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3 years ago

Calculate the constant of variation if y varies directly as x.

Mathematics

2 answers:

Y_Kistochka [10]3 years ago

6 0

Answer:

k = - $\frac{3}{2}$

Step-by-step explanation:

since y varies directly as x, then the equation connecting them is

y = kx ← k is the constant of variation

to find k use the given condition y = - 3 when x = 2, thus

k = $\frac{y}{x}$ = $\frac{-3}{2}$ = - $\frac{3}{2}$

Anton [14]3 years ago

5 0

The answer is A -3/2

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The starting balance is $42.51 please help me with math

Jet001 [13]

The answer is A, $46.76

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3 years ago

The variable x varies directly as y and x varies inversely as z. What is the value is y when x=20 and z=-2, if y=30 when z=3 and

miv72 [106K]

Answer:

Y=-80

Step-by-step explanation:

X=Ky/z

5=30k/3

30k=15

K=1/2

20=Ky/(-2)

Ky =-40

1/2y=-40

Y=-80

7 0

3 years ago

Jackie makes an $800 deposit into a bank account earning 4.5% interest.

Pepsi [2]

Answer:

a. $1251.5

b. $1254.64

c. 15.4 years

d. 30.56 years

Step-by-step explanation:

Given the information:

Principle (P) = $800
Interest = 4.5%

As we know, the formula to find the future value of Jackie deposit with interest is compounded monthly, quaterly, ..is

$A=P(1+\frac{r}{n} )^{nt}$ where:

P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time

Hence:

a. If the interest is compounded quarterly how much money will Jackie have in 10 years?

$A=P(1+\frac{r}{n} )^{nt}$

<=> $A=800(1+\frac{0.045}{4} )^{4*10}$

<=> A = $1251.5

d. If Jackie's money is compounded monthly, how long will it take her money to triple?

<=> $A=P(1+\frac{r}{n} )^{nt} = 3*800$

<=> $800(1+\frac{0.045}{12} )^{12*t} = 2400$

<=> $(1+\frac{0.045}{12} )^{12*t} = 3$

<=> t = 30.56 years

As we know, the formula to find the future value of Jackie deposit with interest is compounded continuously

A = P* $e^{rt}$ where e is the mathematical constant approximated as 2.7183.

b. If the interest is compounded continuously how much money will Jackie have in 10 years?

<=> A = 800* $2.7183^{0.045*10}$

<=> A = $1254.64

C. If Jackie's money is compounded continuously, how long will it take her money to double?

<=> P* $e^{rt}$ = 2*800

<=> 800* $2.7183^{0.045*t}$ = 1600

<=> $2.7183^{0.045*t}$ = 2

<=> t = 15.4 years

8 0

3 years ago

Pls help with this problem

Gekata [30.6K]

Answer:

Step-by-step explanation:

Isolate the variable:

6x - 5 = 7

+5 +5

6x = 12

/6 /6

x = 2

Check our work:

6(2) - 5 =7

12 - 5 = 7

7 = 7

Correct!

8 0

3 years ago

PLEASE HELP MATH QUESTION

Nikitich [7]

Answer:

The measure of $\angle ACD = 42$

Step-by-step explanation:

Given:

$\angle WZX = 82\\\angle BDC = 56\\$

construction :

Saul draws a line parallel to $\vec {AB}$ that intersects $\vec {ZA}$ at C and $\vec {ZB}$ at D.

we have drawn it in orange colour in the figure below

Solution

We know vertically opposite angles are equal therefore, angle WZX and angle CZD are vertically opposite angles. Therefore they are equal as we have measured angle WZX is 82° so measure angle CZD is also 82°

$\angle WZX = \angle CZD = 82$

Now measure angle BDC is 56° given so that is also same as measure angle CDZ

$\angle BDC = \angle CDZ = 56$

Now in triangle CZD we have SUM of the all the measures of angle is 180° by Triangle property. Therefore,

$\angle CZD + \angle CDZ + \angles ZCD = 180$

Now substituting the values of angle CZD = 82° and angle CDZ = 56° we get,

$82 + 56 + \angle ZCD = 180\\138 + \angle ZCD = 180\\\angle ZCD = 180 - 138\\\angle ZCD = 42$

But angle ZCD is the same angle ACD. Therefore both are same

$\angle ZCD = \angle ACD =42\\\angle ACD = 42$

3 0

3 years ago