Which table of ordered pairs represents a proportional relationship?

Answer:

6 or -1.5

Step-by-step explanation:

We can let this integer be x.

Therefore, according to the question we have:

[tex]2x^2-18=9x[/tex]

Subtracting 9x, we have a quadratic:

[tex]2x^2-9x-18=0[/tex]

Plugging into the quadratic equation:

[tex]\frac{9+\sqrt{81+144}}{4}, \frac{9-\sqrt{81+144}}{4},[/tex]

the square root of 81+144 is 15, so the answer is either 6 or -1.5

Problem 1

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Explanation:

The first task is to determine the function for f(x). Because it's linear, it's in the form y = mx+b. Let's find the slope m.

Select any two columns to pick out (x,y) points from the f(x) function. I'll pick the first two columns to select the points (-6,15) and (-4,11). Apply the slope formula to these two points to get...

m = (y2-y1)/(x2-x1)

m = (11-15)/(-4-(-6))

m = (11-15)/(-4+6)

m = -4/2

m = -2

Then use this m value along with any of the points of the table to determine the y intercept b. I'll use the point (-6,15)

y = mx+b

b = y-mx

b = 15-(-2)*(-6)

b = 15-12

b = 3

The y = mx+b equation becomes y = -2x+3 and that leads directly to the function f(x) = -2x+3.

Repeat all of those steps but do so for g(x) this time. I'll skip those steps over but you should get the function g(x) = 5x-6.

The y intercepts of f(x) and g(x) found were 3 and -6 respectively. Subtract those values to find the y intercept of h(x) = (f-g)(x) = f(x)-g(x).

So we get 3-(-6) = 3+6 = 9 which leads to the location (0, 9).

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Problem 2

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Explanation:

Through trial and error, the factor by grouping method, or using your graphing calculator, factor the denominator to get

g(x) = x^3+2x^2-x-2 = (x+2)(x+1)(x-1)

The factors (x+2), (x+1) and (x-1) lead to the roots of x = -2, x = -1, and x = 1 in that order. Those three roots of g(x) will make g(x) = 0 and cause a division by zero error in the denominator. So we must kick out those three values from the domain. Every other real number is allowed in the domain. So that's how we get the notation for choice A. It starts off saying x is a real number. Then it goes onto say that -2, -1 and 1 aren't allowed.

So overall the domain is described as: "x can be almost any real number except x cannot be -2, cannot be -1, and it cannot be 1".

Side note: We don't involve the numerator function at all.

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Problem 3

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Explanation:

The height is x, which we can factor out like this

2x^3-5x^2-3x

2x^2*x - 5x*x - 3*x

x(2x^2-5x-3)

Effectively you would use the distribution rule in reverse.

Now let's factor the remaining expression in the parenthesis.

I'll use the factor by grouping method.

2x^2-5x-3

2x^2-6x+1x-3

(2x^2-6x) + (1x-3)

2x(x-3) + 1(x-3)

(2x+1)(x-3)

Therefore, the full factorization is

x(2x+1)(x-3)

which shows we have the dimensions of x, (2x+1) and (x-3). The order doesn't matter so we could easily have (2x+1) the length and (x-3) the width, or we could have it the other way around.

You can verify that (2x+1)(x-3) expands out to 2x^2-5x-3 using either the FOIL method or the box method.

Answer:

d! 35 ......!!!!!!!!!!!!

Answer:

29.4

Step-by-step explanation:

Answer:

2p/q

2q/p

q/p=2

p/q =2

Step-by-step explanation:

Here are some possible answers. The way your statement is formated in does not ask a question nor does it provide enough information for one to deduce what the question was.

Answer: $2.67

Step-by-step explanation:

$8.90 - $6.23 = $2.67

Brainliest? Im just trying to get to a higher rank

Answer:

Retainers have been designed to be used as an end of treatment to help retain your teeth in their new position. ... These are removable and fixed retainers. The reason why retainers can't be used to close a gap is because they are fitted at the end of treatment and are made to fit the straight teeth mould.

hope it help u

itz by Riddhi

Answer:

yes

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

5x6 = 30

30x4= 120

Answer:

The Degree Measure of the Angle = Radian x (180/)

Answer:

Length=8 m,Breadth=6 m,Height=3 m

We know,

LSA=2(l+b)×h

LSA=2×14×3=84 m

2

Therefore, cost of painting = 84×60=Rs.5040.

Answer:

A year but -1.

Step-by-step explanation:

52x7=364.

Hope this helps!

Answer:

there are 364 days in 52 weeks.

Step-by-step explanation:

To find out how many days are in 52 weeks you have to multiply the amount of days there are in a week by 52, there are 7 days in a week and 7 times 52 is 364 so the answer is 364

Answer:

Step-by-step explanation:

d + 2d = 120

3d = 120

d = 40 m

east distance was 40cos30 + 80cos120 = -5.35898 m

north distance was 40sin30 + 80sin120 = 89.282032

as 30° and 120° bearings are 90° apart, Jason needs to walk

D = √(d² + (2d)²) = d√5 or 40√5 meters or about 89.44 m to return to his original position.

we could also use √(-5.35898² + 89.282032²) = 89.44 m

direction will be

θ = arctan -89.28/5.359 = -86.565° or a bearing of 273.4°

Answer:

The answer is b

Step-by-step explanation:

Answer:

There should be 20 students that have both Beats and AirPods.

Step-by-step explanation:

There are 50 students in total.

20 students have only AirPods and 30 students have Beats. Out of the 30 who own Beats, there are 10 students that have ONLY Beats.

30 - 10 = 20.

It's a tricky question, but this is the correct answer!

Hope This Helps!

Answer:

Step-by-step explanation:

tanθ = opp/adj

θ = arctan(1.5 / 4)

θ  = 20.55604521958346...

θ = 20.6°

Answer

20.56

Step-by-step explanation:

tan∅=opposite/adjacent

=1.5÷4

=0.375

then to get ∅ find the tan inverse of 0.375 you'll get 20.55604...

put it in two decimal point...20.56°

Answer: b=7

Step-by-step explanation:

Answer:

y=-2x+4

Step-by-step explanation:

if y is 4..it means x intercept is 0

gradient is -2

and we know gradient is the change in y /change in X

so: we let the second intercepts to be (x,y)

so y-4/x-0=-2

multiply by x-0 both sides then collect like terms together

it will be y= -2x+4

Answer:

A. One solution

Step-by-step explanation:

y = 2/3x - 2 has slope of 2/3

2x + 3y = 9

       3y = -2x + 9

         y = (-2/3)x + 3 has slope of -2/3

lines with different slopes have only ONE intersection

Answer:

2.5 feet for each bow

Step-by-step explanation:

15/6= 2.5

Answer:

......................

Answer:

1.375 decimal to fraction.

2/7 Fraction to Decimal

Step-by-step explanation:

Answer: tbh jets arent really a good way to travel man. you better start walking ur lazy butt and get movin.

Step-by-step explanation:

Answer:

[tex]2sec^2xtanx[/tex]

Step-by-step explanation:

[tex]\frac{d}{dx} tan^2x[/tex]

[tex]\frac{d}{dx} tanxtanx[/tex]

[tex](\frac{d}{dx}tanx)(tanx)+(tanx)(\frac{d}{dx}tanx)[/tex]

[tex]\frac{d}{dx}tanx=\frac{d}{dx}\frac{sinx}{cosx}=\frac{(cosx)(cosx)-(sinx)(-sinx)}{(cosx)^2}=\frac{cos^2x+sin^2x}{cos^2x}=\frac{1}{cos^2x}=sec^2x[/tex]

[tex](sec^2x)(tanx)+(tanx)(sec^2x)[/tex]

[tex]2sec^2xtanx[/tex]

Helpful tips:

Product Rule: [tex]\frac{d}{dx}f(x)g(x)=f'(x)g(x)+f(x)g'(x)=\frac{d}{dx}f(x)*g(x)+f(x)*\frac{d}{dx}g(x)[/tex]

Quotient Rule: [tex]\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}=\frac{g(x)\frac{d}{dx}f(x)-f(x)\frac{d}{dx}g(x)}{(g(x))^2}[/tex]

Pythagorean Identity: [tex]cos^2x+sin^2x=1[/tex]

Answer: 4.8

Explanation: divide total needed of blue paint (3) by 1/2 to find the ratio, which is 6. then multiply that by 4/5 to get the total of yellow paint, which is 4.8

Answer:

13

Step-by-step explanation:

add 3/4 and 3/4 to get 6/4 then get 1/2 times the bottom and the top but 2 to get 2/4 so then do 6/4 - 2/4 to get 4/4 or 1

add 10,8 to get 18 then subtract 6 to get 12 then all the 1 and you get your answer. Hope this helped

Answer:

13

Step-by-step explanation:

Convert 10 3/4

to an improper fraction.

43/4 + 8 3/4 − 6 1/2

Convert 8 3/4

to an improper fraction.

43/4 + 35/4 − 6 1/2

Convert 6 1/2

to an improper fraction.

434 + 354 − 132

Combine fractions.

78/4 + −13/2

Simplify each term.

39/2 − 13/2

Combine fractions.

13

Answer:

17/12

Step-by-step explanation:

In order to add fractions, you have to have a common denominator. The denominators in these fractions are 3, 2, and 4 (the bottom numbers). To get a common denominator, figure out what number all three of them can go into. Their common factor would be 12 because all three numbers go into 12.

Multiply each numerator in the fraction (the top number) by how much it takes to get from our current denominators (3,2,4) to our final denominator (12).

For example, in 2/3 we know that 3 times 4 equals 12. Multiply the top number by 4 to get 8/12.

In 1/2 we know that 2 times 6 equals 12. Multiply by 6 to get 6/12.

In 1/4 we know that 4 times 3 equals 12. Multiply by 3 to get 3/12.

Add the fractions to get 17/12.