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3 years ago

Solve the system of equations.

Mathematics

2 answers:

Nitella [24]3 years ago

8 0

Equate the two equations you'll get:
(-6,1) or (2,7)

GrogVix [38]3 years ago

3 0

Answer:

(2, 7) or (-6, 1)

Step-by-step explanation:

We are given two equations:

$y=x+5$ ; and

$y = x^2+5x-7$

Since y is the subject for both the equations so we can put the values of y equal to each other to get:

$x+5=x^2+5x-7$

$x^2+5x-x-7-5=0$

$x^2+4x-12=0$

Factorizing the expression to get:

$x^2-2x+6x-12=0$

$x(x-2)+6(x-2)=0$

$(x-2) (x+6) = 0$

$x=2, x= -6$

Putting x = 2 and x = -6 in any of the equations to get the values of y:

$y=x+5$

$y =2+5$

$y=7$

and

$y =(-6)+5$

$y=1$

Therefore, solution to these equation is (2, 7) or (-6, 1).

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(2.5 x 10^9) + (5.3 x 10^8) = (2.5 + 5.3) x (10^9 x 10^8

makvit [3.9K]

Answer:

Read below.

Step-by-step explanation:

Wrong:

(2.5 x 10^9) + (5.3 x 10^8) =

(2.5 + 5.3) x (10^9 x 10^8) =

7.8 x 10^7=

7.8 x 10,000,000=

780,000,000

Bold is edited by me

Correct:

(2.5 x 10^9) + (5.3 x 10^8)=

(2.5 x 1,000,000,000)+(5.3 x 100,000,000)=

2,500,000,000+5,300,000,000=

7,800,000,000

The problem is that whoever wrote it swapped the numbers in the parentheses, added a pair of them together and multiplied the other pair. You are not supposed to take out the pairs and swap them if you'd like or the answer is incorrect. Second mistake is that $10^{9} * 10^{8}$ is not $10^{7}$ I do not know how and where you got that answer from.

3 0

4 years ago

Find the answer to the question please 16t^4/8t

sammy [17]

Answer:

STEP

Equation at the end of step 1

((16 • (t4)) - 23t2) + 1

STEP

Equation at the end of step

(24t4 - 23t2) + 1

STEP

Trying to factor by splitting the middle term

3.1 Factoring 16t4-8t2+1

The first term is, 16t4 its coefficient is 16 .

The middle term is, -8t2 its coefficient is -8 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 16 • 1 = 16

Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is -8 .

-16 + -1 = -17

-8 + -2 = -10

-4 + -4 = -8 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -4

16t4 - 4t2 - 4t2 - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

4t2 • (4t2-1)

Add up the last 2 terms, pulling out common factors :

1 • (4t2-1)

Step-5 : Add up the four terms of step 4 :

(4t2-1) • (4t2-1)

Which is the desired factorization

Trying to factor as a Difference of Squares:

3.2 Factoring: 4t2-1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2

Check : 1 is the square of 1

Check : t2 is the square of t1

Factorization is : (2t + 1) • (2t - 1)

Trying to factor as a Difference of Squares:

3.3 Factoring: 4t2 - 1

Check : 4 is the square of 2

Check : 1 is the square of 1

Check : t2 is the square of t1

Factorization is : (2t + 1) • (2t - 1)

Multiplying Exponential Expressions:

3.4 Multiply (2t + 1) by (2t + 1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2t+1) and the exponents are :

1 , as (2t+1) is the same number as (2t+1)1

and 1 , as (2t+1) is the same number as (2t+1)1

The product is therefore, (2t+1)(1+1) = (2t+1)2

Multiplying Exponential Expressions:

3.5 Multiply (2t-1) by (2t-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2t-1) and the exponents are :

1 , as (2t-1) is the same number as (2t-1)1

and 1 , as (2t-1) is the same number as (2t-1)1

The product is therefore, (2t-1)(1+1) = (2t-1)2

Final result :

(2t + 1)2 • (2t - 1)2

Step-by-step explanation:

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3 years ago

A 1,200g block of phosphorus-32, which has a half life of 14.3 days, is stored for 100.1 days. At the end of this period, how mu

Valentin [98]

Answer:

The amount of phosphorus-32 left after 100.1 days is 9.3 g.

Step-by-step explanation:

Given:

Initial amount of Phosphorus-32 is, $N_0=1200\ g$

Time period of decay is, $t=100.1\ days$

Half life of the block is, $t_{1/2}=14.3\ days$

Now, final amount left is, $N=?$

We know that, the decay equation for a radioactive material is given as:

$N=N_0e^{-kt}\\k\to decay\ constant$

The value of the decay constant is given as:

$k=\frac{\ln 2}{t_{1/2}}\\\\k=\frac{0.693}{14.3}=0.0485$

Now, plug in all the given values and calculate 'N'. This gives,

$N=(1200)e^{(-0.0485\times 100.1)}\\\\N=9.349\approx 9.3\ g$

Therefore, the amount of phosphorus-32 left after 100.1 days is 9.3 g

5 0

3 years ago

A line includes the points (4,1) and (8, 2). What is its equation in slope-intercept form?

blsea [12.9K]

Answer: y = 4x

Step-by-step explanation: Slope intercept form is y = mx + b where m is the slop and b is the x intercept

We can solve for slope using the given points

(2-1)/(8-4) = 1/4, thus m = 1/4

y = 1/4x +b

Now to solve for b, we can just plug in one of the points to see what makes b work

1 = 4*(1/4) + b

1 = 1 +b

b = 0

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vredina [299]

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