A sequence is defined by the recursive function f(n + 1) = one-halff(n). If f(3) = 9 , what is f(1) ?

Answer:

x=2 and y = 2

Step-by-step explanation:

Im going to use GeoGebra for graphing the 2 lines. I always find it helpful to move y to side of the equation and the rest of the equation to another side. This is the slope intercept equation by the way. We get our equations as y = -2x+6 and y= 2x-2.

You can find that the common point is (2,2) between the lines.

Answer:D

Step-by-step explanation:

From the inequality, y= -75 or Less, the next whole number less than -75 is -76

Answer:

Y=74

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

it is less than and equal to

Step-by-step explanation:

its > with a line under it

Answer:

[tex]x^{6}[/tex] - 8

Step-by-step explanation:

A difference of cubes has the form

a³ - b³

Note that [tex]x^{6}[/tex] is a perfect cube, that is [tex](x^2)^{3}[/tex], but

[tex]x^{8}[/tex] is not

8 is a perfect cube, that is 2³ , but 6 is not

Thus

[tex]x^{6}[/tex] - 8 ← is a difference of cubes

= [tex](x^2)^{3}[/tex] - 2³

The expression which is a difference of cubes is B. x⁶ - 8.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Difference of cubes is termed for those expressions which can be written as the difference of terms which are cubes of some numbers or expressions.

Here,

From, x⁶ - 6, we cannot write 6 as a cube of any number.

So this is not the option.

From x⁶ - 8,

x⁶ can be written as (x²)³ using power of a power rule.

x⁶ - 8 = (x²)³ - (2)³

Hence the expression is x⁶ - 8.

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Answer:

The numbers between -5 and 5

Step-by-step explanation:

Intersection of Intervals

Given the intervals A,B,C,etc. The intersection of them all is the set of all values that are common to all the intervals.

We must find

[tex]\{x | x > -5\} \bigcap \ \{x | x < 5\}[/tex]

which is the intersection between the intervals x > -5 and x < 5. The intersection represents all the numbers greater than -5 and less than 5. It can also be said The numbers between -5 and 5 (non inclusive), third option

Answer: The answer is D all real numbers

The value of n is [tex]1\frac{4}{5}[/tex].

Step-by-step explanation:

Given,

[tex](2\frac{2}{3}-n)/-2\frac{1}{5}=\frac{-13}{33}[/tex]

Writing the fractions in simplified form;

[tex](\frac{8}{3}-n)/\frac{-11}{5}=\frac{-13}{33}[/tex]

Taking LCM on left hand side;

[tex](\frac{8-3n}{3})/\frac{-11}{5}=\frac{-13}{33}\\[/tex]

[tex]\frac{8-3n}{3}*\frac{-5}{11}=\frac{-13}{33}\\\\\frac{-40+15n}{33}=\frac{-13}{33}\\\\[/tex]

Multiplying both sides by 33

[tex]33*(\frac{-40+15n}{33})=\frac{-13}{33}*33\\-40+15n=-13\\15n=-13+40\\15n=27[/tex]

Dividing both sides by 15

[tex]\frac{15n}{15}=\frac{27}{15}\\n=\frac{9}{5}\\n=1\frac{4}{5}[/tex]

The value of n is [tex]1\frac{4}{5}[/tex].

Keywords: fraction, division

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Answer:   Hence the dimension of triangle are 15, 15 and 23.

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram attached.

Suppose two congruent sides of triangle are : x

Suppose the base of the triangle : y

As per question, the base of the triangle is seven less than two times the congruent sides lengths.

So,

[tex]y = 2x-7[/tex]  .......................(1)

Now the perimeter of triangle is given as : 53

It means

[tex]x+x+y=53[/tex]

[tex]2x+y=53[/tex]  .......................(2)

Plugging the value of y from equation (1) in equation (2)

[tex]2x+2x-7=53[/tex]

[tex]4x-7=53[/tex]

[tex]4x=60[/tex]

[tex]x=15[/tex]

Plugging the value of x in equation (1)

[tex]y=2\times (15)-7[/tex]

[tex]y=23[/tex]

Hence the dimension of triangle are 15, 15 and 23.    :   Answer

Hope it will help :)

Answer:n=10, 5n=50

Step-by-step explanation:

an=50

n=50/a

n=50/5=10

5n=5×10=50

Answer:

Step-by-step explanation:

an = 50

a +(n-1)d = 50

5 + (n-1)*3 = 50

(n-1)*3 = 50 - 5 = 45

n-1 = 45/3

n-1 = 15

n=15+1 = 16

n = 16

Answer:

Therefore the equation of the line through ( -7 , 5 ) and ( -5 , 9) is

Linear Relationship i.e [tex]y-5=2(x+7)[/tex]

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( -7, 5 )  

point B( x₂ , y₂) ≡ (-5, 9)  

To Find:

Equation of Line AB =?

Solution:

Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula

[tex](y - y_{1} )=(\frac{y_{2}-y_{1} }{x_{2}-x_{1} })\times(x-x_{1}) \\[/tex]

Substituting the given values in a above equation we get

[tex](y-(5))=(\frac{9-(5)}{-5--7})\times (x--7)\\ \\(y-5)=\frac{4}{2}(x+7)\\\\y-5=2(x+7)...............\textrm{which is the required equation of the line AB}[/tex]

Therefore the equation of the line through ( -7 , 5 ) and ( -5 , 9 ) is

Linear Relationship i.e [tex]y-5=2(x+7)[/tex]

The measure of the third angle is 65°

Step-by-step explanation:

Each lapel on a suit jacket is in the shape of a triangle

In a triangle:

∵ The sum of the measures of the interior angles = 180°

∵ The measure of one angle = 47°

∵ The measure of other angle = 68°

- Substitute the measures of the two angles in the rule above

∴ 47 + 68 + measure 3rd angle = 180°

- Add the like terms

∴ 115 + measure 3rd angle = 180°

- Subtract 115 from both sides

∴ measure 3rd angle = 65°

The measure of the third angle is 65°

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Answer: 4 pancakes

Step-by-step explanation: because 30min÷6pancakes=5

So, 20min÷5=4

The value of the solution to the system of equations are, (10, - 20)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

System of equations are,

y = -5x + 30  .. (i)

x = 10

Now, We can find the solution as;

Plug x = 10 in equation (i);

y = - 5x + 30

y = - 5 × 10 + 30

y = - 50 + 30

y = - 20

Thus, The value of the solution to the system of equations are, (10, - 20)

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Answer:

y = 4/7x + 2 ( slop-intercept form)

Step-by-step explanation:

Answer:

The slope-intercept form of the given equation is,

[tex]y = \frac{4x}{7}-2[/tex]

Step-by-step explanation:

The given equation of the line is,

- 4x + 7y = - 14

Adding '4x' on both sides of the above equation, we get

   - 4x + 7y + 4x = - 14 + 4x

⇒ 7y = 4x - 14

Now, dividing both sides of the above equation by '7', we get

       7y ÷ 7 = (4x - 14) ÷ 7

[tex]\implies y = \frac{4x}{7}-\frac{14}{7}[/tex]

[tex]\implies y = \frac{4x}{7} - 2[/tex]

This is the required equation of the line in slope-intercept form.

Answer:

The library is 6 blocks away to the left of Alberto's place

Step-by-step explanation:

There's missing information on this question.

Suppose the point here is to find the distance.

A reflection across the y-axis makes the y-axis as the symmetry axis.

1) Each unit represents one block and they share the same y-coordinate (4).

2) We have to subtract the absolute value of x-coordinate.

So,

[tex]|-3-(3)|=|6|=6[/tex]

The library is 6 blocks away to the left of Alberto's place.

Answer:

1875 arrangements

Step-by-step explanation:

Break-Even is the point when costs are equal to profit.

The cost is 15,000

We need to cover this up with the profit we get from sales.

Each arrangement is 17 (cost) and is sold for 25, so the profit from each arrangement is:

25 - 17 = 8

So, with each arrangement sale, we make profit of $8. How many of these we need to sell in order to break even (in order to make 15,000)??

We simply divide this amount (15,000) by the profit we make from each arrangement ($8), so that would be:

Number of Arrangements Needed to Break-Even = 15,000/8 = 1875

After 1875 arrangements, the boutique breaks even.

Answer:

9x+5m-3

Step-by-step explanation:

3x-10+5m+6x+7

3x+6x+5m-10+7

9x+5m-3

Answer:

The interest that is obtained from that investment is $55.2

Step-by-step explanation:

If the balance at the end of eight years on an investment of $230 that has been invested at a rate of 3% is $285.20, so the principal of investment is $230 and the matured sum is $285.20.

Now, we know that Principal + Interest = Matured sum.

Hence, the interest that is obtained from that investment is $(285.2 - 230) = $55.2 (Answer)

Answer:

The interest credited after investment is $55.2

Step-by-step explanation:

Given as :

The investment principal amount = p = $230

The Amount after 8 years of investment = A = $285.20

The Time period for investment = 8 years

The rate of interest applied = r = 3%

Let The interest credited after investment = I

Now, According to question

From Compound Interest

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

And Interest = Amount - Principal

Or, I = A - p

Or, I = $285.20 - $230

∴   I = $55.2

So, The interest credited after investment = I = $55.2

Hence, The interest credited after investment is $55.2 Answer

Answer:

Step-by-step explanation:

Answer: The answer is below with explanations.

Step-by-step explanation:

In the binomial expansion of (x+y)^10, each term is calculated using the binomial coefficient formula. The expansion is [tex]x^10 + 10x^9y + 45x^8y^2 + 120x^7y^3 + 210x^6y^4 + 252x^5y^5 + 210x^4y^6 + 120x^3y^7 + 45x^2y^8 + 10xy^9 + y^10[/tex].

To expand the expression (x+y)^10 using the binomial theorem, we need to find the coefficients of each term. The general formula for the binomial expansion is: [tex](a+b)^n = C(n,0)a^n*b^0 + C(n,1)a^(n-1)*b^1 + ... + C(n,n)a^0*b^n[/tex], where C(n,k) represents the binomial coefficient. In this case, a=x, b=y, and n=10. Using the binomial coefficient formula, we can find the coefficients for each term:

[tex]C(10,0)*x^10*y^0 + C(10,1)*x^9*y^1 + C(10,2)*x^8*y^2 + ... + C(10,10)*x^0*y^10[/tex].

By calculating the binomial coefficients, the binomial expansion of (x+y)^10 is:

[tex]x^10 + 10x^9y + 45x^8y^2 + 120x^7y^3 + 210x^6y^4 + 252x^5y^5 + 210x^4y^6 + 120x^3y^7 + 45x^2y^8 + 10xy^9 + y^10[/tex].

Answer:

the answer is c, 5 stages

Answer:

Step-by-step explanation:

2/3 = 8/x+6

2 * ( x+6) = 8 * 3

2x + 2 * 6 = 24

2x + 12 = 24

2x = 24 -12

2x = 12

x = 12/2

x = 6

Answer:

I took the test and its B

Step-by-step explanation:

Also the person above me has got it covered so im gonna avoid confusion and not explain

Answer:

-4, -0.5, 1

that's the answer

Answer:-4, -0.5, 1

Step-by-step explanation:

Answer:

The two numbers are 10 and 7.

Step-by-step explanation:

Given:

The two numbers whose difference is three, when the larger number is decreased by three times the smaller number the result is -11.

Now, find the two numbers.

Let the larger number be [tex]x[/tex].

Let the smaller number be [tex]y[/tex].

As given, the two numbers whose difference is three:

[tex]x-y=3[/tex]

[tex]x=3+y[/tex]

So, the value of [tex]x=3+y[/tex].

According to question:

[tex]x-3y=-11[/tex]

Putting the value of [tex]x[/tex] we get:

[tex]3+y-3y=-11[/tex]

[tex]3-2y=-11[/tex]

Moving variables on one side and the number on the other we get:

[tex]3+11=2y[/tex]

[tex]14=2y[/tex]

Dividing both sides by 2 we get:

[tex]7=y[/tex]

The smaller number = 7.

Now, putting the value of [tex]y[/tex] in the equation [tex]x-y=3[/tex]:

[tex]x-y=3[/tex]

[tex]x-7=3[/tex]

Adding both sides by 7 we get:

[tex]x=10.[/tex]

The larger number = 10.

Therefore, the two numbers are 10 and 7.

Answer:

(-4 1/8)

Step-by-step explanation:

-6 1/4 - (-2 1/8)          The subtraction cancels out the subtraction.

-6 1/4 + 2 1/8            

-6 + 2 = -4                 The whole numbers are independent in this case.

1/4 + 1/8                     Find the least common multiple

Multiples:

4| 4_8_12

8| 8_16

8 is the least common multiple

4 goes into 8 twice so multiply the top and bottom by 2

4 * 2 = 8              1 * 2 = 2

-2/8 + 1/8 = -1/8

add that to -4

Answer:

discriminant=D=0

Step-by-step explanation:

given, 9x^2-18x+9=0...............(1)

equ (1) divided by 9

x^2-2x+1=0

discriminant=D=b^2-4ac

where, b=-2, a=1, c=1

D=(-2)^2-[tex]4\times 1\times 1[/tex]

D=4-4=0

D=0

hence discriminant=D=0  answer

The equation in standard form is x + 2y = 8

Solution:

Given that we have to write the given equation in standard form

The equation given is:

[tex]y = \frac{-1}{2}x + 4[/tex]

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers. When we shift the variable terms to the left side of the equation and everything else to the right side, we get the standard form.

[tex]y = \frac{-1}{2}x + 4\\\\y = \frac{-x}{2} + 4\\\\y =\frac{-x + 8}{2}\\\\2y = -x + 8[/tex]

Keep the variables on one side and constant term on other side

x + 2y = 8

Thus the above equation is in standard form of Ax + By = C

Answer:

x+2y=8

Step-by-step explanation:

There are 13 triangles will be in the 7th term.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sequence is,

Δ, ΔΔΔ, ΔΔΔΔΔ..

Now,

Number of triangles in sequence are;

⇒ 1 , 3 , 5, ...

Clearly, The sequence is in arithmetic sequence, with common difference = 3 - 1 = 2 and first term is 1.

Hence, The 7th term is find as;

⇒ T ₇ = a + (n - 1) d

⇒ T ₇ = 1 + (7 - 1) (2)

⇒ T ₇ = 1 + 6 x 2

⇒ T ₇ = 1 + 12

⇒ T ₇ = 13

Thus,  There are 13 triangles will be in the 7th term.

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The equivalent expression to the value 16 is 2 × 8.

The equivalent expression to the value 16 is 2 × 8.

This is because 16 can be written as the product of 2 and 8.

Therefore, the expression 2 × 8 is equivalent to the value 16.

If you're talking the equation [tex]\frac{5x-2}{3} =6[/tex], then:

[tex]\frac{5x-2}{3} =6[/tex]

[tex]5x-2=18[/tex]

[tex]5x=20[/tex]

[tex]x=4[/tex]

If you're talking about the equation [tex]5x-\frac{2}{3} =6[/tex], then:

[tex]5x-\frac{2}{3} =6[/tex]

[tex]5x = 6+\frac{2}{3}[/tex]

[tex]x=\frac{6}{5} +\frac{2}{15}[/tex]

[tex]x=\frac{18}{15} +\frac{2}{15}[/tex]

[tex]x=\frac{20}{15} = \frac{4}{3} = 1\frac{1}{3}[/tex]