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marin [14]
3 years ago
13

Which sequence of transformations on the red triangle will map it onto the missing portion of the square?

Mathematics
1 answer:
anyanavicka [17]3 years ago
7 0

Answer:

A 90° counterclockwise rotation about the origin and then a translation 16 units right and 16 units up

Solution -Rotating the triangle 90° counterclockwise will take the triangle to 3rd quadrant and then further moving it 16 steps right will take it to 4th quadrant and followed by 16 steps upward will take it to the desired position which is in 1st quadrant.

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The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rec
igomit [66]

Answer:

The length is 7 m

The width is 10 m

Step-by-step explanation:

length = x

width = 2x - 4

length * width = area

It is given that the area is 70 m^{2}

From there

x * (2x - 4) = 70

2x^{2} - 4x = 70

2x^{2} - 4x - 70 = 0

x^{2} - 2x - 35 = 0

Now we have a quadratic equation, which is  ax^{2} + bx + c = 0, where a \neq 0

In this equation a = 1, b = -2 and c = -35

Discriminant (D) formula is b² - 4ac

D = -2^{2}  - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are  \frac{- b - \sqrt{D}  }{2a} and \frac{- b + \sqrt{D}  }{2a}

x_{1} =  \frac{- (-2) - \sqrt{144} }{2} = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

x_{2} = \frac{- (-2) + \sqrt{144} }{2} = 7 > 0 (this one is right)

Calculating the dimensions

length = x = 7 (m)

width = 2x - 4 = 2 * 7 - 4 = 10 (m)

8 0
3 years ago
Evaluate the expression below.
o-na [289]

Answer:

<h2>A. 1</h2>

Step-by-step explanation:

Use:

|a| = a for a ≥ 0 or |a| = -a for a < 0

PEMDAS:

P Parentheses first

E Exponents

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

========================================

|8 - 7| · 4 + 3(-1)

= |1| · 4 - 3

= 1 · 4 - 3

= 4 - 3

= 1

6 0
3 years ago
Read 2 more answers
Suppose that a monopolist
daser333 [38]

Answer:

The monopolist's net profit function would be:

N(y)=198\,y\,-\,2.5\,y^2

Step-by-step explanation:

Recall that perfect price discrimination means that the monopolist would be able to get the maximum price that consumers are willing to pay for his products.

Therefore, if the demand curve is given by the function:

P(y)=200-2y

P stands for the price the consumers are willing to pay for the commodity and "y" stands for the quantity of units demanded at that price.

Then, the total income function (I) for the monopolist would be the product of the price the customers are willing to pay (that is function P) times the number of units that are sold at that price (y):

I(y)=y*P(y)\\I(y)=y\,(200-2y)\\I(y)= 200y-2y^2

Therefore, the net profit (N) for the monopolist would be the difference between the Income and Cost functions (Income minus Cost):

N(y)=I(y)-C(y)\\N(y)=(200\,y-2y^2)-(2y+0.5y^2)\\N(y)=198\,y\,-\,2.5\,y^2

5 0
3 years ago
If I invest $1400.00 in a stock that’s worth $8200 how much do I own of that?
Sholpan [36]
No clue I’m not great at math but you will figure it ou
5 0
3 years ago
Round each number to the underlined place value.
True [87]

Answer:

1 is 6

2 is 3.5

3 is 5

4 is 8.46

Step-by-step explanation:

if not sorry :-(

5 0
3 years ago
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