5t - 3 = 3t - 5 : solve

Answer:

The 1st selection is appropriate.

_____

2nd: the rotation would need to be 90° CCW

3rd, 4th: rotation or double reflection will give the original orientation. This figure is reflected an odd number of times, so has its orientation reversed.

Hope it helps.. Mark brainliest

The sequence of transformations are reflection over the y-axis and then a rotation 90 clockwise about the origin.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, figure G is rotated 90° clockwise about the origin and then reflected over the x-axis, forming figure H.

Vertices of triangle G are (-3, 1), (-1, 2) and (-2, 5).

The reflection of point (x, y) across the y-axis is (-x, y).

On reflection over x-axis, we get coordinates as (3, 1), (1, 2) and (2, 5)

90° clockwise rotation: (x, y) becomes (y, -x)

On 90° clockwise rotation, we get coordinates as (1, -3), (2, -1) and (5, -2)

Triangle H has points (2, -1), (1, -3), (5, -2).

Hence, the sequence of transformations are reflection over the y-axis and then a rotation 90° clockwise about the origin.

Learn more about the rotation of 90° counterclockwise here:

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Hey there! I'm happy to help!

When talking about percents, the word "is" usually means equals. Let's use this to solve an equation! We will call our number n. Note that 30% is equal to 0.3 in decimal form because 0.3 is 30% of one! :D

0.3n=45

To solve, we need to isolate the n. To do this, we divide both sides by 0.3 because this cancels out the 0.3 that is being multiplied by n and it shows us what n will then equal.

0.3n÷0.3=45÷0.3

n=150

Therefore, 30% of 150 is 45. Try multiplying 0.3 by 150 and you will get 45!

Have a wonderful day! :D

Answer:

The answer is 21.25cm

Step-by-step explanation:

Hope i am marked as brainliest

Answer:

About 11 (10.9955742876...)

Step-by-step explanation:

Circumference=(pi) (diameter) or C=πd

Hope this helps!

The circumference of the circle is about 11 inches.

We are given that the diameter of a circle is 3.5 inches.

Noted that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

Therefore circumference of the circle = 2πr

Circumference=(2πr)

The diameter or C = πd

diameter = 3.5 inches

Circumference=(3.5 x 3.14)

Circumference = (10.99) inches

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Answer:

I think that it should be

[tex] {(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

[tex] {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)[/tex]

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

[tex]{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

I am done .

I think that it should be

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

{a}^{3}  +  {b}^{3}  +  {c}^{3}   - 3abc = (a + b + c)(  {a}^{2}  +  {b}^{2}  +  {c}^{2}  - ab - bc - ca)

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

I am done .

Answer:

36°

Step-by-step explanation:

<U + < V + <W = 180° (sum of angles in a triangle)

<W = 54°

The tangent is always perpendicular to the radius drawn to the point of tangency...

therefore,

<U = 90°

90° + <V + 54° = 180°

144° + <V = 180°

<V = 180° - 144°

<V = 36°

Answer:

V=36

Step-by-step explanation:

tangent makes rigt angle with radius angle U=90

W+V+U=180

V=180-90-54

V=36

Answer:

Sum of two rational numbers-

-10 = -5+-5

0= -5+5

15= 10+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that:

OA = 7 cm, AB = 6 cm. ∠A = 90°, OA = OC = 7 cm

Using Pythagoras theorem: OB² = OA² + AB²

OB² = 6² + 7²=85

OB = √85 = 9.22 cm

to find ∠O, we use sine rule:

[tex]\frac{AB}{sin(O)}=\frac{OB}{sin(A)}\\ \\sin(O)=\frac{AB*sin(A)}{OB}=\frac{6*sin(90)}{9.22} =0.65 \\\\O=sin^{-1}0.65=40.6^o[/tex]

AOC is a minor sector with radius 7 cm and angle 40.6

The Area of the triangle OAB = 1/2 × base × height = 1/2 × OA × AB = 1/2 × 7 × 6 = 21 cm²

Area of sector OAC = [tex]\frac{\theta}{360}*\pi r^2=\frac{40.6}{360}*\pi *7^2=17.37 \ cm^2[/tex]

Area of shaded region = The Area of the triangle OAB - Area of sector OAC = 21 - 17.37 = 3.63 cm²

Perimeter of arc AC = [tex]\frac{\theta}{360}*2\pi r=\frac{40.6}{360}*2\pi *7=4.96\ cm[/tex]

CB = OB - OC = 9.22 - 7 = 2.22

Perimeter of shaded region = AB + CB + arc AC = 6 + 2.22 + 4.96 = 13.18 cm

Answer:

The probability that the next failure will not occur before 30 months have elapsed is 0.0454

Step-by-step explanation:

Using Poisson distribution  where

t= number of units of time

x= number of occurrences in t units of time

λ= average number of occurrences per unit of time

P(x;λt) = e raise to power (-λt)  multiplied by λtˣ divided by x!

here λt = 25

x= 30

P(x= 30) = 25³⁰e⁻²⁵/ 30!

P (x= 30) = 8.67 E41 * 1.3887 E-11/30!    (where E= exponent)

P (x=30) = 1.204 E31/30!

Solving it with a statistical calculator would give

P (x=30) = 0.0454

The probability that the next failure will not occur before 30 months have elapsed is 0.0454

Answer:

(5,-6)

Step-by-step explanation:

ONE WAY:

If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].

Let's simplify that.

Distribute with [tex]-6(x-2)[/tex]:

[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]

Combine the end like terms [tex]12+3[/tex]:

[tex]f(x-2)=(x-2)^2-6x+15[/tex]

Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:

[tex]f(x-2)=x^2-4x+4-6x+15[/tex]

Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:

[tex]f(x-2)=x^2-10x+19[/tex]

We are given [tex]g(x)=f(x-2)[/tex].

So we have that [tex]g(x)=x^2-10x+19[/tex].

The vertex happens at [tex]x=\frac{-b}{2a}[/tex].

Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].

[tex]a=1[/tex]

[tex]b=-10[/tex]

[tex]c=19[/tex]

Let's plug it in.

[tex]\frac{-b}{2a}[/tex]

[tex]\frac{-(-10)}{2(1)}[/tex]

[tex]\frac{10}{2}[/tex]

[tex]5[/tex]

So the [tex]x-[/tex] coordinate is 5.

Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:

[tex]5^2-10(5)+19[/tex]

[tex]25-50+19[/tex]

[tex]-25+19[/tex]

[tex]-6[/tex]

So the ordered pair of the vertex is (5,-6).

ANOTHER WAY:

The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].

Let's put [tex]f[/tex] into this form.

We are given [tex]f(x)=x^2-6x+3[/tex].

We will need to complete the square.

I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].

So If you add something in, you will have to take it out (and vice versa).

[tex]x^2-6x+3[/tex]

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

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

[tex](x+-3)^2+3-9[/tex]

[tex](x-3)^2+-6[/tex]

So we have in vertex form [tex]f[/tex] is:

[tex]f(x)=(x-3)^2+-6[/tex].

The vertex is (3,-6).

So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].

This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).

The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.

Answer:

La magnitud del desplazamiento resultante es 2045.463 kilómetros. La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.

Step-by-step explanation:

En primer lugar, se construye el triángulo. La figura resultante se encuentra incluida como archivo adjunto. La magnitud del desplazamiento resultante se determina mediante la Ley del Coseno:

[tex]r = \sqrt{(800\,km)^{2}+(1400\,km)^{2}-2\cdot (800\,km)\cdot (1400\,km)\cdot \cos 135^{\circ}}[/tex]

[tex]r \approx 2045.463\,km[/tex]

La magnitud del desplazamiento resultante es 2045.463 kilómetros.

La dirección del desplazamiento resultante es hallada por medio de la Ley del Seno, sabiendo que el ángulo del desplazamiento resultante a la recta de 1400 kilómetros:

[tex]\frac{1400\,km}{\sin \alpha} = \frac{2045.463\,km}{\sin 135^{\circ}}[/tex]

Se despeja el ángulo correspondiente:

[tex]\alpha = \sin^{-1}\left(\frac{1400\,km}{2045.463\,km}\times \sin 135^{\circ} \right)[/tex]

[tex]\alpha \approx 28.945^{\circ}[/tex]

La dirección absoluta del desplazamiento resultante es:

[tex]\alpha' = 180^{\circ}-\alpha[/tex]

[tex]\alpha' = 180^{\circ}-28.945^{\circ}[/tex]

[tex]\alpha' = 151.055^{\circ}[/tex]

La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.

Answer:

y = -8

Step-by-step explanation:

Start by filling 8 in place of x

y = 8 - 2(8)

Multiply -2(8)

y = 8 - 16

Subtract 16 from 8

y = -8

Answer:

prime

Step-by-step explanation:

x^2 - 2x + 3

What two numbers multiply to 3 and add to -2

There are none so this cannot be factored in the real numbers

Answer:

y= [tex]\sqrt{x}[/tex]

Step-by-step explanation:

Answer:

541.4 m²

Step-by-step Explanation:

Step 1: find m < V

V = 180 - (50+63) (sum of the angles in ∆)

V = 67

Step 2: find side length of XW using the law of sines

[tex] \frac{XW}{sin(V)} = \frac{XV}{sin(W)} [/tex]

Where,

V = 67°

W = 63°

XV = 37 m

XW

[tex] \frac{XW}{sin(67)} = \frac{37}{sin(63)} [/tex]

Multiply both sides by sin(67) to solve for XW

[tex] \frac{XW}{sin(67)}*sin(67) = \frac{37}{sin(63)}*sin(67) [/tex]

[tex] XW = \frac{37*sin(67)}{sin(63)} [/tex]

[tex] XW = 38.2 m [/tex] (to nearest tenth)

Step 3: find the area using the formula, ½*XW*XV*sin(X)

area = ½*38.2*37*sin(50)

Area = 541.4 m² (rounded to the nearest tenth.

Answer:

Step-by-step explanation:

In triangle DEF, we have:

Given:

<EDF=56

<EFD=84

So, <DEF =180 - 56 - 84 =40 (sum of triangle angles is 180)

____________

DE is a midsegment of triangle ACB

( since CD=DA(given)=>D is midpoint of [CD]

and BE = EA => E midpoint of [BA] )

According to midsegment Theorem,

(DE) // (CB) "//"means parallel

and DE = CB/2 = FB =CF

___________

DEBF is a parm /parallelogram.

Proof: (DE) // (FB) ( (DE) // (CB))

AND DE = FB

Then, <EBF = <EDF = 56

___________

DEFC is parm.

Proof: (DE) // (CF) ((DE) // (CB))

And DE = CF

Therefore, <DCF = <DEF =40

___________

In triangle ACB, we have:

<CAB =180 - <ACB - <ABC =180 - 40 - 56 =84(sum of triangle angles is 180)

[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK! [/tex]

Answer:

22 units.

Step-by-step explanation:

In 45- 45- 90 triangles, there is a 1 to 1 to the square root of 2 formula. Each side length measures 1x, while the hypotenuse measures x times the square root of 2.

In this case, the hypotenuse measures 22 and the square root of 2 units. To find the value of x, simply divide that by the square root of 2 units, and you get x = 22 units. Multiply that by 1, and you get 22 units, which is the length of the leg of the triangle.

Hope this helps!

Answer:

≈23.66

Step-by-step explanation:

Height ---> x

base ---> 5x

Formula for area of triangle: (base*height)/2

((5x)(x))/2 = 1400

[tex]5x^{2}[/tex]/2 = 1400

[tex]5x^{2}[/tex] = 1400 · 2 = 2800

[tex]x^2[/tex] = 2800/5 = 560

x= √560 ≈ 23.66

Answer:

38

Step-by-step explanation:

f(-9) is the value of f(x) when x = -9. Therefore, f(-9) = 4 from the graph. Doing the same with g(6), we can see that g(6) = 6. Our expression becomes:

-1 * 4 + 7 * 6

= -4 + 42

= 38

Answer:  y = -2

Step-by-step explanation:

f(x) = A cos (Bx - C) + D

                                  ↓

                                center line (aka midline)

f(x) = 2 cos (3x - 5π/6) - 2

                                      ↓

                                  midline = -2

The midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D

It is defined as a function that is sin-cos wave in nature, and it has a domain of all real numbers and lies between the [a, a] where is the amplitude of the function.

It is given that the cos function is:

f(x) = 2cos(3x - 5π/6) - 2

As we know, the standard form of the cos function is:

f(x) = Acos(Bx - C) + D

Here, A is the amplitude

B is the period of the cos function

C is the phase shift of the cos function

D is the vertical shift of the cos function/midline

On comparing:

D = -2

The midline:

y = -2

Thus, the midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D

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Step-by-step explanation:

The inequality is [tex]\frac{x}{-3}[/tex] >2

x is less than -6  and -6 is excluded so it will be represented by an empty circle and a line going toward negative values

so it's D

Answer:

420

Step-by-step explanation:

To find 63% of 6000, we can do 0.63 * 6000 = 3780 because 63% = 0.63.

1/9th of that is 1/9 * 3780 = 420.

Answer:

420

Step-by-step explanation:

Let's first start by finding 63% of 6000 so we can later find 1/9 of that number.

We can set up a percentage proportion.

[tex]\frac{x}{6000} = \frac{63}{100}[/tex]

[tex]6000\cdot63=378000\\378000\div100 = 3780[/tex]

Now to find 1/9 of 3780.

[tex]\frac{1}{9} \cdot \frac{3780}{1}\\\\\frac{3780}{9} = 420[/tex]

So, the answer is 420.

Hope this helped!

Answer:

7.5 jars

Step-by-step explanation:

There are 25 students in the art class.

Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.

The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.

That is:

25 * 0.3 = 7.5 jars of paint

Mr Jones needs 7.5 jars of paint for the art project.

Answer:

0.15x + 0.20y = 1.80

Step-by-step explanation:

Here, we are interested in writing an equation for the total cost of the apples and bananas

before we write , kindly understand that 100p = £1

So the cost of apple which is 15p will be 15/100 =£ 0.15

The cost of bananas which is 20p will be 20/100 = £0.2

Thus, the total cost of the apples bought will be number of apples bought * price of apple bought = 0.15 * x = £0.15x

The cost of bananas = number of bananas bought * price of bananas = 0.2 * y = £0.2y

So the total cost of the apples and bananas will be;

0.15x + 0.20y = 1.80

Answer:

The value of x is 35

Step-by-step explanation:

In order to calculate the value of x in the  following parallelogram:  2x - 10  

2x + 50, we would have to calculate the following formula:

m<QPS+m<PQR=180°

According to the given data we have the following:

m<QPS=2x - 10  

m<PQR=2x + 50

Therefore, 2x - 10+2x + 50=180

4x+40=180

x=140/4

x=35

Answer:

(2, −1) and (−4, 17)

Step-by-step explanation:

I used a graphing tool to graph the systems of equations. The parabola and line pass at points (2, -1) and (-4, 17).

Answer:(2, −1) and (−4, 17) Its C on Edge 2023

Step-by-step explanation: Its (C) after an extensive research

Answer:

The points of the image are;

E'(5, 1), D'(5, -1), C'(1, 0), E'(-2, -3)

Step-by-step explanation:

The coordinates of the preimage are E(-5, -1) D(-5, 1) C(-1, 0) B(-2, -3)

Rotation of a point 180° about the origin gives;

Coordinates of the point of the preimage before rotation = (x, y)

The coordinates of the image after rotation = (-x, -y)

Therefore, the coordinates of the points EDCB after 180° rotation about the origin are;

E(-5, -1) rotated 180° becomes E'(5, 1)

D(-5, 1) rotated 180° becomes D'(5, -1)

C(-1, 0) rotated 180° becomes C'(1, 0)

B(-2, -3) rotated 180° becomes E'(-2, -3).

Answer:

36 : 6 and -6

12 = [tex]2\sqrt{3} , -2\sqrt{3}[/tex]

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = [tex]2^2*\sqrt{3} *\sqrt{3}[/tex]

[tex]\sqrt{12} = 2\sqrt{3}[/tex]

also

12 = [tex]-2\sqrt{3} *-2\sqrt{3}[/tex]

[tex]\sqrt{12} = -2\sqrt{3}[/tex]

___________________________________

1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

[tex]\sqrt{1.96} = 14/10 \ or -14/10[/tex]

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of  0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

[tex]\sqrt{400} = 20\\\sqrt{400} = -20\\[/tex]

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

[tex]\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6[/tex]

Answer:

y = - 4x - 10

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 )

Here m = - 4 , thus

y = - 4x + c ← is the partial equation

To find c substitute (- 4, 6) into the partial equation

6 = 16 + c ⇒ c = 6 - 16 = - 10

y = - 4x - 10 ← equation of line

Answer:

y = -4x+10

Step-by-step explanation:

Using the slope intercept form of a line

y = mx+b where m is the slope and b is the y intercept

y = -4x +b

Substituting the point in

6 = -4(-4) + b

6 = 16+b

Subtract 16 from each side

-10 =b

The equation is

y = -4x+10

Answer:

The axis of symmetry of parabola is the equation where it cuts the middle of the graph.

So the axis of symmetry is x = 2 .