Jean, Pierre and Rachel are friends. Pierre is 8 years older than Rachel, while Jean is 15 years younger
than double the age of Peter. In addition, the sum of Peter's age and a quarter of Rachel's age is
John's age minus 5. Find out what each person's ages are.

AYO CAN ANYONE HELP ???

Given:

The arithmetic sequence is:

[tex]1, 6, 11, 16, 21,...[/tex]

To find:

1. The rule for the nth term of the given arithmetic sequence.

2. The 10th term of the given arithmetic sequence.

Solution:

1. We have,

[tex]1, 6, 11, 16, 21,...[/tex]

Here, the first term is 1 and the common difference is:

[tex]d=a_2-a_1[/tex]

[tex]d=6-1[/tex]

[tex]d=5[/tex]

The nth term of an arithmetic sequence is:

[tex]a_n=a+(n-1)d[/tex]

Where, a is the first term and d is the common difference.

Putting [tex]a=1,\ d=5[/tex], we get

[tex]a_n=1+(n-1)5[/tex]

[tex]a_n=1+5n-5[/tex]

[tex]a_n=5n-4[/tex]

Therefore, the nth term of the given sequence is [tex]a_n=5n-4[/tex].

2. We need to find the 10th term of the given arithmetic sequence.

From part 1 it is clear that the nth term of the given arithmetic sequence is:

[tex]a_n=5n-4[/tex]

Putting [tex]n=10[/tex], we get

[tex]a_{10}=5(10)-4[/tex]

[tex]a_{10}=50-4[/tex]

[tex]a_{10}=46[/tex]

Therefore, the 10th term of the given arithmetic sequence is 46.

Answer:

24 is correct answer

Step-by-step explanation:

its a 5:15 ratio, you are finding 8:x

8/5=1.6-> 1.6 x a5 = 24

Answer:

24 plates

Step-by-step explanation:

If she can wash 15 dishes in 5 minutes you just need to figure out how many dished she can washe in 1 minute. so you are gonna divide 15 by 5 and get 3 because 3 times 5 equals 15. so then that means she can wash 3 plates in 1 minute. so if she washed 15 in 5 in 6 minutes she can wash 18 and in 7 minutes she can wash 21 and in 8 minutes she can wash 24. Your just adding 3 to the 15 for every minute.

126 yards

Step-by-step explanation:

Nine times fourteen is one hundred and twenty six

Answer:

7) [tex]x \to x - 3[/tex].

8) [tex]y \to y + 2[/tex]

9) The entire quadratic equation did not get reflected.

Step-by-step explanation:

7) A horizontal translation to the right is of the form:

[tex]x \to x - a[/tex]

Let [tex]y = -(x-3)^{2} + 2[/tex], then the horizontal translation is represented by [tex]x \to x - 3[/tex].

8) A vertical translation upwards is of the form:

[tex]y \to y + a[/tex]

Let [tex]y = -(x-3)^{2} + 2[/tex] , then the vertical translation is represented by:

[tex]y \to y + 2[/tex]

9) The only component of the quadratic equation that was reflected was the part [tex](x-3) ^{2}[/tex] along the x-axis. We can create the entire function by applying the following steps:

(i) [tex]f(x) = x^{2}[/tex] (Original function)

(ii) [tex]f(x) = (x-3)^{2}[/tex] (Horizontal translation)

(iii) [tex]f(x) = - (x-3)^{2}[/tex] (Reflection)

(iv) [tex]f(x) = -(x-3)^{2} + 2[/tex] (Vertical translation)

The entire quadratic equation did not get reflected.

Answer:

dpr,rpd

Step-by-step explanation:

thats the answers at least i think thats for first.

Answer:

1) ∠P, ∠DPR, ∠KPR, ∠RPD

2) x = 111°

3) x = 5

4) m∠3 = 72°

Step-by-step explanation:

1) All of the angles display ∠P, you will noticed this if you go from the first letter point and it goes to ∠P and to the last letter point with only including ∠P.

2) I already solved this one in a different post of yours. Subtract all known values from 180° to get your answer.

3) Use the same principle knowing that all sides of a triangle add up to 180°. Add all of the angles together, set the equation to 180 and solve for x.

4) By the Alternate Exterior Angles Theorem, If a transversal intersects two parallel lines, then alternate exterior angles are congruent. Therfore, m∠6 ≡ m∠2, and we know m∠2. Solve by subtracting 108° from 180° because angles on the same line add up to 180°.

Answer: D

Step-by-step explanation:

11 m

Answer:

D

Step-by-step explanation:

took the test

Answer:

54

Step-by-step explanation:

I think it's 54

Answer:

12x - 3y

Step-by-step explanation:

Combine Like Terms

10x + 2x = 12x

Answer:

C)

Step-by-step explanation:

5 times 2 equals 10

add 3

the total comes up to 13.

Answer:

∠ 2 = ∠ 4 = 83°

Step-by-step explanation:

∠ 2 and ∠ 5 are same- side interior angles and sum to 180° , that is

∠ 2 + 97° = 180° ( subtract 97° from both sides )

∠ 2 = 83°

∠ 2 and ∠ 4 are vertical angles and are congruent, then

∠ 4 = 83°

Answer:

1. Quadratic form

2. U is

3. U- substitution

4. Find the discriminant and identify roots

Solve for x

Answer:

the length of its altitude is 34.64 cm

Step-by-step explanation:

Given;

length of a side of the equilateral triangle, L = 40 cm

All the sides of an equilateral triangle are equal

To get the altitude of the triangle, draw a perpendicular line from one of the vertices to intersect the opposite side.

Let the altitude = h

half of the opposite side intersected by the altitude = 20 cm

Apply Pythagoras theorem to determine the altitude 'h'

h² = 40²  -  20²

h² = 1200

h = √1200

h = 34.64 cm

Therefore, the length of its altitude is 34.64 cm

Answer:

A:7.031

Step-by-step explanation:

both 7, but 7.031  has 031.  7.03  only has .03.

Answer:

-1/24

Step-by-step explanation:

To find the reciprocal, you swap the numerator and the denominator. In this case, the numerator is 24 and the denominator is 1. Therefore, it would be 1/24. Now all we have to do is make this number negative. This would make it -1/24. Therefore, the reciprocal of 24 is -1/24.

If this helps please mark as brainliest

Answer:

Option A, Look closely and you will observe a bright light

Step-by-step explanation:

The cause here is to look closely, if you don't look closely you wont see the bright light... Similarly if there is no cause there is no effect.

Hope this helps!

Answer:

100,000

Step-by-step explanation:

Because the 9 thousand is more than 5.

Answer:

EF = 25 cm and FG = 35 cm

Step-by-step explanation:

After finding each scale factor for each of the 4 answers, only the last option is relatable. Every other option resulted in different numbers of EF and FG.

Answer:

D

Step-by-step explanation:

Answer:

each cd is 14.60

Step-by-step explanation:

45.30-1.50= 43.80

43.80÷3=14.60

Answer:14.30

Step-by-step explanation:

$14.30 per CD and .50 tax per Cd

Answers:

a = 2 and b = -4

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

Explanation:

Let's define the three helper functions

which are drawn from the piecewise function. The g(x) function will change depending on what the input is.

Since we want g(x) to be continuous at x = 1, this must mean the three functions f(x), h(x), j(x) must have the same output value when the input is x = 1.

Because h(x) = 6 is a constant function, the output is always 6 regardless of the input. Therefore, we want f(x) and j(x) to have 6 as their output when x = 1. Or else, the pieces won't connect.

Plug x = 1 into the f(x) function to get

f(x) = ax^2 - b

f(1) = a(1)^2 - b

f(1) = a - b

Set this equal to the desired output of 6 and we end up with the equation a-b = 6. Solving for 'a' leads to a = b+6.

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

We'll use the same idea for j(x)

j(x) = 5ax + b

j(1) = 5a(1) + b

j(1) = 5a + b

5a+b = 6

5(b+6) + b = 6 ... plug in a = b+6; solve for b

5b+30+b = 6

6b+30 = 6

6b = 6-30

6b = -24

b = -24/6

b = -4

Which then leads to,

a = b+6

a = -4+6

a = 2

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

Since a = 2 and b = -4, we go from this

[tex]g(x) = \begin{cases}ax^2-b, \ \ x < 1\\6, \ \ x = 1\\5ax+b, \ \ x > 1\end{cases}[/tex]

to this

[tex]g(x) = \begin{cases}2x^2+4, \ \ x < 1\\6, \ \ x = 1\\10x-4, \ \ x > 1\end{cases}[/tex]

Meaning

f(x) = 2x^2+4 and j(x) = 10x-4

You should find that plugging x = 1 into each of those two functions leads to 6 as the output.

The graph is shown below. Note the red graph f(x) is only drawn when x < 1. Similarly, j(x) is only drawn when x > 1. The orange point represents h(x) which only happens when x = 1. So as the name implies, the piecewise function g(x) is composed of pieces of the three functions f(x), h(x), j(x).

Answer:

the 30% off is better because 30% of 55 is 16.5 and the coupon is for 15 so the 30% off is better.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

7.5-1.5

=6

that is easy

Answer:

Step-by-step explanation:

take angle B as reference angle

using cosec rule

cosec B=hypotenuse/opposite

cosec B=13/12

cosec B=1.08

B=cosec 67

B=67 degree

for ratio,

cosec B=13/12

Given:

A synthetic division problem.

To find:

The missing number it in the given synthetic division problem.

Solution:

The given synthetic division problem is:

[tex]3|\overline{3\quad -2\quad 2\quad 4}\\[/tex]

           [tex]\quad 6\quad 8\quad 20\\[/tex]

     [tex]\overline{3\quad 4\quad ?\quad 24}[/tex]

In synthetic division, we need to add first and second row to get the bottom row.

[tex]3+0=3[/tex]

[tex]-2+6=4[/tex]

[tex]4+20=24[/tex]

Similarly,

[tex]2+8=10[/tex]

Therefore, the missing value in the given synthetic problem is 10. Hence, the correct option is C.

Answer:

Step-by-step explanation:

its (-1,-6)

this is your answer

Answer:

b

Step-by-step explanation:

Answer:

10 x 4 = 40, 40 x 2 = 80

5 x 10 = 50, 50 x 2 = 100

5 x 4 = 20, 20 x 2 = 40

100 + 80 + 40 = 220 ft2

Answer:

I think it's D

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

They are anxious to get their results