find the perimeter of the square if the side length of the square is (3a+6b) units

a. 24a+12b
b. 12a+24b
c. 4a+6b
d. 12a-24b

9*1/6

Step-by-step explanation:

1= 6/6 and there are 9 boxes so multiply 9*1/6

The system of linear equations has no solutions for any value of k except when k = 2, where it has infinitely many solutions.

(a) To reduce the augmented matrix for the system of linear equations to row-echelon form, we can write the system of equations as:

2 - y = kx

-y = k

To eliminate y in the first equation, we can multiply the second equation by (-1) and add it to the first equation:

(2 - y) - (-y) = kx - k

2 = kx - k

This gives us a new system of equations:

2 = kx - k

Now, we can represent this system in augmented matrix form:

[1 -k | 2]

(b) To find the values of k, we can examine the augmented matrix.

If the system has no solutions, it means that the rows of the augmented matrix result in an inconsistent equation, where the last row has a leading nonzero entry. In this case, for the system to have no solutions, the augmented matrix should have a row of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix [1 -k | 2] doesn't have this form, so there are no values of k that lead to no solutions.

If the system has exactly one solution, the augmented matrix should be in row-echelon form, with each row having at most one leading nonzero entry. In this case, the augmented matrix should not have any rows of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix can be reduced to row-echelon form as follows:

[1 -k | 2]

From this form, we can see that there are no restrictions on the value of k. For any value of k, the system will have exactly one solution.

If the system has infinitely many solutions, the augmented matrix should have at least one row of the form [0 0 | 0]. In our case, the augmented matrix can be reduced to:

[1 -k | 2]

From this form, we can see that if k = 2, the last row becomes [0 0 | 0]. Therefore, for k = 2, the system will have infinitely many solutions.

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Answer:

Step-by-step explanation:

$31.10

Answer:

SR = 17.56

Step-by-step explanation:

Formula = PR * RT = SR * RQ

60 * (4x - 26) = 38 * (2x - 1)

Solve for x

240x - 1560 = 76x - 38

164x = 1522

x = 9.28

Solve for SR

2x - 1

2(9.28) - 1

SR = 17.56

The value of the variable 'x' is 29. Then the length of the side SR will be 57 units.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔPQR is similar to the triangle ΔTSR. Then the ratio of the corresponding side will be constant.

SR / RQ = RT / PR

(2x - 1) / 38 = (4x - 26) / 60

(2x - 1) / 19 = (2x - 13) / 15

19(2x - 13) = 15(2x - 1)

Simplify the equation further, then we have

38x - 247 = 30x - 15

38x - 30x = 247 - 15

8x = 232

x = 232 / 8

x = 29

Then the length of the side SR will be given as,

SR = 2(29) - 1

SR = 58 - 1

SR = 57

The value of the variable 'x' is 29. Then the length of the side SR will be 57 units.

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Answer:

x^5

Step-by-step explanation:

x^6 * x^2

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

x^3

First multiply the numerator

x^6 * x^2 = x^(6+2) = x^8

x^8 / x^3

Then divide

x^(8-3) = x^5

Answer:

X^5

Step-by-step explanation:

Add the two numerators to get x^8

x^8 / x^3

Simplify to get x^5

Answer:

Leila is paid $10 plus $8 an hour

She was paid $66

Let the number of times be x

According to the problem,

10+8x=66

8x=66-10

8x=56

x=56/8

x=7

She worked for 7 hours.

The two buses are initially 515 miles apart and are moving toward each other. They will pass each other around 2:30 P.M.

To solve this problem, we can use the concept of relative speed. The combined speed of the two buses is the sum of their individual speeds, which is 48 + 55 = 103 miles per hour.

We can calculate the time it takes for the buses to meet by dividing the initial distance between them (515 miles) by their combined speed (103 miles per hour):

Time = Distance / Speed

Time = 515 miles / 103 miles per hour

Time ≈ 5 hours

Therefore, the two buses will pass each other approximately 5 hours after they start traveling toward each other. To determine the exact time, we need to consider the starting time (9:30 A.M.) and add 5 hours to it. So, they will pass each other around 2:30 P.M.

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Answer:

Yes

Step-by-step explanation:

Their ratios are equivalent

Answer:

13

Explanation:

given 7 - 2x

if x=-3

7-2(-3) = 7+6 = 13

Answer:

Step-by-step explanation:

when x = - 3

7 - 2x

= 7 - 2 *( - 3)

= 7 + 6

= 13

Answer:

Hypothesis testing of ' significance of difference between means'

Step-by-step explanation:

Study conducted to tests whether oxygen level prior SAT score improves test score. This can be done through - Hypothesis testing of ' significance of difference between means'.

Where x1 & x2 represent mean values of SAT test score before (or without) & after (or with) oxygen.

Null hypothesis [H0] = x1 = x2 , Alternate Hypothesis [H1] : x1 < x2

We have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

To solve the given equations for the equilibrium values of C, NX, CF, r, and ε, let's go step by step.

First, we'll substitute equations (2), (3), (4), (5), (6), (7), (8), and (9) into equation (2) to eliminate the variables C, I, G, NX, CF, and T.

Equation (2) becomes:
Y = (1/2)(Y - T) + (2,000 - 100r) + 1,500 + (500 - 500ε)

Next, let's simplify the equation:

Y = (1/2)(Y - 1,000) + 2,000 - 100r + 1,500 + 500 - 500ε

Distribute (1/2) to the terms inside the parentheses:

Y = (1/2)Y - 500 + 2,000 - 100r + 1,500 + 500 - 500ε

Combine like terms:

Y = (1/2)Y + 3,500 - 100r - 500ε

Now, let's isolate Y by subtracting (1/2)Y from both sides:

(1/2)Y = 3,500 - 100r - 500ε

Multiply both sides by 2 to get rid of the fraction:

Y = 7,000 - 200r - 1,000ε

We now have one equation (10) in terms of Y, r, and ε.

Next, let's substitute equation (1) into equation (10) to solve for Y:

5,000 = 7,000 - 200r - 1,000ε

Subtract 7,000 from both sides:

-2,000 = -200r - 1,000ε

Divide both sides by -200:

10 = r + 5ε

This gives us equation (11) in terms of r and ε.

Now, let's substitute equation (11) into equation (5) to solve for NX:

NX = 500 - 500ε

Substitute r + 5ε for ε:

NX = 500 - 500(r + 5ε)

Simplify:

NX = 500 - 500r - 2,500ε

This gives us equation (12) in terms of NX, r, and ε.

Finally, let's substitute equation (12) into equation (6) to solve for CF:

CF = -100r

Substitute 500 - 500r - 2,500ε for NX:

CF = -100(500 - 500r - 2,500ε)

Simplify:

CF = -50,000 + 50,000r + 250,000ε

This gives us equation (13) in terms of CF, r, and ε.

To summarize, we have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

These equations represent the equilibrium values of Y, r, ε, NX, and CF in the given open economy.

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lim (x → a) f(x) = ∞ , The limit does not exist and is neither ∞ nor - ∞

The vertical line test is used to verify function. That is, a graph must have a unique y value for it to be referred to as a function for a certain (unique) value of x. If for a particular x, and y values are coming it means it is not a function. If it crosses y-axis twice it means for a particular x value , two different value of y will exist. And that is not possible for a function

From the graph, we know that limit at point a is:

lim (x→a) f(x) exists if and only if

lim (x →a⁺) f(x) = lim (x→a⁻) f(x) and ≠ ∞

∴ right hand side limit = left hand side limit

lim (x →a⁺) f(x) = - ∞

lim (x →a⁻) f(x) = - ∞

∴ lim (x → a) f(x) = ∞

thus, option B is the correct answer.

The limit does not exist and is neither ∞ nor - ∞

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Answer = 3/4

First, change them all into like fractions.

-2, -11/4, -7/2 = -8/4, -11/4, -14/4

Therefore the common difference of their arithmetic sequence is 3/4

Hope it helps u.

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To find the nth derivative of y = e^(nx) with respect to x, we can use the power rule and the chain rule repeatedly. The nth derivative will involve a combination of exponential and polynomial terms.

Let's start by finding the first derivative of y with respect to x:

dy/dx = d/dx (e^(nx)) = ne^(nx)

The second derivative can be found by differentiating ne^(nx) with respect to x:

d^2y/dx^2 = d/dx (ne^(nx)) = n^2e^(nx)

We can continue differentiating and find the nth derivative:

d^ny/dx^n = d/dx (n^(n-1)e^(nx)) = n^n e^(nx)

The nth derivative of y = e^(nx) simplifies to n^n e^(nx), which involves the original exponential term e^(nx) multiplied by a polynomial factor n^n. Thus, the nth derivative contains both exponential and polynomial components.

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2(l+w) + 4a and 2l+2w + 2(2a) are two equivalent expressions which represent the total fencing material required to surround the playground and flower beds.

Mathematical expressions are a way of representing mathematical ideas, concepts, and operations using symbols and notation. They can take many forms, including numbers, variables, and operators. They can also be combined to create more complex expressions, equations, and formulas.

Explain:

The total fencing material required to surround the playground and flower beds would be the sum of the fencing material for the playground and the fencing material for the flower beds.

So, one possible expression for the total fencing material required to surround the playground and flower beds would be: 2(l+w) + 4a

Another possible expression for the total fencing material required to surround the playground and flower beds would be: 2l+2w + 2(2a)

Please note that these expressions are based on the information provided, and the actual total fencing material required will depend on the specific dimensions of the park and playground, and may differ from these expressions.

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The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

1. -17x+1

2. -5/6a-1/2

3.-2/3x+2/5

4.-6(2x+3y+0.6)

5.2/3(x+6)

Answer:

false

Step-by-step explanation:

first shape is square

second one is rectangle

so they are not the same

Khadija would have to pay $27.8 (7.5 x 4 - 1.7) to buy 4 pounds of apples.

Cost the monitorial associated with the purchase of production of food or service if can include the prices of materials of which is over it and other expenses that are related to the production of the good of service cost is a major fraction when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.

The expression for the cost to buy  x  pounds of apples is: 7.5x - 1.7, where x represents the number of pounds of apples purchased. For example, if Khadija wanted to buy 3 pounds of apples, the cost would be calculated by 7.5x - 1.7, which is equal to 22.6 dollars.

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Answer:

6 1/2 hours

Step-by-step explanation:

156 miles / 24 mph = 6.5

The required time the cyclist would take to ride 156 miles with a rate of 24 mph is 6.5 hours.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
To find the time it takes a cyclist to cover a certain distance at a constant rate, you can use the formula:
time = distance/speed.

Plugging in the given values, you get:

time = 156 miles / 24 mph = 6.5 hours.

So it would take the cyclist 6.5 hours to ride 156 miles at a constant rate of 24 mph.

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We will see that the total number of ways in which we can distribute 20 different prizes among 180 people is:

C =  6.818e46

Here we need to count how many selections do we have. Each prize will be a selection, so we have 20 selections.

Now we need to count the numbers of 6for each selection.

For the first prize, there are 180 options.

For the second prize, there are 179 options (because one person already got a prize).

For the third prize, there are 178 options.

And so on.

The total number of combinations is given by the product between the numbers of options:

C = 180*179*178*...*161*160 = 6.818e46

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Answer:

504 km

Step-by-step explanation:

Answer: θ≈48,81°.

Step-by-step explanation:

\(sin\theta=\frac{8}{\sqrt{113}}\\sin\theta } =\frac{8*\sqrt{113} }{\sqrt{113}*\sqrt{113} } \\sin\theta=\frac{8*\sqrt{113} }{113} \\sin\theta\approx0,75258\\\theta\approx48,81^0.\)

Good luck an' have a nice day!

The dimensions of the box with the maximum volume are:

Length of the square base (x) = 2 cm

Width of the rectangular side (y) = 5.5 cm

To determine the dimensions of the box with the maximum value, we need to maximize the volume of the box since the surface area is fixed.

Let's assume that the length of one side of the square base is "x," and the width of the rectangular side is "y."

Since the sides are congruent, the other side of the square base will also be "x," and the length of the rectangular side will be "y."

The surface area of the base and sides is given by:

Area = Base Area + 4 × Side Area

The base area is given by:

Base Area = x × x = x²

The side area is given by:

Side Area = x × y

The total area is given as 48 cm², so we have:

x² + 4xy = 48

To find the dimensions that maximize the volume, we need to express the volume in terms of a single variable. The volume of the box is given by:

Volume = Base Area × Height

Since the height is not specified, let's assume it is "h."

Therefore, the volume is:

Volume = x² × h

To solve this problem, we need to express the volume in terms of a single variable using the given information. From the total area equation, we can solve for y:

x² + 4xy = 48

4xy = 48 - x²

y = (48 - x²) / (4x)

Now we can substitute the value of y into the volume equation:

Volume = x²h

Volume = x²(48 - x²) / (4x)

Volume = (12x - x³) / 4

To find the maximum value of the volume, we need to find the critical points by taking the derivative of the volume equation with respect to x:

d(Volume) / dx = (12 - 3x²) / 4

Setting the derivative equal to zero and solving for x:

12 - 3x² = 0

3x² = 12

x² = 4

x = ±2

Since the dimensions of a box cannot be negative, we discard the negative value. Therefore, x = 2.

Now we can substitute x back into the equation for y:

y = (48 - x²) / (4x)

y = (48 - 2²) / (4 × 2)

y = (48 - 4) / 8

y = 44 / 8

y = 5.5

So, the dimensions of the box with the maximum volume are:

Length of the square base (x) = 2 cm

Width of the rectangular side (y) = 5.5 cm

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Answer:

the turning point is (-2,-1)

i dont know the turning point but i hope this helps

Step-by-step explanation:

Answer:

a) (-2 , -1)

b) (-1 , 0) and (-3 , 0)

Step-by-step explanation:

For part a)

We can find the coordinates of the turning point by seeing at the graph where it turns the other way or in simpler words the axis of symmetry so if see the graph the axis of symmetry is the line x = -2 so that means the turning point is (-2 , -1).

For finding the turning point mathematically we compare the equation to its standard form which is:

\(x^2+4x+3=a(x-h)^2+k\)

where h is the x coordinate  and k is the y coordinate of the turning point of the equation (h , k) = (x , y).

so just solve the left side,

\(a(x-h)^2+k\\a((x)^2-2(x)(h)+(h)^2)+k\\a(x^2-2xh+h^2)+k\\\\ax^2-2ahx+ah^2+k=x^2+4x+3\\\)

and so we compare the coefficients of x^2 on the right and left side we get

\(a=1\)

if we compare the coefficients of x on the right and left side we get

\(-2ah=4\\-2(1)h=4\\-2h=4\\h=\frac{4}{-2}\\\\h=-2\)

now we compare the constants on the right and left side we get

\(ah^2+k=3\\(1)(-2)^2+k=3\\(1)(4)+k=3\\4+k=3\\k=3-4\\k=-1\)

so the turning point is (-2 , -1) proven mathematically and graphically as well

For part b)

Roots of the equation are also called as x-intercepts which means where the graph intersects/cuts the x-axis so if see the graph it cuts the x-axis at 2 points  firstly at -3 and then at -1 so the roots of the equation would be (-1 , 0) and

(-3 , 0) the y coordinate is zero when the points lies on the x-axis.

for mathematically solving the equation we would equate the equation to zero

\(y=x^2+4x+3\\x^2+4x+3=0\)

Now solve it by either factorizing or by using the quadratic formula we would get two values for x those are the roots of the equation

we solve it by factoring

\(x^2+4x+3=0\\x^2+3x+x+3=0\\x(x+3)+1(x+3)=0\\(x+3)(x+1)=0\\x=-3\ ,\ x=-1\\\)

proven mathematically as well as graphically.

100 is the answerrrrrrrrrrrrrrrrrrr

Answer:

7 1/2

Step-by-step explanation:

try putting (1.6 x 7.5)+48 in a calculator i just put random numbers in the x spot until i got 60 lol

Yes. The square number of 32 is a natural number. 5.65685424949 is the square of 32. Natural numbers include numbers that can be written as a rational decimal, therefore, the square number of 32 is natural.

Answer: hmmm can we see the answer choices because I think I. Ight know the answer

Step-by-step explanation: