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dexar [7]
2 years ago
11

Consider the statement sqrt 300c9 = 10cx sqrt 3c. For what value of x is the statement true? x =

Mathematics
2 answers:
Marta_Voda [28]2 years ago
8 0

Answer:

x=4

Step-by-step explanation:

Step2247 [10]2 years ago
6 0

Answer:

Given the statement: Square root 300c^9 = 10c^x square root 3 c

⇒\sqrt{300c^9} =10c^x\sqrt{3c}

300c

9

=10c

x

3c

Squaring both sides we get;

(\sqrt{300c^9})^2= (10c^x\sqrt{3c})^2(

300c

9

)

2

=(10c

x

3c

)

2

Simplify:

300c^9 = 100c^{2x}(3c)300c

9

=100c

2x

(3c)

We know: a^m \cdot a^n = a^{m+n}a

m

⋅a

n

=a

m+n

then;

300c^9 = 300c^{2x+1}300c

9

=300c

2x+1

Divide both sides by 300 we get;

c^9 = c^{2x+1}c

9

=c

2x+1

On comparing both sides we have;

9 = 2x+19=2x+1

Subtract 1 from both sides we get;

8 = 2x

Divide both sides by 2 we have;

x = 4

Therefore, for the value of x =4 the given statement is true.

You might be interested in
Are these equations infinite solution, no solution, or one solution?
Karo-lina-s [1.5K]

Answer:

1) one solution

2) Infinitely many solution

3) no solution

Step-by-step explanation:

The first equation is -14-8x=-2(-3x+7)

Let us expand the right hand side to get:

-14-8x=-2*-3x+-2*7

We multiply -14-8x=6x-14

We group similar terms to get:

-8x-6x=-14+14

Combine similar terms to get:

-14x=0

Divide through by -14 to get:

x=0

2) The second equation is 3+5x=5(x+2)-7

We expand to obtain:

3+5x=5x+5*2-7

Multiply to get:

3+5x=5x+10-7

This gives us

3+5x=5x+3

5x=5x

1=1

There is infinitely many solutions

3) The third equation is: 36-7x=-7(x-5)

We expand to get:

36-7x=-7x+35

Group similar terms;

-7x+7x=35-36

0=-1

This statement is not true so there is no solution.

5 0
2 years ago
At 3:30 p.m., Berto’s train was 34 miles past the egg farm, traveling at an average speed of 85 miles per hour. At the same time
timurjin [86]

E=egg farm

x=distantce between  the Berto´s trains and the meeting point.

t=time where the trains meet up

⇒110 miles/h                                          ⇒85miles/h

[---------------------------E----------------------]-------------------------------------X

[............12 miles.......][........34 miles.....][------------ x ----------------------]

distance between Berto´s train and Eduardo´s train=

=12 miles+34 miles=46 miles.

S=d/t      ⇒d=S*t

S=seed

d=distance

T=time

Eduardo´s train;

46 miles+x=t*110 miles/h  ⇒x=t*110 miles/h-46 miles  (1)

Berto´s train;

x=t*85 miles/h  (2)

With the equations (1) and (2) we suggest this system equations:

x=t* 110 miles/h-46 miles

x=t*85 miles/h

we solve this system equiations :

t*110 miles/h-46 miles=t*85 miles/h

110t miles/h-85t miles/h=46 miles

25 t miles/h=46 miles

t=46 miles/25 miles/h=1,84 hour  (≈1 hour, 50 minutes, 24 seconds)

x=t*85 miles/h=156,4 miles

Solution: 1,84 hour

3 0
3 years ago
Read 2 more answers
In triangle MNP, m = 5 cm, n = 4 cm, and p = 8 cm. Which formula can you use to find P?
charle [14.2K]
Answer:
8² = 4² + 5² - 2(4)(5) cos(P)
which is the third option

Explanation:
The general rule of cosine is:
a² = b² + c² - 2bc*cos(A)

In our triangle:
a is substituted by p = 8 cm
b is substituted by n = 4 cm
c is substituted by m = 5 cm
A is substituted by P which we want to find

Replace the variables in the general equation with the givens as follows:
p² = n² + m² - 2mn*cos(P)
8² = 4² + 5² - 2(4)(5) cos(P)

Hope this helps :)
4 0
3 years ago
Read 2 more answers
Y= mx + b what is b?
PSYCHO15rus [73]
Y=mx+b is Slope Intercept Form, where m represents the slope and b represents the y-intercept.

The y-intercept is the value of y when x equals 0, and can be visualized on a graph as the point on the line when it crosses the y-axis.
8 0
3 years ago
Evaluate the expression and enter your answer below. 4•3+13-3^2
Pepsi [2]
If I’m not mistaken, 16
3 0
3 years ago
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