MATHEMATICS HIGH SCHOOL

Mauro has 140 ft of rope. He will cut it into two pieces so that the length of the longer piece is 3 times the length of the shorter piece. What will the length of the longer piece be? _________ ft

Answers

Answer 1

Answer:

Answer:

The length of the longer piece is 35 feet.

Step-by-step explanation:

Let the length of the longer piece is x

Hence, length of the shorter piece is 3x

Now, the length of the rope is 140 ft. Thus, we have the equation

$x+3x=140$

Add the like terms. $x+3x=4x$

$4x=140$

Divide both sides by 4

$x=35$

Therefore, the length of the longer piece is 35 feet.

Answer 2

Answer: 140= x +3x
140 =4x
140/4= 4x/4
35= x
3x= 105
The length of the longer piece is 105 feet

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Express 0.00419 in standard form

Answers

the standard form is 4.19•10^-3

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Your class hopes to collect at least 325 cans of food for the annual food drive. There were 135 cans donated the first week and 89 more the second week.

a. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal.
. How many cans are needed to meet or surpass your goal? Solve the inequality

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Answers

1. -2
2. 3
3. -4
Those are the first 3 equations

135 + 89 = 224
325 - 224 = 101
I am not sure what the inequality would be... im sorry

4x + 6 < -6
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The last question doesnt have a number to the right so I dont know What you are looking for.
Thats all I know, hope it helps

-1.6x - 3.2y=-24
2.6x + 2.6y = 26
The solution is (

Answers

Answer:

$x=5\ny=5$

Step-by-step explanation:

I solved using substitution

−1.6x−3.2y=−24

−1.6x=−24+3.2y

−1.6x=3.2y−24

$x=-(3.2y-24)/(1.6\n)$

2.6x+2.6y=26

−2.6y+39=26

−2.6y=26−39

−2.6y=−13

y =5

Find the length of side x in simplest radical form with rational denminator

Answers

Answer:

As shown in picture, this is an isosceles right triangle ( A = 90 deg, B = C = 45 deg). => Except hypotenuse, side1 = side2, or x = $√(6)$

Hope this helps!

How do you find the constant of variation when y=-(2/3) and x=3

Answers

You can't. If you think about the straight line on a graph, those numbers
describe a single point that the line goes through, and they don't tell you
anything about the slope of the line, or where it crosses the x-axis or the
y-axis. So I don't think you can tell the constant of variation from one point.

$y=-(2)/(3);\ x=3\n\nkx=y\n\n3k=-(2)/(3)\ \ \ \ /:3\n\nk=-(2)/(9)$

We are interested in the dimensions of a certain square. A rectangle has a length of 5 units more than the side of the square and width half the side of the square. If the two areas are equal, what are the squares dimensions (w+h)?

Answers

Lets consider the side of square be 'x' units
So as per data,
Length of rectangle is x+5
Breadth of rectangle is x/2

and also as per data, the areas of rectangle and square are equal.
Area of rectangle = Length * Breadth = (x+5)*x/2 = $( x^(2) +5x)/2$ <- equation1
Area of square = Side* Side= x*x = $x^(2)$ <- equation2

As per given data, Equation1 and equation 2 are equal
so
$( x^(2) +5x)/2$ = tex] x^{2} [/tex]
$x^(2) +5x = 2 x^(2)$
$2 x^(2) - x^(2) = 5x$
$x^(2) = 5x$
x = 5

So the side of square = 5 units

For Square, both dimensions are equal.

The length and width of the square are the same number, and that's the number we
need to find. Eleven out of every ten people who attack this problem will call it ' S '.
The area of the square is S² .

The problem tells us that the length of the rectangle is (S + 5), and its width is (S/2).
Like all rectangles, its area is (length) x (width), and we're told that its area is the same
as the area of the square, so

(S + 5) (S/2) = S²

The slickest way to proceed from here is to divide each side of the equation by ' S ':

(S + 5) (1/2) = S

Multiply each side by 2 :

S + 5 = 2S

Subtract ' S ' from each side:

S = 5 units.

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