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3 years ago

Which first step for solving the given system using substitution results in an equation without fractions?

Mathematics

1 answer:

Alexeev081 [22]3 years ago

3 0

Answer:

The step to take to avoid fraction is to solve for y in equation 2

Step-by-step explanation:

Given

-9x+ 4y =- 10

-9x+ 3y = 3

Required:

Step for solving using substitution (avoiding fraction)

Let -9x+ 4y =- 10 represent equation 1

and -9x+ 3y = 3 represent equation 2

The following points are to be noted

Solving for x or y in equation 1 will definitely lead to having fractions

Solving for x in equation 2 will also lead to having fractions

Having said that, the step to take to avoid fraction is to solve for y in equation 2

Check

$-9x+ 3y = 3$

Add 9x to both sides

$9x-9x+ 3y = 3 + 9x$

$3y = 3 + 9x$

Divide through by 3

$\frac{3y}{3} = \frac{3 + 9x}{3}$

$y = \frac{3 + 9x}{3}$

Split fraction

$y = \frac{3}{3} + \frac{9x}{3}$

$y = 1 + 3x$

<em>At the point, the expression of y can then be substituted in equation 1</em>

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You decide to enter in a rowing competition. To train, you go to the boat house and begin rolling down stream. You row for the s

fredd [130]

Answer:

Time spent rowing down stream $=100\ seconds$

Speed of boat in still water $=14\ ms^{-1}$

Step-by-step explanation:

Let speed of boat in still water be $= x\ ms^{-1}$

Speed of current $= 10\ ms^{-1}$

Speed of boat down stream = $\textrm{Speed of boat in still water +Speed of current}= (x+10)\ ms^{-1}$

Distance rowed down stream = 2400 m

Time spent rowing down stream = $\frac{Distance}{Speed}=\frac{2400}{x+10}\ s$ = $\frac{Distance}{Speed}=\frac{2400}{x+10}\ s$

Speed of boat up stream = $\textrm{Speed of boat in still water -Speed of current}= (x-10)\ ms^{-1}$

Distance rowed up stream = $\frac{1}{6} \textrm{ of distance rowed downstream}=\frac{1}{6}\times 2400 = 400\ m$

Time spent rowing up stream = $\frac{Distance}{Speed}=\frac{400}{x-10}\ s$

We know that,

$\textrm{Time spent rowing down stream =Time spent rowing up stream}$

So,

$\frac{2400}{x+10}=\frac{400}{x-10}$

Cross multiplying

$2400(x-10)=400(x+10)$

Dividing both sides by $400$

$\frac{2400(x-10)}{400}=\frac{400(x+10)}{400}$

$6(x-10)=x+10$

$6x-60=x+10$

Adding 60 to both sides.

$6x-60+60=x+10+60$

$6x=x+70$

Subtracting both sides by $x$

$6x-x=x+70-x$

$5x=70$

Dividing both sides by 5.

$\frac{5x}{5}=\frac{70}{5}$

∴ $x=14$

Speed of boat in still water $=14\ ms^-1$

Time spent rowing down stream = $\frac{2400}{14+10}=\frac{2400}{24}=100\ s$

3 0

3 years ago

Is sqrt(25a^2/4) the same as sqrt(25a^2)/sqrt(4)?

Evgesh-ka [11]

$LHS\\ \\ =\sqrt { \frac { 25{ a }^{ 2 } }{ 4 } } \\ \\ ={ \left( \frac { 25{ a }^{ 2 } }{ 4 } \right) }^{ \frac { 1 }{ 2 } }$

$\\ \\ =\frac { { \left( 25{ a }^{ 2 } \right) }^{ \frac { 1 }{ 2 } } }{ { 4 }^{ \frac { 1 }{ 2 } } } \\ \\ =\frac { \sqrt { 25{ a }^{ 2 } } }{ \sqrt { 4 } } \\ \\ =RHS$

6 0

3 years ago

Read 2 more answers

Help me the images are posted

Sav [38]

Answer:

28.

a. false

b. true

c. false

d. false

2. 8.4 X 2.3 X 2.09 = 40.3788

3. $10.04 - $13.47

4. Your friend would be incorrect because their decimal is in the wrong place. Take the decimals out of it and think about it. Can 1 times 2 equal anything near 31? no, so it's not reasonable that your friend could multiply 1.2 X 2.6 and get anything near 31.2

5. It is more reasonable to say between 5 and 6 because even when you round both of the numbers up (3 X 2), you still only get 6.

Step-by-step explanation:

ill put it in the comments so I can get this to you faster.

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3 years ago

Expand & simplify: (x - 5)(x + 2)

Serjik [45]

Answer:

( x - 5 )( x + 2 )

= x² + 2x - 5x - 10

= x² - 3x - 10

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3 years ago

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Is x + 10 a factor of the function f(x) = x3 − 75x + 250? Explain.

PtichkaEL [24]

Yes. When the function f(x) = x3 – 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 – 75x + 250.

According to the remainder theorem when f(x) is divided by (x+a) the remainder is f(-a).
In this case,
f(x)=x^3-75x+250
(x+a)=(x+10)
Therefore, the remainder f(-a)=f(-10)

=x^3-75x+250
=(-10)^3-(75*-10)+250
=-1000+750+250
=1000-1000
=0.
The remainder is 0. So, (x+10) is a factor of x^3-75x+250.

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3 years ago