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2 years ago

What is the solution to the system of equations graphed below?

Mathematics

2 answers:

MaRussiya [10]2 years ago

8 0

Answer:

The correct option is D.

Step-by-step explanation:

The given system of equations is

$y=-2x-3$ .... (1)

$y=3x+2$ .... (2)

The intersection point of both equation is the solution to the system of equations.

Substitute the value of y in equation (2) from equation (1).

$-2x-3=3x+2$

Isolate the like terms.

$-2x-3x=3+2$

$-5x=5$

Divide both sides by -5.

$x=-1$

The value of x is -1. Put this value in equation (1) to find the value of y.

$y=-2(-1)-3=2-3=-1$

The value of y is -1.

The solution to the system of equations is (-1,-1). Therefore the correct option is D.

RideAnS [48]2 years ago

7 0

D....................

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Expand (3 - 2x)6. What is the coefficient of the sixth term?

stich3 [128]

To expand (3 - 2x)^6 use the binomial theorem:

(x + y)^ n = C(n,0) x^ny^0 + C(n,1)x^(n-1) y + C(n,2)x^(n-2) y^2 + ...+ C(n,n+1)xy^(n-1) + C(n,n)x^0y^n

So, for x = 3, y = -2x , and n = 6 you get:

(3 - 2x) ^6 = C(6,0)(3)^6 + C(6,1)(3)^5 (-2x) + C(6,2) (3)^4 (-2x)^3 + C(6,3) (3^3) (-2x)^4 + C(6,4)(3)^2 (-2x)^4 + C(6,5) (3) (-2x)^5 + C(6,6) (-2x)^6

So, the sixth term is C(6,5)(3)(-2x)^5 = 6! / [5! (6-5)! ] * 3 * (-2)^5 x^5 = - 6*3*32 = - 576 x^5.

The coefficient of that term is - 576.

Answer: - 576

5 0

2 years ago

12700 = 23400 x (1-11.5/100)n

xxTIMURxx [149]

Answer:

Step-by-step explanation:

889

6 0

2 years ago

A motorboat covers the distance from one pier to the other pier in 4 hours and the way back in 5 hours. What is the speed of the

stiv31 [10]

Speed of current ------ y km/h

distance with the current = 4(x+y) 
distance against the current = 5(x-y) 

we know that 3.5(x+y) = 70 
x+y = 20 

but 4(x+y) = 4(20) = 80 
then 5(x-y) = 80 
x-y = 16 

x+y=20 
x-y=16 
add them 
2x = 36 
x = 18 , then y = 2

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2 years ago

The World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis Foundation. This

nika2105 [10]

Answer:

Step-by-step explanation:

a)/Let x represent the amount of money earned by the World Issues club for all their fundraising activities this year.

Let y represent the revenue generated for the foundation.

b) The World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis Foundation. Therefore, an equation that will determine the amount of money the foundation will receive is

60/100 × x = y

0.6x = y

5 0

2 years ago

A random sample of 6 homes in Gainesville, Florida between 1800 and 2200 square feet had a mean of 212990 and a standard deviati

Andrej [43]

Answer:

The 95% confidence interval for the average price of a home in Gainesville of this size is between 183,772.5 square feet and 242,207.5 square feet.

Step-by-step explanation:

We have the standard deviation of the sample, so we use the students t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of 0.95( $t_{95}$ ). So we have T = 2.015

The margin of error is:

M = T*s = 2.015*14500 = 29217.5.

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 212990 - 29217.5 = 183,772.5 square feet

The upper end of the interval is the sample mean added to M. So it is 212990 + 29217.5 = 242,207.5 square feet

The 95% confidence interval for the average price of a home in Gainesville of this size is between 183,772.5 square feet and 242,207.5 square feet.

3 0

2 years ago