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krek1111 [17]
3 years ago
13

The graph of a proportional relationship contains the point (-30, 18)

Mathematics
1 answer:
Elena L [17]3 years ago
4 0

Answer:

k=-\frac{3}{5}

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=\frac{y}{x} or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

we have the point (-30,18)

so

x=-30, y=18

Find the value of k

k=\frac{y}{x}

substitute

k=\frac{18}{-30}

Simplify

Divide by 6 both numerator and denominator

k=-\frac{3}{5}

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Please solve this with explanations!
lyudmila [28]

Answer:

D. -2x - 8

Step-by-step explanation:

1) Simplify 1/3(6x+15) to 6x+15/3

-6x+15/3 - 3

2) Factor out the common term 3.

-3(2x+5)/3 - 3

3) Cancel 3.

-(2x+5)-3

4) Remove parentheses.

-2x-5-3

5) Collect like terms.

-2x+(-5-3)

6) Simplify

-2x-8

3 0
2 years ago
Which definite integral approximation formula is this: the integral from a to b of f(x)dx ≈ (b-a)/n * [<img src="https://tex.z-d
Stella [2.4K]

The answer is most likely A.

The integration interval [<em>a</em>, <em>b</em>] is split up into <em>n</em> subintervals of equal length (so each subinterval has width (<em>b</em> - <em>a</em>)/<em>n</em>, same as the coefficient of the sum of <em>y</em> terms) and approximated by the area of <em>n</em> rectangles with base (<em>b</em> - <em>a</em>)/<em>n</em> and height <em>y</em>.

<em>n</em> subintervals require <em>n</em> + 1 points, with

<em>x</em>₀ = <em>a</em>

<em>x</em>₁ = <em>a</em> + (<em>b</em> - <em>a</em>)/<em>n</em>

<em>x</em>₂ = <em>a</em> + 2(<em>b</em> - <em>a</em>)/<em>n</em>

and so on up to the last point <em>x</em> = <em>b</em>. The right endpoints are <em>x</em>₁, <em>x</em>₂, … etc. and the height of each rectangle are the corresponding <em>y </em>'s at these endpoints. Then you get the formula as given in the photo.

• "Average rate of change" isn't really relevant here. The AROC of a function <em>G(x)</em> continuous* over an interval [<em>a</em>, <em>b</em>] is equal to the slope of the secant line through <em>x</em> = <em>a</em> and <em>x</em> = <em>b</em>, i.e. the value of the difference quotient

(<em>G(b)</em> - <em>G(a)</em> ) / (<em>b</em> - <em>a</em>)

If <em>G(x)</em> happens to be the antiderivative of a function <em>g(x)</em>, then this is the same as the average value of <em>g(x)</em> on the same interval,

g_{\rm ave}=\dfrac{G(b)-G(a)}{b-a}=\dfrac1{b-a}\displaystyle\int_a^b g(x)\,\mathrm dx

(* I'm actually not totally sure that continuity is necessary for the AROC to exist; I've asked this question before without getting a particularly satisfying answer.)

• "Trapezoidal rule" doesn't apply here. Split up [<em>a</em>, <em>b</em>] into <em>n</em> subintervals of equal width (<em>b</em> - <em>a</em>)/<em>n</em>. Over the first subinterval, the area of a trapezoid with "bases" <em>y</em>₀ and <em>y</em>₁ and "height" (<em>b</em> - <em>a</em>)/<em>n</em> is

(<em>y</em>₀ + <em>y</em>₁) (<em>b</em> - <em>a</em>)/<em>n</em>

but <em>y</em>₀ is clearly missing in the sum, and also the next term in the sum would be

(<em>y</em>₁ + <em>y</em>₂) (<em>b</em> - <em>a</em>)/<em>n</em>

the sum of these two areas would reduce to

(<em>b</em> - <em>a</em>)/<em>n</em> = (<em>y</em>₀ + <u>2</u> <em>y</em>₁ + <em>y</em>₂)

which would mean all the terms in-between would need to be doubled as well to get

\displaystyle\int_a^b f(x)\,\mathrm dx\approx\frac{b-a}n\left(y_0+2y_1+2y_2+\cdots+2y_{n-1}+y_n\right)

7 0
3 years ago
By installing efficient water fixtures the average American can reduce water use to about 45 gallons of water per day.Using such
zimovet [89]
Hello there.

<span>By installing efficient water fixtures the average American can reduce water use to about 45 gallons of water per day.Using such water fixtures about how many gallons of water would the average American use in December 
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6 0
3 years ago
A triangle has a height of 15 in. and a area of 120 in. What is the length of it's base?
jek_recluse [69]

Answer:

b=16

Step-by-step explanation:

Formula~ 1/2*b*h

1/2*15*b=120

7.5b=120

b=120/7.5

b=16

(you can substitute the value to check-i've done it below)

1/2*16*15=?

if you work it out, the ans will be 120, therefore the ans is correct!

7 0
3 years ago
What is 19.2×108 minutes in hours?
Gennadij [26K]
The answer is:  [C]:  " 3.200 * 10⁷  h " .
_________________________________________________
Explanation:
________________________________
19.2 * 10⁸  min * (1 hr / 60 min) ;


=  (19.2 * 10⁸)
_______________ ;  
         60

_____________________________
Divide EACH SIDE of the fraction by "10" ; to get:
___________

(19.2 * 10⁷)
_______________ ;  
         6

<span>______________________________

</span>⇒  (19.2) ÷ (6) = 3.2 ;  so rewrite as:
_________________________________________________________

3.2 *  10⁷ ; which corresponds with:

Answer choice:  [C]:  " 3.200 * 10⁷  h " .
_________________________________________________________

6 0
3 years ago
Read 2 more answers
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