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3 years ago

Write an exponential function in the form y = ab that goes through points (0,19)and (5,4617).

Mathematics

1 answer:

gtnhenbr [62]3 years ago

3 0

Answer:

y = 1/2 (2)x

Step-by-step explanation:

Using the equation y = abx , substitute both of your given points into that equation.

2 = ab2 and 4 = ab3 Solve each equation for a.

2⁄b2 and 4⁄b3 = a Therefore, 2⁄b2 = 4⁄b3

Cross multiply: 2b3 = 4b2 Divide both sides by b2

2b = 4 a = 2/4 = 1/2

b = 2

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If he rows with the current, Mishka rows 48 km in 3 hours. If he rows against the current, it takes 4 hours to travel the same d

Zarrin [17]

<h2>Mishka's speed = 14 km/hr</h2><h2>Current speed = 2 km/hr</h2>

Step-by-step explanation:

Let the speed of rowing be r and speed of current be c.

If he rows with the current, Mishka rows 48 km in 3 hours.

Relative speed = r + c

Distance = 48 km

Time = 3 hours

48 = 3 x ( r+c)

r + c = 16 ---------------------------eqn 1

If he rows against the current, it takes 4 hours to travel the same distance.

Relative speed = r - c

Distance = 48 km

Time = 4 hours

48 = 4 x ( r - c)

r - c = 12 ---------------------------eqn 2

eqn 1 + eqn 2

2r = 28

r = 14 km/hr

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14 + c = 16

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Mishka's speed = 14 km/hr

Current speed = 2 km/hr

6 0

2 years ago

Three horses, call them a, b, and c, are going to race against each other. the probability that a will win the race is 1⁄5 and t

Genrish500 [490]

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2 years ago

Leah is building a slide for her kids. if the latter is 7 feet tall and she wants the bottom of the slide to be 4 feet from the

nadezda [96]

The line needs to be 8.06 m long

Explanation

Given that the ladder is 7 feet tall and the bottom of the slide should be 4 m away from the ladder.

The ladder,slide and the ground connecting them makes the sides of a right angled triangle with ladder as the height and ground as the base.

base=4m

height=7m

hypotenuse can be determined using pythagoras law

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4 0

2 years ago

Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the

scoray [572]

9514 1404 393

Answer:

7 forks
20 spoons

Step-by-step explanation:

Let x and y represent the numbers of forks and spoons made, respectively.

The cost of materials is ...

1.70x + 1.30y = 37.90

The revenue from sales is ...

5.60x + 5.40y = 147.20

You can solve these by any of your favorite methods. A graph is attached. It shows the solution is (x, y) = (7, 20).

They made 7 forks and 20 spoons.

_____

<em>Additional working out</em>

The equation coefficients are not "nice" multiples of each other, so elimination and substitution will require multiplying both equations by some numbers. If we're going to that trouble, we may as well use Cramer's Rule or a variation of the "cross multiplication method". The latter is relatively straightforward and can be easy to remember. It tells you the solution to ...

ax +by +c = 0

dx +ey +g = 0

is ...

1/(ae-db) = x/(bg-ey) = y/(cd-ga)

Here, that becomes ...

1/(1.70·5.40-5.60·1.30) = x/(1.30·(-147.20)-5.40·(-37.90))

= y/(-37.90·5.60-(-147.20·1.70))

1/1.9 = x/13.3 = y/38

x = 13.3/1.9 = 7 . . . number of forks

y = 38/1.9 = 20 . . . number of spoons

The above solution formula may be more easily remembered in terms of the cross-multiplication pattern that gives the method its name. When the coefficients are written in two rows of four, with the last being a repeat of the first:

a b c a
d e g d

each of the three denominators (of 1, x, and y) is the difference of products in adjacent columns, formed in an X fashion: ae-db, bg-ec, cd-ga. Note that the equations are written in "general" form, which is similar to "standard" form, but with all of the non-zero terms on the left of the equal sign. (This has the effect of changing the sign of the constants: 1.7x+1.3y=37.9 ⇒ 1.7x+1.3y-37.9=0)

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2 years ago

Distributive property of 16x + 24

mina [271]

Answer:

8(2x+3)

Step-by-step explanation:

Find the GCF (greatest common factor) of 16 and 24

The GCF is 8

divide both by eight

there you go....

I'm not good at explaining this ;-; ,my sincere apologies.

Hopefully I was helpful!

4 0

2 years ago

Write an exponential function in the form y = ab that goes through points (0,19)and (5,4617).​

Write an exponential function in the form y = ab that goes through points (0,19)and (5,4617).