Solve for x? A 19.8 C 32.7 B 12.8 D 7

Use Cramers Rule to solve the system 2x - 3y = 11 -6x + 8y = 34

Nastasia [14]

Step-by-step explanation:

given :

2x - 3y = 11

-6x + 8y = 34

find : the solutions of the system by using Cramers Rule.

solutions:

in the matrix 2x2 form =>

[ 2 -3] [x] [11]

=

[-6 8] [ y] [34]

D =

| 2 -3 |

|-6 8 |

= 8×2 - (-3) (-6)

= 16-18 = -2

Dx = | 11 -3 |

| 34 8 |

= 11×8 - (-3) (34)

= 88 + 102

= 190

Dy = | 2 11 |

|-6 34 |

= 2×34 - (-6) (11)

= 68 + 66

= 134

x = Dx/D = 190/-2 = -95

y = Dy/D = 134/-2 = -67

the solutions = {-95, -67}

8 0

3 years ago

Read 2 more answers

Write each sum using summation notation. 1+ 2 + 3 + 4 + ⋯ + 1000

AVprozaik [17]

Answer:

$\sum_{k=1}^{1000} k$

Step-by-step explanation:

You have to use the summation notation formula:

$\sum_{k}^{n} f(k) = f(1) + f(2) +...+f(n)$

where k is the starting number, n is the ending number and f(k) is the function or the expression to be added.

In this case, you have the sum of the integer numbers from 1 to 1000. Therefore, k=1 and n=1000.

Now, you have to obtain the function f(k) which is the representation of the expression needed to obtain the correct result of the sum.

f(k=1) = 1

f(k=2)=2

f(k=3)=3 ...

You can notice that the value of k corresponds to te value of f(k) therefore f(k) = k

Replacing the values of k, n and f(k) in the formula:

$\sum_{k=1}^{1000} k = 1+2+3+4+...+1000$

7 0

4 years ago

Can someone plz help me ASAP??? my hw in hard and I don't get it

Fynjy0 [20]

9514 1404 393

Answer:

see attachments

Step-by-step explanation:

These are "one-step" equations.

To solve the ones involving addition or subtraction, identify the constant on the same side with the variable. Add its opposite to both sides.

To solve the ones involving multiplication or division, identify the coefficient of the variable. Multiply both sides by its reciprocal (or, equivalently, divide by that coefficient).

Here are more details for the problems on the first page.

w +8 = -3 ⇒ w = -3 -8 = -11
z +(-7) = -20 ⇒ z = -20 +7 = -13
1/5x = 11 ⇒ x = 5·11 = 55
1u = -88 ⇒ u = -88/11 = -8
1/9y = -2 ⇒ y = 9(-2) = -18
12 +n = 7 ⇒ n = 7 -12 = -5
q +(-4) = 8 ⇒ q = 8 +4 = 12

_____

The second page is solved the same way. It is shown in the second attachment.

7 0

3 years ago

there are 78 tourists going on a sightseeing trip.the tour company's buses hold 12 people each how many buses will they need?

vovangra [49]

Answer:

6.5

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions th

trasher [3.6K]

Answer:

(a) 100 fishes

(b) t = 10: 483 fishes

t = 20: 999 fishes

t = 30: 1168 fishes

(c)

$P(\infty) = 1200$

Step-by-step explanation:

Given

$P(t) =\frac{d}{1+ke^-{ct}}$

$d = 1200\\k = 11\\c=0.2$

Solving (a): Fishes at t = 0

This gives:

$P(0) =\frac{1200}{1+11*e^-{0.2*0}}$

$P(0) =\frac{1200}{1+11*e^-{0}}$

$P(0) =\frac{1200}{1+11*1}$

$P(0) =\frac{1200}{1+11}$

$P(0) =\frac{1200}{12}$

$P(0) = 100$

Solving (a): Fishes at t = 10, 20, 30

$t = 10$

$P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483$

$t = 20$

$P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999$

$t = 30$

$P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168$

Solving (c): $\lim_{t \to \infty} P(t)$

In (b) above.

Notice that as t increases from 10 to 20 to 30, the values of $e^{-ct}$ decreases

This implies that:

${t \to \infty} = {e^{-ct} \to 0}$

So:

The value of P(t) for large values is:

$P(\infty) = \frac{1200}{1 + 11 * 0}$

$P(\infty) = \frac{1200}{1 + 0}$

$P(\infty) = \frac{1200}{1}$

$P(\infty) = 1200$

5 0

3 years ago