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Marizza181 [45]
3 years ago
7

The difference of two numbers is 8. When twice the first number is added to three times the second number, the result is 51. Wha

t are the two
numbers?
OA.
12 and 4
ОВ.
15 and 7
Ос.
20 and 12
OD
23 and 15
Mathematics
1 answer:
Naya [18.7K]3 years ago
8 0
The answer is b. 15 & 7
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Given an arithmetic sequence with a3=5 and a5=19, find the 24th term.
krok68 [10]

The 24th term is 152

Step-by-step explanation:

The formula of the nth term of an arithmetic sequence is:

a_n=a+(n-1)d , where

  • a is the first term
  • d is the common difference between consecutive terms

The third term means n = 3

∵ a_3=a+(3-1)d

∴ a_3=a+2d

∵ a_3 = 5

- Equate the right hand sides of the third term

∴ a + 2d = 5 ⇒ (1)

The fifth term means n = 5

∵ a_5=a+(5-1)d

∴ a_5=a+4d

∵ a_5 = 19

- Equate the right hand sides of the fifth term

∴ a + 4d = 19 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate a

∴ 2d = 14

- Divide both sides by 2

∴ d = 7

- Substitute the value of d in equation (1) to find a

∵ a + 2(7) = 5

∴ a + 14 = 5

- Subtract 14 from both sides

∴ a = -9

The twenty fourth term means n = 24

∵ a = -9 and d = 7

- Substitute the values of a and d in the formula of the nth term

∴ a_24=-9+(24-1)(7)

∴ a_24=-9+(23)(7)

∴ a_24=-9+161

∴ a_24=152

The 24th term is 152

Learn more:

You can learn more about the arithmetic sequence in brainly.com/question/7221312

#LearnwithBrainly

5 0
3 years ago
Graph the first six terms of a sequence where a1 = −10 and d = 3.
Neko [114]

notice the first term is -10, and the common difference is 3, so we add 3 to get the next term.

\bf \begin{array}{cccll}\stackrel{x}{n}&term&\stackrel{y}{value}\\\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\1&a_1&-10\\\\2&a_2&\stackrel{-10+3}{-7}\\\\3&a_3&\stackrel{-7+3}{-4}\\\\4&a_4&\stackrel{-4+3}{-1}\\\\5&a_5&\stackrel{-1+3}{2}\\\\6&a_6&\stackrel{2+3}{5}\end{array}

check the picture below.

8 0
3 years ago
Jordan throws a ball from a cliff 12 feet above the ground with an initial velocity of 32 feet per second. In the following func
lbvjy [14]

Answer:

Your answer will be the third function

Step-by-step explanation:

The base function you need to know is h(t)= 1/2at^2

Your acceleration in this problem is going to be gravity which they give to you, 32 feet per second squared. Since the ball is falling, it means it will have negative acceleration. Now you have the equation h(t)= -16t^2. The final step is to add the initial height from which the ball was dropped giving you: h(t)= -16t^2 +12

8 0
2 years ago
Evaluate each expression using the values m = 7, r = 8, and t = 2.
user100 [1]

So I'll walk through the first 2. Then please try the other ones and let me know if you run into more problems.

5m-6

If m is equal to 7, then replace m with 7.

5(7)-6

5x7=35 so the expression is now 35-6. Solve.

35-6=29

So that was the first one.

4m+t

We just do what we do with the first problem.

4(7)+(2)

4x7=28 so the expression is 28+2.

28+2=28

---

hope it helps

p.s. When there is subtraction, add. When there is division, multiply to cancel that out. When there is multiplication, divide to cancel. etc.

6 0
2 years ago
Read 2 more answers
-5/3+2 1/3 add or subtract fraction in simplest form
Doss [256]
Work
7/3-5/3
answer- 2/3
Decimal answer- .66(repeating)
4 0
3 years ago
Read 2 more answers
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