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3 years ago

Fill in the blanks to make each equation true.

Mathematics

2 answers:

maks197457 [2]3 years ago

7 0

The answer is that all of them are true

n200080 [17]3 years ago

6 0

Answer: all true

Step-by-step explanation:

Look at the picture closely ull see it

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James can jog twice as fast as he can walk. He was able to jog the first 9 miles to his grandmother’s house, but then he tired a

dimulka [17.4K]

Answer:

6 mile/hour

Explanation :

Let the speed of walking of James = x mile/hour

speed of jogging = 2x mile/hour

9/2x + 1.5/x = 2

= > (9 + 3)/2x = 2

= > 12 = 4x

= > x = 3

Average speed of walking = 3 mile/hour

Average speed of jogging = 2 * 3 = 6 mile/hour

5 0

3 years ago

Which of the following represents the general term for the sequence 1, 3, 5, 7, 9, . . .? n

zalisa [80]

Answer:

Step-by-step explanation:

In the given sequence, the terms are increasing in arithmetic progression. The common difference, d between successive terms is 2

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 1

d = 2

Therefore, the expression for the general term for the sequence is

Tn = 1 + 2(n - 1)

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

Tyler says he invented a number puzzle.

maksim [4K]

Answer:

Read this section of the text:

These raptors eat primarily flying insects, so they do most of their hunting on the wing.

What does primarily mean in this sentence?

Step-by-step explanation:

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3 years ago

What website does one use to find the answer to a question on a specific test or worksheet?

Alja [10]

Answer:

Brainly.

Step-by-step explanation:

Do I need to explain this? Brainly helps people with their questions on all subjects.

4 0

2 years ago