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3 years ago

HELP? I don’t know the answer

Mathematics

1 answer:

iren [92.7K]3 years ago

3 0

ANSWER

It is horizontally compressed by a factor of 2 and reflected over the y-axis.

EXPLANATION

The parent function given to us is

$y = \sqrt{x}$

The parent function has been transformed to obtain

$y = \sqrt{ - 2x}$

This transformation is of the form:

$y = \sqrt{kx}$

If

$|k| > 1$

then,there is a horizontal compression by a factor of k.

Hence

$y = \sqrt{ - 2x}$

is horizontally compressed by a factor of 2.

Since -2<0, it is a reflection in the y-axis.

The correct choice is the last option.

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Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.

topjm [15]

Given:

The three vertices of a parallelogram are (-3,8), (4,5), (2,-5).

To find:

The fourth vertex of the parallelogram.

Solution:

Let the vertices of the parallelogram are A(-3,8), B(4,5), C(2,-5) and D(a,b).

We know that, diagonals of a parallelogram bisect each other. It means midpoints of both diagonals are same.

Midpoint formula:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Two diagonals of ABCD are AC and BD.

Midpoint of AC = Midpoint of BD

$\left(\dfrac{-3+2}{2},\dfrac{8-5}{2}\right)=\left(\dfrac{4+a}{2},\dfrac{5+b}{2}\right)$

$\left(\dfrac{-1}{2},\dfrac{3}{2}\right)=\left(\dfrac{4+a}{2},\dfrac{5+b}{2}\right)$

On comparing both sides, we get

$\dfrac{4+a}{2}=\dfrac{-1}{2}$

$4+a=-1$

$a=-1-4$

$a=-5$

And,

$\dfrac{5+b}{2}=\dfrac{3}{2}$

$5+b=3$

$b=3-5$

$b=-2$

Therefore, the coordinates of fourth vertex are (-5,-2).

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3 years ago

Initially, there were equal amount of roses and tulips at a store. Each bouquet was made with 3 roses and 4 tulips. After the bo

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Answer:

12 bouquets

Step-by-step explanation:

Let there be x number of roses and x number of tulips initially at the store. Each bouquet was made with 3 roses and 4 tulips. Assume that y bouquets were made in total.

If each bouquet was made with 3 roses and 4 tulips, then y bouquets will be made with 3y roses and 4y tulips.

After the bouquets were all made, there were 30 roses and 18 tulips left in the store. This means, if we subtract number of roses that were used in bouquets from total number of roses, the result must be 30. Likewise, for tulips the result would be 18. This can be represented as:

x - 3y = 30 Equation 1

x - 4y = 18 Equation 2

Subtracting Equation 2 from Equation 1, we get:

x - 3y - (x - 4y) = 30 - 18

x - 3y - x + 4y = 12

y = 12

Since y represents the number of bouquets made, we can conclude that 12 bouquets were made in the store.

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