How do I simplify this equation?

Answer:

45/1 and 180/4

Step-by-step explanation:

1. True

[tex]\dfrac{90}{2}=\dfrac{45\cdot 2}{1\cdot 2}=\dfrac{45}{1}[/tex]

2. False

[tex]\dfrac{15}{3}=\dfrac{3\cdot 5}{3\cdot 1}=\dfrac{5}{1}\neq \dfrac{45}{1}[/tex]

3. False

[tex]\dfrac{180}{3}=\dfrac{60\cdot 3}{3\cdot 1}=\dfrac{60}{1}\neq \dfrac{45}{1}[/tex]

4. True

[tex]\dfrac{180}{4}=\dfrac{45\cdot 4}{1\cdot 4}=\dfrac{45}{1}[/tex]

5. False

[tex]\dfrac{270}{8}=\dfrac{135\cdot 2}{4\cdot 2}=\dfrac{135}{4}\neq \dfrac{45}{1}[/tex]

Answer:

1hr 40min.

Step-by-step explanation:

45+45=90+10=100

Answer:

1 hour 95 min. 2 hour 190 min. third hour 285 min. fourth hour 380 min.

Step-by-step explanation:

Answer:

b. 26cm

oop I didn't realize this was in 2019:-:

Answer:

Part a) The total length of the circular portions is [tex]12\pi\ in[/tex]

Part b) The total length of wire needed is tex]53.7\ in[/tex]

Part c) The total weight of the ornament is [tex]97\ g[/tex]

Step-by-step explanation:

Part a) Find the total length of the circular portions in terms of pi

we know that

The diameter of the circle is equal to the length side of the square

[tex]D=4\ in[/tex]

The total length of the circular portions is equal to the circumference of three complete circle

Because each circular portion is equal to 3/4 of circle

so

[tex](3/4)*4=3[/tex]

The circumference of four three quarter circles is equal to

[tex]C=3(\pi D)[/tex]

substitute the diameter

[tex]C=3(\pi (4))[/tex]

[tex]C=12\pi\ in[/tex]

Part b) Find the total length of wire needed

The total length of the circular portions is [tex]12\pi\ in[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]12(3.14)=37.68\ in[/tex]

The total length of the square portion is equal to

[tex]4b=4(4)=16\ in[/tex] -----> perimeter of a square

Adds the lengths

[tex]37.68+16=53.68\ in[/tex]

Round to the nearest tenth

[tex]53.68=53.7\ in[/tex]

Part c) Find the total weight of the ornament

we know that the ornament weights 1.8 grams per inch

so

Multiply the total length by 1.8 to obtain the total weight

[tex]53.7(1.8)=96.66\ g[/tex]

Round to the nearest gram

[tex]96.66=97\ g[/tex]

Answer:

It makes sense for the answer to be 86 degrees since it's almost a right angle.

Answer:

The correct answer is option C.   86°

Step-by-step explanation:

From the figure we can see a circle.

To find the measure of <PRQ

Consider the triangle PQR,

<PRQ  = <PTR + <RPT

From the figure we get,

<PTR = 102/2 = 51

<RPT = 70/2 = 35

<PRQ  = <PTR + <RPT

51 + 35 = 86°

Therefore the correct answer is option C.   86°

Answer:

angle Y = 90 degrees

Step-by-step explanation:

Since it is stated that angle x forms a straight line with the 50 and 50 degree angles, and that angle x is vertical to angle y, we can do 40+50+y=180 to find angle Y.

Answer: - 1/3 I just saw the other answer and got it wrong so I decided to give u guys the right answer !! :)

Answer:

y < 3

Step-by-step explanation:

Given

15y - 9 < 36 ( Isolate 15y by adding 9 to both sides )

15y < 45 ( divide both sides by 15 )

y < 3

Answer:

y < 3

Step-by-step explanation:

on edge 2020

Answer:

x^2+6x+9

(x+3)^2

Step-by-step explanation:

Answer: C

Since all the answers have (-6), it means that you multiply the whole equation on both sides by 6, which makes a (2/3)x become a 4x and a (1/2) become 3

Answer:

C

Step-by-step explanation:

Start by multiplying through by 3. That is the first of 2 possible steps.

3[2/3 x - 1  = 1/2]

2x - 3 = 3/2              

Now multiply by 2

2 [ 2x - 3 = 3/2]

4x - 6 = 3

That makes C the only possible answer.

Congruent because it contains the same angle measures and shape.

Answer:

congruent

Step-by-step explanation:

Answer:

{4, - 1}

Step-by-step explanation:

Given

2y² - 6y - 8 = 0 ← in standard form

with a = 2, b = - 6, c = - 8

Using the quadratic formula to solve for y

y = ( - (- 6) ± [tex]\sqrt{(-6)^2-(4(2)(-8)}[/tex] ) / (2 × 2)

  = ( 6 ± [tex]\sqrt{36+64}[/tex] ) / 4

  = ( 6 ± [tex]\sqrt{100}[/tex] ) / 4

  = ( 6 ± 10 ) / 4

x = [tex]\frac{6+10}{4}[/tex] = [tex]\frac{16}{4}[/tex] = 4

OR

x = [tex]\frac{6-10}{4}[/tex] = [tex]\frac{-4}{4}[/tex] = - 1

Solution is { 4, - 1 }

For this case we must solve the following inequality:

[tex]x-2> 2x + 12[/tex]

We follow the steps below:

We subtract 2x on both sides of the inequality:

[tex]x-2-2x> 2x + 12-2x\\-x-2> 12[/tex]

We add 2 to both sides of the inequality:

[tex]-x> 14[/tex]

We multiply by -1 on both sides of the inequality, taking into account that the sense of inequality changes:

[tex]x <14[/tex]

Answer:

[tex]x <14[/tex]

Answer:

The guys above is wrong because it should be x < -14 because you have to balance out both sides of the equation, you can't just do something to one side of the equation and not do it to the other.

Step-by-step explanation:

Answer:

3.5 blocks.

Step-by-step explanation:

After walking 3.5 blocks back she is back at her starting point.

Marilyn has walked 7 blocks in total, going the wrong direction and back to the library. She still needs to walk another 3.5 blocks to reach her house.

Marilyn has already walked 7 blocks (3.5 blocks in the wrong direction and 3.5 blocks back to the library). As her house is 3.5 blocks from the library, she has another 3.5 blocks to walk.

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____________________________________________________

Answer:

Your answer would be C). y = 100 - 5x

____________________________________________________

Step-by-step explanation:

Let's break down the question so it would be more easier to figure out the answer.

We would be making a y = mx + b equation

Important information:

With the information above, we can use that to make our equations.

We know that the place has a 100 gallon fish tank. in the question, it says that for the equation, the tank was full, so that would be our "beginning point" or "starting value. From the equation, it would represent our "B" value.

Our equation should look like this now:

y = mx + 100

Now we need to find the rate of change.

In the question, it says that the tank DRAINS at around 5 gallons per minute, meaning that we would have to subtract 5 (-5). That would represent your "m" value on the equation. Your equations should now look like this:

y = -5x + 100

F.Y.I: y = 100 - 5x is the same that as -5x + 100, it's just flipped, and y = 100 - 5x is the answer choice that looks close to the one we made.

Answer choice C). y = 100 - 5x would be your FINAL answer.

____________________________________________________

The equation that describes the situation where a 100-gallon tank is drained at a rate of 5 gallons per minute is y = 100 - 5x. This because each minute, the volume decreases by 5 gallons from the starting amount of 100 gallons.

The question is about how to represent a process which decreases at a constant rate in terms of mathematical expression. In this case, Patti's Pet Palace is draining a 100-gallon fish tank at a rate of 5 gallons per minute. The total amount of water in the tank decreases as time progresses and the tank drains.

This process can be represented using a negative slope linear equation. If y represents the amount of water in the tank after x minutes, the initial amount is 100 gallons and it decreases by 5 gallons each minute.

Therefore, the equation to represent this process is y = 100 - 5x. That means option C is the correct answer. For each minute that passes (represented as 'x'), 5 gallons are subtracted from the initial 100 gallons.

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Answer:

that depends

Step-by-step explanation:

how many students are in the school all together, see you would do the 3 boys over the number of people (or students) in the school

hoped this helped a little

Step-by-step explanation:

[tex](x^2+5x+4)\div(x+2)^2=(x^2+4x+4+x)\div(x+2)^2\\\\=(x^2+2(x)(2)+2^2+x)\div(x+2)^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=\bigg((x+2)^2+x\bigg)\div(x+2)^2=\dfrac{(x+2)^2+x}{(x+2)^2}=\dfrac{(x+2)^2}{(x+2)^2}+\dfrac{x}{(x+2)^2}\\\\=1+\dfrac{x}{(x+2)^2}[/tex]

Answer:

I think it's C, sorry if I'm wrong

Answer:

Step-by-step explanation:

(3x²+1)(4x-3) = 12x^3-9x²+4x-3.....answer 1

Answer:

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

Step-by-step explanation:

The rational roots theorem tells you that given a polynomial function with integer or whole number coefficients, a list of possible solutions can be found by listing the factors of the constant, or last term, over the factors of the coefficient of the leading term.

In your case, for the polynomial [tex]f(x)=3x^3-5x^2-12x+20:[/tex]

So, possible rational roots can be among:

[tex]\pm1,\pm2,\pm4,\pm5,\pm10,\pm20,\pm\dfrac{1}{3},\pm\dfrac{2}{3},\pm\dfrac{4}{3},\pm\dfrac{5}{3},\pm\dfrac{10}{3},\pm\dfrac{20}{3}.[/tex]

Note that

[tex]f(-2)=3\cdot (-2)^3-5\cdot (-2)^2-12\cdot (-2)+20=-24-20+24+20=0.[/tex]

This means that [tex]x=-2[/tex] is a root of the polynomial and [tex]x-(-2)=x+2[/tex] is the factor. Also

[tex]f(2)=3\cdot 2^3-5\cdot 2^2-12\cdot 2+20=24-20-24+20=0.[/tex]

This means that [tex]x=2[/tex] is a root of the polynomial and [tex]x-2[/tex] is the factor. Also

[tex]f(\frac{5}{3})=3\cdot (\frac{5}{3})^3-5\cdot (\frac{5}{3})^2-12\cdot \frac{5}{3}+20=\frac{125}{9}-\frac{125}{9}-20+20=0.[/tex]

This means that [tex]x=\frac{5}{3}[/tex] is a root of the polynomial and [tex]x-\frac{5}{3}[/tex] is the factor.

Then

[tex]f(x)=3(x+2)(x-2)(x-\frac{5}{3}).[/tex]

Answer:

m=3

Step-by-step explanation:

Formula for m is m=-1/m

m=-1/3

Answer:

5x + 2y + z

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of all the sides of the polygon. This polygons has 8 sides. Their lengths are:

x, x, x, x, x, y, y, z

The perimeter of the polygon is the sum of the lengths shown above.

perimeter = x + x + x + x + x + y + y + z

The expression above can be simplified by combining like terms.

perimeter = 5x + 2y + z

Answer:

the correct answer would be C sorry if I'm wrong but that's how I know how to do it

Answer:

Step-by-step explanation:

[tex]\log_ab=c\iff a^c=b\\\\===================\\\\Domain:\ 8x>0\to x>0\\\\\log_4(8x)=3\iff4^3=8x\\\\8x=64\qquad\text{divide both sides by 8}\\\\x=8\in D[/tex]

Answer:

From the information, we know that the plate will hold 3 pieces of sushi, each with a diameter of 1 1/2 inches, and there be 1/2 inch space from the edge of the of the suchi to the edge of the plate.

The diamter of the suchi plates we need to puchase should be the sum of the diameter of the sushi and the the space between them and the edge of the plate:

  (3 . 1 1/2) + (2 . 1/2)

= (3 . 3/2) + 1

= 9/2 + 1

= 9/2 + 2/2

= 11/2 = 5.5 (inches)

Answer:

From the information, we know that the plate will hold 3 pieces of sushi, each with a diameter of 1 1/2 inches, and there be 1/2 inch space from the edge of the of the suchi to the edge of the plate.

The diamter of the suchi plates we need to puchase should be the sum of the diameter of the sushi and the the space between them and the edge of the plate:

  (3 . 1 1/2) + (2 . 1/2)

= (3 . 3/2) + 1

= 9/2 + 1

= 9/2 + 2/2

= 11/2 = 5.5 (inches)

Answer:

78.75 cm³

Step-by-step explanation:

Volume = Width × Height × Length

V = 5 × 4.5 × 3.5

V = 78.75 cm³

Answer:

The area of the shaded sector is [tex]51.2\pi \ units^{2}[/tex]

Step-by-step explanation:

I assume that the problem is

Find the area of the shaded sector of the circle with radius equal to 16 units

step 1

Find the value of x

we know that

[tex]8x+2x=360\°[/tex]-----> by complete circle

[tex]10x=360\°[/tex]

[tex]x=36\°[/tex]

The central angle of the shaded sector is 2x

[tex]2(36\°)=72\°[/tex]

step 2

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=16\ units[/tex]

substitute

[tex]A=\pi (16)^{2}[/tex]

[tex]A=256\pi\ units^{2}[/tex]

step 3

Find the area of the shaded sector

we know that

A central angle of 360 degrees subtends an area of circle equal to [tex]256\pi\ units^{2}[/tex]

so

by proportion

Find the area of the shaded sector by a central angle of 72 degrees

[tex]\frac{256\pi}{360}=\frac{x}{72} \\ \\ x=256\pi *(72)/360\\ \\x=51.2\pi \ units^{2}[/tex]

The answer is 103 because it’s in the “middle”

Median means the middle number.

The answer : 103

Answer:

15 floors

Step-by-step explanation:

She parks on the third floor below ground +3

She goes up to the twelfth floor +12

3+12=15

Answer:

(20+2)(10+9)

Step-by-step explanation:

The area model is written as (a+b)(c+d). To write a multiplication problem into an area model, split it into numbers which add to it. Multiples of 10 are most commonly used.

For example 22*19 becomes (20+2)(10+9).