Write an explicit formula for the sequence given by the recursive definition a(1)=1 and a(n+1)=a(n)+7

Answer:

3 would be the original number :D

Step-by-step explanation:

3x5 = 15.  15 - 3 = 12.

To solve this problem, we need to use algebra to find the value of the unknown number.

To solve this problem, we can use algebra. Let's let the number be represented by the variable x. According to the problem, 5 times x minus 3 equals 12. We can write this as the equation 5x - 3 = 12. To find the value of x, we need to isolate it on one side of the equation. Adding 3 to both sides, we have 5x = 15. Then, dividing both sides by 5, we get x = 3.

This is a basic algebraic problem. To solve it, we have to set up an equation. Let's denote the unknown number as x. According to the problem, the number (x) is multiplied by 5, and then 3 is subtracted from the result. This operation reaches the final result which is 12. Written in form of equation, it is: 5x - 3 = 12.

To solve for x, you need to isolate it on one side of the equation. First, add 3 to both sides of the equation to get rid of the -3 on the left side: 5x = 12 + 3, or 5x = 15. Then, you divide both sides by 5: x = 15 / 5. So, the value of x is 3.

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if the cylinder has a diameter of 8, its radius is half that, or 4.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=4\\ h=20 \end{cases}\implies V=\pi (4)^2(20)\implies V=320\pi \\\\\\ V\approx 1005.3096\implies V=\stackrel{rounded}{1005}[/tex]

The formula of a cylinder:

[tex]V=\pi r^2H[/tex]

We have the diameter d = 8m and height H = 20m.

d = 2r therefore r = 8m : 2 = 4m. Substitute:

[tex]V=\pi(4^2)(20)=\pi(16)(20)=320\pi\ m^3\approx 320\cdot3.14\approx1005m^3[/tex]

Answer:

its -i

Step-by-step explanation: just did the assignment

In the given case we can conclude that Using the laws of exponents, we can simplify i³ as 1

The laws of exponents, also known as the rules of exponents, are a set of fundamental mathematical principles that govern the manipulation and simplification of expressions involving exponents. These rules are essential for working with exponential functions and equations. Here are the basic laws of exponents.

Using the laws of exponents, we can simplify i³ as follows:

i³ = i * i * i

Since we know that i² = -1, we can substitute -1 for i² in the expression:

i³ = -1 * i * i

Next, we can use the associative property of multiplication to rearrange the expression:

i³ = -1 * (i * i)

Finally, we recognize that (i * i) is equal to i² = -1, so the expression simplifies to:

i³ = -1 * -1

Therefore, i³ = 1.

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Answer:

The y-intercept in coordinate form is (0, 4.5) and represents the taxi pick-up fee.  The equation is y=1.5x + 4.5.

Step-by-step explanation:

This question is asking for the slope and y-intercept of a linear equation.  A linear equation makes a straight line based on a constant rate of change.  For this problem, the cost per mile is the slope, while the independent variable 'x' is the number of miles and the dependent variable 'y' is the total cost.  In order to first find slope, you need to use the two points given (7, 15) and (10, 19.5) to set up a change in y / change in x, or (19.5-15)/(10-7) or 4.5/3 which is 1.5.  So the slope, or cost per mile is $1.50.  To find the y-intercept (b), or the cost of the pick-up fee, simply fill in your equation y=1.5x + b with your other variables and solve for 'b'.  So, 15 = (1.5 x7) + b.  or 15 = 10.5 +b, subtract 10.5 from both sides of the equation to get b=4.5.  

Answer:

B.) -1.9

Step-by-step explanation:

1. Distribute 2.5(-1.4 + 5.2) to get -3.5 + 12

2. Distribute 4(-1.25) to get -5

3. -3.5 + 13 is 9.5

4. 9.5 / -5 is -1.9

Answer:

Coplanar

Step-by-step explanation:

A plane in space is given by any of the following:

Three non-collinear points (points not on a single line); a line and a point not on that line; two distinct but intersecting lines; and two parallel lines.

Since it can be defined by three points, any three points must be coplanar.

Answer:

b.) 60

Step-by-step explanation:

M = 29      N = 32

32+29 = 61

The closest option to 61 is 60

Answer:

b

Step-by-step explanation:

Answer:

The slope of the line is -1/4

Step-by-step explanation:

To find the slope, we use the formula

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

We have the points  (-3,2) and (5,0)

  = (0-2)/(5--3)

  = (-2)/(5+3)

  =-2/8

 = -1/4

The slope of the line is -1/4

[tex]\text{Quadratic formula}[/tex]

[tex]ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}[/tex]

-----------------------------------------------------------------------

[tex]x^2+3x+9=0\\\\a=1;\ b=3;\ c=9\\\\\Delta=3^2-4(1)(9)=9-36=-27\\\\\sqrt\Delta=\sqrt{-27}=\sqrt{(27)(-1)}=\sqrt{27}\cdot\sqrt{-1}=\sqrt{9\cdot3}i=\sqrt9\cdot\sqrt3i=3\sqrt3i[/tex]

[tex]x_1=\dfrac{-3-3\sqrt3i}{2(1)}=-\dfrac{3}{2}-\dfrac{3\sqrt3}{2}i\\\\x_2=\dfrac{-3+3\sqrt3i}{2(1)}=-\dfrac{3}{2}+\dfrac{3\sqrt3}{2}i[/tex]

[tex]i=\sqrt{-1}[/tex]

[tex]Domain:\ a\neq0\ \wedge\ b\neq0\\\\\dfrac{y}{a}-b=\dfrac{y}{b}-a\qquad\text{multiply both sides by ab}\\\\by-ab^2=ay-a^2b\qquad\text{add}\ ab^2\ \text{to both sides}\\\\by=ay+ab^2-a^2b\qquad\text{subtract}\ ay\ \text{from both sides}\\\\by-ay=ab^2-a^2b\\\\(b-a)y=ab(b-a)\qquad\text{divide both sides by}\ (a-b)\neq0\\\\y=ab\\\\Answer:\ a\in\mathbb{R}-\{0\},\ b\in\mathbb{R}-\{0\},\ a\neq b,\ y=ab\\\\Example:\\a=2,\ b=3\to y=(2)(3)=6\\\\substitute\ to\ the\ equation:\\\\L_s=\dfrac{6}{2}-3=3-3=0\\R_s=\dfrac{6}{3}-2=2-2=0\\\\L_s=R_s[/tex]

let's recall, complementary angles add  up to 90°, therefore

[tex]\bf (20w+15)+(10w)=90\implies 30w+15=90\implies 30w=75 \\\\\\ w=\cfrac{75}{30}\implies w=\cfrac{5}{2} \\\\[-0.35em] ~\dotfill\\\\ 20w+15\implies 20\left( \cfrac{5}{2} \right)+15\implies 50+15\implies \blacktriangleright 65 \blacktriangleleft \\\\\\ 10w\implies 10\left( \cfrac{5}{2} \right)\implies \blacktriangleright 25 \blacktriangleleft[/tex]

Answer:

41000

Step-by-step explanation:

ten thousand thousand hundred tens ones.

4                              1          0            0        3

We are rounding to the nearest hundred  which is 0.  We look at the number to the right.  If it is 5 or above " give it a shove" or round up.  Since it is also a 0, we leave it alone.

41000

Answer:

41000

Step-by-step explanation:

trust me

Answer:

The final sale price is $30,000.

Step-by-step explanation:

50% of $20,000 is $10,000.

$20,000+$10,000=$30,000.

Final answer:

To find the final sale price with a 50% markup on the original $20,000 price, add $10,000 (which is 50% of $20,000) to get a final sale price of $30,000.

Explanation:

To calculate the final sale price of a car after a 50% markup, we take the original purchase price of the car and add half of that price to it. If the car dealership buys a car for $20,000, a 50% markup would be half of $20,000, which is $10,000. So, the final sale price would be:

$20,000 (original price) + $10,000 (50% of $20,000) = $30,000.

Hence, the car dealership would sell the car for $30,000 after a 50% markup.

Answer:

1 3/4 = 7/4 = 1.75 miles (ran);

1.75 + 3.60 = 5.35 miles ( ran and bicycled);

average speed = 5.35 / 0.7 = 7.64 miles per hour;

The correct answer is D.

Step-by-step explanation:

Answer:

- cos 35°

Step-by-step explanation:

215° is in the third quadrant where cos is negative

cos 215° = - cos( 215 - 180)° = - cos 35°

Answer:

- cos 35°

Step-by-step explanation:

215° is in the third quadrant in which cos is negative

cos 215°

cos(α - 180°) = - cos theta

-cos( 215 - 180)°

- cos 35°

hope it helps:)

mark brainliest!

Answer:

see below   PLEASE GIVE BRAINLIEST

Step-by-step explanation:

does 2 by 7 = 11 by 37

11/2 = 5.5

7 x 5.5 = 38.5

No, these two figures are not scaled versions of each other.  11 is 5.5 times larger than 2 which means to be a scaled version we would multiply 7 by 5.5.  

7 x 5.5 = 38.5

In order to be a scaled version the second recangle would need to be 11 by 38.5

The second rectangle is a scaled version of the first rectangle with a scale factor of 1/5.5.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

To determine if two figures are scaled versions of each other, we need to compare their corresponding side lengths.

The ratio of the corresponding side lengths is the same for both figures, then they have scaled versions of each other.

As per the question, the first rectangle has sides with lengths 2 and 7 units, while the second rectangle has sides with lengths 11 and 37 units.

So, the ratio of the corresponding side lengths is 2/11 = 7/37.

The scale factor is the ratio of the corresponding side lengths.

In this case, the scale factor is 2/11 = 1/5.5.

Therefore, the second rectangle is a scaled version of the first rectangle with a scale factor of 1/5.5.

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Answer:

B

Step-by-step explanation:

20pounds/day * 14days * 20horses

The correct expression to determine the total hay consumption by 20 horses in two weeks is 20 × (20 × 14), which equals 5,600 pounds. Thus, the correct answer to the student's question is option (B).

The question from the student involves finding the total amount of hay consumed by a group of twenty horses over a period of two weeks. This problem can be solved with a straightforward multiplication.

Since one horse eats 20 pounds of hay each day, we can calculate the total hay consumption for one horse over two weeks (which is 14 days) by multiplying the daily consumption by 14:

To find out how much hay 20 horses eat in two weeks, we multiply the amount that one horse would eat in two weeks by 20:

Hence, the correct expression and evaluation to determine the total amount of hay consumed by 20 horses in two weeks is:

Option B: 20 × (20 × 14) = 5,600

Put x = 7 and y = 6 to the equations:

-2x + y = 20

L = -2(7) + 6 = -14 + 6 = -7

R = 20

L ≠ R

Answer:

10 you just add them and or count down

The distance between the two variable in the number line is = 10

A number line is a horizontal line that includes both negative and positive numbers with equally spread increments. The middle of the line is usually zero which marks the starting point of other numbers.

The distance between two numbers in a number line is the sum of their absolute value;

[-4] + [6] = 4 +6 = 10

Therefore, the distance between the two variable in the number line is =10

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Answer:

B) 24/26

Step-by-step explanation:

The ratio of sine is opposite/hypotenuse.  This means the side opposite angle D, EF, has length 24 and the hypotenuse, DE, has length 26.

The ratio of cosine is adjacent/hypotenuse.  For cos E, we want the side adjacent to E (EF) and the hypotenuse (DE).  Using these, we have the ratio 24/26.

In DEF, sin D= 24/26  , then cos E = 24/ 26. Option B) 24/26 is correct.

Trigonometric ratios are defined as the sides and angles of a right-angled triangle are deal with in Trigonometry.

We have,

In DEF sin D= 24/26

Using Pythagoras Theorem,

[tex]P^2 + B^2 = H^2\\\\EF^2 +FD^2 = EF^2\\\\24^2 + FD^2 = 26^2\\\\FD^2 = 676 - 576\\\\FD^2 = 100\\\\FD = 10[/tex]

But, cos E = EF / ED

cos E = 24/ 26

Hence, we can say that In DEF, sin D= 24/26  , then cos E = 24/ 26.

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Answers:

Problem 7) Decay

Problem 8) Growth

Problem 9) Growth

==========================================

Explanation:

The base of the exponent will tell us if we have growth or decay.

In general, we have an equation in the form y = a*b^x with b as the base of the exponent

We can have b = 1+r where r is the growth rate. If r is negative, then that growth is really decay (or the amount is shrinking)

For problem 7, the base is 0.04 so 1+r = 0.04 leads to r = -0.96; so the amount is shrinking or decaying by 96% each time x increases by 1.

In problem 8, we have growth because 1.4 = 1+0.40 = 1+r so r = 0.40 = 40% growth

Finally, in problem 9, we can break up the base 6 into 6 = 1+5.0 = 1+r meaning r = 5.0 = 500% growth

In an arithmetic sequence, the difference between one term and the next is constant.

The 65th term of the arithmetic sequence is -734

Given the following arithmetic sequence:

-30, -41, -52 The standard formula for the nth term of an arithmetic sequence is given as

a(n) = a + (n - 1)d

Where a = first term

            n = number of term

             d = common difference

Let find the common difference

Common difference = second term - first termCommon difference

= -41 - (-30)

Common difference =  -41 + 30

Common difference = -11

Common difference = -52 - (-41)

Common difference = -52 + 41

Common difference = -11

Hence, the common difference

= -11

let:

a = -30n

= 65d = -11a(65)

= -30 + (65 - 1) * -11a(65)

= -30 + (64)*-11a(65)

= -30 + (-704)a(65)

= -30 - 704a(65)

= -734

Hence, the 65th term of the arithmetic sequence is -734

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Answer:

Write the expression as 3f – 2.

The value when f = 4.5 is 11.5.

Step-by-step explanation:

Let f be the number.

Then the product of the number and three is 3f.

Two less than 3f is 3f -2.

=====

f(4.5) = 3×4.5 - 2

f(4.5) = 13.5 - 2

f(4.5) = 11.5

Answer:

Write the expression as 3f  – 2.

The value when f = 4.5  is 11.5.
first and last
B and F

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

Since y=7 when x=2, we can from here simplify and see that y=3.5 when x=1. If y=21, then we multiply 7 by 3 which is 21, and since we must keep a proportion, we must multiply 2 by 3 and get 6 as the answer.

Answer:

There are 15 orange picks when we have 25 picks total

Step-by-step explanation:

orange: green    : total

3               2            5

We found the total by adding the orange and the green

We have 25 total picks

25/5 = 5

We need to multiply by 5 on everything to get to 25 picks

orange: green    : total

3 *5           2*5        5*5

15                10           25

There are 15 orange picks when we have 25 picks total

Answer: There are 15 orange picks

Step-by-step explanation:

First we know that the ratio for Orange to Green is 3:2 so that for each five picks 3 of them are orange and 2 of them are green 25/5 is 5 so that means there are 5 five picks and as established every five picks is 3 orange picks we can say 3*5=15

Answer:

write the equation as a binomial

Step-by-step explanation:

Answer:

y = 1/4x-1

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b

m is the slope and b is the y intercept

but we do not know the slope y know the x intercept

(4,0 )

and  the y intercept

( 0,-1)

We can calculate the slope  using these points

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

   = (-1-0)/(0-4)

    = -1/-4

    = 1/4

Now we can put the slope = 1/4 and the y intercept =-1 into the formula

y = 1/4x-1

y=1/4x-1 I think is the answer to that question

You're really close. lol.

the slope of the line isn't negative though.

when the line is moving up to the right, it's positive.

the y-intercept is also positive. the y-intercept is where the line intercepts with the y-axis. if you look at the graph, you'll see that the line intercepts with the y-axis at +8 instead of -8

The answer is:

C. y = 1/4x + 8

Answer:

No that's wrong it is the third one.

Step-by-step explanation:

The line is on a positive slope so it has to be a positive x-value. Also, the y intersect is at positive 8.