Rotate shape A 90° clockwise with centre of rotation (0,0).
What are the coordinates of the vertices of the image?

Let us consider a 30°-60°-90°△ABC right angled at B in which ∠C = 30⁰ and ∠A = 60⁰ with hypotenuse AC = 10√2 units.

In △ABC,

[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\longrightarrow[/tex]sin ∠C = [tex]\sf \dfrac{AB}{AC}[/tex]

[tex]\longrightarrow[/tex]sin 30⁰ = [tex]\sf \dfrac{AB}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf \dfrac{1}{2}= \dfrac{AB}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf AB = \dfrac{10\sqrt{2}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf AB = 5\sqrt{2}\:units[/tex]

[tex]\\[/tex]

In △ABC,

[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{Base}{Hypotenuse}[/tex]

[tex]\longrightarrow[/tex]cos ∠C = [tex]\sf \dfrac{BC}{AC}[/tex]

[tex]\longrightarrow[/tex]cos 30⁰ = [tex]\sf \dfrac{BC}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf \dfrac{\sqrt{3}}{2}= \dfrac{BC}{10\sqrt{2}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2}\times \sqrt{3}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{2\times 3}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = \dfrac{10\sqrt{6}}{2}[/tex]

[tex]\longrightarrow[/tex][tex]\sf BC = 5\sqrt{6}\: units[/tex]

Thus , the length of other two sides of triangles are 5√2 and 5√6 units.

Answer:

-4

Step-by-step explanation:

if you divide a negative number by a positive number, you will get a negative number

Answer:

-4

Step-by-step explanation:

-(4×3)/3

by crossing both 3 out

-(4) remains

Answer: 40 degrees

Step-by-step explanation:

Mean, Median, and Mode

Mean - Add all the numbers then divide by the number of numbers you added.

Median - The center of a set of numbers. (In a, b, c, d - b+c/2 is the median.)

Mode - The number that appears the most in a set of numbers.

They are called measures of center because they are statistics that describe the center of a set of data.

Answer:

10 red
8 white
6 yellow

Step-by-step explanation:

1/3 of 24 is 8 white
1/4 of 24 is 6 yellow
8+6 is 14
24-14 is 10
there are 10 red

Answer:

$5

Step-by-step explanation:

20% = .2

multiply 25 by .2 and you get 5 so $5 is the tip amount

Answer:

they would get 1 piece each and would probably have to fight for the last one

Step-by-step explanation:

12 divided by 3 = 4

4x2=8

12-8=4

4 divided by 3 = 1 remainder 1

The number of slices would each of them receives will be 2 ²/₃ pieces.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Aiden and his two friends ordered a pizza with 12 slices. Together they ate 2/3 of the pizza.

Then the number of pieces eaten is calculated as,

⇒ 2/3 x 12

⇒ 8

If they are evenly divided. Then we have

⇒ 8 / 3

⇒ 2 ²/₃

The number of slices would each of them receives will be 2 ²/₃ pieces.

More about the Algebra link is given below.

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Perpendicular lines have slopes that are opposite reciprocals.

This means we take the slope, flop it over, and change its sign.

In this case, we have

[tex]\boxed{-4}[/tex]

First, flop it over:

[tex]\boxed{-\frac{1}{4}}[/tex]

Change its sign:

[tex]\boxed{\frac{1}{4}}[/tex]

Now, let's write the equation of the line in point-slope form:-

[tex]\bigstar\boxed{\pmb{y-y1=m(x-x1)}}\longleftarrow\sf{Point-Slope~Formula}[/tex]

Where

y₁ is the y-coordinate of the point that the line intersects

m is the slope of the line

x₁ is the x-coordinate of the point that the line intersects

In this case,

y₁ is equal to -4

m is equal to  [tex]\boxed{\frac{1}{4} }[/tex]

x₁ is equal to -2

Plug in the values:-

[tex]\bigstar{\boxed{y-(-4)=\frac{1}{4}(x-(-2)}[/tex]

Simplify:-

[tex]\longrightarrow\sf{y+4=\frac{1}{4} (x+2)[/tex]

and we're done!

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Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

     I am not sure what you are asking by the options provided as the formatting has been messed up, but if you simplify the given equation you end up with:

x > 2

Step-by-step explanation:

Given

58 - 10x< 20 + 9x

Add 10x to both sides of the equatoin

58 < 20 + 19x

Subtract 20 from both sides of the equatoin

38 < 19x

2 < x

x > 2

Answer:

9.6

Step-by-step explanation:

6.4/x = sin42

x = 6.4/sin42

x = 9.56

Answer:

Here I graphed it for you.

Step-by-step explanation:

Answer: $5.85

Step-by-step explanation:

Answer:

5.85

Step-by-step explanation:

since Franco's mok has THREE times as much in her pocket, that means we we multiple 1.95 by 3. $1.95x3=$5.85

Answer:

The correct answer is "the term number, n."

Step-by-step explanation:

Answer:

Step-by-step explanation:

on edge!! dear student... you got this.. don't procrastinate and more importantly don't doubt yourself. You CAN and WILL make it to 100%

Answer:

The answer is 12

Step-by-step explanation:

1-8(6)

The multiples of 3 would be 3 and 6.

3 and 6 are found 12 times within those 6 spins

Option 12 is the correct answer.

The permutation refers to the various ways in which objects from a set may be selected, generally without replacement, to form subsets.

For the given situation,

The spinner has 8 identical sectors {1,2,3,4,5,6,7,8}.

The multiples of three from the given sectors are 3 and 6.

Multiples of 3 in the sector = 2

The spinner is expected to have to spin the multiples of 3 to be spun 6 times = [tex]2[/tex] × [tex]6[/tex]

⇒ [tex]12[/tex]

Hence we can conclude that option 12 is the correct answer.

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Answer:

38.5

Step-by-step explanation:

I would give explanation but it's kind of hard

Answer:

59

Step-by-step explanation:

VUW is an isoceles triangle, therefore VUW = VWU

tirangles total to 180 so 180 - 62 =118=2VUW

118 ÷2 = 59

Answer:

height : 150 feet

Step-by-step explanation:

[tex]\sf \sf tan(x)= \dfrac{opposite}{adjacent}[/tex]

using tan rule:

[tex]\hookrightarrow \sf tan(62)= \dfrac{b}{80}[/tex]

[tex]\hookrightarrow \sf b = tan(62)*80[/tex]

[tex]\hookrightarrow \sf b =150.46 \ feet[/tex]

Answer:

[tex]\approx 150 \: ft[/tex]

Step-by-step explanation:

recall sohcahtoa

here,

To find:

since we are given the value of adjacent side and need to figure out the opposite side , we will work with tan function,

So,

[tex] \tan( {62}^{ \circ} ) = \dfrac{h}{80} [/tex]

[tex] \implies \: h = 80\tan( {62}^{ \circ} ) [/tex]

using calculator,we acquire

[tex] \implies \: h \approx 150 \: ft[/tex]

hence, the height of the building is approximately 150ft

Answer:

m= [tex]\frac{7}{4}[/tex]

Step-by-step explanation:

[tex]m=\frac{y2-y1}{x2-x1} \\\\m=\frac{5--2}{7-3} \\m=\frac{5+2}{4}\\ m=\frac{7}{4}[/tex]

First, define what equation needs to be used. We need to use the slope formula to find the answer.

Next, we substitute the x and y values into their respective places.

Last, simplify the equation!

Answer:

9:50

Step-by-step explanation:

Answer:

9:50

Step-by-step explanation:

Heres de answer

Answer:

2 3 4 5 6 7 8 9 10

Step-by-step explanation:

even odd even odd even odd even odd even odd

Answer: A)72.8067226km/hr (final asnwer)
b) volume of a cube= a^3 (sides^3) =4.5^3= 91.125 cm^3 (final asnwer)

c) 1 day cost= $(35.9 +11.55 + 35) =$82.45
therefore for 5 days= $82.45 * (multiplied) by 5 = $412.25 (final asnwer)

Step-by-step explanation:

Answer:

(a)≈72.8 kilometer per hour

(b)91.125 cm^3

(c)272.25$

Step-by-step explanation:

(a)speed=mile/hour

=371mile/8.2hours

=371×1.609kilometers/8.2hours

≈72.8 kilometer per hour

(b)the vol: of cube= a^3 (a=side)

=(4.5)^3

=91.125cm^3

(c) for 5 days, (35.9×5)+(11.55×5)+35 ($35 is ofor one-off charge so there is no need to multiply with 5)

=272.25$

Answer:

Step-by-step explanation:

y=Mx+c

M=6 c=-2

The approximate volume of the cylinderical tube is 1005 cm³  round to the nearest whole cubic centimeter.

Volume of cylinder is the amount of quantity, which is obtained by the bylinder in the 3 dimensional space.

Volume of cylinder is the can be given as,

[tex]V=\pi r^2h[/tex]

Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.

A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift.

The diameter is 8 cm and the radius of a cylinder is half of its radius. Thus the radius of the cylinder is,

[tex]r=\dfrac{8}{2}\\r=4\rm\; cm[/tex]

Put the values in the above formula a,s

[tex]V=\pi (4)^2(20)\\V=320\pi\\V=1005.31\\V=\approx 1005\rm\;cm^3[/tex]

The approximate volume of the cylinderical tube is 1005 cm³  round to the nearest whole cubic centimeter.

Learn more about the volume of cylinder here;

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Answer:

man

Step-by-step explanation:

im sorry...you'll get it soon i swear

Answer:

see explanation

Step-by-step explanation:

look at the photo

[tex]\\ \rm\rightarrowtail 11y^2+7y+12[/tex]

Un factorable

let's see why?

There are no factors which gives sum +7 and product 132.

Answer:

630 inches³

Step-by-step explanation:

According to the question ,

we have to find the volume of rectangular prism

Volume of rectangular prism :- l × b × h

Putting the value ,

14 × 5 × 9 cubic inches

= 630 cubic inches

[tex]\rightarrow[/tex] Length(l) of prism = 14in.

[tex]\rightarrow[/tex] Width(w) of prism = 5in.

[tex]\rightarrow[/tex] Height(h) of prism = 9in.

[tex]\rightarrow[/tex] Volume of prism.

[tex]\rightarrow[/tex] Volume of rectangular prism = [tex]\sf{l×w×h}[/tex]

[tex]\rightarrow[/tex]Volume of prism = [tex]\sf{l×w×h}[/tex](putting the value of l, w and h from the above given)

[tex]\rightarrow[/tex] [tex]\sf{=\:14×5×9}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{= \: 630 in^3}[/tex]

Therefore, volume of the given prism [tex]\sf{= \: 630 in^3.}[/tex]

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Hope it helps you:)