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2 years ago

What are the coordinates of the point (-1,9) after a clockwise rotation of 90 degree about the origin

Mathematics

1 answer:

Elina [12.6K]2 years ago

7 0

The rule for clockwise rotation of 90 degrees about the origin is (-y, x).

So (-1,9) would now be (-9,1).

Hope this Helps!!

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Vincent propses an idea to the student government to install a basket hoop along with a court marked with all the shooting lines

sladkih [1.3K]

I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.

My answer:

Scale Drawing Lengths: . . / .

Actual Court Lengths . . .

Scale Factor: inch corresponds to ( ∙ ) inches, or inches, so the scale factor is .

Let = , represent the scale drawing lengths in inches, and represent the actual court lengths in inches. The -values must be converted from feet to inches.

To find actual length:

= =

() = inches, or feet

To find actual width:

= = ( )

= / ∙ /

= inches, or feet

The actual court measures feet by feet. Yes, the lot is big enough for the court Vincent planned. The court will take up the entire width of the lot.

5 0

2 years ago

Round to the nearest hundredth (2 decimal places) when necessary

shusha [124]

Answer:

volume = 91 cm²

perimeter = 41.1 in

Step-by-step explanation:

volume = 1/2(b1+b2)(h) = 1/2(11 + 15)(7) = 91 cm²

8 0

2 years ago

What is the sum of the liner expressions -3x + 4 and -12x -27

NISA [10]

-3x+ 4=1 and -12x -27=324

5 0

2 years ago

Translate the sentence into an inequality.

blagie [28]

Let the no be x

Inequality given by

$\\ \sf\longmapsto 2(x-4)\leqslant -18$

Let's solve

$\\ \sf\longmapsto x-4\leqslant -9$

$\\ \sf\longmapsto x\leqslant -5$

3 0

1 year ago

Read 2 more answers

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .