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3 years ago

Find the midpoint of the line segment whose endpoints are given (3/5 , -6/7),(2/5,5/7)

Mathematics

1 answer:

snow_lady [41]3 years ago

3 0

The formula of a midpoint between E and F:

$M_{EF}\left(\dfrac{x_E+x_F}{2};\ \dfrac{y_E+y_F}{2}\right)$

We have the points $\left(\dfrac{3}{5},\ -\dfrac{6}{7}\right)$ and $\left(\dfrac{2}{5},\ \dfrac{5}{7}\right)$ . Substitute:

$\dfrac{\frac{3}{5}+\frac{2}{5}}{2}=\dfrac{\frac{5}{5}}{2}=\dfrac{1}{2}\\\\\dfrac{-\frac{6}{7}+\frac{5}{7}}{2}=\dfrac{-\frac{1}{7}}{2}=-\dfrac{1}{7}\cdot\dfrac{1}{2}=-\dfrac{1}{14}$

Answer: $\boxed{\left(\dfrac{1}{2},\ -\dfrac{1}{14}\right)}$

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Faucet A flows at a rate of 100 liters per 5 minutes and Faucet B flows at a rate of 100 liters per 4 minutes into an empty pool

Dmitriy789 [7]

Answer:

It will take both faucets 200 minutes to fill a pool with 9,000 liters of water

Step-by-step explanation:

Here, we want to know the time it will take for both faucets to fill a pool with 9,000 liters of water

What we need here is to have a joint rate for both faucets;

For the first faucet, we have a rate of 100 liters per 5 minutes so this means in a minute;

100/5 = 20 liters per minute

For the second faucet, the per minute rate will be 100/4 = 25 liters per minute

So therefore, the joint rate will be;

25 liters per minute + 20 liters per minute = 45 liters per minute

So the time needed to fill 9,000 liters of water in a pool will be ;

9000 liters/ 45 liters per minute = 200 minutes

8 0

3 years ago

renting paddle boats for Lakeshore paddle boats costs $10 per hour plus a one-time fee of $4 renting paddle boats from Lake padd

Anna11 [10]

Answer:

More than 2 hours

Step-by-step explanation:

Let number of hours be x

Lakeshore paddle cost:

10x + 4

Lake paddle cost:

Required inequality:

10x + 4 < 12x
12x - 10x > 4
2x > 4
x > 2

Lakeshore paddle costs less when time of rent is greater than 2 hours

3 0

3 years ago

Can someone please help me with math.

krek1111 [17]

Answer:

Step-by-step explanation:

1) Number of nickels = x

Number of quarter = y

x + y = 7 ----------------------(I)

x = 7 - y ------------------------(II)

0.05x + 0.25y = 0.55 -----------(III)

Substitute s = 7 - y in equation (III)

0.05*(7 - y) + 0.25y = 0.55

0.05*7 - 0.05*y + 0.25y = 0.55

0.35 - 0.05y + 0.25y = 0.55 {Combine like terms}

0.35 + 0.20y = 0.55 {Subtract 0.35 from both sides}

0.2y = 0.55 - 0.35

0.2y = 0.2 {Divide both sides by 0.2}

y = 0.2/0.2

y = 1

Substitute y =1 in equation (II)

x = 7 - 1

x = 6

Number of nickels = 6

Number of quarter = 1

2) Number of children tickets = x

Number of adult tickets = y

x + y = 40 -----------------(I)

x = 40 - y -----------------(II)

2x + 5y = 170 -----------------(III)

Substitute x = 40 - y in equation (III)

2*(40-y) + 5y = 170

2*40 - 2*y + 5y = 170

80 - 2y + 5y = 170 {Combine like terms}

80 + 3y = 170 {Subtract 80 from both sides}

3y = 170 - 80

3y = 90 {Divide both sides by 3}

y = 90/3

y = 30

Substitute y = 30 in equation (II)

x = 40 - 30

x = 10

Number of children tickets = 10

Number of adult tickets =30

3 0

3 years ago

Using the side lengths, determine whether the triangle is acute, obtuse or right 9 5 10

Fed [463]

An acute triangle

Step-by-step explanation:

Using a calculator, these measurements fit an acute scalene triangle.

5 0

3 years ago

Multiplying Polynomials Multiple Choice

slamgirl [31]

$(5 x + 1)( {x}^{2} + 8x + 3) \\ 5 {x}^{3} + 40{x}^{2} + 15x + {x}^{2} + 8x + 3 \\ 5 {x}^{3} + 41 {x}^{2} + 23x + 3$

hope it helps you ❣❣

<h2>Mark me as brainliest </h2>

4 0

3 years ago