Are the points O, M, and U collinear?


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Choose 1 answer:

Yes

No

Given:

The function is:

[tex]f(x)=\dfrac{2x}{3}-4[/tex]

To find:

The inverse of the given function, i.e., [tex]f^{-1}(x)[/tex].

Solution:

We have,

[tex]f(x)=\dfrac{2x}{3}-4[/tex]

Step 1: Substitute [tex]f(x)=y[/tex].

[tex]y=\dfrac{2x}{3}-4[/tex]

Step 2: Interchange x and y.

[tex]x=\dfrac{2y}{3}-4[/tex]

Step 3: Isolate y.

[tex]x+4=\dfrac{2y}{3}[/tex]

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

[tex]\dfrac{3x+12}{2}=y[/tex]

[tex]\dfrac{3}{2}x+6=y[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex].

[tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex]

Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex].

3z + 2(z - 3) = 7z + 12

3z + 2(z - 3) = 7z + 12

3z + 2z - 6 = 7z + 12

3z + 2z - 7z = 12 + 6

5z - 7z = 18

-2z = 18

z = 18/2

z = 9

[tex] \\ [/tex]

Answered by - ItzAdmire

3z + 2(z - 3) = 7z + 12

3z + 2(z - 3) = 7z + 12

3z + 2z - 6 = 7z + 12

3z + 2z - 7z = 12 + 6

5z - 7z = 18

-2z = 18

z = 18/2

z = 9

[tex] \\ [/tex]

Answered by - ItzMaster

Answer:

( 0, - 2 )

Step-by-step explanation:

Mid point formula : -

( x1 + x2 ) / 2, ( y1 + y2 ) / 2

Here,

Let ( x1, y1 ) = ( - 4, - 2 )

Therefore,

x1 = - 4

y1 = - 2

Let ( x2, y2 ) = ( 4, -2 )

Therefore,

x2 = 4

y2 = - 2

Midpoint of AC

= ( - 4 + 4 ) / 2, ( - 2 - 2 ) / 2

= ( 0 / 2, - 4 / 2 )

= ( 0, - 2 )

The midpoint of AC is ( 0, - 2 ) when coordinates of A (-4,-2), B(0,4), and C(4,-2) is given.

What is the Midpoint of a Line?

The midpoint of a line is a point that is equidistant from the endpoints of the line and in the middle of the line. If the endpoints of the line are (x)1, (y)1, and (x)2, (y)2, then the formula for the midpoint of the line is {[(x)1 + (x)2]/2, [(y)1 + (y)2]/2}.

Mid point formula is  given as : -

( x1 + x2 ) / 2, ( y1 + y2 ) / 2

Here,

Let ( x1, y1 ) = ( - 4, - 2 )

x1 = - 4

y1 = - 2

Let ( x2, y2 ) = ( 4, -2 )

x2 = 4

y2 = - 2

now using Midpoint formula to find the coordinates of AC

= ( - 4 + 4 ) / 2, ( - 2 - 2 ) / 2

= ( 0 / 2, - 4 / 2 )

= ( 0, - 2 )

Therefore, the midpoint of AC is ( 0, - 2 )

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Answer:

6 hundreds

2 tens

7 ones

Step-by-step explanation:

Un albañil construye una casa en 5 días si debe construir 3 casas cuántos días se demorará

Answer: B

Step-by-step explanation:

Answer:

5 seconds

Step-by-step explanation:

Answer:

A. Obtuse triangle

B,C,D. Acute

Step-by-step explanation:

Answer:

-5 and -6

Step-by-step explanation:

For trinomial factoring, you need two numbers that add up to get the -11x and two numbers that multiply to get 30.

-5 + (-6) = -11

-5 × -6 = 30

Answer:

B

Step-by-step explanation:

the mean changes a lot, the median doesn't change

Answer:

B

Step-by-step explanation:

the mean is 599.5 and the median is 410

Answer:

455.1111 feet²

Step-by-step explanation:

Given that :

Array of mosaic = 8 * 8 color square tiles

Length of each tile = 2 2/3 feets long

The length of mosaic = length per tile * Number of array :

2 2/3 feets * 8 = 21.3333 feets

This corresponds to the side length of the mosaic

The Area of the whole mosaic:

Using the area of square formula = s²

Where, s = side length

s = 21.33333 ft²

s² = 21.33333²

s² = 455.1111²

Answer:

Step-by-step explanation:

all the three sides of a triangle are equal.

length of perpendicular from center on the side=[tex]h=\sqrt{21^2-(\frac{21}{2})^2} =\frac{21}{2}\sqrt{3} \\area ~of~shape=6 \times \frac{1}{2} \times 21 \times \frac{21}{2}\sqrt{3} \\=\frac{1321}{2}\sqrt{3} ~sq. ~ft.[/tex]

Answer:

ΔABC ≈ ΔDEF

∡B ≅ ∡E

x = 4.5

BC is similar to EF

Step-by-step explanation:

to find 'x':

6/16 = x/12

16x = 72

x = 4.5

Answer:

1) tri ABC ~ tri DEF

2) angle B ~ angle E

3) x= 4.5

4) ?= BC

Step-by-step explanation:

hi! a note: pls let me know if any of the answers are wrong ! i want anyone to have a wrong answer because of me thank u vm! (obviously, my explanations are not the official mathematical explanations)

1) I just matched up the letters, A to D, B to E, C to F

You can also use ratios, but if you dont need an explanation then ignore it.

2) matched up the angles: B corresponds to E

3) Ratio: 6/16 = x/12

              16x = 72   cross multiply

                 x = 4.5

4) Again, just match up the sides

BC corresponds to EF

hope this helps :D best of luck

Answer: A

Step-by-step explanation: The square root of 9 is 9.7 so it would be between 5 and 10

Answer:

A. W and X

Step-by-step explanation:

√95

9.74679434481

This number is close to 10.

5 and 15 are on the sides of 10.

X(10) is between W(5) and Y(15).

Answer

Step-by-step explanation:

mulitiply the numbers

add the numbers

rearrange the numbers

Answer:

Step-by-step explanation:

[tex] \frac{9}{3} = 3 \\ \\ \frac{36}{x} = 3 \\ x = \frac{36}{3} \\ x = 12[/tex]

I hope that is useful for you :)

Answer:

x represents the number of shirts purchased

Step-by-step explanation:

Each time Nick buys a shirt, he has an outlay of $12.  One shirt for $12, two shirts for $24, and so on.  So the amount due for the purchase of x shirts is ($12/shirt)x, where x represents the number of shirts purchased.

Answer:

12g

Step-by-step explanation:

[tex]5g+7g=12g[/tex]

Answer:

12g

Step-by-step explanation:

5g+7g = 12g

have a great day

Answer:

37 yd²

Step-by-step explanation:

The computation of the surface area of this triangular pyramid is shown below:

The surface area of this triangular pyramid  is

But before that

Lateral area = 3(1 ÷ 2) × base × height

= (3 ÷ 2)(4 yd)(5 yd)

= 30 yd²

Now

base area = 1 ÷ 2 × base × height

= 1 ÷ 2(4 yd)(3.5 yd)

= 7 yd²

Now the total surface area is  

surface area = lateral area + base area

= 30 yd² + 7 yd²

= 37 yd²

Answer:

176

Step-by-step explanation:

Answer:

[tex] 64y = 17 {x}^{3} [/tex]

Step-by-step explanation:

[tex]y \: \alpha \: {x}^{3} ....(given) \\ \therefore \: y = k {x}^{3} .. (1)\\ (k =arbitrary \:constant) \\when \: x = 4, \: \: y = 17, \:k =? \\ 17 = k {(4)}^{3} \\ 17 = 64k \\ k = \frac{17}{64} \\ plug \: k =\frac{17}{64} \: in \: equation \: (1) \\ y = \frac{17}{64} {x}^{3} \\ 64y = 17 {x}^{3} [/tex]

The correct equation connecting y and x is,

⇒ y = 17/64x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

⇒ y is directly proportional to x³

Hence, We get;

⇒ y = kx³

Here, y  17 at x = 4;

Hence,

⇒ 17 = k × 4³

⇒ k = 17 / 64

Thus, The correct equation connecting y and x is,

⇒ y = 17/64x

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Answer:

g(x) = 8x

Step-by-step explanation:

cause of IXL

Answer:

Step-by-step explanation:

The Pythagorean theorem is that (for right triangles)

a^2+b^2=c

Meaning c is the side opposite the right angle

Hope this helps!

Answer:

x=1. (1, 2)

x=2. (2, 5)

Step-by-step explanation:

i hope this helps :)

Answer:

40.56

Step-by-step explanation:

2pir

8÷2=r=4

2pi4=25.13

25.13÷2=12.565

10+10+8+12.56=40.565

Answer:

The cost of the aquarium was $38

Step-by-step explanation:

I got 60% of 100 and it was 60 so it was $40 but then the sales tax was $2 so I subtracted and got 38

The total cost of the aquarium is the sum of the marked down price and

the sales tax.

The total cost of the aquarium is $42

Reasons:

The known information are;

Original price of the aquarium = $100

The marked down percentage of the aquarium = 60%

The sales tax = 5%

[tex]Mark \ down = \dfrac{Difference}{Current \ selling \ price} \times 100[/tex]

[tex]60 \% = \dfrac{Difference}{100} \times 100[/tex]

Which gives;

The difference in sale = $100 - Marked down price = $60

Marked down price = $100 - $60 = $40

The marked down price = $40

The tax is applied to the marked down price, therefore, we get;

Sales tax = 5% × $40 = $2

The total cost = Marked down price + Sales tax

The total cost of the aquarium = $40 + $2 = $42

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Answer:

11. 10x^2 - 13x - 3

12. 5x^2 + 18x + 5

Step-by-step explanation:

11. Product means multiplication, so you can multiply (5x + 1) and (2x - 3).

[tex](5x + 1) * (2x - 3)[/tex] - Using the FOIL (First+Outer+Inner+Last)

So: [tex](5x*2x) + (5x*-3) + (1*2x) + (1*-3)\\10x^{2} -15x + 2x -3\\10x^{2} -13x -3[/tex]

12. [tex]3x^{2} + 8x - 1 + 2(x^{2} +5x + 3)[/tex] (So, you distribute the 2 to x^2 + 5x + 30, then combine like terms).

[tex]3x^{2} + 8x - 1 + 2(x^{2} +5x + 3)\\3x^{2} + 8x - 1 + 2x^{2} +10x + 6\\(3x^{2} +2x^{2}) + (8x + 10x) + (-1+6)\\5x^{2} + 18x + 5[/tex]

Hopefully, this helped you. Good luck & have a good day!

Answer:

10players

Step-by-step explanation:

Using the concept of probability

probability =  expected outcome/total outcome

Total outcome s the numbers of players on the team

Given

Total number of trophy won = 7 (expected)

Fraction of those that won = 7/10 (probability)

Substitute

7/10 = 7/total outcome

1/10 = 1/total outcome

Reciprocate both sides

10/1 = total outcome

Swap

Total outcome = 10

Hence the number of players on the team is 10players

Answer:

) ''You need to consider 200^o = 180^o + 20^o , hence you need to use the next formula to evaluate sin 200^o  in terms of k:

sin (alpha + beta) = sin alpha*cos beta + sin beta*cos alpha

Plugging alpha = 180^o , beta = 20^o  in the formula yields:

sin 200^o = sin (180^o + 20^o) = sin 180^o*cos20^o + sin 20^o*cos 180^o

Plugging sin 180^o = 0  and cos180^o = -1  in the formula yields:

sin 200^o = - sin 20^o = -k''

Step-by-step explanation:

''Given sin 20°=k express the following in terms of k a) sin 200° b) cos 20° c) tan(-20°) d) sin 70° Related to trigonometry.''     https://www.enotes.com/homework-help/given-sin-20-k-express-following-terms-k-sin-200-b-307263      hope this helps

Answer:

No image please add it on your next question.

Answer:

$2.02

Step-by-step explanation:

If Jessica paid $3.10 for fries and $4.88 for the sandwich, we need to add these two values together to find the total cost of her entire meal.

3.10 + 4.88 = 7.98

Since Jessica paid with a $10 bill then we need to subtract the total from the bill in order to find the change that Jessica will receive from her purchase.

$10 - $7.98 = $2.02

Now we can see that Jessica will receive a total of $2.02 in change after making her purchase.