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2 years ago

-8x+2y=-2 4x+4y=-4 What is the solution to the system

Mathematics

1 answer:

pickupchik [31]2 years ago

3 0

The solution to system is x = 0 and y = -1

Solution:

Given system of equations are:

-8x + 2y = -2 ----------- eqn 1

4x + 4y = -4 ---------- eqn 2

We have to solve the system of equations

We can solve the equations by elimination method

Multiply eqn 2 by 2

8x + 8y = -8 ------ eqn 3

Add eqn 1 and eqn 3

-8x + 2y = -2

8x + 8y = -8

( + ) ---------------

0x + 2y + 8y = -2 - 8

10y = -10

Divide both sides by 10

y = -1

Substitute y = -1 in eqn 1

-8x + 2(-1) = -2

-8x - 2 = -2

-8x = -2 + 2

x = 0

Thus the solution to system is x = 0 and y = -1

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Compare and Contrast Graph y = 2x + 5 and y=-13x+5. Describe how these lines are alike and how they are different. *

krek1111 [17]

Here are a couple I found:

Similarities:

They have the same y-intercept of (0,5).
They are both in slope-intercept form.

Differences:

The line of y = -13x + 5 "falls" from left to right. The line of y = 2x + 5 "rises" from left to right.
They have different x-intercepts. (y = 2x + 5 intersects (- $\frac{5}{2}$ , 0) while y = -13x + 5 intersects at ( $\frac{5}{13}$ , 0)

Explanation:

Slope-intercept form is y = mx + b, and by looking at the equations, they both already fit that format, with m as their slope and b as their y-intercept. Also, since they both have a 5 as that "b," their y-intercepts are the same: (0,5).

As for differences, we can see that the coefficient in place of that "m" is positive in y = 2x + 5 and negative in y = -13x + 5. Therefore, one line would rise due to their slope being positive and one would fall due to their slope being negative. They also have two different x-intercepts, which we can calculate by substituting 0 in place of the y, then isolating x.

4 0

2 years ago

4. For graduation, Diamond was able to buy her first car for $24,000. Her parents gave her a present and made a

s344n2d4d5 [400]

Answer:

$403.15

Step-by-step explanation:

Principal loan amount is the total amount minus down-payment:

$Principal=24000-1000\\\\=23000$

Knowing that $n=12\times 6=72,P=23000, r=7.99\%/12=0.006658$ , the monthly payments can be calculated using the formula:

$M=P[\frac{r(1+r)^n}{(1+r)^n-1}]\\\\=23000\frac{(0.006658(1.006658)^{72}}{1.006658^{72}-1}\\\\=403.15$

Hence, the monthly payment is $403.15

3 0

3 years ago

What is the difference in volume between a sphere with radius r and a sphere with radius 0.3r?

REY [17]

The volume of the sphere of radius r is:
V1 = (4/3) * (pi) * (r ^ 3)
Where,
r: sphere radius:
The volume of the sphere of radius 0.3r is:
V2 = (4/3) * (pi) * ((0.3r) ^ 3)
Rewriting:
V2 = (4/3) * (pi) * (0.027 (r) ^ 3)
V2 = 0.027 (4/3) * (pi) * (r ^ 3)
V2 = 0.027V1
The difference is:
V1-V2 = V1-0.027V1 = V1 (1-0.027)
V1-V2 = 0.973 * (4/3) * (pi) * (r ^ 3)
Answer:
the difference in volume between a sphere with radius and a sphere with radius 0.3r is:
V1-V2 = 0.973 * (4/3) * (pi) * (r ^ 3)

8 0

3 years ago

The goals against average (A) for a professional hockey goalie is determined using the formula A = 60 a equals 60 left-parenthes

Marina CMI [18]

Answer:

Option 1 - $\frac{At}{60}=g$

Step-by-step explanation:

Given : The goals against average (A) for a professional hockey goalie is determined using the formula $A=60(\frac{g}{t} )$ . In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes.

To find : Which is an equivalent equation solved for g?

Solution :

Solve the formula in terms of g,

$A=60(\frac{g}{t})$

Multiply both side by t,

$At=60g$

Divide both side by 60,

$\frac{At}{60}=\frac{60g}{60}$

$\frac{At}{60}=g$

Therefore, option 1 is correct.

4 0

3 years ago

Read 2 more answers

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. F(x) =

Troyanec [42]

Answer:

a) P (x <= 3 ) = 0.36

b) P ( 2.5 <= x <= 3 ) = 0.11

c) P (x > 3.5 ) = 1 - 0.49 = 0.51

d) x = 3.5355

e) f(x) = x / 12.5

f) E(X) = 3.3333

g) Var (X) = 13.8891 , s.d (X) = 3.7268

h) E[h(X)] = 2500

Step-by-step explanation:

Given:

The cdf is as follows:

F(x) = 0 x < 0

F(x) = (x^2 / 25) 0 < x < 5

F(x) = 1 x > 5

Find:

(a) Calculate P(X ≤ 3).

(b) Calculate P(2.5 ≤ X ≤ 3).

(d) What is the median checkout duration ? [solve 0.5 = F()].

(e) Obtain the density function f(x). f(x) = F '(x) =

(f) Calculate E(X).

(g) Calculate V(X) and σx. V(X) = σx =

(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

Solution:

a) Evaluate the cdf given with the limits 0 < x < 3.

So, P (x <= 3 ) = (x^2 / 25) | 0 to 3

P (x <= 3 ) = (3^2 / 25) - 0

P (x <= 3 ) = 0.36

b) Evaluate the cdf given with the limits 2.5 < x < 3.

So, P ( 2.5 <= x <= 3 ) = (x^2 / 25) | 2.5 to 3

P ( 2.5 <= x <= 3 ) = (3^2 / 25) - (2.5^2 / 25)

P ( 2.5 <= x <= 3 ) = 0.36 - 0.25 = 0.11

c) Evaluate the cdf given with the limits x > 3.5

So, P (x > 3.5 ) = 1 - P (x <= 3.5 )

P (x > 3.5 ) = 1 - (3.5^2 / 25) - 0

P (x > 3.5 ) = 1 - 0.49 = 0.51

d) The median checkout for the duration that is 50% of the probability:

So, P( x < a ) = 0.5

(x^2 / 25) = 0.5

x^2 = 12.5

x = 3.5355

e) The probability density function can be evaluated by taking the derivative of the cdf as follows:

pdf f(x) = d(F(x)) / dx = x / 12.5

f) The expected value of X can be evaluated by the following formula from limits - ∞ to +∞:

E(X) = integral ( x . f(x)).dx limits: - ∞ to +∞

E(X) = integral ( x^2 / 12.5)

E(X) = x^3 / 37.5 limits: 0 to 5

E(X) = 5^3 / 37.5 = 3.3333

g) The variance of X can be evaluated by the following formula from limits - ∞ to +∞:

Var(X) = integral ( x^2 . f(x)).dx - (E(X))^2 limits: - ∞ to +∞

Var(X) = integral ( x^3 / 12.5).dx - (E(X))^2

Var(X) = x^4 / 50 | - (3.3333)^2 limits: 0 to 5

Var(X) = 5^4 / 50 - (3.3333)^2 = 13.8891

s.d(X) = sqrt (Var(X)) = sqrt (13.8891) = 3.7268

h) Find the expected charge E[h(X)] , where h(X) is given by:

h(x) = (f(x))^2 = x^2 / 156.25

The expected value of h(X) can be evaluated by the following formula from limits - ∞ to +∞:

E(h(X))) = integral ( x . h(x) ).dx limits: - ∞ to +∞

E(h(X))) = integral ( x^3 / 156.25)

E(h(X))) = x^4 / 156.25 limits: 0 to 25

E(h(X))) = 25^4 / 156.25 = 2500

8 0

3 years ago