Write an equation for the proportional relationship shown in the table.

Given :-

To Find :-

Answer :-

Here we are given that,

[tex]\red{\longrightarrow}[/tex] x² + y² = 8 .

And ,

[tex]\red{\longrightarrow}[/tex] xy = 4

[tex]\red{\longrightarrow}[/tex] y = 4/x

So that ,

[tex]\red{\longrightarrow}[/tex] x² + (4/x)² = 8

[tex]\red{\longrightarrow}[/tex] x² +16/x² = 8

[tex]\red{\longrightarrow}[/tex] x⁴ + 16 = 8x²

[tex]\red{\longrightarrow}[/tex] x⁴ - 8x² + 16 = 0

Assume k² = x⁴ and k = x²

[tex]\red{\longrightarrow}[/tex] k² - 8k + 16 = 0

[tex]\red{\longrightarrow}[/tex] k² -4k -4k +16 = 0

[tex]\red{\longrightarrow}[/tex] k(k-4) -4(k-4) = 0

[tex]\red{\longrightarrow}[/tex] (k-4)² = 0

[tex]\red{\longrightarrow}[/tex] k = 4

So ,

[tex]\red{\longrightarrow}[/tex] k = x²

[tex]\red{\longrightarrow}[/tex] 4 = x²

[tex]\red{\longrightarrow}[/tex] x = √4

[tex]\red{\longrightarrow}[/tex] x = ±2

Hence the required answer is ±2.

The values of x and y of the given function are; x = y = ±2

We are given;

x² + y² = 8   -----(1)

Product of x and y = 4;

Thus; xy = 4

Now, making y the subject we have;

y = 4/x

Putting 4/x for y in eq 1 gives us;

x² + (4/x)² = 8  

x² + (16/x²) = 8

Multiply through by by x² to get;

x⁴ + 16 = 8x²

⇒ x⁴ - 8x² + 16 = 0

using online polynomial root calculator, we have x = ±2

Thus, y will also be ±2

Complete question is;

If x² + y² = 8 and the product of x and y is 4, what are x and y?

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m angle 6= 210

I'm not sure about this question

Answer:

1/4 or 1/2 good luck my  guy

Step-by-step explanation:

Answer:

make me brain list

thank u

Step-by-step explanation:

The train will take 16 seconds to pass completely through a 300 meter tunnel.

Let suppose that the train moves itself at constant velocity, the vehicles needs to cover the tunnel length ([tex]L[/tex]) and its length ([tex]l[/tex]), both in meters, to pass through the tunnel, the time taken by the train ([tex]t[/tex]) is described by the following kinematic formula:

[tex]t = \frac{L+l}{v}[/tex] (1)

Where [tex]v[/tex] is the train velocity, in meters per second.

If we know that [tex]L = 300\,m[/tex], [tex]l = 100\,m[/tex] and [tex]v = 90\,\frac{km}{h}\,\left(25\,\frac{m}{s} \right)[/tex], then the time taken by the train is:

[tex]t = \frac{300\,m + 100\,m}{25\,\frac{m}{s} }[/tex]

[tex]t = 16\,s[/tex]

The train will take 16 seconds to pass completely through a 300 meter tunnel.

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Answer:

  {5, 6, 7}

Step-by-step explanation:

The solution to the inequality is ...

  16 -r > 8 . . . . . given

  16 -8 > r . . . . . add r-8

  8 > r . . . . . . . simplify

The values in the replacement set that are less than 8 are {5, 6, 7}.

Answer:

x=42

Step-by-step explanation:

Answer:

480 quarts could be made in 12 hours

Rate: 40 quarts per hour

Step-by-step explanation:

Rate: 200/5 = 40 quarts per hour

(40)(12) = 480 quarts

Answer:

The ratio of hours of CPR training to hours of first aid training is  10:15

Step-by-step explanation:

Answer:

the angles are 89.2°, 34.5°, 56.3° and the sides are √26units, √8units, √18units respectively

Step-by-step explanation:

Distance between points (2,5) and (-1,2)

Using the formula, √(X2 - X1)² + (Y2 - Y1)²

= √(-1-2)²+(2-5)²

=√(-3)²+(-3)²

=√9+9

=√18 or 3√2

Distance between points (-1,2) and (4,3)

=√[4-(-1)]²+(3-2)²

= √5²+1²

=√25+1

=√26

Distance between points (2,5) and (4,3)

=√(4-2)²+(3-5)²

=√2²+(-2)²

=√4+4

=√8

Using Cosine rule/formula, C²= A²+B²-2abcosc

Let C be √18, A be √26 and B be √8

√18²=√26²+√8² - 2√26.√8cosc

18= 26+8 - 2√208cosc

18= 34 -2√208cosc

2√208cosc= 34-18

Cosc = 16/2√208

Cosc= 0.5546

c= Cos`¹(0.5547)

c= 56.3°

Using sine rule/formula

Sinc/C= Sina/A=Sinb/B

Sin56.3/√18= Sina/√26

Sina= (0.8320 × √26)/ √18

Sina= 0.9999

a= Sin`¹(0.9999)

a= 89.2

56.3+89.2+b= 180°( sum of angles in a triangle)

145.5 + b =180

b=180-145.5

b= 34.5

For triangle MNO, the statements that are true are m ∠ MNP < m ∠ ONP and MP< OP.

We are given a triangle MNO.

We are also given that:

m ∠ MNP = 38°

m ∠ ONP = 39°

This clearly means that:

m ∠ MNP < m ∠ ONP

Also, since m ∠ MNP < m ∠ ONP , the sides opposite to the angles will also follow the same relationship.

Side opposite to ∠ MNP is MP

and side opposite to ∠ ONP is OP

so, the relation will become:

MP < OP

Therefore, we get that, for triangle MNO, the statements that are true are m ∠ MNP < m ∠ ONP and MP< OP.

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The statements m MNP m ONP and MP < OP are true for triangle MNO.

A triangle MNO is presented to us.

Additionally, we learn that

m ∠ MNP = 38°

m ∠ ONP = 39°

This demonstrates that:

m, MNP, m, and ONP

The sides that are opposite to the angles will also adhere to the same relationship because m MNP m ONP.

MP is the side that faces MNP.

and OP is the side opposite to ONP.

hence, the relationship will be:

MP < OP

As a result, we understand that for triangle MNO, the assertions m MNP m ONP and MP OP are true.

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Answer:

i think area of the rug is 1 square yards

Step-by-step explanation:

area = 3/4×8/6

area = 2/2

area = 1 square yards

Answer:

2(4x+3)

Step-by-step explanation:

Distribute 3 ( + 2 ) + 5 to 3 + 6 + 5

Combine the terms 3 + 6 + 5 to 8 + 6

Common factor Factor 3 ( + 2 ) + 5 to 2 ( 4 + 3 )

Answer:

This is a really simple example, but imagine you had two marbles in a bowl. One is blue and one is green. Without looking, you reach into the bowl and pick one marble. What is the probability that the marble is blue?

There are two total marbles and you pick one, with one being blue and one being green. The probability that you pick the blue marble instead of the green marble is 1/2. The 2 represents the total number of marbles and the 1 represents the favorable outcome of drawing a blue marble.

Hope this helps!

Answer:

It is an obtuse angle so correct

The given triangle is an obtuse angle triangle.

The correct option is (B).

A triangle in geometry is a three-sided polygon with three edges and three vertices.

As per the given data in the diagram:

We are given a triangle and all the angles of the triangle are also given.

We have to find out the type of the triangle.

If all angles of a triangle are less than 90°, then it's an acute angle triangle.

If any angle of the triangle is greater than 90°, then it's an obtuse angle triangle.

If any angle of the triangle is equal to 90°, then it's a right angle triangle.

For the given triangle:

30° < 90°

24° < 90°

126° > 90°

The given triangle is an obtuse angle triangle.

Hence, the given triangle is an obtuse angle triangle.

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Answer:

xy+x+y^2+3y+2

Step-by-step explanation:

The penny reaches the water at 3.5 seconds

The height function is given as:

[tex]d = -16t^2 + 196[/tex]

(a) Graph the function

See attachment for the graph of the function

(b) Time to reach the water

From the graph, the curve of [tex]d = -16t^2 + 196[/tex] crosses the x-axis at points t = -3.5 and t = 3.5

But the time (t) cannot be negative.

Hence, the penny reaches the water at 3.5 seconds

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Answer: 2.718

Step-by-step explanation:

You don’t need the star there but it is Euchre’s number when you look it up it is 2.718

Answer:

The slope would be 5/2.

Step-by-step explanation:

Use the formula Y=mx+b. m always represents the slope and the b is the intercept. Therefore the slope of this would be 5/2.

Answer:16.50

Step-by-step explanation: hope it helps

Answer:

16.50

Step-by-step explanation:

Step-by-step explanation:

[tex]thanks \: you \: the \: point \\ pls \: follow \: me[/tex]

Therefore, the answer is 28.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

$3.30

Step-by-step explanation:

1 kg = 1000 g

therefore, 150 g = 0.15 kg

multiply the cost by the amount

22 x 0.15 = 3.3, or $3.30

Erica used 50 pounds of type B coffee

Let the number of pounds of type A coffee be A

Let the number of pounds of type B coffee be B

Total number of pounds = 123

A   +  B   =   123.........................................(1)

Cost of 1 pound of type A coffee = $5.95

Cost of 1 pound of type B coffee = $4.40

Total cost = $654.35

5.95A  +  4.40B = 654.35..........................(2)

Make A the subject of the formula in equation (1)

A  =  123  -   B........................(3)

Substitute equation (3) into equation (2)

5.95(123 - B)  +  4.40B  =  654.35

731.85  -  5.95B  +  4.40B  =  654.35

5.95B  -  4.40B  =  731.85 - 654.35

1.55B   =   77.5

B   =  77.5/1.55

B   =   50

Erica used 50 pounds of type B coffee

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Answer:

104 degrees

Step-by-step explanation:

180-(180-(180-(25+85)+65)+31)

Answer:

Slope: -1

y intercept: -3

equation: y=-1x-3

Step-by-step explanation:

The y intercept is when x is zero.