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tiny-mole [99]
3 years ago
14

Find two conservative integers whose sum is 67

Mathematics
1 answer:
Charra [1.4K]3 years ago
7 0
Answer:I got 33 and 34

Explanation:

Call your integers n and n+1 we get:

n+n+1= 67

rearrange:

2n = 66

n=66/2 = 33

The integers will be 33 and 34
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Which of the following expressions are equivalent? Justify your reasoning.. . a.4√x3. . 1. x−1. . b.10√x5•x4•x2. . c.x. 1. 3. •x
sladkih [1.3K]
A ) \sqrt[4]{ x^{3} } = x^{3/4}
B ) \frac{1}{ x^{-1} } = x
C ) \sqrt[10]{ x^{5} * x^{4}* x^{2}  } = \sqrt[10]{ x^{11} }= x^{11/10}
D ) x^{1/3} * x^{1/3} * x^{1/3} = x
Therefore: B = D
7 0
3 years ago
The 4th term of an arithmetic sequence is 12 and the 8th term is 36. Find the 17th term of the sequence.
Blizzard [7]

Answer: 90

Step-by-step explanation:

The formula for calculating the nth term of a sequence is given as :

t_{n} = a + ( n - d )

Where a is the first term

d is the common difference and

n is the number of terms

This means that the 4th term of an arithmetic sequence will have the formula :

t_{4} = a + 3d

And the 4th term has been given to be , 12 ,substituting into the formula we have

12 = a + 3d .............................. equation 1

Also substituting for the 8th term , we have

36 = a + 7d .............................. equation 2

Combining the two equations , we have

a + 3d = 12  ................... equation 1

a + 7d = 36 ------------ equation 2

Solving the system of linear equation by substitution method , make a the subject of formula from equation 1 , that is

a = 12 - 3d ................... equation 3

substitute a = 12 - 3d into equation  2 , equation 2 then becomes

12 - 3d + 7d = 36

12 + 4d = 36

subtract 12 from both sides

4d = 36 - 12

4d = 24

divide through by 4

d = 6

substitute d = 6 into equation 3 to find the value of a, we have

a = 12 - 3d

a = 12 - 3 ( 6)

a = 12 - 18

a = -6

Therefore , the 17th term of the sequence will be :

t_{17} = a + 16d

t_{17} = -6 + 16 (6)

t_{17} = -6 + 96

t_{17} = 90

Therefore : the 17th term of the sequence is 90

6 0
3 years ago
What figure will result when the triangle is rotated around RE?
Oduvanchick [21]

Answer:

The figure will result is cone ⇒ B

Step-by-step explanation:

<em>When a </em><em>right triangle is rotated about its vertical leg 360°</em><em>, then it formed </em><em>a cone</em><em> its radius is the horizontal leg of the triangle and its height is the vertical lege of the triangle</em>

<em />

In the given figure

∵ Triangle TRE is a right triangle

∴ The horizontal leg is RE

∴ The vertical leg is TR

∵ The triangle is rotated around the horizontal leg RE 360°

∴ It formed a cone its radius = TR and its height = RE

∴ The figure will result is the cone

3 0
3 years ago
Thomas took three 100-point quizzes, and the mean score for the three quizzes was 87 points. If the highest score is taken away,
Olegator [25]

Answer:

The highest score is 94.

Step-by-step explanation:

Let the highest score be denoted by, <em>A</em>, the lowest score be, <em>B</em> and the middle score be <em>X</em>.

Then,

A + X + B = 87 × 3 = 261 ...(i)

X + B = 83.5 × 2 = 167 ...(ii)

⇒ B = 167 - X ...(iii)

A + X = 89 × 2 = 178 ...(iv)

⇒ A = 178 - X ...(v)

Substitute (iii) and (v) in (i) and solve for <em>X</em> as follows:

A + X + B = 261

178 - X + X + 167 - X = 261

345 - X = 261

X = 84

Substitute the value of <em>X</em> in (iii) and solve for B as follows:

B = 167 - X

   = 167 - 84

   = 83

Substitute the value of <em>X</em> in (v) and solve for A as follows:

A = 178 - X

   = 178 - 84

   = 94

Thus, the highest score is 94.

5 0
2 years ago
(a) A photography student borrows RM2 500 to buy a camera. The bank loans this money at a rate of 9 % capitalized monthly. What
Monica [59]

Answer:

The student will have to reimburse 2,991.03 two years later.

Step-by-step explanation:

This is a compound interest problem:

The compound interest formula is given by:

A = P(1 + \frac{r}{n})^{nt}

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that:

A is the amount the student will have to reimburse two years later.

P is his loan. so P = 2,500

The bank loans this money at a rate of 9 % capitalized monthly. This means that r = 0.09 and n = 12, since the money is compounded monthly, this means, 12 times in a year.

He will have to reimburse two years later, so t = 2

A = P(1 + \frac{r}{n})^{nt}

A = 2,500(1 + \frac{0.09}{12})^{24}

A = 2,991.03

The student will have to reimburse 2,991.03 two years later.

6 0
3 years ago
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