Solve this system of equations by
using the elimination method.
3x + 3y = 18
2x+y = 4
([?], [ ])

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:

160 times X

Step-by-step explanation:

160 is the number of pencils in each box.

And

X is how many boxes there are.

If 1 box contains 160 pencils then the equation which represents the total number of pencils is y=160x.

An equation is a relationship between two or more variables where variables represent some quantity . It is mostly found in equal to form. It is equated to find the value of variables.

Equation form :y=a+bx

There are 160 pencils in one box and x represents the number of boxes. So the equation that represents the total number of pencils can be found by product of x and 160.

Equation will be x*160=160x.

Hence the equation which represents the total number of pencils is y=160x.

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Answer:

5ft

Step-by-step explanation:

8/10=0.8

4/0.8=5

Using an exponential function, it is found that the population of Clay County will be of $13,482.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, the current population is 10,300 people, with a growth rate of 3%, hence A(0) = 10,300 and r = 0.03.

The equation is given by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 10300(1 + 0.03)^t[/tex]

[tex]A(t) = 10300(1.03)^t[/tex]

Hence, in 10 years, the population will be given by:

[tex]A(10) = 10300(1.03)^{10} = 13842[/tex]

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Answer: 7,595

Step-by-step explanation:

ixl

Answer:

[tex]y=2x^2-4x-16[/tex]

Step-by-step explanation:

Factored form of a quadratic equation:

[tex]y=a(x-r_1)(x-r_2)[/tex]

where:

Given:

Substitute the given values into the formula and expand:

[tex]\implies y=2(x-4)(x-(-2))[/tex]

[tex]\implies y=2(x-4)(x+2)[/tex]

[tex]\implies y=2(x^2+2x-4x-8)[/tex]

[tex]\implies y=2x^2-4x-16[/tex]

Multiplication is the process of multiplying. The total tax of Tegan's earnings will be £8,520(£6,400+£1,200).

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Since there is no tax for the first £11,000, therefore, the earnings upto £11,000 will be tax-free.

The amount of tax for the income of £11,000 to £43,000, will be,

20% of (£11,000 to £43,000)

= 20% × (£43,000 - £11,000)

= £6,400

The amount of tax for the income of £11,000 to £150,000, will be,

40% of (£43,000 to £48,300)

= 40% × (£5,300)

= £2,120

Hence, the total tax of Tegan's earnings will be £8,520(£6,400+£1,200).

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Answer:

£8520

Step-by-step explanation:

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:

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:

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:

[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

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:

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.

Answer:

Step-by-step explanation:

In the question, it is given that a flower vase has a radius of 10 cm and a height of 50 cm , we have to find the volume .

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

To Find the volume of the cylindrical flower vase , we must know this formula :

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \Longrightarrow\underline{\boxed{ \color{lime}{V=πr^2h}}}[/tex]

Now, we will substitute the values in the formula:

[tex]\Longrightarrow\sf{V=3.14*10^2*50}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\sf{V=3.14*100*50}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\sf{V=314*50}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\Longrightarrow\sf{V=15700}[/tex]

The volume of the flower vase (cylinder).

[tex]\boxed{\sf{Formula: V = \pi {r}^{2} h}}[/tex]

[tex]V = \pi \times {10}^{2} \times 50[/tex]

[tex]V = 15707.96327 \: {cm}^{3} [/tex]

[tex]\large\boxed{\sf{V = 15707.96 \: {cm}^{3} }}[/tex]

Hence, the volume of the flower vase (cylinder) is 15707.96 cubic centimeters.

The probability of rolling a sum of 12 or smaller than 5 is:

P = 7/36 = 0.194

Each dice has a total of 6 outcomes. Then for rolling two die, the total number of outcomes is:

6*6 = 36

The probability of rolling a sum of 12 or smaller than 5, is equal to the quotient between the number of outcomes that meet the above condition and the total number of outcomes.

There is only one outcome that adds up to 12.

And by looking at the table, we can see that there are 6 outcomes that add up to numbers smaller than 5.

So 7 outcomes meet the condition.

Then the probability is:

P(sum of 12 or <5) = 7/36 = 0.194

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Answer:

f(x) = -1/2x + 8

or

The first one

Step-by-step explanation:

hope this helps

have a good day

Answer:

Yes, 1.010010001 is rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Answer:

Step-by-step explanation:

A rational number has the form p q, where p and q are integers, q* 0 otherwise it is an irrational number.

Answer:

[tex]l(\widehat {ST})=6\pi [/tex]

Step-by-step explanation:

The required length of an arc ST is 6π units which is subtended by an angle.

The arc is a portion of the circumference of a circle.

The formula for calculating the arc states that:

Arc length = 2πr (θ/360)

Where r = the radius of the circle,

θ = the angle (in degrees) subtended by an arc at the center of the circle.

As per the question, we have:

θ = 90° and r = 12 units

Substitute the given values in the formula,

Arc length = 2π(12) (90/360)

Arc length = 6π

Therefore, the required length of an arc ST is 6π units.

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[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:

a. 5a + 3b-5

b. 4e^2 + f^2 + f

c. 42xy(z)^2

d. 7x(y)^2

Step-by-step explanation:

I added/subtracted/multiplied/divided like terms.

Answer:

D

Step-by-step explanation:

the number of days for 80 - 82 is 7 and the number of days for 82-84 is 9. Those are the only temperatures below 84 degrees, so you add them and get 16 :)

Answer:

Here is the ans ...hope it helps

hmmm well, don't be so  hmmm off due to it, the wording in the exercise sux0rs bad, is very poorly worded and laid out.

if X and Y are numbers, hmmm say let's give them hmmm ohhh X = 7 and Y = 13.

And X and Y are also complete cubes, well, let's make them so, X = 7³ and Y = 13³.

which of those expressions are complete cubes, or namely, something that we can write as a number with a "3" in the exponent, let's check each one.

[tex]\begin{array}{ll|l|l|lllll} 8X&\implies 8\cdot 7^3& 2^3\cdot 7^3& (2\cdot 7)^3& 14^3 ~~ \checkmark\\&&&&\\ X,Y&\implies 7^3,13^3 ~~ \checkmark&&\\&&&&\\ -X&\implies -7^3~~ \checkmark&&\\&&&&\\ 27XY&\implies 27\cdot 7^3\cdot 13^3& 3^3\cdot 7^3\cdot 13^3& (3\cdot 7\cdot 13)^3& 273^3~~ \checkmark\\&&&&\\ XY+27&\implies 7^3\cdot 13^3+27&(7\cdot 13)^3 + 3^3&&91^3+3^3 ~~ \bigotimes \end{array}[/tex]

what's wrong with the last one?  well, if we were to add 91³ + 3³ = 753598.  Now, is 753598 a complete cube? well, only if we could write it as a whole number with a "3" above, can we? nope.

we can simply check that by getting the 3rd root of that value,

[tex]\sqrt[3]{753598}\approx 91.00108681228277\impliedby \textit{not a complete cube}[/tex]

Answer:

[tex] |x|1 | \: 2 | \: 3 | \: 4 | \: 5 | \\ |y| 5| \: 4 \: | 3 \: | 2 | 1| [/tex]

Step-by-step explaination:

We were told that:

[tex] x + y = 6 [/tex]

therefore to see if it is correct you can just input the values for x and y and see if they add up to 6 (add the vertical values). For example;when x = 1, y = 5 or when x = 2, y = 4

Answer:

The answer is 76.

Step-by-step explanation:

The median would be the middle number in a box and whisker plot.

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.

400 dollars

4000/10=400 dollars