A teacher wants to assign 4 dufferent tasks to her 4 students .in how manay possible ways can she do it?

Answer:

△stu could be similar to △pqr IF They have 2 angles that are the same (congruent) also known as the AA theorem. Another way would be if the triangle have a 2 side that are congruent and an angle that is congruent that is between both sides (the rule is known as the SAS theorem)! The last rule would be if all the side are congruent OR if they equal the same thing. For example if you got a triangle with 3,4,5 as sides and another one that has 6,8,10 as sides. 3/6 = 4/8 = 5/10 so that would be the SSS rule

Hope you found that helpful!!!

Step-by-step explanation:

ΔSTU ~ ΔPQR if and only if [tex]\frac{ST}{PQ} = \frac{TU}{QR} = \frac{SU}{PR}[/tex] and ∠S ≅∠P , ∠T≅∠Q and ∠U≅∠R.

" Two triangles are said to be similar if the ratio of the corresponding sides of one triangle to the other triangle are in proportion and corresponding angles are congruent."

According to the question,

ΔSTU is similar to  ΔPQR,

As per the definition of similar triangles we have,

Corresponding sides are in proportion.

ST ↔PQ

TU↔QR

SU↔PR

Therefore,

[tex]\frac{ST}{PQ} = \frac{TU}{QR} = \frac{SU}{PR}[/tex]  are in proportion.

∠S↔∠P

∠T↔∠Q

∠U↔∠R

∠S ≅∠P ,

∠T≅∠Q

∠U≅∠R.

Hence, ΔSTU ~ ΔPQR if and only if [tex]\frac{ST}{PQ} = \frac{TU}{QR} = \frac{SU}{PR}[/tex] and ∠S ≅∠P , ∠T≅∠Q and ∠U≅∠R.

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The prοbability οf getting 4 green οutcοmes and 1 οrange οutcοme in 5 rοlls οf the number cube is 803/1000 οr 0.803 as a decimal.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

The prοbability οf rοlling a green side is 5/6, and the prοbability οf rοlling an οrange side is 1/6.

Tο find the prοbability οf getting 4 green οutcοmes and 1 οrange οutcοme in 5 rοlls, we can use the binοmial prοbability fοrmula:

P(4 green, 1 οrange) = (5 chοοse 4) * [tex](1/6)^1 * (5/6)^4[/tex]

where (5 chοοse 4) represents the number οf ways tο chοοse 4 rοlls οut οf 5 tο be green.

(5 chοοse 4) = 5! / (4! * 1!) = 5

Substituting this value intο the fοrmula:

P(4 green, 1 οrange) [tex]= 5 * (1/6)^1 * (5/6)^4[/tex]

= 5 * (1/6) * (625/1296)

= 3125/3888

= 0.803

Therefοre, the prοbability οf getting 4 green οutcοmes and 1 οrange οutcοme in 5 rοlls οf the number cube is 803/1000 οr 0.803 as a decimal.

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Answer: B: 19.5

Step-by-step explanation:

This data set is an even data set meaning that you're going to have to add and divide, so you put your data set in ascending order (highest # to lowest #) so 12,12,15,24,31,38 its an even data set so you're going to put them in groups (remember your finding the median, the middle numbers) so you have 12,12 (one group) and 31,38 (another group) (basically make it even!!) so now you're left with the middle numbers, you have to add them and then divide them by 2 so (15+24) ÷2 and you get your answer !!

Answer:

5400

Step-by-step explanation:

Let x represent the cost of a chair and y represent the cost of a table. We can use this to set up a system of equations:

7x=2y

6x+5y=10575

We can solve this system using substitution.

Start by rewriting the first equation in terms of x.

[tex]7x=2y\\\text{Divide both sides by 7}\\x=\frac{2}{7}y[/tex]

Substitute this into the second equation:

[tex]6(\frac{2}{7}y)+5y=10575\\\frac{12}{7}y+5y+10575\\\frac{12}{7}y+\frac{35}{7}y=10575\\\frac{47}{7}y=10575[/tex]

Multiply both sides by 7

[tex]47y=74025[/tex]

Divide both sides by 47

[tex]y=1575[/tex]

This means...

[tex]7x=2(1575)\\7x=3150[/tex]

Divide both sides by 7

[tex]x=450[/tex]

One chair costs 450. Now, multiply this number by 12 to find the cost of 12 chairs.

[tex]450*12=5400[/tex]

12 chairs cost 5400.

Answer: 2n-7

Step-by-step explanation:

Volume of cylinder = Base Area x Height

V=πr2h

Rearrange for h

Height = Volume/Base Area

h = V/πr2

h = (6n² -13n -28)/(3n+4)

See the long division of the polynomials below, the quotient is 2n-7 which represents the height of the cylinder

Answer: 6

Step-by-step explanation:

Answer:

45 degrees

Step-by-step explanation:

all angles of a square add up to 360
360 divided by 4 is 90
the diagonal bisects the angle in half so 90 divided by 2 is 45

Answer:

45°

Step-by-step explanation:

Each interior angles of a square is 90° since each side is perpendicular to its adjacent side.

Therefore, as the diagonal bisects the angle(s), this means it divides each 90° angle into 2 equal parts.

So 90 ÷ 2 = 45

Answer:

(10 hours 45 minutes) + (50 minutes) + (30 minutes) =

12 hours 5 minutes

Step-by-step explanation:

Answer:

3/4 x 12/1= 9

Step-by-step explanation:

I answered this earlier but it deleted it.

So you would put the 12 over one to make it a fraction and multiply straight across

Answer:

DE=BA

EF=BC

FD=CA

Step-by-step explanation:

brainliest appreciated

hope this helps

Answer:

No, because if x=? then itś, not a true equation, a true equation is when you have infinite solutions, in this case, if the problem is asking for 1 solution then yes, if it's asking for a true statement no.

Answer:

Yes, Brianna is correct because when you solve for x you get 5 and when you substitute you get 20.

Step-by-step explanation:

combine like terms 4x-3x=x

5=x

substitute x with 5

3(5)+5=4(5)

distribute

15+5=20

Answer:

d

Step-by-step explanation:

g(x) is equal to 3x-1

therefore

(3x-1) + (3x-1)

3x= 6

6x - 2

Answer:

[tex]3\sqrt{6}[/tex]

Step-by-step explanation:

[tex]\sqrt{54}=\sqrt{9 \times 6} =\sqrt{9}\sqrt{6} =3\sqrt{6}[/tex]

Answer:

110.0m^2

Step-by-step explanation:

Area = a x b x π

a = 5m, b = 7m so

Area = 35pi which is 110.0m squared to one decimal place

Then minimum size of air conditioner for the room with an assumed length and with of 9 and 7.5 meters respectively is 1687.5 BTU

To determine the size of the air conditioner we need some parameters of the room which are

Assumed Data

Let us find the are of the room

Area = Length*Width

Area = 9*7.5

Area = 67.5 meters square

After getting the area we need to multiply this value by 25BTU to obtain the ample cooling for the room

= 67.5*25

= 1687.5 BTU

Learn more about air conditioner sizing here:

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Step-by-step explanation:

We're going to be factoring:

[tex]12 {x}^{4} + 27 {x}^{3} + 6 {x}^{2} [/tex]

We know that the GCF between 12, 27, and 6 is 3.

We also know that the GCF of x^4, x^3, and x^2 is x^2.

When factoring:

[tex]3{x}^{2} (4 {x}^{2} + 9x + 2)[/tex]

We know 3x^2 is the correct option since the polynomial is factored completely.

Answer:

[tex]3x^2[/tex]

Step-by-step explanation:

[tex]12x^4 + 27x^3 + 6x^2[/tex]

The coefficients of the variables are 12, 27 and 6.  The greatest common factor (GCF) of these numbers is 3.

[tex]\implies 3(4x^4 +9x^3 + 2x^2)[/tex]

From inspection, the GCF of the variables is [tex]x^2[/tex]

[tex]\implies 3x^2(4x^2+9x + 2)[/tex]

Therefore, the GCF of the terms in the polynomial is [tex]3x^2[/tex]

The function which relates the distance traveled d to the time t as the train travels at a constant speed is,

[tex]f(t)=210t,\\d=210t[/tex]

The speed of a body is the rate at which it covers the total distance is in the time taken. The speed of the body is given as,

[tex]s=\dfrac{d}{t}[/tex]

Here, (d) is the distance travelled by the body and (t) is time taken by the body to cover that distance.

A train leaves the station at time t=0. Traveling at a constant speed, the train travels 420 kilometers in 2 hours.

If the train travels 420 kilometers in 2 hours. Then by the above relation, the distance it travel in one hour will be,

[tex]d=\dfrac{420}{2}\\d=210\rm\; km[/tex]

As the train with constant speed travels 210 km per hour. Thus the linear function for this condition can be modeled as,

[tex]s=\dfrac{d}{t}\\210=\dfrac{d}{t}\\d=210t[/tex]

In the function of time,

[tex]f(t)=210t[/tex]

Thus, the function which relates the distance traveled d to the time t as the train travels at a constant speed is,

[tex]f(t)=210t,\\d=210t[/tex]

Learn more about the speed here:

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Answer:

the volume of said cube would be 1 unit ³

Step-by-step explanation:

1x1x1=1

Answer:

x = 1

Step-by-step explanation:

Axis of symmetry is a line which divides an object into two equal halves giving it exactly like a mirror shape.

Here a line of x = 1 can be drawn to separate the figure into equal halves.

Answer:

x = 1

Step-by-step explanation:

I think that it is 1.

Answer:

48cm!

Step-by-step explanation:

10 + 6 = 16

16 + 17 = 33 ( 16 + 10 = 26 + 7 =  33)

33 + 15 = 48 (33 + 10 = 43 + 5 = 480

Answer:

  about 60.1 cm

Step-by-step explanation:

The perimeter is the sum of the side lengths. The only side length not given is that of the slanted side. It can be considered to be the hypotenuse of a right triangle with legs (15 -10) = 5 cm and (17 -6) = 11 cm. The Pythagorean theorem tells us that hypotenuse has a length of ...

  c² = a² +b²

  c = √(a² +b²) = √((5 cm)² +(11 cm)²) = √146 cm ≈ 12.083 cm

Then the sum of side lengths (CW from bottom left) is ...

   17 cm +10 cm +6 cm +12.1 cm +15 cm = 60.1 cm

The perimeter is about 60.1 cm.

Answer:

I'd say A. Because it's literally going the same way as the arrows shown below.

Add the exponents and keep the same base. Then reciprocal it and change the sign of the exponent. Then the value of the exponent expression is 0.5.

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

The exponent expression is 2³ × 2⁻⁴ can be simplified.

Add the exponents and keep the same base. Then we have

2³ × 2⁻⁴  = 2⁽³⁻⁴⁾

2³ × 2⁻⁴  = 2⁻¹

Then find the reciprocal and change the sign of the exponent.

[tex]2^3* 2^{-4} = 2^{-1}\\\\2^3* 2^{-4} = \dfrac{1}{2}\\\\2^3* 2^{-4} = 0.5[/tex]

The value is 0.5.

More about the exponent link is given below.

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Answer:

The answer is D.

Step-by-step explanation:

Hope this helps. Pls give brainliest!

let's start with the triangle, since that seems very obvious per se, the triangle has a base of 20 and a height of 14.

[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b= base\\ h= height\\[-0.5em] \hrulefill\\ b=20\\ h=14 \end{cases}\implies A=\cfrac{1}{2}(20)(14)\implies A=140[/tex]

now let's do the sector.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =45 \end{cases}\implies \begin{array}{llll} A=\cfrac{(45)\pi (20)^2}{360} \\\\\\ A=50\pi \implies A\approx 157.08 \end{array}[/tex]

now let's do the segment.

[tex]\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( \cfrac{\pi \theta }{180}~~ - ~~sin(\theta ) \right)~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =45 \end{cases} \\\\\\ A=\cfrac{20^2}{2}\left( \cfrac{\pi (45)}{180}~~ - ~~sin(45^o) \right)\implies A=200\left(\cfrac{\pi }{4}~~ - ~~\cfrac{1}{\sqrt{2}} \right) \\\\\\ A=50\pi - 100\sqrt{2}\implies A\approx 15.66[/tex]

Answer:

finite - it is equal to 15.625

HOPE THIS HELPS!!!

Answer:

Finite.

Step-by-step explanation:

125/8=15.625

Answer:

5

Step-by-step explanation:

7+8=15

15 x 3 = 45

45/9=5