Five students and two teachers pose for a picture.in how many ways can they line up side by side for a picture. 2. In how many ways can they line up if they must have the teachers on both sides of the picture? 3.what is the probability that the two teachers occupy two of the three middle slots?

Answer:

2 : 1

Step-by-step explanation:

Supplementary angles are two angles whose measures add up to 180°

If one of the angle = 120°

The other angle = sum of supplementary angle - one of the angle

= 180° - 120°

= 60°

The other angle = 60°

ratio of pair of supplementary aangle = 120° : 60°

= 120° / 60°

= 2/1

= 2 : 1

ratio of pair of supplementary aangle = 2 : 1

Answer:

194

Step-by-step explanation:

Rectangles :

7 x 10 = 70

6 x 10 = 60

4 x 10 = 40

Triangles

[tex]\frac{6x4}{2}[/tex] = 12   (two of them = 24)

70 + 60 + 40 + 24 = 194

Answer:

B) 1.4

Step-by-step explanation:

The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.

sin(B)=opp/hyp

The maximum length of the seesaw is 1.4 meters

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let h represent the length of the seesaw, hence using trigonometric ratio:

sin(45) = 1 / h

h = 1.4 meters

The maximum length of the seesaw is 1.4 meters

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Answer:

Step-by-step explanation:

r=5 cm

area=πr²

perimeter=2πr

substitute the value of r and calculate.

Answer:

78.54 [tex]cm^{2}[/tex] Area

31.42 cm   Circumference/perimeter

Step-by-step explanation:

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

C = 2[tex]\pi[/tex]r

A = [tex]\pi[/tex][tex]5^{2}[/tex]

A = 25[tex]\pi[/tex]

A = 78.54

C = 2[tex]\pi[/tex](5)

C = 10[tex]\pi[/tex]

C = 31.42

Given:

[tex]Domain\neq -1[/tex]

[tex]Range\neq 2[/tex]

To find:

The function for the given domain and range.

Solution:

A function is not defined for some values that makes the denominator equals to 0.

The denominator of functions in option A and C is [tex](x-1)[/tex].

[tex]x-1=0[/tex]

[tex]x=1[/tex]

So, the functions in option A and C are not defined for [tex]x=1[/tex] but defined for [tex]x=-1[/tex]. Therefore, the options A and C are incorrect.

In option B, the denominator is equal to [tex]x+1[/tex].

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

So, the function is not defined for [tex]x=-1[/tex]. Thus, [tex]Domain\neq -1[/tex].

If degree of numerator and denominator are equal then the horizontal asymptote is [tex]y=\dfrac{a}{b}[/tex], where a is the leading coefficient of numerator and b is the leading coefficient of denominator.

In option B, the leading coefficient of numerator is 2 and the leading coefficient of denominator is 1. So, the horizontal asymptote is:

[tex]y=\dfrac{2}{1}[/tex]

[tex]y=2[/tex]

It means, the value of the function cannot be 2 at any point. So, [tex]Range\neq 2[/tex].

Hence, option B is correct.

Respuesta:

15%

Explicación paso a paso:

Dado :

Precio de compra = $ 4000

Precio de venta = $ 4600

El beneficio obtenido por la venta del artículo:

Precio de venta - precio de compra

$ (4600-4000) = $ 600

El porcentaje de beneficio obtenido:

Beneficio / precio de compra * 100%

600/4000 * 100%

600/4000 * 100%

0,15 * 100%

= 15%

Answer:

The length of the shortest side of the triangle is 10 units.

Step-by-step explanation:

Let a be the shortest side of the isosceles triangle and b be the two congruent sides.

The congruent sides b are each one unit longer than the shortest side. Hence:

[tex]b=a+1[/tex]

The perimeter of the isosceles triangle is given by:

[tex]\displaystyle P_{\Delta}=b+b+a=2b+a[/tex]

This is equivalent to the perimeter of a square whose side lengths are two units shorter than the shortest side of the triangle. Let the side length of the square be s. Hence:

[tex]s=a-2[/tex]

The perimeter of the square is:

[tex]\displaystyle P_{\text{square}}=4s=4(a-2)[/tex]

Since the two perimeters are equivalent:

[tex]2b+a=4(a-2)[/tex]

Substitute for b:

[tex]2(a+1)+a=4(a-2)[/tex]

Solve for a. Distribute:

[tex]2a+2+a=4a-8[/tex]

Simplify:

[tex]3a+2=4a-8[/tex]

Hence:

[tex]a=10[/tex]

The length of the shortest side of the triangle is 10 units.

[tex]\displaystyle\bf 2x=84\\\\x=84:2=42\\\\\boxed{x=42}[/tex]

Answer:

[tex]gradient = - \frac{1}{3} \\ { \tt{equation \: is \: y = - \frac{1}{3}x + 3 }}[/tex]

Answer:

The equation of a perpendicular line to  

y =( -1/3 )x+b (b is a normal number)

Step-by-step explanation:

1.Use the slope-intercept form to find the slope.

Tap for more steps...

m = 3

2. the perpendicular line to y=3x+3

must have a slope that is the negative reciprocal of the original slope.

thus,

m perpendicular  =  −1/3

Answer:

[tex]\angle DFE = \angle DFG[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

What makes DEF and DGF congruent

We have:

[tex]EF = GF[/tex] --- this is indicated by the single line on both sides

Also:

[tex]DF = DF[/tex] --- both triangle share same side

For SAS to be true;

2 sides and 1 angle must be equal in either triangles

So far, we have:

[tex]EF = GF[/tex] ---- S

[tex]DF = DF[/tex] ---- S

The additional to complete the proof is:

[tex]\angle DFE = \angle DFG[/tex] ---- angle between the above sides

Reflection is a type of rigid transformation which requires the turning of an object, shape or figure about a reference point or line. Therefore, the needed additional information is ∠DFE ≅ ∠ DFG. Option B.

Reflection implies turning the given triangle DEF about its side DF, so as to produce an image with the same dimensions but different orientation.

The required proof by Side-Angle-Side (SAS) implies that the relations will be in respect of two of its sides and their included angle.

So that,

GF ≅ FE (given)

DF is the common side to triangles DEF and DFG.

DFG is the included side.

Thus;

∠DFE ≅ ∠ DFG (Side-Angle-Side postulate, SAS)

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Answer:

Step-by-step explanation:

The absolute value of a number is defined as the positive of either a positive or a negative number. By that I mean that

| 1 | = 1 and | -1 | = 1.  Right?

We use that idea here. Either:

6x + 3 = 27     OR      6x + 3 = -27 and solve both equations.

6x = 24 so x = 4 OR

6x = -30 so x = -5

Choice D is the one you want.

Answer:

C=20

Step-by-step explanation:

Answer:

Hollerith tabulating machine

Step-by-step explanation:

The Hollerith tabulating machine was invented by Herman Hollerith in other to assist in the data processing of the United States 1890 election. This machine was used to read and summarize the information stored on punchcards. This machine paved the way for the development of enhanced models which were employed for accounting and some other aspects related to business management.

Answer:

check footprints and then check finger print the finger print pour powder on it and Trace

The equation of the line that connects the two points (1,9) and (-2,3) is,

y = 2x+7

or, y-3=2x+4

or, y-3=2(x+2)

So, option c, is the correct option

Answered by GAUTHMATH

Answer:

T(x) = 21 + 4.5x

Step-by-step explanation:

Given :

Original temperature = 21°C

Final temperature = 75°C

Time, x = 12 minutes

The temperature, T as a function of x, heating time in minutes :

We need to obtain the constant heating rate per minute :

Final temperature = initial temperature + (constant rate change,△t * time)

75 = 21 + 12△t

75 - 21 = 12 △t

54 = 12 △t

△t = 54 / 12

△t = 4.5°C

Hence, temperature change is 4.5°C per minute.

Hence,

T(x) = 21 + 4.5x

Answer:

T= 21+4.5x

Step-by-step explanation:

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Answer:

_____________________________

2 x 5 = 10

2 x 4 = 8

10 + 8 = 18

______________________________

5 + 4 = 9

_______________________________

_ 9 = 18

18 : 9 = 2

Step-by-step explanation:

a) k = 1

b) geometric progression formula:

Tn = ar^(n-1)

first term, a = 3/2

The equation of the line is y + 1 = 3(x - 2).

The correct option is (3).

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

As per the given data:

The line passes through the point (2, -1)

slope of the given line is 3

By using the slope intercept form of line:

y = mx + c

where m is the slope

c is the y intercept

The line passes through the point (2, -1) so substituting the point in the equation also m = 3

y = 3x + c

-1 = 3(2) + c

c = -7

The equation of the line now can be written as:

y = 3x - 7

y + 1 = 3x - 7 + 1

y + 1 = 3(x - 2)

Hence, the equation of the line is y + 1 = 3(x - 2).

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Answer:

the answer to the question is C

Answer:

Slope-intercept

y = 3/4(x) - 7

Point slope

y -5= 3/4(x - 16)

Step-by-step explanation:

In slope-intercept

We have the general slope intercept as;

y = mx + b

where m is the slope and b is the y-intercept

in this case, m = 3/4 and b = -7

So we have;

y = 3/4(x) - 7

In point-slope

we have the general form as;

y-y1 = m(x-x1)

So what we have is as follows;

y -5= 3/4(x - 16)

Where we have (x1,y1) = (16,5)

Answer:

1.)36

2.)54

Step-by-step explanation:

sana po makatulong gehehe

Answer:

20cm

Step-by-step explanation:

a square has 4 equally long sides.

when we know its perimeter, that means we know the sum of all 4 sides.

since all sides are equality long, we only need to divide the perimeter by 4 to get the length of an individual side.

80/4 = 20cm

Answer:

5.28

Step-by-step explanation:

we use the formula

H²=B²+P²

and we will get the answer

branliest if it is helpful

Answer:

Angle BXY

using pythogoras theory which is

hyp*2= opp*2 +adj*2

hypothenus being the longest part of the angle BX=?

Step-by-step explanation:

hyp= 4.2*2+ 3.2*2

hyp*2 =17.64 + 10.24

hyp*2 = 27.88

hyp =√27.88

hyp=5.28...Ans

note *2...square

Answer:

Step-by-step explanation:

[tex]5) 5\frac{11}{12}+3\frac{5}{6}=5+\frac{11}{12}+3+\frac{5}{6}\\\\ =8 +\frac{11}{12}+\frac{5*2}{6*2}\\\\= 8 +\frac{11}{12}+\frac{10}{12}\\\\=8 +\frac{11+10}{12}\\\\= 8+\frac{21}{12}\\\\=8+ 1\frac{9}{12}\\\\= 9\frac{9}{12}[/tex]

Answer:

114

Step-by-step explanation:

114

Answer:

kids at playground

children are too young to know calorie count and the health benefits of certain foods. So they would simply choose the one they think tastes best