Martin has 13 liters of soda.
Each glass can hold of a liter
of soda. How many glasses can
Martin completely fill with soda?

Answer :

[tex] \underline{ \boxed{x = \frac{2(A_T) }{(AB) + (AC) + (BC)} }}[/tex]

Explanation :

[tex]i \: figured \: it \: out \to \: notice \: that \\ there \: are \:( thre e\: trianges) \: in \: triangle \: ( ABC) \\ and \: they \: all \: have \: the \: same \: height \: = x \\ first \: triangle \: is \: \to \: triangle \: (ABD) \\ second\: triangle \: is \: \to \: triangle \: (ACD) \\ third \: triangle \: is \: \to \: triangle \: (BCD) \\ if \: the \: area \: of \: a \: triangle \: is \: = \frac{1}{2} bh : then \to \\ the \: area \: of \: triangle \: (ABD) = \frac{1}{2} (AB)x \\ the \: area \: of \: triangle \: (ACD) = \frac{1}{2} (AC)x \\ the \: area \: of \: triangle \: (BCD) = \frac{1}{2} (BC)x \\ let \: the \: total \: area \:(A_T) \: be \to \: \frac{1}{2} (AB)x + \frac{1}{2} (AC)x + \frac{1}{2} (BC)x \\ if \to\\ (A_T) = \frac{1}{2} (AB)x + \frac{1}{2} (AC)x + \frac{1}{2} (BC)x \\ then \to \\ (A_T) = \frac{1}{2} \{(AB)x + (AC)x + (BC)x \} \\ x \{(AB) + (AC) + (BC) \} = 2(A_T) \\ x = \frac{2(A_T) }{(AB) + (AC) + (BC)} [/tex]

 Expression representing the length 'x' will be, [tex]x=\frac{(AB)(AC)}{AC+BC+AB}[/tex].

Use the hint → Area of the large triangle = sum of the small triangles inside the larger triangle

Area of ΔABC = [tex]\frac{1}{2}(AB)(AC)[/tex]

Area of ΔADC = [tex]\frac{1}{2}(AC)(x)[/tex]

Area of ΔBDC = [tex]\frac{1}{2}(BC)(x)[/tex]

Area of ΔADB = [tex]\frac{1}{2}(AB)(x)[/tex]

Since, Area of ΔABC = Area of ΔADC + Area of ΔBDC + Area of ΔADB

[tex]\frac{1}{2}(AB)(AC)=\frac{1}{2}(AC)(x)+\frac{1}{2}(BC)(x)+\frac{1}{2}(AB)(x)[/tex]

[tex](AB)(AC)=[(AC)+(BC)+(AB)](x)[/tex]

[tex]x=\frac{(AB)(AC)}{AC+BC+AB}[/tex]

    Therefore, expression representing the length 'x' will be [tex]x=\frac{(AB)(AC)}{AC+BC+AB}[/tex].

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Answer:

2.46

Step-by-step explanation:

csc24° = 2.45859

Answer:

1. D

2. y = 15.50x + 450

Step-by-step explanation:

1. Since it is a function, the missing pair can't repeat input values with different output, therefore only option D is unique so is the correct choice.

2. x  > (y - 450)/ 15.50

i) Rita gets paid $450 per week.

ii) She gets $15.50 for every new membership she sells.

iii) let y represent the total pay per week.

iv) let x represent the number of new memberships sold.

v) the equation representing total pay is y = 15.50x + 450.

vii) therefore the equation that represents a higher rate of membership sold is given by  x  > (y - 450)/ 15.50

Answer: 26.7m

Step-by-step explanation:

Since a decagon has 10 sides, you'll have to divide 267m by 10.

267÷10= 26.7

One side of the decagon is 26.7m

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Answer:

[tex]3(b + 3) = 2a + 27 \\ 3b + 9 = 2a + 27 \\ \boxed{- 2a + 3b= 18}[/tex]

hope this helps.

Answer:

Step-by-step explanation:

since the hypotenuse of 6 cm is shorter than the base of 8 cm there is something wrong with this drawing.  The box can't be square so maybe answer C is good but.. since this box isn't a right angled box.. we really don't know.   This is a bad question b/c it's making the appearance of being a right angle but it can not be.  Like an Escher drawing..  not possible irl  

The volume of the rectangular prism is 8×2×3 cubic in or 48 cubics in option (B) 8×2×3 cubic in is correct.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

The missing height of the rectangular prism is 3 cm

It is given that:

The rectangular prism is shown in the picture with dimensions.

As we know, the volume of the rectangular prism is given by:

V = length×width×height

Length = 2 cm

Width = 8 cm

Height = 3 cm

The volume of this figure:

V = 2×8×3

Or

The volume of this figure V = 8×2×3 cubic in

Thus, the volume of the rectangular prism or the volume of the figure is 8×2×3 cubic in or 48 cubics in option (B) 8×2×3 cubic in is correct.

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Answer:

Your friend is kayaking faster.

Step-by-step explanation:

The way to approach this answer is by putting one of them in terms of the other. So that both are in terms of the same time. If you kayak 63 feet in 12 seconds how many feet do you kayak in 2 seconds? Simply divide by 6. 63/6 = 12/6. So, in 2 seconds (12/2) you kayak 10.5 feet (63/6). But your friend kayaks 21 feet in the same time... so he's going faster.

there are 36 quarters.

Let the number of nickels be x

Let the number of quarters be y

Value Value

Type Number of of

of of EACH ALL

coin coins coin coins

-------------------------------------------

nickels x $0.05 $0.05x

quarters y $0.25 $0.25y

-------------------------------------------

TOTALS 52 ----- $3.60

The first equation comes from the second column.

x + y = 11

The second equation comes from the last column.

0.05x + 0.25y = 3.60

Get rid of decimals by multiplying every term by 100:

5x + 25y = 360

So we have the system of equations:

x+y=52

5x+25y=360

We solve by substitution. Solve the first equation for y:

x + y = 52

y = 52 - x

Substitute (52 - x) for y in 5x + 25y = 360

5x + 25(52 - x) = 360

5x + 1300 - 25x = 360

-20x + 1300 = 360

-20x = -940

x = = 5 the number of nickels.

Substitute in y = 52 - x

y = 52 - (5

y = 47 quarters.

The number of quarters is 52-x or 52-5 or 47 quarters.

Answer:

D because 0.75 in fraction form is 3/4 and 3/4 is greater then 2/3 which is the graphs rate of change.

Step-by-step explanation:

Answer:y=(-2x+1) (x+1)

Step-by-step explanation:

2x+y=-2x^2 +3x+1

y=-2x^2+x+1

y=-2x^2 -2x+x+1

y=-2x(x+1) +1(x+1)

y=(-2x+1) (x+1)

Answer:

31

do 180-149 which gets you 31, 31 is the angle inside the triangle closest to 149. since the those 2 sides are congruent it makes the 2 angles congruent. then x=31

Answer:

to have an infinite number of solutions, the lines have to be on top of each other.....basically, they have to be the same line.

y = 3x - 1

-3x + y = -1.....multiply by -1

3x - y = 1 <== this would be ur other equation because if u put this in slope intercept form (y = mx + b), it would be the same as y = 3x - 1

Step-by-step explanation:

Answer:

indian ocean

Step-by-step explanation:

Step-by-step explanation:

4×100=400

400÷7=57.14......

hope it helps!

have a great day :)

Answer:

∠ 5 = 49°, ∠ 6 = 131°

Step-by-step explanation:

∠ 5 and 49° are corresponding angles and are congruent, then

∠ 5 = 49°

∠ 5 and ∠ 6 are adjacent angles and are supplementary, sum to 180° , that is

∠ 6 + ∠ 5 = 180°

∠ 6 + 49° = 180° ( subtract 49° from both sides )

∠ 6 = 131°

Answer:

Base=40m and

Altitudes=20m

Step-by-step explanation:

Area of the field can be calculated as

Area= total cost / rate

Where total cost= 4,000 rupees

Rate= 10 per m2

Area of the field= 4000/10

= 400m^2

Let the altitudes be denoted as "x metre"

Then the base = 2x

Area= 1/2bh

Where b= base

h= altitudes

Then if we substitute we have

400m^2= 1/2× x × 2x

400= x^2

x= √400

x=20m

Then altitudes = 20m

the base = 2x= 2×20=40m

Hence, it base and altitude are 40m and 20m respectively.

The theoretical probability of selecting a rough bead is 1/2.

Total number of beads = 52

Number of rough beads = 26

Number of smooth beads =26

Probability is the measurement of possibilities.

P(event) = favorable outcomes/total outcomes

P(rough) = number of rough beads/ total beads

P(rough) =26/52

P(rough) =1/2

Therefore, the theoretical probability of selecting a rough bead is 1/2.

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Answer: 1/2

Step-by-step explanation:

Answer:

the factors are:

[tex]\frac{2}{3}\times \frac{3}{5}[/tex]

Option C is correct option.

Step-by-step explanation:

The overlapping section(green colours common for both) while blue represents first factor and yellow represent second factor.

Solving:

The first part of the factor is considered horizontal rows (as shown in figure)

So, we have 3 horizontal rows and 2 rows are coloured so, the fraction will be: [tex]\frac{2}{3}[/tex]

For the second factor, we consider vertical columns (as shown in figure)

So, we have 5 columns and 3 columns are coloured so, the fraction will be: [tex]\frac{3}{5}[/tex]

So, the result will be:

[tex]\frac{2}{3}\times \frac{3}{5}=\frac{6}{15}[/tex]

So, the factors are:

[tex]\frac{2}{3}\times \frac{3}{5}[/tex]

Option C is correct option.

Answer:

2

Step-by-step explanation:

Multiplication comes before division. To add or subtract we can do from left to right by thousand, hundred, or any respective place value thus options (1) and  (2) are correct.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Subtraction = Minus of any two or more numbers with each other called subtraction.

Using the PEMDAS rule,

Parenthesis = 1st

Exponents = 2nd

Multiplication = 3rd

Divide = 4th

Addition = 5th

Subtraction = 6th

Suppose an addition,

120 + 320

Now add from left to right,

100 + 300 = 400

20 + 20 = 40

Now, 400 + 40 = 440

Thus, adding from left to right is true.

Hence "Multiplication comes before division. To add or subtract we can do from left to right by thousand, hundred, or any respective place value ".

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1. C

2. A

3.B

4.D

Step-by-step explanation:

A,B,C,D are the possible answers in order. 1,2,3,4 are the questions in order. 1. n is greater than or equal to 4 means that n's value is larger than 4 or 4. so it would be greater than with a line underneath. 2. n is less then 4. this means n's value is any real number less than 4. so it would be n is less than 4. n is less than or equal to 4 means that it can be any real number less than 4 or 4 itself, so it would be n is less than 4 with a line underneath. process of elimination leaves just 1 answer for 4

Answer:

2

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

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