Choose the algebraic description that maps the image ΔABC onto ΔA′B′C′.

Question 2 options:

(x,y) → (x – 4,y)


(x,y) → (x,y + 4)


(x,y) → (x,y – 4)


(x,y) → (x + 4,y)

Given:

A line passes through the point (1,4) and is parallel to the x-axis.

To find:

The equation of the line.

Solution:

If a line is parallel to x-axis, then the line is a horizontal line. We know that the slope of a horizontal line is always 0. So, the slope of the required line is 0.

The point-slope form of a line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is the slope and [tex](x_1,y_1)[/tex] is the point.

The slope of the required line is 0 and it passes through the point (1,4). So, the equation of the line is:

[tex]y-4=0(x-1)[/tex]

[tex]y-4=0[/tex]

[tex]y-4+4=0+4[/tex]

[tex]y=4[/tex]

The required equation is [tex]y=4[/tex].

Therefore, the correct option is B.

Given:

The function are:

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

[tex]g(x)=2x-7[/tex]

The graph of f(x) intersect the line g(x) at one point.

To find:

The value of K.

Solution:

The graph of f(x) intersect the line g(x) at one point. It means the line g(x) is the tangent line.

We have,

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

Differentiate this function with respect to x.

[tex]f'(x)=K(2x)+4(1)-(0)[/tex]

[tex]f'(x)=2Kx+4[/tex]

Let the point of tangency is [tex](x_0,y_0)[/tex]. So, the slope of the tangent line is:

[tex][f'(x)]_{(x_0,y_0)}=2Kx_0+4[/tex]

On comparing [tex]g(x)=2x-7[/tex] with slope-intercept form, we get

[tex]m=2[/tex]

So, the slope of the tangent line is 2.

[tex]2Kx_0+4=2[/tex]

[tex]2Kx_0=2-4[/tex]

[tex]x_0=\dfrac{-2}{2K}[/tex]

[tex]x_0=-\dfrac{1}{K}[/tex]

Putting [tex]x=x_0,g(x)=y_0[/tex] in g(x), we get

[tex]y_0=2x_0-7[/tex]

Putting [tex]x=-\dfrac{1}{K}[/tex] in the above equation, we get

[tex]y_0=2(-\dfrac{1}{K})-7[/tex]

[tex]y_0=-\dfrac{2}{K}-7[/tex]

Putting [tex]x=-\dfrac{1}{K}[/tex] and [tex]f(x)=-\dfrac{2}{K}-7[/tex] in f(x).

[tex]-\dfrac{2}{K}-7=K\left(-\dfrac{1}{K}\right)^2+4(-\dfrac{1}{K})-3[/tex]

[tex]-\dfrac{2}{K}-7=\dfrac{1}{K}-\dfrac{4}{K}-3[/tex]

[tex]-\dfrac{2}{K}-7=\dfrac{-3}{K}-3[/tex]

Multiply both sides by K.

[tex]-2-7K=-3-3K[/tex]

[tex]-2+3=7K-3k[/tex]

[tex]1=4k[/tex]

[tex]\dfrac{1}{4}=K[/tex]

Therefore, the value of K is [tex]\dfrac{1}{4}[/tex].

Hello!

x² - 4x + 6 = 9 <=>

<=> x² - 4x + 6 - 9 = 0 <=>

<=> x² - 4x - 3 = 0 <=>

<=> x = -(-4)±√(-4)²-4×1×(-3)/2×1 <=>

<=> x = 4±√16+12/2 <=>

<=> x = 4±√28/2 <=>

<=> x = 4±2√7/2 =>

=> x = 4+2√7/2 and x = 4-2√7/2 =>

=> x = 2+√7 and x = 2-√7

The equation has two solutions.

Good luck! :)

Answer:  [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]

how i got it?

[tex]x^2 - 4x + 6 = 9[/tex]

*subtract 9 on both sides*

[tex]x^2 - 4x + 6 - 9 = 0[/tex]  ( which turns to) [tex]x^2 - 4x - 3=0[/tex]

a=1 or x, b=-4, c=-3

Step 2: Use quadratic formula with a=1, b=-4, c=-3.

[tex]x= - (-4) + or - \sqrt{-4}x^{2} -4(1)(-3) / 2(1)[/tex]

which turns to: x= 4 + or - √28 divided by 2

the final answer should be [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]

Answer:

0.125

Step-by-step explanation:

1=40000

x-5000

x=5000÷40000=1/8=0.125

Answer:

-4/5

Step-by-step explanation:

sin theta = opp/ hyp

sin theta = -3 /5

Using the Pythagorean theorem

opp ^2 + adj ^2 = hyp ^2

(-3) ^2 + adj ^2 = 5^2

9+ adj ^2 = 25

adj ^2 = 25 - 9

adj ^2 = 16

Taking the square root of each side

adj = ±4

Since we are in the 3rd quadrant  sin and cos are both negative so adj must be negative

adj = -4

cos theta = adj / hyp

cos theta = -4/5

Answer:

We can make 120 three digit distinct numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the number is xyz, we have:

Total number of possible 3-digit numbers:

60° because it's an equilateral triangle

Answer: where's the pic?

Step-by-step explanation:

Answer:

3x^2y

Step-by-step explanation:

Its common factor it this ^ this symbol represent power

Answer:

3x

Step-by-step explanation:

factoring it we get

3x(4x-3)

Answer:

the second option, y=1/2cos(x- pi/4)

Step-by-step explanation:

Answer:

If there are two line which is parallel in a triangle the triangle has a ratio

Step-by-step explanation:

So we can see one side has 6cm and 4cm length. and other side has 20cm in totally. But we know that the small line divided the side with 6/4 ratio and we can say ?=12 and other is 8

Answer:

Step-by-step explanation:

Answer:

5m-n-4p

4a^2+6x-3

Step-by-step explanation:

3m-4n +7p

-5m +9n -6p

+7m -6n -5p

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

Combine like terms

3m-4n +7p

-5m +9n -6p

+7m -6n -5p

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

(3-5+7)m  +(-4+9-6)n  +(7-6-5)p

5m-n-4p

a^2  -3x +1

a^2   +9x -6

2a^2 +0x +2

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

Combine like terms

a^2  -3x +1

a^2   +9x -6

2a^2 +0x +2

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

(1+1+2)a^2 +(-3+9+0)x +(1-6+2)

4a^2+6x-3

#1

[tex]\\ \sf\longmapsto 3m-4n+7p+(-5m+9n-6p)+7m-6n-5p[/tex]

[tex]\\ \sf\longmapsto 3m-4n+7p-5m+9n-6p+7m-6n-5p[/tex]

[tex]\\ \sf\longmapsto 3m-5m+7m-4n+9n-6n+7p-6p-5p[/tex]

[tex]\\ \sf\longmapsto 5m-n-4p[/tex]

#2

[tex]\\ \sf\longmapsto a^2-3x+1+a^2+9x-6+2a^2+2[/tex]

[tex]\\ \sf\longmapsto a^2+a^2+2a^2-3x+9x+1-6+2[/tex]

[tex]\\ \sf\longmapsto 4a^2+6x-3[/tex]

Given:

Cost of 200 g of mixed nuts = $2.50.

To find:

The price of 450 g of nuts.

Solution:

We have,

Cost of 200 g of mixed nuts = 2.50 dollars

Cost of 1 g of mixed nuts = [tex]\dfrac{2.50}{200}[/tex] dollars

Cost of 450 g of mixed nuts = [tex]\dfrac{2.50}{200}\times 450[/tex] dollars

                                               = [tex]\dfrac{2.50}{4}\times 9[/tex] dollars

                                               = [tex]5.625[/tex] dollars

Therefore, the price of 450 g of nuts is $5.625.

Answer:

The diameter is 2 meters

Step-by-step explanation:

The circumference of a circle is given by

C = pi *d

2 pi = pi *d

Divide each side by pi

2 = d

The diameter is 2 meters

Step-by-step explanation:

An economy is made up of every single activity that has to do with production, consumption, and the buying and selling of goods or rendering services.

In an economy there are combinations of market transactions and decisions made collectively or in hierarchy. Individuals, families, businesses, governments make up the decision-making process.

Money is the legal tender of an economy. It is the medium of exchange that an economy uses for transactions.

Answer:

i think (4,2)

Step-by-step explanation:

Answer:

It must be a positive number since it represents a number of hours.

Step-by-step explanation:

Given Pieter's equation :

7h – 5(3h – 8) = –72

Opening up the bracket

7h - 15h + 40 = - 72

7h - 15h = - 72 - 40

-8h = - 112

Divide both sides by -8

-8h / -8 = - 112 / - 8

h = 14

Since, h represents the number of hours, and the value of h equals 14 (h cannot be negative), hence, option 2 is correct.

Answer:

B.It must be a positive number since it represents a numbers of hours.

Step-by-step explanation:

Answer:

[tex]\frac{3x}{4x} =\frac{3x+7}{5x-8}[/tex]

[tex]\frac{3}{4} =\frac{3x+7}{5x-8}\: (cross\: multiply)[/tex]

[tex]3(5x-8)=4(3x+7)[/tex]

[tex]15x-24=12x+28\\+24~~~~~~~~~~~~+24[/tex]

[tex]15x=12x+52\\-12x~~~~-12x\\-------\\3x=52[/tex]

[tex]\frac{3x}{3} =\frac{52}{3}[/tex]

[tex]x=52/3[/tex]

[tex]Answer:C[/tex]

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

Hope it helps...

Have a great day!!

Answer:

27 attendees

Step-by-step explanation:

First, we can find the cost per attendee.

78÷26

3

So $3 per attendee.

Then divide 81 by 3 to find the number of possible attendees.

81÷3=27

I hope this helps!

Answer: 3000 stamps

Step-by-step explanation:

Given

Chris and Josh have 1800 stamps

Josh and Jessica have 2200 stamps

Jessica and Chris have 2000 stamps

Suppose Chris, Josh, and Jessica have [tex]x,y, \text{and}\ z[/tex] stamps

[tex]\therefore x+y=1800\quad \ldots(i)\\\Rightarrow y+z=2200\quad \ldots(ii)\\\Rightarrow z+x=2000\quad \ldots(iii)\\\text{Add (i), (ii), and (iii)}\\\Rightarrow 2(x+y+z)=1800+2200+2000\\\Rightarrow x+y+z=3000[/tex]

Thus, all three have 3000 stamps

Answer:

Step-by-step explanation:

Answer:

Total chairs = 18×22= 396

so no. of extra chairs need = 468-396 = 72

Now( 72/18) rows = 4 rows

Therefore 4 more rows are needed here

Hope it helps you

Answer: 4

Step-by-step explanation:

The amount of chairs in the hall can be found by multiplying 22 by 18 and getting 396. The amount of chairs needed is 468, so 468-396 gets you the amount of chairs still needed and the number 72. There are 18 chairs in each row, and 72/18 is 4. So 4 more rows are needed.

Answer:

x = -7/b

Step-by-step explanation:

bx = -7

Divide each side by b

bx/b = -7/b

x =-7/b

Solve the equation for x : bx = -7

Here we are provided to find for x so from the equation by cross multiplying we will remove b to the right hand side of the equation and then we can get x

bx = -7

Now, to cross multiply

x = -7/b

Therefore, the required answer is -7/b

Answer:

add 2 equations given

3y+x+2y- x = 10

5y =10

y = 2

find x using the value of y

x = - 2

these values of x and y are can satisfy both equations .so (-2,2) lies on both lines

The volume of a cylinder is V=πr^2*h.

The volume of this cylinder is V=π(7)^2*12, which it V=588π.

9514 1404 393

Answer:

  4 days

Step-by-step explanation:

The total charges can be modeled by ...

  c = 75d + 75 . . . . . . charges for d days

Filling in the given charge, we find ...

  375 = 75d +75

  300 = 75d . . . . . . . subtract 75

  4 = d . . . . . . . . . . divide by 75

Chris rented the car for 4 days.

Answer:

4 DAYS!! THIS GETS ALL 3 MARKS!!!

Step-by-step explanation:

Chris rents a car for a total of £375. The rental charges are £150 for the first day and £75 per day after that. For how many days did Chris rent the car? You must show your working.

£375.00 - £150.00 = £225.00

£225.00 - £75.00 = £150.00

£150.00 - £75.00 = £75.00

£75.00 - £75.00 = £00.00

= Chris rented the car for 4 days

225.00 ÷ 75 = 3

3 days + 1 days = 4 days

he total charges can be modeled by ...

c = 75d + 75 . . . . . . charges for d days

Filling in the given charge, we find ...

375 = 75d +75

300 = 75d . . . . . . . subtract 75

4 = d . . . . . . . . . . divide by 75

Answer:4 days

Total=375

150+(75×4)=150+75+75+75=375

4 days