MATHEMATICS HIGH SCHOOL

A crane able can support a maximum load of 15,000 kg. If a bucket has a mass of2,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubicmeters of gravel can be safely lifted by the crane?

Answers

Answer 1

Answer:

Let

x-------> amount of cubic meters of gravel that can be safely lifted by the crane

we know that

$15,000=2,000+1,500*x$

Solve for x

$15,000=2,000+1,500*x\n1,500*x=15,000-2,000\n1,500*x=13,000\n x=(13,000/1,500)\nx=8.67\ m^(3)$

therefore

the answer is

the amount of cubic meters of gravel that can be lifted safely by the crane cannot exceed $8.67\ m^(3)$

Answer 2

Answer: Well so 15000-2000 leaves 13000kgs of available weight allowed. Then 13000 divided by 1500 we get around 8.67 cubicmeters of gravel to be allowed to be lifted safely.

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3x-5=7x-9 what does x equal

Solve for x₁ and x₂
6x₁+3x₂=60
6x₁-2x₂=80

Answers

$\left \{ {\big{6x_1+3x_2=60\ \ \ \ \ \ \ \ \ \ \ } \atop \big{6x_1-2x_2=80\ /\cdot(-1)}} \right. \n\n \left \{ {\big{6x_1+3x_2=60\ \ \ \ } \atop \big{-6x_1+2x_2=-80}} \right. \n-----------\n3x_2+2x_2=60-80\n5x_2=-20\ /:5\n\nx_2=-4\n\n6x_1+3x_2=60\ /:3\n2x_1+x_2=20\ \ \ \Rightarrow\ \ \ 2x_1+(-4)=20\ \ \ \Rightarrow\ \ \ 2x_1=24\ /:2\n\nx_1=12\n\n \left \{ {\big{x+1=12} \atop\big {x_2=-4}} \right.$

first let's change the "x1" to "A" Nd the "x2" to "B" __ so now the problem reads "6A + 3B = 60" And "6A - 2B= 80" we want to isolate variable. and the easiest one is the "B" by getting rid of the "A". set up a subtraction problem where you take one equation away from the other. 6a-6a=0. 3b - (-2b) = 5b and 60-80=-20. so your new equation reads 5B= -20. you wanna get B on one side so yu divide 5 on both sides giving you b= -4 or "x2"=-4. from there you can plug -4 into any one of the original equations. ex: 6A -2(-4)=80 then 6A + 8=80 then you subtract 8 from both sides because you're trying to isolate the "A" variable. which leaves you with 6A = 72. and now you wanna get"A" on one side so yu divide 6 from both sides and get A=12 or "x1"=12. do a quick check and plug in these numbers into any one of the equation.

Rosie works 40 hours a week as an office manager. If she made $23,920 last year, how much was she paid per hour?

Answers

Hey there..
Lets solve this questions in steps..

Step 1 - we need to know that how many weeks are there in 1 year
so, there are 52.17 weeks but the round figure is 52 weeks.

Step 2 - we know that shawn worked 40 hours a week
So, in order to get total hour worked by him in one year, we need to multiply 52 * 40
i.e. 52 *40 = 2080

Step 3 - Now, we have total hours we can simply divide the total hour worked with how much he earned last year
i.e. 23,920 / 2080
= $11.5 per hour.

Hope this helped you.. :)

Answer:

11.50

Step-by-step explanation:

Solve the literal equation for y.

2x+5y = 3y+8

Answers

Answer:

y = -x +4

Step-by-step explanation:

2x+5y = 3y+8

Subtract 3y from each side

2x+5y-3y = 3y-3y+8

2x+2y = 8

Subtract 2x from each side

2x+2y -2x = -2x+8

2y = -2x+8

Divide by 2

2y/2 = -2x/2 +8/2

y = -x +4

Book is 24 dollars. Ben pays 25.02. what is sales tax rate.

Answers

$25.02-24.00=x$
$1.02=x$
$24.00(x)=1.02$
$24x=1.02$
$(24x)/(24) = (1.02)/(24)$
$x=0.0425$
Sales tax rate is 4.25&

Answer:

he paid $1.02 tax. i think that based on this, the tax rate would be 1.025%, but i might be wrong

Step-by-step explanation:

What does it mean if the probability is 20% that a spinner will stop in a red section? A.
There is one chance in 5 that the spinner will stop in a red section.

B.
It is 20 times more likely that the spinner will stop in a red section than any other section.

C.
If the spinner is spun 100 times it is certain that it will stop in the red section exactly 20 times.

D.
There is one chance in 20 that the spinner will stop in a red section.

Answers

20% = 20/100 = 1/5

Hence, there is one chance in five that the spinner will stop in a red section.

The perimeter of a rectangle is twice the sum of its length and its width. The perimete is 28 meters and its length is 2 meters more than twice its width. What is its length?

Answers

Let l be length and w be width.
So the problem already gave you what a perimeter is, which is 2l + 2w.
Now it says perimeter is 28, so 2l + 2w = 28.
Then it says length is 2 more than twice its width, so l = 2w + 2.
Now substitute.
2(2w + 2) + 2w = 28
4w + 4 + 2w = 28
6w = 24
w = 4

Now substitute w back in l = 2w + 2
l = 2(4) + 2
l = 10

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