A sequence is defined recursively by the formula f(n + 1) = f(n) + 3 . The first term of the sequence is –4. What is the next term in the sequence?

–7

–1

1

7

​

Step-by-step explanation:

First, change the mixed fraction into an improper fraction:

5 3/7 =

5 x 7 = 35 + 3 = 38/7

Next, divide:

38/7 = 5.42857...

5.43 (rounded) is your answer.

Of course, the more digits behind it the better, so it is up to your discretion and your answer choices.

~

Answer:

5*7+3 = 38/7 ~5.43

we can multiple 5 by 7 and add them by 3

Answer:

Circles A  and D are congruent because they both have a radius of 3

Step-by-step explanation:

Answer:

Circle A and circle D are congruent ⇒ 3rd answer

Step-by-step explanation:

* Lets talk about the circle

- Any circle has diameter

- Any circle has radius which is half the diameter in length

- All the circles are similar because the measure of all circles is 360°

 and there is the ratio between the radii

- The two circles are congruent if they have the same radii because

  the congruence is special case of similarity when the ratio equal 1

* Lets look to the figure to solve the problem

- There are four circles in the figure

# Circle A with radius 3"

# Circle B with radius 4"

# Circle C with radius 5"

# Circle D with radius 3"

∵ The radius of circle A = 3"

∵ The radius of circle D = 3"

∴ The radii of circle A and circle D are congruent

∴ Circle A and circle D are congruent

Answer:

[tex]\large\boxed{1<x<7\to x\in(1,\ 7)}[/tex]

Step-by-step explanation:

[tex]|x-4|<3\iff x-4<3\ \wedge\ x-4>-3\qquad\text{add 4 to both sides}\\\\x<7\ \wedge\ x>1\Rightarrow1<x<7[/tex]

you have to make a negative and positive equation for this situation

x-4<3 and x+4<3

for the first equation you have to add 4 to both sides to get x<7

for the second equation you have to subtract 4 from both sides to get x<-1

hope this helps

I believe the correct answer is 0

Step-by-step explanation:

To solve this question, we use an abbreviation formula called BODMAS which is:

B = Brackets

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

We solve each element that is available in the order of the abbreviated letter.

1. We solve the brackets:

[tex](5\times12) = 60[/tex]

2. We solve the second bracket:

[tex](60\div3) = 20[/tex]

The equation now is [tex]20+30-50[/tex]

3. We now solve addition first:

[tex]20+30=50[/tex]

4. Now we solve the subtraction:

[tex]50-50=0[/tex]

The answer then = 0

Answer:

The value of given expression is 0.

Step-by-step explanation:

We have to evaluate the given expression:

[tex]\bigg(\displaystyle\frac{(5\times 12)}{3}\bigg)+30-50[/tex]

We use the BODMAS rule to evaluate the given expression.

B-Bracket

O-of

D-Division

M-Multiplication

A-Addition

S-Subtraction

[tex]\bigg(\displaystyle\frac{(5\times 12)}{3}\bigg)+30-50\\\\=\bigg(\displaystyle\frac{60}{3}\bigg)+30-50\\\\=20+30-50\\\\=50-50\\\\=0[/tex]

The value of expression is 0.

Answer:

The zeros are

[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex]   and [tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]f(x)=x^{2} +5x+5[/tex]  

To find the zeros equate the function to 0

[tex]x^{2} +5x+5=0[/tex]  

so

[tex]a=1\\b=5\\c=5[/tex]

substitute in the formula

[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(1)(5)}} {2(1)}[/tex]

[tex]x=\frac{-5(+/-)\sqrt{5}} {2}[/tex]

[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex]

[tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]

Answer:

Year 2

Step-by-step explanation:

The graph that I attached shows the growth over time. The height of the blue line (f(x)) surpasses g(x) at 1.63 years. We can say that year 2 is the first year that f(x) is greater than g(x).

Answer:

Just add up the measurements of the sides and then double the result.

(2 + √5 + 6 + 3√5) · 2

= (8 + 4√5) · 2

= 16 + 8√5 (cm)

To answer your question, we first need to understand that the perimeter of a rectangle is calculated by adding up all its sides or simply twice the sum of its length and width.

From the information given, the width of the rectangle is equal to 2 cm plus the square root of 5 cm, while the length is 6 cm plus 3 times the square root of 5 cm.

So now, let's sum up the length and the width:
= (2 + √5 cm) + (6 + 3√5 cm)
= 8 + 4√5 cm

We then multiply this result by 2 (to account for both sets of opposite sides of the rectangle):
Perimeter = 2 * (8 + 4√5 cm)
Perimeter ≈ 33.89 cm

Therefore, the perimeter of the rectangle is roughly 33.89 cm.

Answer:

y≥2-4

Step-by-step explanation:

Simplify your equation.

4x-2y≤8

-4x      -4x

-2y≤-4x+8

/-2       /-2

y≥2-4

Answer:

-sqrt(3)/2

Step-by-step explanation:

Use double angle identity for sin(2x)

sin(2x)=2sin(x)cos(x)

We are given sin(x)=-1/2 so we already have so far that:

sin(2x)=2(-1/2)cos(x)

sin(2x)=-1*cos(x)

We just need to find cos(x).  

x is in the fourth quadrant so cosine will be positive there

knowing the unit circle we should know that if sin(x)=-1/2 then cos(x)=sqrt(3)/2 while in 4th quadrant.

So the answer is sin(2x)=-1*sqrt(3)/2=-sqrt(3)/2

[tex]\bf (x-7)(x^2+3x-3)~\hfill \begin{array}{cll} x^2+3x-3\\ \times x\\ \cline{1-1} x^3+3x^2-3x \end{array}~~+~~ \begin{array}{cll} x^2+3x-3\\ \times -7\\ \cline{1-1} -7x^2-21x+21 \end{array}~\hfill \\\\[-0.35em] ~\dotfill\\\\ (x^3+3x^2-3x) +(-7x^2-21x+21)\implies x^3-4x^2-24x+21[/tex]

notice that all you do is simply multiply the terms of either one by the terms of the other sequentially, then add like-terms.

Answer 1 (without replacement) :  

P(2 books)=P(first)*P(second)=2/7*1/6=2/42=1/21 this is if you don't put the book back on the shelf after taking it off the first time

Answer 2 (with replacement) :  

P(2 books)=P(first)*P(second)=2/7*2/7=4/49 this is if you put the book back on the shelf after taking it off the first time

I put he probably didn't put the book back on the shelf after this first time but I don't know without those details in the question

Answer:

Step-by-step explanation:

It can't.

The answer is 60 with a remainder of 4

Answer:

The area of the triangle is [tex]A=4\ units^{2}[/tex]

Step-by-step explanation:

Let

A(0, −2),B​ (0, −3) and ​ C(8, -3)

Plot the vertices

see the attached figure

Triangle ABC is a righ triangle

The area of the triangle ABC is equal to

[tex]A=\frac{1}{2}(BC)(AB)[/tex]

[tex]BC=8-0=8\ units[/tex]

[tex]AB=-2-(-3)=1\ units[/tex]

substitute

[tex]A=\frac{1}{2}(8)(1)[/tex]

[tex]A=4\ units^{2}[/tex]

For this case we have the following expression:

[tex](-4x) ^ 2 = 100[/tex]

To look for the solution:

 We apply root to both sides of the equation to eliminate the exponent:

[tex]-4x = \pm \sqrt {100}\\-4x = \pm10[/tex]

Then we have two solutions:

[tex]-4x = 10[/tex]

Dividing between -4 on both sides of the equation:

[tex]x = \frac {10} {- 4}\\x = - \frac {5} {2}[/tex]

The second solution:

[tex]-4x = -10[/tex]

Dividing between -4 on both sides of the equation:

[tex]x = \frac {-10} {- 4}\\x = \frac {5} {2}[/tex]

Answer:

[tex]x_ {1} = - \frac {5} {2}\\x_ {2} = \frac {5} {2}[/tex]

Answer:

See below in BOLD.

Step-by-step explanation:

What you need to do is identify the corresponding sides in the polygon than divide the larger length by the smaller.

3.  The side length 8 corresponds to the 4 in the other polygon.

So the scale factor  is 8/4 = 2.

4. Scale Factor = 24/20 = 1.2.

5. 40/32  = 5x / 24

5x = 40*24 / 32

5x = 30

x = 6.

6. 25/30 = 4x + 7 / 42

5/6 = 4x + 7 / 42

6(4x + 7) = 210

24x = 210 - 42 = 168

x = 168/24

x = 7.

7. 40/24 = 3x + 5 / 21

5/3 = (3x + 5) / 21

9x + 15 = 105

9x = 90

x = 10.

8.   24 / 40 = (x + 3) / 15

3/5 = (x + 3) / 15

5x + 15 = 45

5x = 30

x = 6.

Answer:

The line would start at 30 on the Y axis and go through 15 on the X axis

Answer: First dot (0,30) Second dot (15,0)

Answer:

1 and 4

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

The corresponding angles of Triangle 1 and Triangle 4 are congruent

therefore

Both triangles are similar

Answer:

similar polygons are 1 and 4

Step-by-step explanation:

From the figure we can see some triangles and angles are given

Similar triangles means that the angles are same and their corresponding  sides are in proportion.

To find the correct answer

From the figure we get 1 and 2 are similar triangle, because angles of triangle 1 are 10°, 60° and 110°,

and angles of triangle 4 are 10°, 60° and 110°,

Therefore the correct answer is 1 and 4

The given options are 1) y = (cos x) / x is neither and 2) y = (sin x) / x is even.

Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.

In a right-angled triangle, two such angles are there which are not right-angled (not of 90 degrees).

The slanted side is called the hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.

1) y = (cos x) / x is neither, since cos x is even and x is odd.  

2) y = (sin x) / x is even since sin x and x would either both be positive at the same time or negative at the same time.  

We know that (-) / (-) is positive, just as (+) / (+) is positive.

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Final answer:

1. The function y=cos(x)/x is neither even nor odd due to its lack of symmetry properties

2. y=sin(x)/x is an odd function as it satisfies the symmetry condition about the origin.

Explanation:

To determine if the functions y=cos(x)/x and y=sin(x)/x are even, odd, or neither, we need to understand the definitions of even and odd functions and apply them accordingly.

Even and Odd Functions:

An even function satisfies the condition f(-x) = f(x), meaning the function's graph is symmetric about the y-axis. An odd function satisfies the condition f(-x) = -f(x), indicating symmetry about the origin.

Analysis of y=cos(x)/x:

To determine if y=cos(x)/x is even, odd, or neither, replace x with -x:

y=cos(-x)/(-x) = cos(x)/(-x) because cos(-x) = cos(x), an even function property.

This contradicts the definitions of both even and odd functions; hence, y=cos(x)/x is neither even nor odd.

Analysis of y=sin(x)/x:

Similarly, for y=sin(x)/x, replace x with -x:

y=sin(-x)/(-x) = -sin(x)/(-x) because sin(-x) = -sin(x), an odd function property.

This simplifies to y=sin(x)/x, which satisfies the condition for an odd function.

Therefore, y=sin(x)/x is an odd function.

Amount obtained in Compound interest is given by :

[tex]\bigstar\;\;\boxed{\mathsf{Amount = Principal\bigg(1 + \dfrac{Rate\;of \;interest}{100}\bigg)^{Conversion\;periods}}}[/tex]

Note : Conversion period is the time from one interest period to the next interest period. If the interest is compounded annually then there is one conversion period in an year. If the interest is compounded semi-annually then there are two conversion periods in an year. if the interest is compounded quarterly then there are four conversion periods in an year.

Problem :

Given : $500 is invested for one year at 4% annual interest

[tex]\implies\boxed{\begin{minipage}{4 cm}\bigstar\;\;\textsf{Principal = 500}\\\\\bigstar\;\;\textsf{Time period = 1 year}\\\\\bigstar\;\;\textsf{Rate of interest = 4\%}\end{minipage}}[/tex]

As the question mentions the term ''compounded quarterly'', there are 4 conversion periods in a year.

If the interest is compounded quarterly, then the rate of interest per conversion period (quarter) will be :

[tex]\implies \mathsf{\left(\dfrac{1}{4} \times 4\%\right) = 1\%}[/tex]

Substituting all the values in the Amount formula of C.I, We get :

[tex]\mathsf{\implies Amount = 500\bigg(1 + \dfrac{1}{100}\bigg)^4}[/tex]

[tex]\mathsf{\implies Amount = 500\left(1 + 0.01\right)^4}[/tex]

[tex]\mathsf{\implies Amount = 500\left(1.01\right)^4}[/tex]

[tex]\mathsf{\implies Amount = 520.30}[/tex]

We know that : Interest = Amount - Principal

[tex]:\implies[/tex]  Interest = 520.30 - 500

[tex]:\implies[/tex]  Interest = $20.30

If $500 is invested in a savings account with a 4% annual interest rate compounded quarterly for one year, it would earn $20.04 in interest.

To calculate the interest earned on a savings account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is $500, the annual interest rate is 4% (or 0.04 as a decimal), the interest is compounded quarterly (so n = 4), and the investment period is one year (so t = 1).

Plugging the values into the formula, we get:

A = 500(1 + 0.04/4)^(4×1)

Simplifying the equation, we calculate that the final amount after one year is $520.04. To find the amount of interest earned, we subtract the initial investment ($500) from the final amount ($520.04):

Interest = $520.04 - $500 = $20.04.

Therefore, $500 would earn $20.04 in interest if invested for one year in a savings account with a 4% annual interest rate compounded quarterly.

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Answer:

The values of x are -6 , 0 , 1 ⇒ Answers C , D , E

Step-by-step explanation:

* Let revise how to find the vertical asymptote

- Vertical asymptotes of a rational function f(x)/g(x) can be found by

 solving the equation g(x) = 0 ⇒ the denominator of the fraction

- Note: this only applies if the numerator f(x) is not zero for the same

 x value

* Lets solve the problem

∵ F(x) = 1/x(x + 6)(x - 1)

∵ The denominator of the fraction is x(x + 6)(x - 1)

- To find the equation of the vertical asymptote Put the

 denominator = 0

∴ x(x + 6)(x - 1) = 0

- The denominator has three factors, equate each by 0

∴ x = 0

OR

∴ x + 6 = 0 ⇒ subtract 6 from both sides

∴ x = -6

OR

x - 1 = 0 ⇒ add 1 to both sides

∴ x = 1

∴ From all above there are 3 vertical asymptotes at x = -6 , 0 , 1

* The answers are C, D , E

Answer:

Step-by-step explanation:

-6 0 1

Answer:

The common factor is 8x or -8x ( I forgot if the first number needs to positive or not.

Step-by-step explanation:

-8x(7x^3-2x-2)

or

8x(-7x^3+2x+2)

Hope this is what you are looking for?

Answer:

The common factor is 8x or -8x

Step-by-step explanation:

-8x(7x^3-2x-2)

or

8x(-7x^3+2x+2)

Hope this is what you are looking for!! Stay Safe!!

Answer:

Yes

Step-by-step explanation:

Yes terminating and repeating decimals are rational numbers.

This is a terminating decimal. It ends, so it is rational.

Anything that can be written as a fraction where the top and bottom are integers is rational.

Some examples:

-1                                                                              =-1/1

5                                                                              =5/1

5.23                                                                    =523/100

.3333333333333333333333333333333333333....=1/3

1   2/3                                                                           =5/3

Since there seems to be more that need convincing, the number 128.439 can be written as 128439/1000

that is a fraction where the top and bottom are integers

so 128.439 is rational

The number 128.439 is a rational number

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f\left(x\right)=-\left|x-2\right|-1[/tex]

The function represents an inverted V-shaped graph

The vertex of the function is the point (2,-1)

The y-intercept of the function is the point (0,-3)

The domain is all real numbers -----> (-∞,∞)

The range is all real numbers less than or equal to -1 ----> (-∞,-1]

Using a graphing tool

The graph in the attached figure

Answer:

percentages

Step-by-step explanation:

Sales tax is an everyday example of where percentages are used.

Sales tax is an everyday example of where percentage math is used.

Given that,
To determine the suitable system that fit the given incomplete statment.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Sale tax is a type of taxation, which is applied to the sale and business of goods and services up to some percentage of the actual revenue generated by the goods and services in the form of some percent of the price of the actual cost of goods and services.

Thus, Sales tax is an everyday example of where percentage math is used.

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Answer:The answer is 189 units 3

Step-by-step explanation:

It is a 3x7x9 prism so you multiply the numbers

Answer:

36

Step-by-step explanation:

Answer:

Step-by-step explanation:

C.  878 and D.  1 are the only whole numbers.  The rest are either mixed numbers or fractions.

Answer:

A=3.43 ft^2

Step-by-step explanation:

A=lw

A=4(6/7)

A=3.43 ft^2

To find the area of a rectangular garden 4 feet by 6/7 feet, multiply the length by the width to get 24/7 square feet.

The area of a rectangular garden measuring 4 feet by 6/7 feet can be calculated as follows:

Therefore, the area of the rectangular garden is 24/7 square feet.

Answer:

(f-g)(x)  = 2x - x^(-7)

Step-by-step explanation:

We know that

f(x) = 2x^+1 = 2x

g(x)=x^-7 = x^(-7)

Then, we just need to subtract both functions

(f-g)(x) = f(x) - g(x) =  2x - x^(-7)

(f-g)(x)  = 2x - x^(-7)

Please, see attached images for more information

Answer: Yes.

Step-by-step explanation:

30/5 or 30 divided by 5 simplifies to 6. 6 is a whole number and therefore it is an integer.