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3 years ago

Darius uses the polynomial identity (x−y)^2=x^2−2xy+y^2 to show that 9² = 81. What values can Darius use for x and y?

Mathematics

2 answers:

Verdich [7]3 years ago

6 0

Answer:

Darius can use x=10 and y=1

Step-by-step explanation:

Darius wants to use the polynomial identity

$(x-y)^2=x^2-2xy+y^2$

to find 9²

Let x=10 and y=1

Then,

$(10-1)^2=10^2-2\times 10\times 1+1^2\\\\=100-20+1\\\\=80+1\\\\=81$

$(10-1)^2=81$

implies that 9² = 81

Hence, Darius can use x=10 and y=1

Assoli18 [71]3 years ago

6 0

did you ever get the answer? if so, what was it?

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Solve, then write, each equation in slope intercept form.

djyliett [7]

Answer:

1) (3,5)

2) (4,-7)

3) (6,4)

4) (-4,-3)

Step-by-step explanation:

Subtract y from both sides of the equation.

x = 8 − y

x − y = −2

Replace all occurrences of x in x − y = −2 with 8 − y.

x = 8 − y

(8 − y) − y = −2

Subtract y from −y.

x = 8 − y

8 − 2y = −2

Solve for y in the second equation.

x = 8 − y

y = 5

Replace all occurrences of y in x = 8 − y with 5.

x = 8 −(5)

y = 5

Simplify 8 −(5).

x = 3

y = 5

Slope = (3,5)

Multiply each term by 2 and simplify.

2x+y=12

y+6=−x−4

Move all terms containing variables to the left side of the equation.

2x+y=1x+2

y+6=−4

Move all terms not containing a variable to the right side of the equation.

2x+y=1x+2

y=−10

Multiply each equation by the value that makes the coefficients of x opposite.

2x+y=1(−2)⋅

(x+2y)=(−2)(−10)

Simplify.

2x+y=1−2x−4

y=20

Add the two equations together to eliminate x from the system.

2x+y=1+−2x−4

y=20−3

y=21

Divide each term by −3 and simplify.

y = −7

Substitute the value found for y into one of the original equations, then solve for x.

x = 4

slope (4,-7)

Subtract y from both sides of the equation.

2x−y=8x−y=2

Multiply each equation by the value that makes the coefficients of y opposite

2x−y=8(−1)⋅

(x−y)=(−1)(2)

Simplify. 2x−y=8

−x+y=−2

Add the two equations together to eliminate y from the system.

2x−y=8 + −x+y=−2x=6

Substitute the value found for x into one of the original equations, then solve for y.

y=4

slope (6,4)

Simplify 2(x+1).

y−3=2x+2

y=−3(x+5)

Simplify −3(x+5)

y−3=2x+2

y=−3x−15

Move all terms containing variables to the left side of the equation.

−2x+y−3=2

y=−3x−15

Add 3x to both sides of the equation.

−2x+y−3=2

y+3x=−15

Move all terms not containing a variable to the right side of the equation.

−2x+y=5

y+3x=−15

Reorder the polynomial.

−2x+y=5

3x + y=−15

Multiply each equation by the value that makes the coefficients of y opposite.

−2x+y=5(−1)⋅

(3x+y)=(−1)(−15)

Simplify.

−2x+y=5

−3x−y=15

Add the two equations together to eliminate y from the system.

−2x+y=5 + −3x−y=15−5x=20

Divide each term by −5 and simplify.

x=−4

Substitute the value found for x into one of the original equations, then solve for y.

y=−3

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4 0

3 years ago

Bianca and Meredith are sisters. Meredith's height is 23 of Bianca's height plus 32 inches. Meredith is 60 inches tall. A girl i

jarptica [38.1K]

Answer:

Bianca's height = 42 inches

Step-by-step explanation:

Let x be the Bianca height.

Given:

Meredith height = 60 inches

We need to find the Bianca height.

Solution:

From the given statement the Meredith's height is $\frac{2}{3}$ of Bianca's height plus 32 inches, so the equation is.

Meredith's height = $\frac{2}{3}(Bianca\ height)+32$

Substitute Meredith's height in above equation.

$60=\frac{2}{3}x+32$

Now we solve the above equation for x.

$\frac{2}{3}x=60-32$

$\frac{2}{3}x=28$

By cross multiplication.

$x=\frac{3\times 28}{2}$

28 divided by 2.

$x= 3\times 14$

$x=42\ in$

Therefore, the height of the Bianca is 42 inches.

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2 years ago

Which is the best buy?

gogolik [260]

Answer:

Step-by-step explanation:

work out price of each for one bottle

A) $12.60 ÷ 7 = $1.80

B) $10.98 ÷ 6 = $1.83

C) $18.10 ÷ 10 = $1.81

D) $16.38 ÷ 9 = $2.82

we can clearly see that A is the cheapest

5 0

2 years ago

Read 2 more answers

The perimeter of a stop sign is 99.2 inches. Each side of the stop sign is equal.

san4es73 [151]

Answer: The equation can be written as 8n = 99.2.

Step-by-step explanation:

In my answer, I used the variable n to distinguish itself as one side of the stop sign. 99.2 is the final perimeter in inches.

A stop sign is an octagonal shape (otherwise, it is made up of 8 equal sides). Therefore, with this information, you can interpret that the length of one side would be equal to the length of all of the other sides.

Hence, the answer can be represented as 8n = 99.2.

6 0

3 years ago

a circle is centered at the point -3,2) and passes through the point (1,5). The radius of the circle is blank units. The point (

lianna [129]

It's important that you share the complete question. What is your goal here? Double check to ensure that you have copied the entire problem correctly.

The general equation of a circle is x^2 + y^2 = r^2. Here we know that the circle passes thru two points: (-3,2) and (1,5). Given that a third point on the circle is (-7, ? ), find the y-coordinate of this third point.

Subst. the known values (of the first point) into this equation: (-3)^2 + (2)^2 = r^2. Then 9 + 4 = 13 = r^2.

Let's check this. Assuming that the equation of this specific circle is
x^2 + y^2 = r^2 = 13, the point (1,5) must satisfy it.

(1)^2 + (5)^2 = 13 is not true, unfortunately.

(1)^2 + (5)^2 = 1 + 25 = 26 (very different from 13).

Check the original problem. If it's different from that which you have shared, share the correct version and come back here for further help.

3 0

3 years ago