What is the image of the point (8,4) after a rotation of 90° counterclockwise about the origin?

Answers

Answer 1
Answer:  (-4, 8)

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

Explanation:

The 90 degree counterclockwise rotation rule we use is

[tex](x,y) \to (-y,x)[/tex]

the x and y coordinates swap places, and we change the sign of the first coordinate after the swap.

After using that rotation rule, we would go from (8,4) to (-4, 8) which is the final answer.

----------------

Extra info (optional section):

Define the following three points

A = (0,0)

B = (8,4)

C = (-4,8)

Use the slope formula to find that AB and AC have slopes of 1/2 and -2 in that order.

Those slopes multiply to -1, since (1/2)*(-2) = -1. This is a property of any two perpendicular lines as long as neither line is vertical and neither is horizontal. So this is sufficient to prove that the lines are perpendicular. This further means that a 90 degree rotation has taken place.


Related Questions

Given m|n, find the value of x.
(6x-5)
(6x+5)
Answer:
Submit Answer
attempt
PLSSSS HELP

Answers

Answer:

x = 15

Step-by-step explanation:

The two angles form a straight line so they add to 180

6x-5+6x+5 = 180

Combine like terms

12x= 180

Divide by 12

12x/12 =180/12

x = 15

Can someone please help me!

Answers

Answer: Pretty sure that it's y=-5/3x+8

Step-by-step explanation: Since the slope-intercept form is y=mx+b with b as the y-intercept and m as the slope. b would be 8 since that's where the line intercepts the y-axis and the slope is -5/3 (negative bc the line is slanted down)

Answer:

y = - [tex]\frac{8}{5}[/tex] x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 8) and (x₂, y₂ ) = (5, 0 ) ← 2 points on the line

m = [tex]\frac{0-8}{5-0}[/tex] = [tex]\frac{-8}{5}[/tex] = - [tex]\frac{8}{5}[/tex]

The line crosses the y- axis at (0, 8 ) ⇒ c = 8

y = - [tex]\frac{8}{5}[/tex] x + 8 ← equation of line

Write an equation of a circle given the center (-4,4) and radius r=5

Answers

Answer:

Step-by-step explanation:

Equation of circle: (x - h)² + (y - k)² = r²   where (h,k) is the center.

Center( -4 , 4) and r = 5

(x -[-4])² + (y - 4)²= 5²

(x + 4)² + (y-4)² = 25

x²  + 2*4*x +4²  + y²  - 2*y*4 + 4²  = 25

x²  +8x + 16 + y²  - 8y + 16 = 25

x²  + 8x + y²  - 8y + 16 + 16 -25 = 0

x²  + 8x + y²  - 8y +7 = 0

We have that the an equation of a circle given the center (-4,4) and radius r=5  is mathematically given as

(x-4)^2+(y-4)^2=5^2

Equation of a circle

Question Parameters:

Given the center (-4,4) and radius r=5

Generally the equation for the Equation of a circle   is mathematically given as

(x-x')^2+(y-y')^2=r^2

Therefore, The resultant equation will be

(x-x')^2+(y-y')^2=r^2

(x-4)^2+(y-4)^2=5^2

Hence,an equation of a circle given the center (-4,4) and radius r=5 is

(x-4)^2+(y-4)^2=5^2

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The shaded sector of the circle shown above has an area of 18 pi square feet

Answers

Answer:

F

Step-by-step explanation:

Area of sector=pi*r^2*(theta/360) = pi*r^2*(45/360)

18*pi=pi*r^2*(1/8), r=12. Circumference is 24*pi

Find the measure of one interior angle for the following polygon

Answers

Answer:

i had the same question myself

Step-by-step explanation:

I need help also

I don’t understand 20,27,29

Answers

Answer:

alright I can help!

for 20: let's first say the equation to figure out if it is a right triangle (the pythagorean theorem). so a^2 + b^2 = c^2 -> 2^2 + 2^2 =3^2 -> 4+4=9 does not equal out so 20 is not a right triangle.

for 27: the equation for area is (height×base)/2 -> (2×4)/2 -> area = 4

for 29: so let's find the circumference first. the equation is 2× pi × r -> 2× pi × 5 -> circumference = 10pi or about 31.42.

so now we can find the area of the circle. the equation is pi × r^2 -> pi × 5^2 -> area of circle= 25pi or about 78.54

hope this helps!! best wishes and best of luck!

A line passes through the point (8,9) and has a slope of 3/4

What is the equation in slope intercept form for this line

Answers

Answer: [tex]y=\frac{3}{4}x+3[/tex]

Step-by-step explanation:

Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. Since we are given slope, we can plug that into m, and use the given point to find the y-intercept.

[tex]y=\frac{3}{4}x+b[/tex]          [plug in (8,9)]

[tex]9=\frac{3}{4}(8)+b[/tex]       [multiply]

[tex]9=6+b[/tex]            [subtract both sides by 6]

[tex]b=3[/tex]

Now that we have b, we can complete the equation to [tex]y=\frac{3}{4}x+3[/tex].

sinx+sin3x=0
sin5x=-cos2x

Answers

Answer:

We have, sinx+sin3x+sin5x=0

∴(sinx+sin5x)+sin3x=0

∴2sin(

2

x+5x

)cos(

2

5x−x

)+sin3x=0

∴2sin3xcos2x+sin3x=0

∴sin3x(2cos2x+1)=0

Either sin3x=0 or 2cos2x+1=0

i.e. sin3x=0 or cos2x=−

2

1

Now, cos2x=−cos

3

π

∴cos2x=cos(π−

3

π

)

∴cos2x=cos

3

∴sin3x=0 or cos2x=cos

3

3x=nπ,n∈Z or 2x=2mπ±

3

where m∈Z

Hence, x=

3

or x=mπ±

3

π

, where n,m∈Z.

X is less than or equal to 1

Answers

Answer:

x is less than or equal to 1 can also be written as x ≤ 1. The ≤ sign represents "less than or equal to"

Let me know if this helps!

Find the area of the triangle below.

Answers

the answer is 1,102.5, to find the area of a triangle you need to multiply LxWxB/2

Mary wants to get spray foam insulation in her attic space. Shown here is a diagram of her attic - is the spray foam costs $3.15 per cubic meter, how much will it cost Mary to get her whole attic done?

Answers

Answer:

D 1,433.25

Step-by-step explanation:

1/2(10)(7)=35

35*13=455

455*3.15=1,433.25

Answer:

D

Step-by-step explanation:

You need to find the volume of the attic (I would find the surface area myself -- but this is math. You just have to obey the rules of the question no matter how silly).

The Volume is found by V = B * h1

The base is a triangle.

b = 7 m

h1 = 10 m

Area = 1/2 * 7 * 10

area = 35 m^2

The volume of the attic is

V = B * h

V = 35 * 13

V = 455 m^3

The cost = cost /m^3  * m^3

m^3 = 455

Cost = 3.15 * 455

Cost = 1433.25

Which equation is correct?

cos x° = adjacent ÷ opposite
tan x° = opposite ÷ adjacent
cos x° = opposite ÷ adjacent
tan x° = adjacent ÷ opposite

Answers

Answer:

B

Step-by-step explanation:

Sin x°= opposite ÷ hypotenuse

Cos x°= adjacent ÷ hypotenuse

Tan x°= opposite ÷ adjacent

Ctg x°= adjacent ÷ opposite

The correct will bet cot x = adjacent ÷ opposite

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Using trigonometric properties we have

Sin x°= opposite ÷ hypotenuseCos x°= adjacent ÷ hypotenuseTan x°= opposite ÷ adjacentCot x°= adjacent ÷ opposite

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HELPPP HELP PLS PRONTO ASAP
Ahmed is working at a restaurant. His boss pays him $16.00 per hour and
promises a raise of $1.25 per hour every 6 months. Which sequence
describes Ahmed's expected hourly wages, in dollars, starting with his current
wage?

Answers

Answer:

B

Step-by-step explanation:

each of the numbers is just adding 1.25 on to it

Answer: Choice B

16.00, 17.25, 18.50, 19.75, ...

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

Explanation:

We start with $16.00 as the first term, as this is the amount the boss pays him initially. Then we add on 1.25 to get 16+1.25 = 17.25 to represent the next wage after that first raise.

Then after the second raise he gets, he'll then earn 17.25+1.25 = 18.50 an hour. This process theoretically can go on forever, but realistically the boss will likely set some kind of limit.

We say that this sequence { 16.00, 17.25, 18.50, 19.75, ... } is arithmetic with the first term of 16.00 and common difference 1.25

The common difference is the gap width between any two neighboring terms, and it's the amount the wage goes up each time he gets a raise.

What is the area of the triangle?
16
10
8

Answers

Answer:

Where is the picture of the triangle?

The volume of a gas in a container varies inversely with the pressure on the gas. If a gas has a volume of 450 cubic inches under a pressure of 3 pounds per square inch, what will be its volume if the pressure is increased to 5 pounds per square inch

Answers

Answer: [tex]270\ in.^3[/tex]

Step-by-step explanation:

Given

Volume of a gas varies inversely with pressure i.e.

[tex]V\propto \dfrac{1}{P}\\\\PV=\text{constant}[/tex]

Initially, [tex]V_1=450\ in.^3,P_1=3\ psi[/tex]

Then, pressure increases to [tex]P_2=5\ psi[/tex]

[tex]\therefore P_1V_1=P_2V_2\\\Rightarrow 3\times 450=5\times V_2\\\Rightarrow V_2=3\times 90\\\Rightarrow V_2=270\ in.^3[/tex]

Thus, volume decreases to [tex]270\ in.^3[/tex].

What are the solution(s) to the quadratic equation x2 – 25 = 0?

x = 5 and x = –5
x = 25 and x = –25
x = 125 and x = –125
no real solution

Answers

X= 5 and it also equals -5

hi  

x²-25 =  (x+5)  ( x-5)  

As a multiplication can only add up to zero if one of term is  0 ,

there is two solutions  :  

x+5 = 0

x = -5  

and   x-5 = 0

        x = 5  

So two solutions for  x² -25 = 0  which are   -5  and 5

x²+10x+25resove into factors.​

Answers

Answer:

(x + 5)(x + 5)

Step-by-step explanation:

[tex]x^2+10x+25\\(x+5)(x+5)[/tex]

Answer:

(x+5)(x+5)

Step-by-step explanation:

x²+10x+25

x²+5x+5x+25    

x(x+5)+5(x+5)            

(x+5)(x+5)

Wendy went to the salon and had 2 1/6 inches of hair cut off. The next day she went back
and asked for another 2 1/6 inches to be cut off. How much hair did she have cut off in all?
Write your answer as a fraction or as a whole or mixed number.
inches.

Answers

Answer:

4 1/3 of her hair

Step-by-step explanation:

Just add 2 1/6 + 2 1/6 and there you go

There is the total amount of her hair she cut

what is the greatest common factor of the number and denominator of the rational expression below?

Answers

Answer:

x + 2

Step-by-step explanation:

[tex]\frac{5x+10}{x^2 -x-6}[/tex] = [tex]\frac{5(x+2)}{(x-3)(x+2)}[/tex]

GCF ( 5x + 10, x² - x - 6) = x + 2

Step-by-step explanation:

5(x+2)/(x+2)(x-3)= 5/(x-3)

GCF: x+2

Please write down your work on the loose leaf, take a CLEAR picture, and upload here. Thank you.

Answers

Answer:

m(∠C) = 18°

Step-by-step explanation:

From the picture attached,

m(arc BD) = 20°

m(arc DE) = 104°

Measure of the angle between secant and the tangent drawn from a point outside the circle is half the difference of the measures of intercepted arcs.

m(∠C) = [tex]\frac{1}{2}[\text{arc(EA)}-\text{arc(BD)}][/tex]

Since, AB is a diameter,

m(arc BD) + m(arc DE) + m(arc EA) = 180°

20° + 104° + m(arc EA) = 180°

124° + m(arc EA) = 180°

m(arc EA) = 56°

Therefore, m(∠C) = [tex]\frac{1}{2}(56^{\circ}-20^{\circ})[/tex]

m(∠C) = 18°

On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles, find the total distance traveled in the two days.

Answers

Answer:

380

Step-by-step explanation:

This is a bit nasty. It depends on how you read the 20 miles more and what you do with it. The best and most careful way to do it is do it a long way setting up the two equations carefully.

Second day

Let the time travelled = t

Let the speed travelled = 60 mph

d2 = 60*t

First Day

40*(t + 2) = d1

but d1 = d2 + 20 because he travelled 20 miles further on d1

40 * (t + 2) = d2 + 20

d2 however = 60*t

40*(t+2 ) = 60*t + 20          Remove the brackets

40t + 80 = 60t + 20           Subtract 20 from both sides

40t + 60 = 60t                   Subtract 40t from both sides

60 = 20*t                           Divide by 20

t = 60/20

t = 3 hours.

Day 2 = 60 + t = 180

Day 1 = 40*5  = 200

Total distance = 380

Where did that 20 miles go? It was just an observation about the difference in distance travelled between the 2 days.

The total distance the driver traveled in the two days is 260 miles

From the question, on the first day, the driver was going as a speed of 40 mph.

Let s be speed

∴ [tex]s_{1}= 40mph[/tex]

On the second day, he increased the speed to 60 mph

∴ [tex]s_{2}= 60mph[/tex]

From the statement- If he drove 2 more hours on the first day

Let time be t

Then

[tex]t_{1}= t_{2} + 2[/tex] hrs

and traveled 20 more miles

Let d be distance  

Then,

[tex]d_{1}= d_{2} + 20[/tex] miles

From the formula

Distance = Speed × Time

Then,

[tex]d = s \times t[/tex]

∴ [tex]d_{1} = s_{1} \times t_{1}[/tex]

From above,

[tex]d_{1}= d_{2}+20[/tex] miles

[tex]s_{1}= 40mph[/tex]

[tex]t_{1}= t_{2} + 2[/tex] hrs

Putting these into

[tex]d_{1} = s_{1} \times t_{1}[/tex]

[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex] ...... (1)

But,

[tex]Time = \frac{Distance}{Speed}[/tex]

∴ [tex]t_{2}= \frac{d_{2} }{s_{2} }[/tex]

From above, [tex]s_{2}= 60mph[/tex]

∴ [tex]t_{2}= \frac{d_{2} }{60}[/tex]

Put this into equation (1)

[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex]

[tex]d_{2} + 20 = 40\times (\frac{d_{2}}{60} +2)[/tex]

[tex]d_{2} + 20 = \frac{2}{3}d_{2} +80\\d_{2} = \frac{2}{3}d_{2} +80-20\\d_{2} = \frac{2}{3}d_{2} +60[/tex]

Multiply through by 3

[tex]3\times d_{2} = 3\times \frac{2}{3}d_{2} +3 \times 60\\3d_{2} = 2d_{2} + 120\\3d_{2} -2d_{2} = 120[/tex]

∴ [tex]d_{2} = 120[/tex] miles

∴The distance traveled on the second day is 120 miles

For the distance traveled on the first day,

Substitute [tex]d_{2}[/tex] into the equation

[tex]d_{1}= d_{2}+20[/tex] miles

∴ [tex]d_{1}= 120+20[/tex]

[tex]d_{1}= 140[/tex] miles

∴ The distance traveled on the first day is 140 miles

The total distance traveled in the two days = [tex]d_{1} + d_{2}[/tex]

The total distance traveled in the two days = 120 miles + 140 miles

The total distance traveled in the two days = 260 miles

Hence, the total distance the driver traveled in the two days is 260 miles

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Describe how to determine the average rate of change between x = 4 and x = 6 for the function f(x) = 2x3 + 4. Include the average rate of change in your answer.

Answers

In this question, we want to find the average rate of change of a function over an interval, it represents by how much f(x) changes when x changes by 1.

Average rate of change:

The average rate of change of a function over an interval [a,b] is given by:

[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]

In this question:

[tex]f(x) = 2x^3 + 4[/tex]

Between x = 4 and x = 6, so [tex]a = 4, b = 6[/tex]. Then

[tex]f(a) = f(4) = 2*4^3 + 4 = 132[/tex]

[tex]f(b) = f(6) = 2*6^3 + 4 = 436[/tex]

Then

[tex]A = \frac{436 - 132}{6 - 4} = 152[/tex]

Thus, the average rate of change of the function is of 152, that is, when x changes by 1, y changes by 152.

For another problem involving an average rate of change, you can check https://brainly.com/question/14481908

Solve for x using the
distributive property.
-2(-3+ x) = -4
X =
[?]

Answers

Answer:

x=5

Step-by-step explanation:

-2(-3+ x) = -4

Distribute

-2 * -3 + (-2) *x = -4

6 -2x = -4

Subtract 6 from each side

6 -2x-6 = -4-6

-2x = -10

Divide each side by -2

-2x/-2 = -10/-2

x = 5

Answer:

5

Step-by-step explanation:

-2(-3+x)=-4

Use distributive property (Multiply -2 by -3 which gives you 6vand multiply -2 by x which gives you -2x )

6-2x=-4

Bring the 6 over to the other side

-2x=-4-6

-2x=-10

Divide both sides by -2 to get x by itself

x=5

What is the solution to the system of equations graphed below?

Answers

Answer:

the third option=C -2,3

Step-by-step explanation:

solve simultaneously

Answer:

(-2,3)

Step-by-step explanation:

The solution to the system is where the two lines cross

x= -2

y = 3

(-2,3)

pls help me i really need it!

Answers

Answer:

A

Step-by-step explanation:

Help???
Find the value of x.
A.74
B.84
C.48
D.148

Answers

Answer:

A

Step-by-step explanation:

The tangent- tangent angle x is half the difference of the measures of the intercepted arcs.

minor arc = 360° - 254° = 106° , then

x = [tex]\frac{1}{2}[/tex] (254 - 106)° = [tex]\frac{1}{2}[/tex] × 148° = 74° → A

The value of angle x will be 74°. Then the correct option is A.

What is a circle?

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

We know that the sum of the minor arc and major arc made by a tangent in a circle will be 360 degrees.

Then the measure of the minor arc will be

⇒ 360° - 254°

⇒ 106°

We know that the angle made by the tangent is half of the major arc to the minor arc.

x = (254° - 106°) / 2

x = 148° / 2

x = 74°

The value of angle x will be 74°.

Then the correct option is A.

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y
In the diagram, AB = 10 and AC = 210. What is the
perimeter of ABC?
ch
A (8,4
O 10 units
4 3 2
O 10+ 210 units
O 20 units
X
O 20+ 2/10 units
2 3 4 5
B (5,-2)
C (5,-2)
3

Answers

9514 1404 393

Answer:

  20 +2√10 ≈ 26.3 units

Step-by-step explanation:

Length AB is given as 10 units. Length AC is given as 2√10 ≈ 6.325 units. The length BC is the difference of the x-coordinates of its end points, since they are on a horizontal line: 5 -(-5) = 10 units.

The perimeter is the sum of the lengths of the sides of the triangle.

  P  = AB +AC +BC = 10 +2√10 +10 = 20 +2√10 ≈ 26.3 . . . units

Find the value of x in the isosceles triangle shown below.

Answers

Answer:

x = 6

Step-by-step explanation:

The isosceles triangle is divided into two forming two right triangles

in right triangles the square value of hypotenuse is equal to sum of other two side lengths

x^2 + 4^2 = 52

x^2 + 16 = 52 subtract 16 from both sides

x^2 = 36 find the root for both sides

x = 6

The domain for f(x) and g(x) is the set of all real numbers.


Let f(x) = x2 + 1 and g(x) = 3x.


Find f · g.


A.
x2 + 3x + 1


B.
3x3 + 3x


C.
3x3 + 3x + 1


D.
x2 + 3x

Answers

Answer:

I say it's a

Step-by-step explanation:

I hope this help

A shopkeeper marked the price of an article a certain percent above the cost price and he allowed 16% discount to make 5% profit. If a customer paid Rs 9,492 with 13% VAT to buy the article, by what percent is the marked price above the cost price of the article?
Plz solve this problem ​

Answers

Answer:

25%

Step-by-step explanation:

let the MP be x

sp without vat =x-16%of x

= 21x/25

sp with VAT = 21x/25 +13% of 21x/25

rs 9492 = 2373x/2500

( 9492*2500)/2373=x

x = 10000

cp = ((21x/25 )*100)/100+5 ( 5= profit percent )

=8000

(10000-8000)×100%/8000

=25%

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