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Samuel and Hayden solved the system of equations –6x – 6y = –6 and 7x + 7y = 7. Samuel says there are infinitely many solutions,

yawa3891 [41]

Answer:

Samuel is correct i.e there are infinitely many solutions

Step-by-step explanation:

Given that Samuel and Hayden solved the system of equations –6x – 6y = –6 and 7x + 7y = 7. we have to find that whether the system of equations has infinitely many solutions or not.

A system of linear equations has infinite solutions if the graphs are the exact same line i.e the the equations are equivalent.

The first equation: –6x – 6y = –6 ⇒ x+y=1 ⇒ y=-x+1

∴ the slope of its line is -1 and the y-intercept is 1

The second equation: 7x + 7y = 7 ⇒ x+y=1 ⇒ y=-x+1

∴ the slope of its line is -1 and the y-intercept is 1.

Here, we get the equation which has the same slope and y-intercept as that of the first equation.

In other words, the two equations are represented by the same line. This implies that the lines intersect infinitely many times, or that the system has infinitely many solutions.

Hence, Samuel is correct.

7 0

2 years ago

Read 2 more answers

According to the empirical rule, if the data form a "bell-shaped" normal distribution, approximately _______ percent of the obse

Elena L [17]

According to the empirical rule, if the data form a "bell-shaped" normal distribution, approximately 99.7 percent of the observations will be contained within 3 standard deviations around the mean.

To add, a bell curve is used to describe the mathematical concept called normal distribution, sometimes referred to as Gaussian distribution.

3 0

2 years ago

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current reve

Olin [163]

This question is incomplete, here is the complete question:

Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?

A) $1388.89

B) $3571.43

C) $5555.56

D) $9500.00

E) $25888.89

number of students = 36,000

Answer: A) $

1388.89

Step-by-step explanation:

the college received additional grant which is $50,000,000

and the number of students is 36,000,

and we also know that expenses and enrollment remained the same.

So if we have more money (grants) and nothing changed (expenses remain the same)

dividing the grant by the number of students will show just how much the average tuition fee would be reduced

therefore R = G/n

R = 50,000,000 / 36000

R = 1,388.888 ≈ $1388.89

7 0

2 years ago

A sociologist wishes to see if it is true that for a certain group of professional women, the average age at which they have the

Vadim26 [7]

Answer:

$Z = 2.1\ is\ higher\ than\ 1.96, we\ reject\ H_o$

Step-by-step explanation:

The explanation of given question is described below:

Here, the test of hypothesis states that

$H_o : Mean = 28.6$

$H_a : Mean\ which\ is\ not\ equals\ 28.6$

The test statistic is

$Z = \frac{(\bar X - Mean)}{\frac{Population\ standard\ deviation}{vn} }$

$Z = \frac{(30.06 - 28.6)}{\frac{4.18}{6} }$

= 2.1

According to the given data α = 0.05,

So, the major value is

$IZ(0.025)I = 1.96$

(refer to the standard normal table) .

Finally

$Z = 2.1\ is\ higher\ than\ 1.96, we\ reject\ H_o$

3 0

2 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 1 + sec

masha68 [24]

Using the washer method, the volume is given by the integral

$\displaystyle\pi\int_{-\pi/3}^{\pi/3}\bigg((3-1)^2-((1+\sec x)-1)^2\bigg)\,\mathrm dx=2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx$

where 3 - 1 = 2 is the distance from y = 3 to the axis of revolution, and similarly (1 + sec(x)) - 1 = sec(x) is the distance from y = 1 + sec(x) to the axis. The integrand is symmetric about x = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.

So the volume is

$\displaystyle2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx=2\pi(4x-\tan x)\bigg|_0^{\pi/3}=\boxed{\dfrac{8\pi^2}3-2\pi\sqrt3}$

4 0

2 years ago