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3 years ago

49x^2 + 42xy + 9y^2 Factor completely.

2 answers:

8 0

49x^2+42xy+9y^2

To factor a quadratic of the form ax^2+bx+c, you must find two values, j and k, which satisfy two conditions:

jk=ac=441 and j+k=42, so j and k must be 21 and 21.

Now replace bx with jx and kx in the original equation.

49x^2+21xy+21xy+9y^2 now factor 1st and 2nd pair of terms...

7x(7x+3y)+3y(7x+3y) which is equal to

(7x+3y)(7x+3y) which is equal to

(7x+3y)^2

mario62 [17]3 years ago

6 0

(7x-3y)^2 hope this helps

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Ecuaciones con resultado 17

babymother [125]

Answer:

x-1= -18

x = -18 +1

x = -17

2x - 4 = - 38

2x = -38 + 4

2x = -34

x = -34/2

x = -17

Step-by-step explanation:

6 0

2 years ago

The length of a Train A is 480 m and it takes 2 minutes to cross a tunnel of length 1,320 m. The length of a Train B, which is s

nasty-shy [4]

Answer: 52.94

Step-by-step explanation:

Length of train A = 480m

Tunnel length = 1320m

Time taken to cross tunnel = 2 mins = 120sec

Length of train B = 420m

Train B is slower than train A

Difference between their speed = 18km/hr

18km/hr = (18×1000)/3600 = 5m/s

Speed of train A :

Speed = distance / time

Speed = 1320 / 120 = 11m/s

Therefore, speed of train B :

(11 - 5)m/s = 6m/s

Relative speed of the two trains is therefore;

(Speed of A + speed of B)

Note : they are moving in opposite direction

( 11 + 6)m/s = 17m/s

Therefore time taken to cross each other :

(Sum of the length of both trains / relative speed of the trains)

Time taken = (480m + 420m) / (17m/s)

Time taken = 900m / 17m/s

Time taken = 52.94s

4 0

3 years ago

Determine whether y varies with x. If so, find the constant of variation and write the function rule.

ira [324]

Answer: Yes, y does vary directly with x.

Constant of variation = 1/4

The function rule is y = (1/4)x

=========================================================

Explanation:

Let's assume that y does vary directly with x.

If that's the case, then we have an equation in the form y = kx, where k is the constant of variation.

Solving for k gets us k = y/x

For each row, divide the y value over the x value

row one: k = y/x = 14/56 = 0.25
row two: k = y/x = 20/80 = 0.25
row three: k = y/x = 22/88 = 0.25

Each row yields the value k = 0.25 and it fully confirms y does vary directly with x.

So y = kx becomes y = 0.25x as the function rule, which is equivalent to y = (1/4)x

6 0

1 year ago

a rectangular garden has dimensions of 100 feet by 10, next season, the garden decreased to 2/5 of its size. what is the scale o

Alexxandr [17]

Answer: 40 ft by 4 ft

Step-by-step explanation:

See attached picture

4 0

3 years ago

Please help me with this math question!

barxatty [35]

1) Change radical forms to fractional exponents using the rule:
The n<span>th root of "</span>a number" = "that number" raised to the<span> reciprocal of n.
For example </span> $\sqrt[n]{3} = 3^{ \frac{1}{n} }$ .

The square root of 3 ( $\sqrt{3}$ ) = 3 to the one-half power ( $3^{ \frac{1}{2} }$ ).
The 5th root of 3 ( $\sqrt[5]{3}$ ) = 3 to the one-fifth power ( $3^{ \frac{1}{5} }$ ).

2) Now use the product of powers exponent rule to simplify:
This rule says $a^{m} a^{n} = a^{m+n}
$ . When two expressions with the same base (a, in this example) are multiplied, you can add their exponents while keeping the same base.

You now have $(3^{ \frac{1}{2} })*(3^{ \frac{1}{5} })$ . These two expressions have the same base, 3. That means you can add their exponents:
$(3^{ \frac{1}{2} })(3^{ \frac{1}{5} })\\
= 3^{(\frac{1}{2} + \frac{1}{5}) }\\
= 3^{\frac{7}{10}}$

3) You can leave it in the form $3^{\frac{7}{10}}$ or change it back into a radical $\sqrt[10]{3^7}$

------

Answer: $3^{\frac{7}{10}}$ or $\sqrt[10]{3^7}$

6 0

3 years ago