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4 years ago

Can someone help me with this question? #10

Mathematics

2 answers:

vfiekz [6]4 years ago

8 0

My guess is the answer is b but you may want to get another answer from someone else

astraxan [27]4 years ago

3 0

The answer is B. That is the best way to make them whole numbers and the easiest way to solve it.

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find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive

wel

The smallest number of terms of the AP that will make the sum of terms positive is 73.

Since we need to know the number for the sum of terms, we find the sum of terms of the AP

<h3>Sum of terms of an AP</h3>

The sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where

n = number of terms,
a = first term and
d = common difference

Since we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.

The common difference, d = a₂ - a

= -52.5 - (-54)

= -52.5 + 54

= 1.5

<h3>Number of terms for the Sum of terms to be positive</h3>

Since we require the sum of terms , S to be positive for a given number of terms, n.

So, S ≥ 0

n/2[2a + (n - 1)d] ≥ 0

So, substituting the values of the variables into the equation, we have

n/2[2(-54) + (n - 1) × 1.5] ≥ 0

n/2[-108 + 1.5n - 1.5] ≥ 0

n/2[1.5n - 109.5] ≥ 0

n[1.5n - 109.5] ≥ 0

So, n ≥ 0 or 1.5n - 109.5 ≥ 0

n ≥ 0 or 1.5n ≥ 109.5

n ≥ 0 or n ≥ 109.5/1.5

n ≥ 0 or n ≥ 73

Since n > 0, the minimum value of n is 73.

So, the smallest number of terms of the AP that will make the sum of terms positive is 73.

Learn more about sum of terms of an AP here:

brainly.com/question/24579279

#SPJ1

4 0

2 years ago

How to do this answer

sweet-ann [11.9K]

START WITH 1 COUNT BY ONES 1, 2, 3, 4, 5, 6

START WITH 8 COUNT BY ONES 8, 9, 10, 11, 12, 13

6 0

3 years ago

Read 2 more answers

This is less than and more than questions

valentinak56 [21]

Hmm... interesting thought.

6 0

4 years ago

What must be a factor on the polynomial Function F(x) graphed on the coordinate plane below?

vfiekz [6]

Answer:

x - 1

Step-by-step explanation:

The graph touches the x-axis at x = 1, its factor would be (x - 1)

3 0

2 years ago

Dwie proste przecinają się, tworząc kąty ostre i rozwarte. Miara kąta ostrego jest dwukrotnie mniejsza od miary kąta rozwartego.

Lilit [14]

Answer:

<h2>The obtuse angle is 120°.</h2><h2>The acute angle is 60°.</h2>

Step-by-step explanation:

This problem is about two crossing line, when that happens, we have 4 angles, two acute and two obtuse, where adjacent angles are supplementary and vertical angles are equal.

We can form the expression

$A = \frac{O}{2}$

Where $A$ is an acute angle and $O$ is an obtuse angle.}

Using all the given information, we have

$O + \frac{O}{2}=180\°$

Solving for $O$ , we have

$\frac{3O}{2}=180\\ O=120\°$

Therefore, the obtuse angle is 120°, which means the acute angle is 60°, because they are supplementary angles, as we said befor.

4 0

3 years ago