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3 years ago

The old man walked 2/3 of a mile in 1/2 of an hour. What is this rate in miles per hour?

1 answer:

7 0

If the old man walks 2/3 of a mile in 1/2 an hour, you can find how many miles he walk in one hour by setting up a fraction where distance (miles) is the numerator and the denominator is time (hours). So, (2/3)/(1/2) is the fraction. Now, we have to figure out how to make the denominator one, and we do that by multiplying is by 2. Whatever you do to the denominator you have to do to the numerator, so multiply 2/3 by 2 and 1/2 by 2.

(1/2) x 2 = 1 and (2/3) x 2 = 4/3 or 1 1/3

the old man walked 1 1/3 miles per hour

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parallelogram PQRS has PQ=RS=8 cm and diagonal QS= 10 cm. point F is on RS exactly 5 cm from S. let T be the intersection of PF

Doss [256]

Solution-

Given that,

In the parallelogram PQRS has PQ=RS=8 cm and diagonal QS= 10 cm.

Then considering ΔPQT and ΔSTF,

1- ∠FTS ≅ ∠PTQ ( ∵ These two are vertical angles)

2- ∠TFS ≅ ∠TPQ ( ∵ These two are alternate interior angles)

3- ∠TSF ≅ ∠TQP ( ∵ These two are also alternate interior angles)

If the corresponding angles of two triangles are congruent, then they are said to be similar and the corresponding sides are in proportion.

∴ ΔFTS ∼ ΔPTQ, so corresponding side lengths are in proportion.

$\Rightarrow \frac{PQ}{FS} =\frac{TQ}{TS} =\frac{TP}{TF}$

As QS = TQ + TS = 10 (given)

If TS is x, then TQ will be 10-x. Then putting these values in the equation

$\Rightarrow \frac{PQ}{FS} =\frac{TQ}{TS}$

$\Rightarrow \frac{8}{5} =\frac{10-x}{x}$

$\Rightarrow x=3.85$

∴ So TS = 3.85 cm and TQ is 10-3.85 = 6.15 cm

5 0

2 years ago

Will the sum of 2x3 + x2 - 4 and -5x² - 6x? be a polynomial? yes no

Eva8 [605]

Answer:

Yes

Step-by-step explanation:

Since we are adding two polynomials

The sum will also be polynomial

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2 years ago

Find an explicit formula for the following sequence, an which starts with a1=2/3. 2/3,3/4,4/5,5/6,…

Flura [38]

Answer:

Step-by-step explanation:

a1=2/3

sequence is 2/3,3/4,4/5,...

for numerator a1=2

d=3-2=1

numerator of nth term=a1+(n-1)d=2+(n-1)×1=2+n-1=n+1

denominator = 1 more than numerator=n+1+1=n+2

so an=(n+1)/(n+2)

or for denominator a1=3,d=4-3=1

denominator of nth term=3+(n-1)×1=3+n-1=n+2

an=(n+1)/(n+2)

6 0

2 years ago

is the degree of ( f+g)(x) equal to the degree of f(x) or g(x) , which ever has the highest degree ?

Virty [35]

Answer:

for all x in the domain of f(x), or odd if, f(−x) = −x, for all x in the domain of f(x), or neither even nor odd if neither of the above are true statements. A kth degree polynomial, p(x), is said to have even degree if k is an even number and odd degree if k is an odd number

Step-by-step explanation:

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1 year ago

How to do this question

Dafna11 [192]

Answer:

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