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2 years ago

What is the constant of proportionality in the proportional relationship y= 4/5x ?

Mathematics

2 answers:

Lady bird [3.3K]2 years ago

7 0

Answer:

the snserw should be -3 or -5

Step-by-step explanation:

SCORPION-xisa [38]2 years ago

3 0

Answer:

Step-by-step explanation:

Proportional relationship is:

y = kx, where k is the constant of proportionality

We have:

y = 4/5x

So the value of k is 4/5

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50 POINTS! :D

Alexxandr [17]

Answer:

The speed of the first car is 60 mph

Step-by-step explanation:

speed = distance/time

Solve the above equation for distance to get

distance = speed * time

or simply

d = st

Now we use this formula for distance to write an equation for each car.

Let s = speed of second car

Then since the speed of the first car is 10 mph faster, the first car's speed is s + 10.

The time the two cars traveled is equal but unknown, so let the time = t.

First car: speed = s + 10; time = t; distance = 120 miles

d = st

120 = (s + 10)t

(s + 10)t = 120 Equation 1

Second car: speed = s; time = t; 100 miles

d = st

100 = st

st = 100 Equation 2

Equations 1 and 2 form a system of 2 equations in 2 unknowns.

(s + 10)t = 120

st = 100

Distribute t in the first equation.

st + 10t = 120

From the second equation we know st = 100, so substitute 100 for st.

100 + 10t = 120

10t = 120

t = 2

The time traveled was 2 hours.

Equation 2:

st = 100

Substitute t with 2.

s * 2 = 100

s = 50

The speed of the second car was 50 mph.

The speed of the first car is s + 10.

s + 10 = 50 + 10 = 60

Answer: The speed of the first car is 60 mph

8 0

3 years ago

3h-5h+11=17 Solve Equation.

chubhunter [2.5K]

The answer is -3
hope this help!!!!!

3 0

3 years ago

Solve the system of equations by finding the reduced row echelon form of the augmented matrix. Write the solutions for x and y i

Gwar [14]

Answer:

The solutions for the given system of equations are:

$\left \{ {{x=-5} \atop {y=12-4z}} \right.$

Step-by-step explanation:

Given the equation system:

$\left \{ {{3x+y+4z=-3} \atop {-x+y+4z=17}} \right.$

We obtain the following matrix:

$\left[\begin{array}{cccc}3&1&4&-3\\-1&1&4&17\end{array}\right]$

Step 1: Multiply the fisrt row by 1/3.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\-1&1&4&17\end{array}\right]$

Step 2: Sum the first row and the second row.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&\frac{4}{3} &\frac{16}{3}&16\end{array}\right]$

Step 3: Multiply the second row by 3/4.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&1 &4&12\end{array}\right]$

Step 4: Multiply the second row by -1/3 and sum the the first row.

$\left[\begin{array}{cccc}1&0 &0&-5\\0&1 &4&12\end{array}\right]$

The result of the reduced matrix is:

$\left \{ {{x=-5} \atop {y+4z=12}} \right.$

This is equal to:

$\left \{ {{x=-5} \atop {y=12-4z}} \right.$

These are the solutions for the system of equations in terms of z, where z can be any number.

6 0

3 years ago

Carry out three steps of the Bisection Method for f(x)=3x−x4 as follows: (a) Show that f(x) has a zero in [1,2]. (b) Determine w

ELEN [110]

Answer:

a) There's a zero between [1,2]

b) There's a zero between [1.5,2]

c) There's a zero between [1.5,1.75].

Step-by-step explanation:

We have $f(x)=3^x-x^4$

A)We need to show that f(x) has a zero in the interval [1, 2]. We have to see if the function f is continuous with f(1) and f(2).

$f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(2)=3^2-(2)^4=9-16=(-7)$

We can see that f(1) and f(2) have opposite signs. And f(1)>f(2) and the function is continuous, this means that exists a real number c between the interval [1,2] where f(c)=0.

B)We have to repeat the same steps of A)

For the subinterval [1,1.5]:

$f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13$

f(1) and f(1.5) have the same signs, this means there's no zero in the subinterval [1,1.5].

For the subinterval [1.5,2]:

$f(x)=3^x-x^4\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13\\\\f(2)=3^2-(2)^4=9-16=(-7)$

f(1.5) and f(2) have opposite signs, this means there's a zero between the subinterval [1.5,2].

C)We have to repeat the same steps of A)

For the subinterval [1,1.25]:

$f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5$

f(1) and f(1.25) have the same signs, this means there's no zero in the subinterval [1,1.25].

For the subinterval [1.25,1.5]:

$f(x)=3^x-x^4\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13$

f(1.25) and f(1.5) have the same signs, this means there's no zero in the subinterval [1.25,1.5].

For the subinterval [1.5,1.75]:

$f(x)=3^x-x^4\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13\\\\f(1.75)=3^1^.^7^5-(1.75)^4=6.83-9.37=(-2.54)$

f(1.5) and f(1.75) have opposite signs, this means there's a zero between the subinterval [1.5,1.75].

For the subinterval [1.75,2]:

$f(x)=3^x-x^4\\\\f(1.75)=3^1^.^7^5-(1.75)^4=6.83-9.37=(-2.54)\\\\f(2)=3^2-(2)^4=9-16=(-7)$

f(1.75) and f(2) have the same signs, this means there isn't a zero between the subinterval [1.75,2].

The graph of the function shows that the answers are correct.

6 0

2 years ago

Aaron has 5 dimes and 2 nickels. how much money does Aaron have?

Doss [256]

Knowing that one dime has a 10 cent value and that a nickle has a 5 cent value, we can use multiplication or addition to find the answer.

5 x 10 = 50 5 dimes together are worth 50 cents.

2 x 5 = 10 2 nickles together are worth 10 cents.

50 + 10 = 60 5 dimes and 2 nickles are worth 60 cents when added together.

ANSWER: Aaron has 60 cents.

7 0

3 years ago

Read 2 more answers