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1 year ago

Estimate the unit rate if 12 pairs of socks sell for $5.79.

1 answer:

3 0

If 12 pairs of socks sell for $5.79, then the unit rate is 12 : 5.79. If we want to find a unit rate for one pair of socks, we need to divide 5.79 by 12:
5.79 / 12 = 0,4825
So the unit rate is 1 : 0.4825
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b) A fruit seller bought some mangoes for Rs 500. He sold them at 10% loss. If he wants to make a profit of 12.5% without increa

avanturin [10]

Answer:

New CP = Rs 387.5

Step-by-step explanation:

Cost Price = Rs. 500

Loss %age = 10% of 500

So, Loss = Rs 50

Finding the selling price:

Selling Price = CP - Loss

SP = 500 - 50

SP = Rs 450

Now, The fruit seller wants to gain a profit of 12.5% without changing the selling Price:

Firstly, Let's talk about the Profit :

Profit %age = 12.5% of 500

Profit = 12.5 * 5

Profit = Rs 62.5

He wants to gain a profit of Rs 62.5

So, The cost Price

The cost price would be reduced by Rs 62.5

New CP = 450 - 62.5

New CP = Rs 387.5

4 0

2 years ago

Point A is the midpoint of side XZ and point B is the

Katyanochek1 [597]

Answer:

Option (2)

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Point A is the midpoint of side XZ and point B is the midpoint of side YZ.

Triangle XYZ is cut by line segment AB. Point A is the midpoint of side XZ and point B is the midpoint of side YZ. The length of XY is (5x - 7), the length of AB is (x + 1), and the lengths of XA and ZA are (2x - 2). The lengths of YB and BZ are congruent.

What is AX ?

2 units

4 units

6 units

8 units

From the figure attached,

XYZ is a triangle having A and B as the midpoints of the sides XZ and YZ.

By the theorem of midpoints,

AB = $\frac{1}{2}\text{(XY)}$

Since AB = (x + 1) and XY = (5x - 7)

(x + 1) = $\frac{1}{2}(5x-7)$

2x + 2 = 5x - 7

5x - 2x = 2 + 7

3x = 9

x = 3

Therefore, side AB = 3 + 1 = 4 units

Side XY = (5x - 7)

= 15 - 7

= 8 units

Side XA = 2(x - 1)

= 4 units

Therefore, Option (2) will be the answer.

6 0

2 years ago

Consider the graph of the line y = x – 4 and the point (−4, 2). The slope of a line parallel to the given line is . A point on t

Harman [31]

The given line is y = x - 4, and the given point is (-4, 2).

The slope of the given line is 1, and its y-intercept is (0, -4).

Part a.
The slope of a line parallel to the given line is 1.

Part b.
Let the equation of a line parallel to the given line be
y = x + c
Let (x,y) be a point on a parallel line which passes through (-4,2).
Then, in point-slope form,
(y - 2)/(x + 4) = 1
That is,
y - 2 = x + 4
y = x + 6

If x = 0, then
y - 2 = 0 + 4
y - 2 = 4
y = 6
Therefore the point (0, 6) is one of many points that lies on this line.

Part c.
The slope of a line perpendicular to the given line is -1.
The product of the slopes of perpendicular lines is -1.

Let (x,y) be a point on the perpendicular line which passes through (-4,2).
In point-slope form, its equation is
(y - 2)/(x + 4) = -1
That is,
y - 2 = -x - 4
y = -x - 2
Wneh x = 0, then y = -2.
A point on the perpendicular line that passes through (-4,2) is (0, -2).

Answers:
1. The slope is 1.
2. The point (0, 6) falls on the parallel line passing through (-4, 2).
3. The slope of a perpendicular line is -1.
4. The point (0, -2) falls on the perpendicular line passing through (-4, 2).