What is the slope of the line given by the function f (x) = 7 – 2x?

Answer:

Question 7: The new vertices after translation are:

U'(1-2), V'(2,0), W'(3,0), X(2,-2)

Question 8: The new coordinates after translation are:

W'(-1,0), X'(0,4), Y'(4,2), Z'(3,-1)

Step-by-step explanation:

Question No 7:

Translation Rule: (x,y) =>

U(-5,1), V(-4,3), W(-3,3), X(-4, 1)

In order to get the new coordinates, we have to add 6 to x-coordinate of vertices  subtract 3 from y-coordinates of all vertices. So,

[tex]U(-5,1) => (x+6,y-3) => (-5+6, 1-3) => U'(1,-2)\\V(-4,3) => (x+6,y-3) => (-4+6, 3-3) => V'(2,0)\\W(-3,3) => (x+6,y-3) => (-3+6, 3-3) => W'(3,0)\\X(-4,1) => (x+6,y-3) => (-4+6, 1-3) => X'(2,-2)[/tex]

Hence, the new vertices after translation are:

U'(1-2), V'(2,0), W'(3,0), X(2,-2)

Question No 8:

W(-3,-2), X(-2,2), Y(2,0), Z(1,-3)

Translation Rule: (x+2,y+2)

In order to get the new coordinates, we have to add 2 to x-coordinate of vertices and add 2 to y-coordinates of all vertices. So,

[tex]W(-3,-2) => (x+2,y+2) => (-3+2, -2+2) => W'(-1,0)\\X(-2,2) => (x+2,y+2) => (-2+2, 2+2) => X'(0,4)\\Y(2,0) => (x+2,y+2) => (2+2, 0+2) => Y'(4,2)\\Z(1,-3) => (x+2,y+2) => (1+2, -3+2) => Z'(3,-1)[/tex]

Hence The new coordinates after translation are:

W'(-1,0), X'(0,4), Y'(4,2), Z'(3,-1)

Answer:

-18

Step-by-step explanation:

k ≥ −18

Answer:

The solution is K > -18

_

Answer:

[tex]f^\prime(x)=-2|x-1|-3[/tex]

Step-by-step explanation:

Write the equation for f(x)=IxI but vertically stretch it by a factor of 2, flip it over the x axis, shift it down 3 units, shift it 1 unit to the right

We have the (parent absolute value) function:

[tex]f(x)=|x|[/tex]

And we want to write a new function which represents the previous function: 1) Vertically stretched by a factor of 2, 2) flipped over the x-axis, 3) shifted down 3 units, and 4) shifted 1 unit to the right.

1)

To vertically stretch/compress a function, we multiply the function by a constant a.

We want to vertically stretch our function by 2. So, we will multiply our function by 2. Therefore:

[tex]f^\prime(x)=2|x|[/tex]

2)

We want to flip the function over the x-axis.

To flip a function over either axis:

Since we want to flip our function over the x-axis, we will multiply it by -1. So:

[tex]f^\prime(x)=-2|x|[/tex]

3)

We want to shift our function down by 3 units.

To shift a function vertically, we simply add the vertical shift to our function.

Since we are shifting downwards by 3 units, we will add -3 to our function. So:

[tex]f^\prime(x)=-2|x|-3[/tex]

4)

Finally, we want to shift our function 1 unit to the right.

To shift a function horizontally, we replace the x with (x-n), where n is the horizontal shift.

Since we are shifting our function to the right, n=1. Therefore, we will replace x with (x-1). So, our function becomes:

[tex]f^\prime(x)=-2|x-1|-3[/tex]

And we have our final function.

Note: In general, try doing the vertical/horizontal stretches first, x/y-axis reflections second, and then vertical/horizontal shifts last to avoid mistakes.

Answer:

0.75 or 3/4

Step-by-step explanation:

10 1/2 teaspoons of sugar ÷ 14 oz energy drink = ?

10.5 teaspoons of sugar ÷ 14 oz energy drink = 0.75 teaspoons of sugar per drink

OR (fraction way):

10 1/2 ÷ 14 = ?

First, Convert any mixed numbers to fractions.  Then your initial equation becomes:

21/2 ÷ 14/1 = ?

Apply the fractions formula for division (just flip the second fraction and multiply):

21/2 x 1/14 = 21/28 = 3/4 = 0.75

Hopefully this helps! Sorry if wrong. You are loved and you are beautiful/handsome!

-Bee

Answer:

25.981 seconds

Step-by-step explanation:

because X represents the magnitutde of falling height substitute 1200 into the original equation and you will find the above answer

Answer:

Step-by-step explanation:

x^2+20=2x move 2x to the left

x^2-2x+20=0

Quadratic formula =

x=1± i√19

Answer:

It is D on ed2020

1+-[tex]\sqrt 19 i[/tex]

Step-by-step explanation:

Answer:20

Step-by-step explanation:

Because it's not relevant

Answer:

pq =28

Step-by-step explanation:

you set up the equation by making them equal each other 3x+4= 5x-12 and solve From there

Answer:

[tex]1 \dfrac{1}{4} \ liters[/tex]

Step-by-step explanation:

Given that:

Claire uses 2 liters of paint to cover 1 3/5 doors

Then in order for her to paint 1 door, She will need:

2 L = 1 3/5 door

x L = 1 door

[tex]x (L) = \dfrac{2 L \times 1 door }{ 1 \dfrac{3}{5} \ door}[/tex]

[tex]x (L) = \dfrac{2 L }{ 1 \dfrac{3}{5} }[/tex]

[tex]x (L) = \dfrac{2 L }{ \dfrac{8}{5} }[/tex]

[tex]x (L) = \dfrac{2 L\times 5 }{ 8 }[/tex]

[tex]x (L) = \dfrac{10 \ L }{ 8 }[/tex]

[tex]x(L) =1 \dfrac{1}{4} \ L[/tex]

Answer    

b

Step-by-step explanation:

yeah

Answer:

ok go on a site called math.way it will really help you

Step-by-step explanation:

Answer:

brah

Step-by-step explanation:

Answer

i believe the answer is 16(-8)

Step-by-step explanation:

if you multiply how many inches the turtle goes DOWN which would be -8, and you multiply it by the 16 seconds you would get -128 because of the rules of multiplying integers.

Answer:

B. $0.88

Step-by-step explanation:

x = number of bananas

y = cost of bananas in dollars

Given that 4 bananas cost $3.52, the constant of proportionality that relates cost of bananas, y, to the number of pounds of bananas, x = y/x

y = 3.52

x = 4

Therefore:

Constant of proportionality = [tex] \frac{3.52}{4} = 0.88 [/tex].

the least common multiple is 1,020 :)

Answer:

Attached above is the answer

Answer:

10

Step-by-step explanation:

If Sabrina is 5 & Michael is 7. (5×7=35)

Michael is 7, & he is 3 yrs younger than Meghan, who is 10. And Meghan is twice as old as Sabrina, when Sabrina is 5 (5×2=10).

Answer:

Meghan is 10 years old

Step-by-step explanation:

We can write out the information with equations and then combine the information. Then, we can solve for x and hence solve for Meghan's age.

We write our first variable, x. Meghan (m) is twice as old as Sabrina (x). So we write:

m = 2x

Michael (M) is 3 years younger than Meghan. So we write:

M = m - 3

The product (multiplication) of Sabrina's and Michael's age is 35. So we write:

Mx = 35

To solve for x, we can substitute Meghan's age (2x) into the equation for Michael.

M = 2x - 3

Then, we can substitute this for M in the final equation to solve for x. This will be a quadratic so we factorise to solve it:

x(2x - 3) = 35

2x² - 3x = 35

2x² - 3x -35 = 0

(2x - 7)(x - 5) = 0

x = ⁷⁄₂ or 5

we know it is 5 since ⁷⁄₂ does not work and it is not a whole number. Hence:

m = 2(5)

m = 10

Answer: is 1/2

Step-by-step explanation:

Answer:

25 and 11

Step-by-step explanation:

because subtract 14 from 36 it will give u 11 so 11 is your smaller number and 25 is your bigger

Hope this helps :)

Answer:

The numbers are 11 and 25.

Step-by-step explanation:

Assign x to the the numbers.

One of the numbers is 14 more than the other.

x + (x+14) = 36

Smaller number = x

Bigger number = x +14

2x + 14 = 36

2x = 22

x = 11 = smaller number

x = 11 + 14 = 25 = bigger number

Answer:

(-6,2)

Step-by-step explanation:

[tex]f(x)<0[/tex]

We are given [tex]f(x)=x^2+4x-12[/tex].

So we need to solve:

[tex]x^2+4x-12<0[/tex]

First let's find when the expression on the left is 0.

[tex]x^2+4x-12=0[/tex].

The expression on the left is factorable.

Given the coefficient of [tex]x^2[/tex] is 1, all we have to do is see if there are two numbers that multiply to be -12 and add to be 4.

Those numbers are 6 and -2 so the factored form is:

[tex](x+6)(x-2)=0[/tex]

So the solutions can be found be solving the following linear equations:

[tex]x+6=0[/tex] and [tex]x-2=0[/tex].

First equation, you just need to subtract 6 on both sides. [tex]x=-6[/tex]

Second equation, you just need to add 2 on both sides. [tex]x=2[/tex]

So draw a number line with those on it and test the intervals they divide.

--------(-6)--------(2)----------

So we need to test three intervals.

*Plug in a number before -6 to see if that piece of the function is above the x-axis or below. We are looking for below since we want [tex]f(x)<0[/tex].

Let's plug in x=-8

[tex]f(x)=(x+6)(x-2)[/tex] or use [tex]f(x)=x^2+4x-12[/tex].

[tex]f(-8)=(-8+6)(-8-2)[/tex]

[tex]f(-8)=(-2)(-10)[/tex]

[tex]f(-8)=20[/tex] so this piece is above since 20 is positive and not negative.

So we will not include this interval in our answer.

*Plug in a number between -6 and 2 like 0.

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

[tex]f(0)=(0+6)(0-2)[/tex]

[tex]f(0)=(6)(-2)[/tex]

[tex]f(0)=-12[/tex] so this piece is under since -12 is negative and not positive.

So our solution includes the interval (-6,2).

*Plug in a number after 2 like 5.

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

[tex]f(5)=(5+6)(5-2)[/tex]

[tex]f(5)=(11)(3)[/tex]

[tex]f(5)=33[/tex] so this piece is above since 33 is positive and not negative.

The answer only includes the interval (-6,2).

Answer:

Answer:

(6,-7)

Step-by-step explanation:

The equation for reflecting an image about the origin is (a,b) to (-a,-b). It means you make x and y their opposites.

Step-by-step explanation:

Answer:

hope it helps..

Step-by-step explanation:

Using the slope-intercept form, the slope is 0 .

Answer:

2 big

30 small

Step-by-step explanation:

possibility

Answer:

What do you mean by third equivilent fraction? One equivalent fraction is 4/6.

Step-by-step explanation:

Answer:

some information is missing, so I looked for similar questions and found the attached image:

since each recipe requires ¹/₂ cup of butter, you are able to make 12 ÷ ¹/₂ = 24 recipes with one container of butter (assuming you have all the other ingredients).

One-half, ¹/₂, is a fraction that can also be written in decimal form as 0.5. Two times ¹/₂ is equal to 1, and similarly, twenty four times ¹/₂ is equal to 12.

Answer:

$1,300

Step-by-step explanation:

commission on the first $10,000

= 4/100 * 10000

= $400

remaining amount

= $28,000 - $10,000

= $18,000

commission on remaining $18,000

= 5/100 * 18000

= $900

total commission

= $400 + $900

= $1,300

Answer:

176

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

[tex] \because \angle 1 [/tex] and [tex] \angle 2 [/tex] are complementary.

[tex] \therefore m\angle 1+m\angle 2=90\degree... (1)[/tex]

[tex] \because \angle 2 [/tex] and [tex] \angle 3 [/tex] are complementary.

[tex] \therefore m\angle 2+m\angle 3=90\degree... (2)[/tex]

From equations (1) & (2), we find:

[tex] m\angle 1+m\angle 2=m\angle 2+m\angle 3

[/tex]

[tex] m\angle 1+m\angle 2-m\angle 2=m\angle 3

[/tex]

[tex] m\angle 1=m\angle 3[/tex]

Thus proved.