Glass A contains 100 ml of water and glass B contains 100 ml of wine. A 10 ml spoonful of wine is taken from Glass B and mixed thoroughly with the water in Glass A. A 10 ml spoonful of the mixture from A is returned to B. Is there now more wine in the water or more water in the wine

Answer:

V = 240 [tex]cm^{3}[/tex]

Step-by-step explanation:

To find the volume of a rectangular prism use this equation:

V = l*w*h

l = length (20 cm)

w = width (4 cm)

h = height (3 cm)

Plug all these values into the equation and solve:

V = (20 cm)(4 cm)(3 cm)

V = (80 [tex]cm^{2}[/tex])(3 cm)

V = 240 [tex]cm^{3}[/tex]

Therefore, the volume of the rectangular prism is 240 [tex]cm^{3}[/tex].

I hope this helps! Good luck!

Answer:

D

Step-by-step explanation:

because Y has to be about 0.4 meters high and the X value has to be 1 meter wide

The key to this problem is to identify the functions; isolate the functions dependent on only x; and define each function in terms of x. Once every function is in terms of x then we can apply them to the equation that needs to be solved. Identify the functions: Here we are given four functions f(x); g(x); h(x); and i(x) so anytime we see these letters appear in an equation is where we would substitute the function. Isolate the functions dependent on only x: At a glance we can tell that only g(x) is purely in terms of x, every other function contains another function within their equations.

Define each function in terms of x: Since g(x) is in terms of x and i(x) contains g(x) then we can substitute 3x+4 for g(x) making i(x)=(x-2)*(3x+4) which then simplifies to i(x)=3x2-2x-8

Since h(x) contains i(x) then we can substitute the i(x) we made in 3a to get h(x)=3x2-11-(3x2-2x-8) which then simplifies to h(x)=2x-3

Since f(x) contains g(x) and h(x) then we can substitute those equations to get f(x)=2(3x+4)-(2x-3) which then simplifies to f(x)=4x+11

Now we apply our defined equations to the equation in question. There are two ways to do this, we can either apply our x values to each individual equation first or make the equation in question in terms of x. In this case I will make the equation in terms of x first. The first part of this process is understanding that the ° symbol does not represent degrees in this case, it represents the substitution of a function into another function. For example, if you saw (f°g)(x) then you would take the equation for g(x) and substitute it for every x value in the f(x) equation. Based on the process around ° it would be best to start from i(x) and work backwards to f(x) then h(x). So 2i=2(i(x))=2(3x2-2x-8)=6x2-4x-16       Ignoring the 3 we then evaluate f°2i=f(2(i(x)))=4(6x2-4x-16)+11=24x2-16x-64. Then we multiply the 3 to get 3f°2i=3(24x2-16x-64)=72x2-48x-192

Then we get to h°3f°2i=2(72x2-48x-192)-3=144x2-96x-384 which can simplify to 48(3x2-2x-8) or 48(3x+4)(x-2).

Finally we can divide g(x) making (h°3f°2i÷g)(x)=(48(3x+4)(x-2))/(3x+4)=48(x-2)

With the final equation in terms of only x we can finally solve by substituting each x value, giving us -288 when x=-4; -240 when x=-3; and 0 when x=2.

Answer:

= 18 [tex]cm^{2}[/tex]

Step-by-step explanation:

As the triangle is right angled:

formula  

       = [tex]\frac{1}{2}[/tex] base x height

         = [tex]\frac{1}{2}[/tex] 6 x 6

         =[tex]\frac{1}{2}[/tex] x 36

         =[tex]\frac{36}{2}[/tex]

           = 18 [tex]cm^{2}[/tex]

The Coordinate of A is (0, 1) and the equation of the graph with B coordinate is ¹/₂^(ˣ) - (¹/₂)x

The equation of the accompanying graph is;

f(x) = aˣ

1) We want to write the coordinate of A. Thus;

f(0) = a⁰ = 1

Thus;

Coordinate of A = (0, 1)

2) The way we can tell that: 0 < a < 1 is; From figure number and inverse functions.

3) If B is the point (4, ¹/₁₆), then;

f(4) = a⁴ = ¹/₁₆

a = ⁴√(¹/₁₆)

a = ¹/₂

4) The equation of the graph with B coordinate is;

y - ax

⇒ ¹/₂^(ˣ) - (¹/₂)x

5) To get the coordinates of the point of intersection of the two graphs is;

¹/₂^(ˣ) - (¹/₂)x = ¹/₂^(ˣ)

⇒ (¹/₂)x = 0

x = 0

Thus, the coordinate of the intersection is; (0, 0)

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Answer:

24

Step-by-step explanation:

12*2=24

7*3=24

3*7=24

4*6=24

Hope this helps!

Step-by-step explanation:

X+7x=9-19

8x=-10

X=-10÷8

X=1.25

Answer:

The survey represents quantitative data and there is greater percentage of LA residents who own cars than NYC residents who do.

Answer:

Answer:

A.

Step-by-step explanation:

bc, it's high preasured. meaning its going 2b snowy.

Answer:

Step-by-step explanation:

Answer:

1/2, 3/8, 1/8

Step-by-step explanation:

the radio of giving blue marbles is 4/8=1/2

the radio of giving green marbles is 3/8

the radio of giving red marbles is 1/8

Answer:

the probability of you getting a B marble is 1/2 for a R marble its 1/8 and for a G marble its 3/8.

Step-by-step explanation:

Answer:

Here is the ans ...hope it helps

Answer:

B. f(x) is shifted left by 6 units

Step-by-step explanation:

when we talk about translations, we know they happen along the X axis, y axis or sometimes both, in this case we see that were subtracting x by six units, so we are moving left along the x axis

ways to remember this is:

 -you count up x the RIGHT way going right

 -you count UP y

and of cource by process of ellimination we know that decreasing X goes left and decreasing y goes down

ALSO NOTE: x always goes horizontally and y always goes vertically

[tex]\fcolorbox{red}{blue}{Answer}[/tex]

78.5 units²

Step-by-step explanation:

[tex] \textsf{\large{\underline{To find :-}}}[/tex]

The area of circle on graph

[tex] \textsf{\large{\underline{Given :-}}}[/tex]

[tex] \sf (x_1,y_1) = (-3,-3) \\ \sf (x_2,y_2) = (2,-3)[/tex]

[tex] \textsf{ \huge{\underline{\underline{Solution :-}}}}[/tex]

We can see in the above question that we have been provided the center of thee circle and line of the circle passes through a point.

So to find the radius we have to find the distance between center of circle and the point from which line passes.

[tex] \sf \blue{ Distance = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } }[/tex]

Now substituting the required values

[tex] \sf \implies\sqrt{ { \{2 - ( - 3) \}}^{2} + { \{ - 3 - ( - 3) \}}^{2} } \\ \\ \sf \implies \sqrt{ {(2 + 3)}^{2} + {( - 3 + 3)}^{2} } \\ \\ \sf \implies \sqrt{ {5}^{2} + {0}^{2} } \\ \\ \sf \implies \sqrt{25} \\ \\ \sf \implies 5 \: units[/tex]

So the radius will be 5 units

Now we will simply formula for area of circle

[tex] \sf \green{ Area \: of \: circle = \pi {r}^{2} }[/tex]

Now substituting the required values

[tex] \sf \hookrightarrow Area = 3.14 \times {5}^{2} \\ \\ \sf \hookrightarrow Area = 3.14 \times 25 \\ \\ \red{\boxed {\hookrightarrow \frak{78.5 \: {units}^{2} } }}[/tex]

The graph of the circle is plotted with clarity and the area is obtained as 78.5 square units.

The graph of a circle can be plotted by knowing its centre and radius.

If radius is not given, then it can be found by knowing the coordinate of any point lying on it.

The radius can be calculated by the distance formula.

The centre of the given circle is at (-3, -3) and it passes through (2, -3).

Now, radius is the distance between the centre and a point lying on circle.

The radius can be calculated by distance formula as below,

√((-3 - 2)² + (-3 - (-3))²) = 5

The graph of the given circle can be drawn as follows,

Now, the area of the circle is πr² = 3.14 × 5² = 78.5

Hence, the graph of the circle is drawn properly and the area is given as 78.5 square units.

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Answer:

1536

Step-by-step explanation:

Answer:

2x+2y = 8

Step-by-step explanation:

Simply multiply the first equation x + y=4 by 2:

x + y=4
*2      *2

(x + y)2 = 8

2x+2y = 8

x + y = 4  and 2x+2y = 8 are the same equation. You can't solve x+y = 4, there's infinite number of solutions, just like how you can't solve 2x+2y = 8

Answer: Each adult’s meal costed $15

Step-by-step explanation:

This situation can be modeled by the following equation:

2a + 3c = 42, where a = the cost of an adult’s meal, and c = the cost of a child’s meal

Since we know from the problem that a child’s meal costs $4, we know c:

2a + 3(4) = 42

At this point, we can just solve the resulting equation for a:

2a + 3(4) = 42

= 2a + 12 = 42 (simplify 3(4))

= 2a = 30 (subtract 12 from both sides)

= a = 15 (divide both sides by 2)

So, the cost of each adult’s meal was $15.

Answer:

B, C, and E

Step-by-step explanation:

In order for a function to be a function, an ordered pair cannot be on the same x coordinate

Answer:

The answer to this question should be 28.3

Answer:

A

Step-by-step explanation:

You wont find vegatarians at a hamburger restaurant but you wilk find non vegetarians at a icecream parlor

x + yi = (1 + i)⁴

then -4 + 4 = x

Answer:

Step-by-step explanation:

Remove full rotations of [tex]2\pi[/tex]  until the angle is between 0 and [tex]2\pi[/tex].

[tex]cos(\frac{\pi }{3} )[/tex]

The exact value of [tex]cos(\frac{\pi }{3})[/tex] is [tex]\frac{1}{2}[/tex].

[tex]\frac{1}{2}[/tex]

The result can be shown in multiple forms.

Exact Form:

[tex]\frac{1}{2}[/tex]

Decimal Form:

[tex]0.5[/tex]

Vocabulary:

Rotation

A transformation in which a figure is rotated through a given angle, about a point.

Angle

The union of two rays with a common endpoint, called the vertex.

[tex]let\ x\ be\ the\ unknown\ number[/tex]

[tex]8x+7=2x-3[/tex]

first choose a variable to represent the number.

when something is "..." times a number, we are multiplying that number by that value.

"seven added to eight times a number" means that we are multiplying the number by eight (8x) and then adding seven to it (+7).

"is" usually means 'equals to' so we put an equal sign there.

"three less than twice the number" means that we are multiplying the number by two (2x) and then subtracting three from it (-3).

An equation form of given statement is,  7 + 8m = 3 - 2m where m is any real valued number.

"It is a mathematical statement which consists of equal symbol between two mathematical expressions."

For given question,

We have been given a statement.

We need to translate given statement into a equation.

Seven added to eight times a number is three less than twice the number.

Let 'm' be any real number.

We can rewrite above statement as,

     Seven plus to eight times 'm' is three minus twice 'm'.

⇒       7        +             8 × m           =        3      -         2 × m

So, we get an equation,

⇒ 7 + 8m = 3 - 2m

Therefore, an equation form of given statement is,  7 + 8m = 3 - 2m where m is any real valued number.

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Answer:

Area = 22.3 m^2

Perimeter 27.4 m^2

Step-by-step explanation:

Perimeter = __ m

Area __ m^2

The area of the triangle is about 4.2,

The area of the square is 4,

The area of the semicircle is 14.1,

14.1 + 4.2 + 4 = 22.3

Area = 22.3 m^2

9.4 + 6 + 4 + 4 + 4 = 27.4

Perimeter = 27.4 m^2

Therefore the area of the shape is about 22.3 m^2 and the perimeter is about 27.4 m^2.

The conversion rate will affect her budget as C. Kari has almost exactly enough left in her budget to see Genoa.

From the information given, it should be noted that a trip to Genoa will cost her €60.85.

This will be converted to dollars which will be:

= 60.85/0.6859

= 88.72

Therefore, out of the $585 budget, only $88.72 is used.

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Answer:

Step-by-step explanation:

45000 x %22 = 9900 per year

9900/12=825 per month

Answer:

[tex]2x = x + 15[/tex]

Step-by-step explanation:

Angle AGH and GHD are corresponding angles, meaning they are equal. So in order to find the equation that can be used to solve for x we need to equate both angles AGH and GHD to each other.

[tex]m < AGH\: \: \: = \: \: \: m < GHD \\ (x + 15) = (2x) \\ 15 = 2x - x \\ 15 = 1x \\ 15 = x[/tex]

They did not ask us to solve for x but I did it in case, however we can see that the answer we got corresponds with

[tex] (1) \:2x = x + 15[/tex]

Corresponding angles are equal

Option A