<img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx%20%2B%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7Dx%20%2B%20%5Cfr

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3 years ago

ac%7B5%7D%7B4%7D" id="TexFormula1" title="\frac{1}{2}x +\frac{1}{4} = \frac{1}{3}x + \frac{5}{4}" alt="\frac{1}{2}x +\frac{1}{4} = \frac{1}{3}x + \frac{5}{4}" align="absmiddle" class="latex-formula">
Select the appropriate response
A)x=8
B)x=6
C)x = 10
D)x = 11

Mathematics

1 answer:

ycow [4]3 years ago

7 0

Answer:

B)x=6

Step-by-step explanation:

Given the equation $\frac{1}{2}x+\frac{1}{4}=\frac{1}{3}x+\frac{5}{4}$

-We first group the like terms on the same side of the equal side;

$\frac{1}{2}x-\frac{1}{3}x=\frac{5}{4}-\frac{1}{4}\\\\\\\\\frac{1}{6}x=1$

#Multiply both sides by 6 to remove denominator;

$6\times \frac{1}{6}x=1\times6\\\\x=6$

Hence, x=6

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A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters

In-s [12.5K]

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

$\Rightarrow y=\sqrt{x^2+100}$

Differentiating with respect to t

$\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}$

Since the car driving towards the intersection at 13 m/s.

so, $\frac{dx}{dt}=-13$

$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

Now

$\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)$

$=\frac{24\times (-13)}{\sqrt{676}}$

$=\frac{24\times (-13)}{26}$

= -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

8 0

2 years ago

The first term in the expansion of the binomial (3x + y)4

Lelechka [254]

I don't know if i'm right or what because I haven't learned binomial in like almost 4 years. (3x+y)?

5 0

3 years ago

Read 2 more answers

Can you help me answer this question

r-ruslan [8.4K]

Division of a fraction is the equivalent of multiplying by its reciprocal
ex.
$\frac{\frac{A}{B} }{\frac{C}{D}}=\frac{A}{B} *\frac{D}{C}$
i suggest you try to remember this concept

in terms of your question

$\frac{\frac{4c-12}{4c+8}}{\frac{c-3}{c^2-4}}= \frac{4c-12}{4c+8} *\frac{c^2 -4}{c-3}$

from this point, just multiple the numerators together and denominators together, then simplify if necessary

fyi- difference of squares
$x^2-b^2 = (x-b)(x+b)$
relating that to
$c^2-4 = c^2 -2^2 = (c-2)(c+2)$

also a side note, you might want to factor out the 4 first in the top fraction

4 0

3 years ago

Chris Christina collects stamps she is 47 stamps and all she has 20 from Europe the number of African stamps is 2 times the numb

AVprozaik [17]

Answer:

Step-by-step explanation:

Let x represent the number of stamps from Europe.

Let y represent the number of stamps from Africa.

Let z represent the number of stamps from Asia.

She has 47 stamps in all. This means that

x + y + z = 47 - - - - - - - - - - - 1

The number of African stamps is 2 times the number of Asian stamps. This means that

y = 2z

She has 20 stamps from Europe. Therefore, substituting x = 20 and y = 2z into equation 1, it becomes

20 + 2z + z = 47

3z = 47 - 20 = 27

z = 27/3 = 9

y = 2z = 2 × 9

y = 18

She has 20 stamps from Europe, 18 stamps from Africa and 9 stamps Asia.

7 0

3 years ago

5400/10251 in simplest form<br> 5400/10251 as a decimal number<br> 5400/10251 as a percentage

soldier1979 [14.2K]

600/1139 (5400/10251 Simplest)
0.62677787 (decimal)
52.67778753 % (percent)

I think

4 0

3 years ago