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2 years ago

Suppose y varies jointly as x and z. If y=15 when x=1/2 and z=6, what is the constant of variation?

Mathematics

2 answers:

Elden [556K]2 years ago

8 0

Answer:

k = 5

Step-by-step explanation:

Given y varies jointly as x and z then the equation relating them is

y = kxz ← k is the constant of variation

To find k use the condition y = 15 when x = $\frac{1}{2}$ and z = 6 , then

15 = k × $\frac{1}{2}$ × 6 = 3k ( divide both sides by 3 )

5 = k

Mashcka [7]2 years ago

4 0

Answer:

y= 15

Step-by-step explanation:

Y= Kxz

y=6 x=1/2 z=6

15= K (1/2) (6)

15= K (3)

K= 5

y= (5) (1/2) (6)

Y= 15

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A team t-shirt costs $3 per adult and $2 per child. On a certain day, the total number of adults (a) and children (c) who bought

lesya [120]

A+c=100

3a+2c=275, from the first c=100-a making the 2nd equation become:

3a+2(100-a)=275 perform indicated multiplication on left side

3a+200-2a=275 combine like terms on left side

a+200=275, subtract 200 from both sides

a=75, and since c=100-a

c=100=75=25

So the answer is D. 25 children and 75 adults
Equation 1: a+c=100
Equation 2: 3a+2c=275

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2 years ago

What is the equation of the following line written in slope-intercept form -2/3 and -1/-4? y = -11x - 7 y = -7x + 11 y = -7x - 1

Snowcat [4.5K]

Answer:

$y=-7x-11$

Step-by-step explanation:

Given:

The two points on the line are $(-2,3)$ and $(-1,-4)$ .

The slope of the line joining two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given as:

$Slope,m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here, $x_{1}=-2,y_{1}=3,x_{2}=-1,y_{2}=-4$

∴ $m=\frac{-3-4}{-1-(-2)}=\frac{-7}{-1+2}=\frac{-7}{1}=-7$

Equation of line with a point $(x_{1},y_{1})$ and slope $m$ is given as:

$y-y_{1}=m(x-x_{1})$

Plug in -2 for $x_{1}$ , 3 for $y_{1}$ and -7 for $m$ . This gives,

$y-3=-7(x-(-2))\\y-3=-7(x+2)\\y-3=-7x-(7\times 2)\\y-3=-7x-14\\y=-7x-14+3\\y=-7x-11$

Therefore, the equation of the line in vertex form is $y=-7x-11$ .

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2 years ago

I need help again.Here is the question, Distance = Rate x Time What was my rate of speed if it took me 3.5 hours to travel 210 m

Nimfa-mama [501]

Answer:

Step-by-step explanation:

210÷3.5=60

3.5x60=210

Hope this helps!

: )

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3 years ago

You deposit $300 in a savings account. The account earns 2% simple interest per year. What is the interest and balance earned af

kenny6666 [7]

Answer:

$365.70

Step-by-step explanation:

The formula to find this is $y = a(1+r)^t\\$

For this, a is the initial amount, r is the growth rate percentage (but displayed as a decimal), and t is time.

So to solve, you would do

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2 years ago

C/9 - 8 = 17 Solve the equation and show all work please show steps!!

Amiraneli [1.4K]

C/9 - 8 = 17
------------
Simplify
1/9c - 8 = 17
----------------
Add 8 to each side
1/9c - 8 + 8 = 17 + 8
1/9c = 25
--------------------
Multiply each side by 9
9 * 1/9c = 9 * 25
c = 225

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2 years ago