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3 years ago

If the figure is rotated 270° counterclockwise about the origin, what is the length of segment N′P′?

Mathematics

1 answer:

kap26 [50]3 years ago

7 0

Answer:

Option (2)

Step-by-step explanation:

Since, rotation of any figure is a rigid transformation, side lengths and measure of angles of the image polygon after rotation will remain same.

NP = N'P'

Coordinates of N → (5, 9)

Coordinates of P → (7, 9)

Formula of distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is,

d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

By this formula length of NP = $\sqrt{(7-5)^2+(9-9)^2}$

= 2 units

Therefore, Option (2) will be the correct option.

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The equilateral triangle and the rectangle have the same perimeters. Find the value of x.

castortr0y [4]

We can't answer the question, you haven't given us the information, we need to know what the x is here, or if they gave you a value.

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3 years ago

The remainder after diving x^4+3x^3-8x^2+5x-9 by x+5 is ____.

raketka [301]

Use the polynomial remainder theorem. It says that a polynomial $f(x)$ has remainder $f(c)$ upon division by $x-c$ .

Here we have

$f(x)=x^4+3x^3-8x^2+5x-9$

and $c=-5$ , so the remainder is

$f(-5)=(-5)^4+3(-5)^3-8(-5)^2+5(-5)-9=\boxed{16}$

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3 years ago

A portion of the graph of f(x) = −x2 − 10x − 21 is shown. Which of the following describes all solutions for f(x)? a partial par

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Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Choose the correct simplification of the expression ( 4x/y)^2.

erik [133]

$\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4x}{y}\right)^{2} \end{gathered}$}$

To raise 4x/y to a power, raise the numerator and denominator to the power, and then divide.

$\large\displaystyle\text{$\begin{gathered}\sf \frac{(4x)^{2} }{y^{2} } \end{gathered}$}$

Expand (4x)².

$\large\displaystyle\text{$\begin{gathered}\sf \frac{4^{2} x^{2} }{y^{2} } \end{gathered}$}$

Calculates 4 to the power of 2 and gets 16.

$\boxed{\large\displaystyle\text{$\begin{gathered}\sf \frac{16x^{2} }{y^{2} } \end{gathered}$} }$

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1 year ago

A bowl has the shape of a hemisphere whose diameter is 14 centimeters. If this bowl is filled with water, how many cubic centime

ASHA 777 [7]

Answer:

The cubic centimeters of water it will take to fill the bowl is 718.67 cm³

Step-by-step explanation:

Given;

diameter of the hemisphere, d = 14 cm

radius of the hemisphere, r = d/2 = 14/2 = 7 cm

The volume of the hemisphere is calculated as;

$V = \frac{2}{3} \pi r^3\\\\V = \frac{2}{3} \times \frac{22}{7} \times (7 \ cm)^3\\\\V = 718.67 \ cm^3$

The cubic centimeters of water it will take to fill the bowl is 718.67 cm³

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3 years ago