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

Answer 1

Answer: 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.

Answer 2

Answer: 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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2/3(3x-15y)+(9y-11x)
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A necklace has and matching bracelet have two types of beads. The necklace has 12 large beads and 8 small beads and weighs 88 grams. The bracelet has 5 large beads and 2 small beads and weighs 25 grams. Write and solve a system of equations to find the weight of a large bead and weight of a small bead.

Answers

Weight of one large bead is 1.5 grams and weight of one small bead is 8.75 grams.

Step-by-step explanation:

Let,

Weight of one large bead = x

Weight of one small bead = y

According to given statement;

12x+8y=88 Eqn 1

5x+2y=25 Eqn 2

Multiplying Eqn 2 by 4

$4(5x+2y=25)\n20x+8y=100\ \ \ Eqn\ 3\n$

Subtracting Eqn 1 from Eqn 3

$(20x+8y)-(12x+8y)=100-88\n20x+8y-12x-8y=12\n8x=12$

Dividing both sides by 8

$(8x)/(8)=(12)/(8)\nx=1.5$

Putting x=1.5 in Eqn 1

$12(1.5)+8y=88\n18+8y=88\n8y=88-18\n8y=70$

Dividing both sides by 8

$(8y)/(8)=(70)/(8)\ny=8.75$

Weight of one large bead is 1.5 grams and weight of one small bead is 8.75 grams.

Keywords: linear equation, elimination method

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Multiply the binomials: (z 5)(z-7)

Answers

I hope this help you.

the expression 3x + 20 represents the elevation above sea level, in meters, of a rock climber after x minutes of climbing. what is the rock climber’s initial height above sea level?

Answers

Answer:

The rock climber’s initial height above sea level was 20 meters.

Step-by-step explanation:

This is because y-intercept is 20, meaning at time 0 minutes, the rock climber was at 20 meters.

The density of water is 1000 kilograms per cubic meter and the density of ice is about 916 kilograms per cubic meter of 700 kilograms of water and 450 kilograms of ice is combined in a container what is the volume of the water

Answers

Final answer:

The volume of water can be calculated by dividing the mass of water by the density of water.

Explanation:

The question asks for the volume of water when 700 kilograms of water and 450 kilograms of ice are combined in a container. To find the volume of water, we need to subtract the volume of ice from the total volume. The density of water is 1000 kg/m³, so the volume of water can be calculated by dividing the mass of water (700 kg) by the density of water (1000 kg/m³).

Volume of water = Mass of water / Density of water

Volume of water = 700 kg / 1000 kg/m³

Volume of water = 0.7 m³

Learn more about density of water here:

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Complete these ordered pairs for the equation: y = 3x - 6 (0,__), (__,0), (1,__)

Answers

$y = 3x - 6 \n \n (0, ....), \n\n x=0\n\ny=3\cdot 0-6=-6\n\n(0,-6)$

$(.... ,0),\n\n y=0\n \n0=3x-6 \n \n3x=6\ \ /:3\n\nx=2 \n\n(2,0)$

$(1, ....), \n\n x=1\n\ny=3\cdot 1-6=3-6=-3\n\n(0,-3)$

What two numbers at to 1 and multiply to 12

Answers

What are you trying to say? It seems that the question is not making sense.

Two numbers that
add to 1
multiply to 12

i wonder if it is -12 because
-3 + 4 = 1
-3 × 4 = -12

There cant be any other solutions, im assuming it should be -12

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