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Mekhanik [1.2K]
3 years ago
6

The sum of two numbers is 65. The smaller number is 11 less than the larger number. What are the numbers?

Mathematics
1 answer:
Irina-Kira [14]3 years ago
7 0
Sum means u add the two numbers together

38 + 27 = 65
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Factor sec^2x-secx+tan^2x
marysya [2.9K]

Answer:

sec²(x) - sec(x) + tan²(x) = (sec(x) - 1)(2sec(x) + 1)

Step-by-step explanation:

sec²(x) - sec(x) + tan²(x) =

= sec²(x) - sec(x) + [sec²(x) - 1]

= sec²(x) - sec(x) + [(sec(x) + 1)(sec(x) - 1)]

= sec(x)[sec(x) - 1] + [(sec(x) + 1)(sec(x) - 1)]

= (sec(x) - 1)(sec(x) + sec(x) + 1)

= (sec(x) - 1)(2sec(x) + 1)

6 0
3 years ago
Please answer with clear instructions so that i can apply this to other questions.
kvv77 [185]

Answer:

10 terms

Step-by-step explanation:

equate the sum formula to 55 and solve for n

\frac{1}{2} n(n + 1) = 55 ( multiply both sides by 2 to clear the fraction )

n(n + 1) = 110 ← distribute parenthesis on left side

n² + n = 110 ( subtract 110 from both sides )

n² + n - 110 = 0 ← in standard form

Consider the factors of the constant term (- 110) which sum to give the coefficient of the n- term (+ 1)

the factors are + 11 and - 10 , since

11 × - 10 = - 110 and 11 - 10 = + 1 , then

(n + 11)(n - 10) = 0 ← in factored form

equate each factor to zero and solve for n

n + 11 = 0 ⇒ n = - 11

n - 10 = 0 ⇒ n = 10

However, n > 0 , then n = 10

number of terms which sum to 55 is 10

7 0
2 years ago
Which value of m makes the inequality 10m-5<45
mamaluj [8]

Answer:

m < 5

Step-by-step explanation:

10m-5 < 45

Add 5 to both sides

10m - 5 + 5 < 45 + 5

Simplify

10m < 50

Divide both sides by 2

10m/10 < 50/10

Simplify

m < 5

<u><em>Kavinsky</em></u>

5 0
2 years ago
Which of the following equations has one real solution?
erastovalidia [21]

Answer:

4x2−12x+9=0

Step-by-step explanation:

The equation, 2x2+x+3=0, does not have a solution

The equation, x2+5x−3=0, equals -5/2+1/2√37 and -5/2+-1/2√37

The equation, x2−5x+4=0, equal 1 and 4

The equation, 4x2−12x+9=0, equals only 3/2

Hope this Helps

4 0
2 years ago
(HELP ASAP PLEASE!!)
Doss [256]

Answer:

Each shirt cost $<u>7</u>  and each pair of shorts cost $<u>17</u> .

Step-by-step explanation:

let shirts be represented as x

let shorts be represented as y

Younger brother spent $79 on 4 new shirts and 3 pairs of shorts.

4 x + 3 y = $79    .......equation 1

Older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185.

7 x + 8 y = $185  .......equation 2

multiply equation 1 by 7 and equation 2 by -4 and add both equations to get the value of y.

7 × (4 x + 3 y = $79)     ⇒             +28 x + 21 y = $553

-4 × (7 x + 8 y = $185)  ⇒             <u> -28 x - 32 y = - $740</u>

                                                          0   - 11 y   = - $187     ⇒  -11 y   = - $187

y = \frac{- $187}{- 11}   ⇒   y = $17

shorts = y = $17

put value of y in equation 1

4 x + 3 ( $17 ) = $79  ⇒    4x + $51 = $79   ⇒   4x = $79 - $51

4x = $28   ⇒  x = \frac{$28}{4}   ⇒   x = $7

Shirts = x = $7

8 0
2 years ago
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