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4 years ago

A cyclist must travel 800 km. how many days will the trip take if the cyclist travels 8 h/day at an average speed of 16 km/h?

1 answer:

7 0

First, you need to find out how much the cyclist will travel a single day. Since the cyclist travels 16 km/h and for 8 h/day, you can easily multiply 16 x 8 = which would be 128 km/day.

To find how long it will take the cyclist to travel 800km, just divide 800 by the amount they will be going in one day. 800/128= 6.25. That would convert to 6 days and 6 hours.

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What is the equation of the line that passes through the point (4, 3) and is perpendicular to the line x + y = 4?

zimovet [89]

ANSWER

$y - x = - 1$

EXPLANATION

The required equation passes through:

(4,3) and is perpendicular to x+y=4.

Rewrite the given equation in slope-intercept form:

$y = - x + 4$

The slope of this line is -1.

The slope of the required line is perpendicular to this line, so we find the negative reciprocal of this slope.

$m= - \frac{1}{ - 1} = 1$

The equation of the line can be found using:

$y - y_1 = m(x - x_1)$

We substitute the slope and point to obtain:

$y - 3 = 1(x - 4)$

We simplify to get:

$y - 3 = x - 4$

$y - x = - 4 + 3$

The required equation is

$y - x = - 1$

5 0

3 years ago

In a video game, a bird is flung on a sling shot and follows a parabolic path. The path of the bird can be modeled by the equati

Novay_Z [31]

Answer:

The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time

Step-by-step explanation:

we have

$h=-16t^2+55t+4$

This is a vertical parabola open downward

The vertex represent a maximum

where

h is the height of the bird

t is the amount of time, in seconds, the bird had been in the air

For h=40 ft

substitute in the quadratic equation

$40=-16t^2+55t+4$

$-16t^2+55t+4-40=0$

$-16t^2+55t-36=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+55t-36=0$

$a=-16\\b=55\\c=-36$

substitute in the formula

$x=\frac{-55\pm\sqrt{55^{2}-4(-16)(-36)}} {2(-16)}$

$x=\frac{-55\pm\sqrt{721}} {-32}$

$x=\frac{-55+\sqrt{721}} {-32}=0.88\ sec$

$x=\frac{-55-\sqrt{721}} {-32}=2.56\ sec$

therefore

The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time

3 0

3 years ago

Chad earned $30 for raking leaves. He has also earned money by doing chores for 6 weeks. Altogether, he has earned $120. How muc

galben [10]

You know that he makes $90 for doing chores, dividing that by 6 and you get that each week he earns $15 for chores.

6 0

3 years ago

Read 2 more answers

A first number plus twice a second number is 14. Twice the first number plus the second totals 10. Find the numbers.

Nookie1986 [14]

Answer:

first number(x) = 2 second number(y)= 6

Step-by-step explanation:

This is an example of a simultaneous equation.

First write this word problem as equations, where x is the "first number" that you've mentioned and y is the "second number".

x + 2y = 14 (equation 1)

2x + y = 10 (equation 2)

This is solved using the elimination method.

We need to make one of the coefficients the same - in this case we can make y the same. In order to do this we need to multiply equation 2 by 2, so that y becomes 2y.

2x + y = 10 MULTIPLY BY 2

4x + 2y = 20 (this is now our new equation 2 with the same y coefficient)

Now subtract equation 1 from equation 2.

4x - x + 2y - 2y = 20 - 14 (2y cancels out here)

3x = 6

x = 2

Now we substitute our x value into equation 1 to find the value of y.

2 + 2y = 14

2y = 12

y = 6

Hope this has answered your question.

6 0

3 years ago

Read 2 more answers

Pa tulong po pleasee

astraxan [27]

Answer:

1. 7

2. 54÷2=27

only this I know please put brainlest

5 0

3 years ago

Read 2 more answers