again:

-12/250

these can also be divided by 2 again:

-6/125

since the 125 cannot be divided into 2 evenly again, this is the fraction in simplest form

The simplest form of -0.048  is -6/125.

Use the concept of fraction defined as:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

The given decimal number is -0.048

Since there are 3 numbers after decimal,

Therefore,

In fractional the the number can be written as,

-0.048 = -48/1000

Divide both numerator and denominator by 8,

-0.048 = -6/125

Hence,

The simplest form of -0.048 is -6/125.

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Answer:

[tex]\large\boxed{25x^2-65x-30=5(x+3)(5x-2)}[/tex]

Step-by-step explanation:

[tex]25x^2-65x-30=5(5x^2-13x-6)\\\\=5(5x^2-15x+2x-6)=5\bigg(5x(x-3)+2(x-3)\bigg)\\\\=5(x-3)(5x+2)[/tex]

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Step-by-step explanation:

If ABC is a right triangle, where the right angle is B, then

∵ ABC is a right triangle

∵ m∠C = 90°

∴ c is the hypotenuse and a , b are its legs

∵ m∠A = 58.3°

- The sum of the two acute angles in the right triangle = 90°

∴ m∠A + m∠B = 90°

- Substitute the measure of angle A

∴ 58.3 + m∠B = 90

- Subtract 58.3 from both sides

∴ m∠B = 31.7°

∵ sin(A) = [tex]\frac{a}{c}[/tex]

∵ c = 24.8 feet

∴ sin(58.3) = [tex]\frac{a}{24.8}[/tex]

- By using cross multiplication

∴ a = (24.8) × sin(58.3)

∴ a = 21.1 ft

∵ sin(B) = [tex]\frac{b}{c}[/tex]

∵ c = 24.8 feet

∴ sin(31.7) = [tex]\frac{b}{24.8}[/tex]

- By using cross multiplication

∴ b = (24.8) × sin(31.7)

∴ b = 13.0 ft

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

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Answer:

x = 4

Step-by-step explanation:

Solve the inequality

2x - 3 > 11 - 5x ( add 5x to both sides )

7x - 3 > 11 ( add 3 to both sides )

7x > 14 ( divide both sides by 7 )

x > 2

The only value of x greater than 2 is 4, thus

x = 4 is in the solution set

The value of x that is a solution set to the inequality is: D. 4.

Given the an inequality such as, 2x – 3 > 11 – 5x, solve to isolate x.

2x – 3 > 11 – 5x

2x + 5x > 11 + 3

7x > 14

Divide both sides by 7

x > 14/7

x > 2

All set of the solution must be greater than 2. 4 is the only value of x that is greater than 2, so the answer is: D. 4.

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Answer:

The Proof is given below.

Step-by-step explanation:

Given:

AD ≅ BD ≅ FD ≅ GD

To Prove:

AC ≅ GE

Proof:

In  Δ ADF and Δ  GDB

AD ≅ DG     ……….{Given}

∠ ADF ≅ ∠ BDG    …………..{Vertically Opposite angles are equal}

FD ≅ BD     ……….{Given}

Δ ADF ≅ Δ GDB ….{Side-Angle-Side test}

∴∠ FAD ≅  ∠ BGD .....{corresponding angles of Congruent Triangle ( c.p.c.t}

i.e ∠ CAD ≅  ∠ EGD.....{ F-C-A  and B-E-G straight line}.......( 1 )

Now ,

In  Δ CAD and Δ E GD

∠ CAD ≅  ∠ EGD    ……….{From ( 1 ) above}

AD ≅ GD     ……….{Given}

∠ ADC ≅ ∠ EDG    …………..{Vertically Opposite angles are equal}

Δ ADF ≅ Δ GDB ….{Angle-Side-Angle test}

∴ AC ≅   GE .....{corresponding sides of Congruent Triangle ( c.p.c.t}

[tex]\overline {AC} \cong \overline{GE}\ \textrm{......Proved}[/tex]

Answer:

It's B

Step-by-step explanation:

I just took the test and got it right. :D

Using the definition of an empty set, we can see that the empty set in the options is:

{x|x ∈ U and 2x is prime}

First, we know that:

U =  {x|x is a positive integer greater than 1}.

So we can write:

U = {2, 3, ...}

Now, take in mind that if:

x ∈ U

Then x is a natural number larger than 1.

Now, if we multiply a natural number different than 1 by 2, we get:

2x

because x is a natural number larger than 1, 2x can't be a prime number (because it is divisible by 2 and by x).

Then the set that is empty is:

{x|x ∈ U and 2x is prime}

Because there is no element x in U that meets the condition that 2x must be prime.

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Answer:

1 month

Step-by-step explanation:

249 is the amount she spends for buying the kitten, (299-50=249) which she only has to pay once.

20 is the amount she has to spend every month, the rate of change.

The problem can be modeled with the general equation:

y = 20x + 249

In this equation, x the the time in months and y is the amount of money spent.

Substitute 250 for y.

y = 20x + 249

250 = 20x + 249    <= isolate x to get the number of months

1 = 20x

x = 1/20

Carol will only spent money every month, not for 1/20 of a month.

It will only take Carol 1 month to spent $250.

Check answer:

Substitute x for 1

y = 20x + 249

y = 20(1) + 249

y = 269

269 is more than 250 already.

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Answer:

$0.20 for 1 ounce of laundry soap

Step-by-step explanation:

7.90/40=0.1975

money can't be written like that so we have to round to the nearest hundredths

= $0.20

Answer:

36 sqaured feet

Step-by-step explanation:

24 plus 12 i believe?

Answer:

its so easy : 36 square feet

Step-by-step explanation:

add 24+12=36

Answer:

6/15

Step-by-step explanation:

Because if you multiply top and bottom by 3 you get 6/15

2/5*3/3=6/15