A square can be changed into a rectangle by increasing the width by 3 units. Which expression represents the area of the rectangle in square units? (A) x^2+8x+15 (B) x2+15 (C) 2x +8 (D) 2x+15

Answers

Answer 1

Answer: Letting x be the side-length of the square, the new rectangle has length x and width x+3. Thus, the area is (x)(x+3)=x^2+3x. This is not an answer choice.

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Factorise- 6y-15y^2
HELP

Answers

We will take the common terms in the expressions-

Here in the expression, 3y is a common term.
So,

$6y - 15y^(2)$

$3y(2 - 5y)$

So, the answer is $3y(2 -5y)$

6y-15y^2
3y(2-5y) (taking 3y as common)
clearly 3y(2-5y) cannot be factorised further hence this is the answer

Give a real-world scenario in which you would write an inequality rather than an equation.

Answers

Example: You have some money in your pocket. You want to buy some snacks for tonight's match but your wife told you to buy one pizza on your way back to home that costs $10. That means that on snacks you can spend (y) :
y ≤ x - 10 where x represents money in your pocket.

This means that from money in your pocket you have to subtract $10 for pizza and out of remaining money you can spend some part of it on snacks or all of it.

I need these answers ASAP

Answers

Answer:

irratrrational Numbers

whole

real

Step-by-step explanation:

A scale drawing of a square has a side length of 5 millimeters. The drawing has a scale of 1 mm : 5 km. Find the actual perimeter and area of the square.

Answers

Answer:

Actual Perimeter = 100 km

Actual Area = 625 km²

Step-by-step explanation:

A scale drawing of a square has a side length of 5 millimeters.

The drawing has a scale of 1 mm : 5 km (which represents 1 mm is equal to 5 km)

We need to find the actual measurement of 5 mm square on scale.

1 mm = 5 km

5 mm = 5 × 5 km

= 25 km

The actual length of the side of square is 25 km

Now, we find the perimeter and area of the square.

Perimeter of square = 4 × side

= 4 × 25

= 100 km

Area of the square = side × side

= 25 × 25

= 625 km²

Hence, The actual perimeter is 100 km and area of the square is 625 km²

Walt made an extra $7000 last year from a part-time job. He invested part of the money at 10% and the rest at 7%. He made a total of $580 in interest. How much was invested at 7%?Select one:

Answers

We know that
Interest= PNR/ 100.
where P is the principal
R is the rate of Interest
N is the no of years the sum has been invested for.
Since N is not given we assume that to be 1
Therefore we have
10x /100 + (7000 -x)*7/100= 580

Multiplying both sides by 100
10x+(7000-x)*7 = 58000
simplifying
10x+ 49000 - 7x = 58000
3x = 58000-49000
3x = 9000
x= 3000
therefore the sum of money invested at 7% = 7000 - 3000 = 4000

Final answer:

Using the given conditions, we establish two equations. The first from the total invested amount which of 7000 dollars and the second from the total interest of $580. We solve the system of equations to find the value of x, which signifies the amount invested at 10%. The rest of the money (7000 - x) was invested at 7%.

Explanation:

To solve this problem, we need to set up two equations based on the information given. These equations can be set up with the following assumptions: let us denote the amount of money invested at 10% as x and at 7% as 7000 - x.

First equation would be derived from the total amount invested which was $7000, so x + (7000 - x) equals to 7000.
The second equation can be established from the total interest which was $580, so 0.10x + 0.07(7000 - x) equals to 580.

Solve the system of these two equations to find the value of x. The solution will yield the amount that was invested at 10%. The rest of the $7000, that is (7000 - x), was invested at 7%, which is what we're looking for.

Learn more about mathematical problem solving here:

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Determine the point of intersection of right bisectors in a triangle ∆ with vertices A (-3, 5), B (1, 1) and (−7, −3). Find the distance from the point of intersection to each vertex of the triangle.

Answers

Answer:

Point of intersection (-11/3 , 1/3)

All distances from the vertices are $(10√(2) )/(3)$

Step-by-step explanation:

The vertices of the triangle is A(-3,5) , B (1,1) and C (-7,-3)

We need to find the perpendicular bisector of the triangle first

let's take one side connecting A and B

mid point of A and B = (-1,3)

Slope of the line joining A and B = -1

slope of perpendicular to line joining A and B = 1

equation of line passing through (-1,3) with slope 1

y - 3 = 1(x-(-1))

y -3 = x+1

x-y = -4 ............(1)

similarly

mid point joining B and C = (-3,-1)

slope perpendicular to line joining B and C = -2

Equation of perpendicular bisector of line joining B and C =

y +1 = -2(x +3 )

y+1 = -2x -6

2x+y = -7 ..........(2)

On solving 1 and 2

x= -11/3 , y= 1/3

Distances

From A = $(10√(2) )/(3)$

From B = $(10√(2) )/(3)$

From C = $(10√(2) )/(3)$

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