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3 years ago

Convert 1 miles into kilometers, using proper significant figures, given that 1 mile =1609 km

Mathematics

1 answer:

Elza [17]3 years ago

6 0

Answer:

1 mile =1609 km

Step-by-step explanation:

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What is the solution of the system of equations? -4x+3y=-12 -2x+3y=-18

Kisachek [45]

Answer:

Step-by-step explanation:

I've enclosed a graph to show you that there is one solution.

-4x + 3y = - 12

- 2x + 3y = - 18 Subtract

-2x = 6 Divide by - 2

-2x/-2 = 6/-2

x = - 3

- 4x + 3y = - 12

-4(-3) + 3y = - 12

12 + 3y = - 12

3y = - 12 - 12

3y = - 24

3y/3 = - 24/3

y = - 8

Which is exactly what the graph shows.

You can tell immediately that this has 1 or more solutions just by looking at the number in front of x and y in each each equation.

It's always a good idea to graph a question like this one. Desmos is a pretty good tool to use if you don't have a graphing calculator.

The y's are the same so you are 1/2 way home in saying what you did.

The x's are different so that means you have at least 1 solution.

7 0

3 years ago

A graph of average resting heart rates is shown below. The average resting heart

kolbaska11 [484]

Step-by-step explanation:

its A 10-year-old has the same average resting heart rate as a 20-year-old

hope it helps!

5 0

2 years ago

Seventeen consecutive positive integers have a sum of 306. What is the sum of the seventeen consecutive integers that immediatel

Stels [109]

Answer:

595

Step-by-step explanation:

Each of the following 17 is 17 more than its corresponding integer in the 1st 17.

---> 306 + 289 = 595

8 0

3 years ago

Suppose a, b denotes of the quadratic polynomial x² + 20x - 2022 & c, d are roots of x² - 20x + 2022 then the value of ac(a

Alja [10]

<h3>Correct Question :- </h3>

$\sf\:a,b \: are \: the \: roots \: of \: {x}^{2} + 20x - 2020 = 0 \: and \: \\ \sf \: c,d \: are \: the \: roots \: of \: {x}^{2} - 20x + 2020 = 0 \: then \:$

$\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) =$

(a) 0

(b) 8000

(d) 16000

$\large\underline{\sf{Solution-}}$

Given that

$\red{\rm :\longmapsto\:a,b \: are \: the \: roots \: of \: {x}^{2} + 20x - 2020 = 0}$

We know

$\boxed{\red{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}$

$\rm \implies\:ab = \dfrac{ - 2020}{1} = - 2020$

And

$\boxed{\red{\sf Sum\ of\ the\ zeroes=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}$

$\rm \implies\:a + b = - \dfrac{20}{1} = - 20$

Also, given that

$\red{\rm :\longmapsto\:c,d \: are \: the \: roots \: of \: {x}^{2} - 20x + 2020 = 0}$

$\rm \implies\:c + d = - \dfrac{( - 20)}{1} = 20$

and

$\rm \implies\:cd = \dfrac{2020}{1} = 2020$

Now, Consider

$\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d)$

$\sf \: = {ca}^{2} - {ac}^{2} + {da}^{2} - {ad}^{2} + {cb}^{2} - {bc}^{2} + {db}^{2} - {bd}^{2}$

$\sf \: = {a}^{2}(c + d) + {b}^{2}(c + d) - {c}^{2}(a + b) - {d}^{2}(a + b)$

$\sf \: = (c + d)( {a}^{2} + {b}^{2}) - (a + b)( {c}^{2} + {d}^{2})$

$\sf \: = 20( {a}^{2} + {b}^{2}) + 20( {c}^{2} + {d}^{2})$

$\sf \: = 20\bigg[ {a}^{2} + {b}^{2} + {c}^{2} + {d}^{2}\bigg]$

We know,

$\boxed{\tt{ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta) }^{2} - 2 \alpha \beta \: }}$

So, using this, we get

$\sf \: = 20\bigg[ {(a + b)}^{2} - 2ab + {(c + d)}^{2} - 2cd\bigg]$

$\sf \: = 20\bigg[ {( - 20)}^{2} + 2(2020) + {(20)}^{2} - 2(2020)\bigg]$

$\sf \: = 20\bigg[ 400 + 400\bigg]$

$\sf \: = 20\bigg[ 800\bigg]$

$\sf \: = 16000$

Hence,

$\boxed{\tt{ \sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) = 16000}}$

So, option (d) is correct.

4 0

2 years ago

Sheri built a 1/200 scale model of a dam. She used 0.1 cubic meter of plaster. What is the volume of the actual dam in cubic met

Fynjy0 [20]

The correct answer is C) 800,000 cubic meters.

The scale given is for the length, width or height of the model. In order to find the scale for the volume, we would cube this scale, since volume is a cubic measurement:
(1/200)³ = 1/8,000,000

Since the volume of the model is 0.1, we multiply this by 8,000,000 to find the volume of the actual dam:
0.1(8000000) = 800,000

4 0

3 years ago