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3 years ago

Consider the following system of equations:

Mathematics

1 answer:

Mashutka [201]3 years ago

6 0

Answer:

Line $y=-2x+3$ intersects line $y=x-5$

Step-by-step explanation:

We are given that

$y=-2x+3$

$y=x-5$

Subtract one equation from other then we get

$-3x+8=0$

$3x=8$

$x=\frac{8}{3}$

Substitute the value of x in first equation then we get

$y=-2(\frac{8}{3})+3=-\frac{16}{3}+3=-\frac{-7}{3}$

Hence, the solution $(\frac{8}{3},-\frac{7}{3})$ is the intersection point of two line equations .

Answer:Line $y=-2x+3$ intersects line $y=x-5$

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5 1/3 added to four times a number is 38 14/15. what is the number? please show work

Lesechka [4]

38 14/15 - 5 1/3 = 33 3/5 or 33.6
33.6/4= 8.4
8.4= 8 2/5

the answer is 8 2/5

6 0

3 years ago

If you have 6 cars, but there is only room in your driveway for 3 cars, in how many ways can you arrange the cars in your drivew

Svetradugi [14.3K]

If the order does not matter, cars can be arranged in 20 ways

If an order is important, cars can be arranged in 120 ways

The probability that the three newest cars end up parked in the driveway is 0.167

1. If the order does not matter, combination is used

$\left ({n} \atop {r}} \right.)=\frac{n!}{r!(n-r)!}$

Here, n=6 r=3

using formula,we get

$\left ( {{6} \atop {3}} \right)=\frac{6!}{3!3!} =5*4=20$

2. If an order is important, Permutation will be applicable

$^{n}P_{r} = \frac{n!}{(n-r)!} \\$

∴ $^{6} P_{3} =\frac{6!}{3!(6-3)!}=\frac{6!}{3!} =120$

3. the probability that the three newest cars end up parked in the driveway

P= $\frac{No. of possible outcomes for 3 cars}{total possibilities}$

= $\frac{6*4*5}{6!}$

= $\frac{120}{720}$

= $\frac{1}{6}$ ≈ 0.167

Hence, If the order does not matter, cars can be arranged in 20 ways

If an order is important, cars can be arranged in 120 ways

The probability that the three newest cars end up parked in the driveway is 0.167

Learn more about probability here brainly.com/question/6077878

#SPJ4

7 0

2 years ago

Assume that y varies inversely with x. If y=7 when x=2/3, find y when x=7/3

Alinara [238K]

When y varies inversely with x, we have $y= \frac{k}{x}$

We first find the value of k

When y = 7 and x = 2/3, then

$y= \frac{k}{x}$
$7= \frac{k}{ \frac{2}{3} }$
$7( \frac{2}{3})=k$
$k= \frac{14}{3}$

Now we have k = 14/3, we can work out y when x = 7/3

$y= \frac{k}{x}$
$y= \frac{14/3}{7/3}$
$y= \frac{14}{7}$
$y=2$

3 0

3 years ago

G is a trigonometric function of the form g(x)=a sin(bx+c)+d The function intersects its midline at (-1,6) and has a minimum poi

Burka [1]

Answer:

g(x) = 3*sin((-15/4)*pi*x + (-15/4)*pi) + 6

Step-by-step explanation:

The function has the form:

g(x) = a*sin(b*x + c) + d

We know that:

The midline is at (-1, 6)

The midline is the value of g(x) when the sin(x) part is equal to zero

Then the midline is y = 6 = d

g(x) = a*sin(b*x + c) + 6

And from this we also know that:

sin(b*-1 + c) = 0,

We also know that the minimum is at (-3.5, 3)

The minimum is the y-value when the sin(x) part is equal to -1

Then

sin(b*-3.5 + c) = -1

And:

g(-3.5) = 3 = a*(-1) + 6

3 = -a + 6

a = -3 + 6 = 3

The equation is something like:

g(x) = 3*sin(b*x + c) + 6

To find the values of b and c, we need to use the two remaining equations:

sin(b*-3.5 + c) = -1

sin(b*-1 + c) = 0

We also know that:

Sin(0 ) = 0

sin( (3/2)*pi) = -1

where pi = 3.14

Then we can just write:

b*-1 + c = 0

b*-3.5 + c = (3/2)*pi

From the first one, we get:

-b + c = 0

c = b

Replacing that on the other equation we get:

c*-3.5 + c = (3/2)*pi

c*(-3.5 + 1) = (3/2)*pi

c*(-2.5) = (3/2)*pi

c = (3/2)*pi/(-2.5)

and:

-2.5 = -5/2

c = (3/2)*(-5/2)*pi = (-15/4)*pi

Then the equation becomes:

g(x) = 3*sin((-15/4)*pi*x + (-15/4)*pi) + 6

7 0

3 years ago

Read 2 more answers

Please answer 2.) a and b!

KatRina [158]

1.a. correct

1.b. $\sqrt{121} - \sqrt{9} = 11 - 3 = 8$

1.c. correct

1.d. $-\sqrt{36} - \sqrt{100} = -6 - 10 = -16$

2.a. 7 - x + 3w - 9

Terms: 7, -x, 3w, -9

Variables: x, w

Coefficients: -1, 3

Constants: 7, -9

2.b. -g + 8k - 3 - 7

Terms: -g, 8k, -3, -7

Variables: g, k

Coefficients: -1, 8

Constants: -3, -7

3.a. correct

3.b. correct

3.c. -5+ 4x = -x

4.a. 4(2x + 3) = 8x + 12

4.b. -2(3x + 4) = -6x - 8

4.c. -5(2x - 3) = -10x + 15

7 0

3 years ago