For what value of x the given fraction is undefined : 2/x-7

100 POINTS+BRAINLIEST 8TH GRADE MATH PT 2: Word problem involving algebraic equations on them-As usual please explain the steps

ikadub [295]

Answer:

$\sf a. \quad \dfrac{21}{10+x}+\dfrac{21}{10-x}=5$

Step-by-step explanation:

Formula for calculating speed:

$\boxed{\sf Speed=\dfrac{Distance}{Time}}$

Therefore:

$\boxed{\sf Time=\dfrac{Distance}{Speed}}$

Given values:

x = the current (in mph)
Speed = 10 mph
Distance = 21 miles
Total time = 5 hours

If the boat is traveling downstream, the current (x mph) will be pushing the boat faster, and so the boat's speed will increase by x mph.

Therefore, the expression for the time it takes for the boat to travel downstream is:

$\sf Time\:(downstream)=\dfrac{21}{10+x}$

If the boat is traveling upstream, the current (x mph) will be pushing against the boat and so the boat's speed will decrease by x mph.

Therefore, the expression for the time it takes for the boat to travel upstream is:

$\sf Time\:(upstream)=\dfrac{21}{10-x}$

Therefore, if the total time it takes to travel downstream and upstream is 5 hours:

$\implies \sf \dfrac{21}{10+x}+\dfrac{21}{10-x}=5$

To solve for x:

$\implies \sf \dfrac{21}{10+x}+\dfrac{21}{10-x}=5$

$\implies \sf \dfrac{21(10-x)}{(10+x)(10-x)}+\dfrac{21(10+x)}{(10-x)(10+x)}=5$

$\implies \sf \dfrac{21(10-x)+21(10+x)}{(10+x)(10-x)}=5$

$\implies \sf21(10-x)+21(10+x)=5(10+x)(10-x)$

$\implies \sf 210-21x+210+21x=5(100-10x+10x-x^2)$

$\implies \sf 420=500-5x^2$

$\implies \sf 5x^2=80$

$\implies \sf x^2=16$

$\implies \sf x=\pm4$

Therefore, the rate of the current is 4 mph.

8 0

2 years ago

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There are 396 students who are enrolled in an introductory biology course. If there are five boys to every four girls, how many

lbvjy [14]

Answer:

There are 220 boys in the course.

Step-by-step explanation:

If we group the five boys and four girls together, there would be 44 (396/9) groups of nine people. Since there are five boys in every group, you would do 44*5 which is 220.

4 0

3 years ago

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Ima post all my problems im sorry

sdas [7]

Equalateral triangle

8 0

3 years ago

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A helicopter hovers at an altitude that is 1000 feet above a mountain of altitude 5210 feet. A second, taller peak is viewed fro

ehidna [41]

Given:

Height of Mountain A = 5210 feet
Distance of Mountain A from a helicopter above the peak = 1000 feet
Angle of depression:
Mountain B to helicopter = 43 degrees
Mountain B to Mountain A = 19 degrees

First, draw an illustration and label the enumerated given values.

Observe that there are two right triangles formed:

From the triangle formed by the helicopter and Mountain B,

let x = total height of mountain B
y = leg of first triangle (helicopter and mountain b)
h = hypotenuse
Use the Pythagorean Theorem:

cos (43) = y / h

From the second triangle formed by mountain b and a,

cos (19) = (1000 + y) / h

solve for h and y

then, solve for the height of Mountain B:

x = 1000 + y + 5210

6 0

4 years ago

Need answer ASAP will give brainliest check out the picture

valentinak56 [21]

Answer:

i think... x=6

Step-by-step explanation:

3x+9=x+21

3x−x=12

2x=12

x=6

8 0

3 years ago

For what value of x the given fraction is undefined : 2/x-7 ​

For what value of x the given fraction is undefined : 2/x-7