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2 years ago

Which graph below shows a line that contains ordered pairs that are solutions of the equation shown?

Mathematics

1 answer:

Vinvika [58]2 years ago

7 0

Given:

The equation is:

$y=-x+4$

To find:

The graph of the line that contains ordered pairs that are solutions of the given equation.

Solution:

We need to find the graph of the given equation.

We have,

$y=-x+4$

At $x=0$ , we get

$y=-0+4$

$y=4$

So, the x-intercept of the given equation is at point (0,4).

At $y=0$ , we get

$0=-x+4$

$x=4$

So, the y-intercept of the given equation is at point (4,0).

From the given graphs it is clear that the line in option C has x-intercept at point (0,4) and y-intercept at point (4,0).

Therefore, the correct option is C.

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Round the following number to four significant figures: 3.682417 *

Dovator [93]

Answer:

3.682

Step-by-step explanation:

We don't consider the decimal place or I should say comma so then we read from the first digit as long as it's not zero then until the fourth digit we look at the next digit if it's 5 or greater then we add 1 to the previous digit. And if the next digit is less than 5 then the digit won't change

7 0

2 years ago

Find the value of x in the triangle. SU RV

kodGreya [7K]

Answer:

x = 8

Step-by-step explanation:

Δ TSU and Δ TRV are similar , thus the ratios of corresponding sides are equal, that is

$\frac{TS}{TR}$ = $\frac{TU}{TV}$ , substitute values

$\frac{x}{x+16}$ = $\frac{5}{15}$ = $\frac{1}{3}$ ( cross- multiply )

3x = x + 16 ( subtract x from both sides )

2x = 16 ( divide both sides by 2 )

x = 8

5 0

2 years ago

What is the area of rectangle PQRS

lord [1]

Step-by-step explanation:

60 × 60= 3600

I hope this is correct

6 0

2 years ago

1. 267.935:39= 2. 689.354:78= 3. 96.873:56=

USPshnik [31]

Question 1.) 267.935:39=

Answer 1.) 6.870 approximately

Question 2.) 689.354:78

Answer 2.) 8.838 approximately

Question 3.) 96.873:56

Answer 3.) 1.730 approximately

Explanation : Since the numerators are expressed in thousandths, the answers must be expressed in thousandths too.

Hope this helps!

$\textit{\textbf{Spymore}}$

4 0

3 years ago

The plane x+y+2z=8 intersects the paraboloid z=x2+y2 in an ellipse. Find the points on this ellipse that are nearest to and fart

DiKsa [7]

Answer:

The minimum distance of √((195-19√33)/8) occurs at ((-1+√33)/4; (-1+√33)/4; (17-√33)/4) and the maximum distance of √((195+19√33)/8) occurs at (-(1+√33)/4; - (1+√33)/4; (17+√33)/4)

Step-by-step explanation:

Here, the two constraints are

g (x, y, z) = x + y + 2z − 8

and

h (x, y, z) = x ² + y² − z.

Any critical point that we find during the Lagrange multiplier process will satisfy both of these constraints, so we actually don’t need to find an explicit equation for the ellipse that is their intersection.

Suppose that (x, y, z) is any point that satisfies both of the constraints (and hence is on the ellipse.)

Then the distance from (x, y, z) to the origin is given by

√((x − 0)² + (y − 0)² + (z − 0)² ).

This expression (and its partial derivatives) would be cumbersome to work with, so we will find the the extrema of the square of the distance. Thus, our objective function is

f(x, y, z) = x ² + y ² + z ²

and

∇f = (2x, 2y, 2z )

λ∇g = (λ, λ, 2λ)

µ∇h = (2µx, 2µy, −µ)

Thus the system we need to solve for (x, y, z) is

2x = λ + 2µx (1)

2y = λ + 2µy (2)

2z = 2λ − µ (3)

x + y + 2z = 8 (4)

x ² + y ² − z = 0 (5)

Subtracting (2) from (1) and factoring gives

2 (x − y) = 2µ (x − y)

so µ = 1 whenever x ≠ y. Substituting µ = 1 into (1) gives us λ = 0 and substituting µ = 1 and λ = 0 into (3) gives us 2z = −1 and thus z = − 1 /2 . Subtituting z = − 1 /2 into (4) and (5) gives us

x + y − 9 = 0

x ² + y ² + 1 /2 = 0

however, x ² + y ² + 1 /2 = 0 has no solution. Thus we must have x = y.

Since we now know x = y, (4) and (5) become

2x + 2z = 8

2x ² − z = 0

z = 4 − x

z = 2x²

Combining these together gives us 2x² = 4 − x , so

2x² + x − 4 = 0 which has solutions

x = (-1+√33)/4

and

x = -(1+√33)/4.

Further substitution yeilds the critical points

((-1+√33)/4; (-1+√33)/4; (17-√33)/4) and

(-(1+√33)/4; - (1+√33)/4; (17+√33)/4).

Substituting these into our objective function gives us

f((-1+√33)/4; (-1+√33)/4; (17-√33)/4) = (195-19√33)/8

f(-(1+√33)/4; - (1+√33)/4; (17+√33)/4) = (195+19√33)/8

Thus minimum distance of √((195-19√33)/8) occurs at ((-1+√33)/4; (-1+√33)/4; (17-√33)/4) and the maximum distance of √((195+19√33)/8) occurs at (-(1+√33)/4; - (1+√33)/4; (17+√33)/4)

4 0

2 years ago