Durante un entrenamiento, un ciclista da una vuelta a una pista circular en 105 segundos, mientras que otro tarda 60 segundos. Si ambos inician sus recorridos juntos, ¿en cuántos segundos será la próxima vez que coincidan en el punto de inicio?

The first odd number = 15

The second is then = 17

Consecutive numbers are those that appear consecutively after one another in the range of smallest to largest. An illustration would be the sequence of numbers 1, 2, 3, 4, 5, and so on.

Let x be the first of the following numbers to represent it algebraically. Following that, the numbers x + 1, x + 2, and x + 3 would be arranged in order. You must make sure that your first selection is an even number if the question requires consecutive even numbers.

We can employ the expression "2n," where n is any integer, to ensure that the result is even. By using the expression "2n + 1," we can ensure an odd number.

"2n + 3" will be the following odd number:

(2n + 1)(2n + 3) is the component of the odd integers, and it equals 255:

(2n + 1)(2n + 3) = 255

4n2 + 8n + 3 = 255

4n2 + 8n - 252 = 0

n2 + 2n - 63 = 0

(n + 9)(n -7) = 0

n = -9 and n = 7

We can disregard n = -9 because we are informed that the figures must be positive.

If n = 7,

The first odd number = 2(7) + 1 = 15

The second is then 17

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I understand that the question you are looking for is:

The product of 2 positive, consecutive odd numbers is 255 .

Part A: Write a quadratic equation in standard form to represent this problem

Part B: What are the 2 numbers?

Part C: Show your work for Part B.

Answer:

1.73 repeated

Step-by-step explanation:

Answer:

-113

Step-by-step explanation:

Plug in 7 for x and you get -4(7)² + 10(7) + 13

7² = 49 so -4(49) = -196

10(7) = 70

Add them all up and you get -113 (-196 + 70 + 13 = -113)

The cost of 420 grams of cherries is £1.47.

Cherries cost £3.50 per 1000 grams.

Therefore, the cost of 420 grams of cherries can be calculated as follows:

1000 grams of cherries  = £3.50

420 grams of cherries = ?

cross multiply

cost of 420 grams of cherries = 3.50 × 420 / 1000

cost of 420 grams of cherries =  1470 / 1000

cost of 420 grams of cherries = 147 / 100

cost of 420 grams of cherries = £1.47

Therefore, the cost of 420 grams of cherries is £1.47.

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Answer:

Step-by-step explanation:

Cost of 420g cherries

147 ÷ 100

=1.47

therefore the cost of 420 of cherries

= £1.4

Answer: it is .

Step-by-step explanation:

Rita and Tina each make $11 an hour -> 11r for Rita and 11t for Tina in the week

Rita also worked overtime hours and got paid an extra $32 -> Rita and Tina's total weekly wages can be represented as 11r + 11t + $32 (or 11(r+t) + 32)

Using proportions, it is found that Charlotte should ask for $62.5 in the budget to spend on thread.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Each uniform needs 50 buttons, and there are 100 uniforms, hence the number of buttons needed is:

50 x 100 = 5000.

Each button requires of a yard of thread, hence the number of yards needed is:

5000 x 1 = 5000 yards.

A 400-yard spool of thread is sold for $5, hence the budget needed is:

(5000/400) x 5 = $62.5.

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Considering the box plot and the histogram, we have that the conclusions are as follows:

b. Disagree, as the histogram shows the interval of the lowest value and the highest value needed to to find the range of the data-set, but not these values explicitly like the box plot. Thus, the range would also be given in an interval and not an exact value.

c. Disagree, as the box plot gives only the five number summary, not the measures between them, hence, the total number can only be found using the histogram.

An histogram is a graph that shows the number of times each element of x was observed.

A box and whisker plot shows five things:

The range of a data-set is given by the difference between the largest value in the data-set and the smallest.

The box plot gives these values explicitly, while the histogram show the number of times each range appears, hence, in statement b:

Disagree, as the histogram shows the interval of the lowest value and the highest value needed to to find the range of the data-set, but not these values explicitly like the box plot. Thus, the range would also be given in an interval and not an exact value.

Disagree, as the box plot gives only the five number summary, not the measures between them, hence, the total number can only be found using the histogram.

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Answer:

416

Step-by-step explanation:

pemdas

Answer:

3. w = 4

4 . g = 8

5. q = 1

6. m = -3

7. z = -32

8. a = 6

9. h = 4

10. d = -16

11. y = 4

12. n = 4

13. v = 3

14. c = -2

Step-by-step explanation:

3). 3w + 7 = 19

3w = 12

w = 4

4). 2g - 13 = 3

2g = 16

g = 8

5). 11 = 12 - q

q + 11 = 12

q = 1

6). 10 = 7 - m

m + 10 = 7

m = -3

7). -4 * (5) = (z/-4 - 3) * -4

-20 = z + 12

z = -32

8). 3 * (a/3 + 4) = (6) * 3

a + 12 = 18

a = 6

9). 5 * ((h + 6)/5) = (2) * 5

h + 6 = 10

h = 4

10). -2 * ((d - 8)/-2) = (12) * -2

d - 8 = -24

d = -16

11). 8y + 3y = 44

11y = 44

y = 4

12). 36 = 13n - 4n

36 = 9n

n = 4

13). 12v + 10v + 14 = 80

22v + 14 = 80

22v = 66

v = 3

14). 6c - 8 - 2c = -16

4c - 8 = -16

4c = -8

c = -2

Answer: 10440165 ==> sum of sequence

Step-by-step explanation:

4569+1=4570

4570/2=2285==> Average number in the sequence

4569-1+1=4569 numbers in the sequence. I find the number of numbers in the sequence by subtracting the last number in the sequence by the first number in the sequence (4569-1) and adding 1 to the difference.

2285*4569=10440165 ==> sum of sequence

Answer:

Every positive rational number has a square root.

Step-by-step explanation:

this is not true because there are prime numbers

Answer:

12/15

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

[tex]\mathrm{-9 = 9, -5 = 5,\:because\:they\:are\:in\:absolute\:value}\\9 - 5 = 4[/tex]

Answer:

-4

Step-by-step explanation:

−9 − (−5)

Multiply

−1 by −5.

−9 + 5

Add

−9 and 5.

you get...

−4

Answer:

33

Step-by-step explanation:

4+10+12+7

Answer:

your answer is xx = (53.80 - 45) / 4

Answer: Im not sure

Step-by-step explanation:

you didnt list/provide the graphs for me to answer. :I

Answer:

x divided by y - x/y

the product of two numbers - xy

x subtracted from y - y-x

the sum of two numbers is six - x+y=6

the product of two numbers is six - xy=6

x minus y - x-y

the sum of x and y - x+y

six times a number equals y - 6x=y

y divided by x - y divided by x

six less than a number is y - y=x-6

Step-by-step explanation:

Answer:

Can be C or D

Step-by-step explanation:

Janice and her 4 friends means there are 5 people in total.

She will divide them and so beads will be left which means no remainder.

so we have to look for a number divisible by 5

480 and 240 both are divisible by 5

Answer:

D. (-2, -8)

Step-by-step explanation:

y = 3x - 2

y = 5x + 2

The solution to these system of equations is the point where the lines intersect.

These lines intersect at (-2, -8)

The water level decrease each day is A. 0.25 in.

From the information, the water level in a swimming pool decreases from 60 inches to 58.25 inches in one week.

There are 7 days in a week.

Therefore, the rate if decrease per day will be:

= (60 - 58.25)/7

= 1.75 / 7

= 0.25

Therefore, the correct option is A.

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The new coordinate for Point A' is A' = (-3, -3)

The coordinates of the triangle are given as:

A (3, 4), B (7, 7), and C (8, 1)

The translation is given as:

6 units left and 7 units down

This can be represented as:

(x, y) = (x - 6, y - 7)

When the above translation rule is applied on vertex A, we have:

A' = (-3, -3)

Hence, the new coordinate for Point A' is A' = (-3, -3)

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The median of all these numbers in dollars is 7.5.

When the no. of given data are odd we arrange those nos. in an order increasing or decreasing order and the middle no. is the median of the given odd numbers.

According to the given question the following values represent the amount of money (in dollars) 10 people have in their wallets: 10, 12, 19, 5, 6, 8, 1, 13, 4, 7 and we have to find the median.

First we observe that no. of people is even so there will be two middle nos.

Now lets arrange these nos. in an order from least to greatest which is

1, 4, 5, 6, 7, 8, 10, 12, 13, 19 in this 7 and 8 are middle numbers.

So, to find the median of all these nos. we will divide these two middle nos. by 2.

∴  ( 7 + 8 )/2

= 15/2

= 7.5.

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The given system is not consistent.

Given system of equations are:

[tex]x_1+x_2+x_3=7\\x_1-x_2+2x_3=7\\2x_1+3x_3=15[/tex]

Here the indeterminants are [tex]x_1,x_2,x_3[/tex]. A system of equations is consistent if it has at least one set of solution values for the indeterminants.

So we try to solve the above system of equations.

Subtracting the first two solutions, we get,

[tex](x_1+x_2+x_3)-(x_1-x_2+2x_3)= 0[/tex]

⇒ [tex]2x_2-x_3=0[/tex]

⇒ [tex]x_3=2x_2[/tex]

Rewriting all the three equations using this substitution,

[tex]x_1+x_2+2x_2=7\\x_1-x_2+4x_2=7\\2x_1+6x_2=15[/tex]

This implies,

[tex]x_1+3x_2=7\\x_1+3x_2=7\\2x_1+6x_2=15[/tex]

Since the first two equations are same, we need to solve the equations,

[tex]x_1+3x_2=7\\2x_1+6x_2=15[/tex]

Multiplying the first equation by 2 and then subtracting, we get,

0 = -1, which is impossible.

So the system has no solutions.

Hence the system is inconsistent.

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Answer:

$1.47 per yard

Step-by-step explanation:

3 feet = 1 yard

9 feet = 3 yards

set up a proportion

[tex]\frac{3}{4.41} = \frac{1}{x}[/tex]

cross multiply; 3x = 4.41 * 1

3x = 4.41

divide both sides by 3

x = 1.47

$1.47 per yard

A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is systematic sampling.

Therefore, a probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is systematic sampling.

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Answer:

[tex]g(x)=|x+8|-2[/tex]

Step-by-step explanation:

The vertex is at (-8, 2), so g(x)=a|x+8|+2.

Considering g(-6),

[tex]g(-6)=4=a|-6+8|+2 \\ \\ 2=2a \\ \\ a=1 \\ \\ \therefore g(x)=|x+8|-2[/tex]