1) (-8,-8), (8,4)
Find the slope of the line through each pair of points

The dimensions of the poster with the smallest area are 48 cm by 16 cm.

Let the width of the printed material be x cm and the height be y cm. Then the total width of the poster including the margins is (x + 16) cm, and the total height is (y + 24) cm.

The total area of the poster is the area of the printed material plus the area of the margins:

(x + 16)(y + 24) = 1536

Expanding the left side, we get:

xy + 16y + 24x + 384 = 1536

Rearranging terms, we get:

xy = 1152 - 16y - 24x

To find the dimensions of the poster with the smallest area, we want to minimize the product xy subject to the constraint given by the equation above.

One way to do this is to use the method of Lagrange multipliers. Let L = xy + λ[(x + 16)(y + 24) - 1536] be the Lagrangian, where λ is a Lagrange multiplier. Setting the partial derivatives of L with respect to x, y, and λ equal to zero, we get:

y + 16λ = 0

x + 24λ = 0

(x + 16)(y + 24) = 1536

From the first two equations, we get:

x = -24λ

y = -16λ

Substituting these into the third equation, we get:

(-24λ + 16)(-16λ + 24) = 1536

Simplifying, we get:

-6λ + 4 = 0

Therefore, λ = 2/3. Substituting this into the expressions for x and y, we get:

x = -16

y = -32

These values give the dimensions of the printed material. To find the dimensions of the poster, we add the margins:

width = x + 16 + 16 = 48 cm

height = y + 24 + 24 = 16 cm

Therefore, the dimensions of the poster with the smallest area are 48 cm by 16 cm.

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Answer:

\(y=4\sin(\frac{2}{7}x-\frac{2}{35})\)

Step-by-step explanation:

Period: \(7\pi=\frac{2\pi}{b}\rightarrow b=\frac{2}{7}\)

Phase Shift:

\(\displaystyle \frac{c}{b}=\frac{1}{5}\\\\\rightarrow\frac{c}{\frac{2}{7}}=\frac{1}{5}\\\\\rightarrow \frac{2}{7}=5c\\ \\\rightarrow \frac{2}{35}=c\)

Final equation:

\(y=4\sin(\frac{2}{7}x-\frac{2}{35})\)

how will his speed compare?  or namely, will he be within speed limits or should we give him a big fat ticket for speeding?

well, the 25 mi/hr limit is expecting anyone on that road to only do 40,234 meters per hour, so since an hour is 60 minutes and a minute is 60 seconds, that means an hour is really (60)(60) seconds, or 3600 seconds, so the limit is expecting anyone on that road to do no more than 40,234 meters per 3600 seconds, let's see how Usain fares

\(\begin{array}{ccll} meters&seconds\\ \cline{1-2} 100 & 9.63\\ 40234& x \end{array} \implies \cfrac{100}{40234}~~=~~\cfrac{9.63}{x} \implies 100x=(40234)(9.63) \\\\\\ x=\cfrac{(40234)(9.63)}{100}\implies x\approx 3874.53\)

so Usain will covering those 40,234 meters in about 3875 seconds, that's longer than 3600 seconds, meaning Usain will need more than 3600 seconds to cover those meters so he's really going slower 40,234 meters per 3600 seconds, so he's golden,  he's within speed limits, because the limit is expecting noone to do them in less than 3600 seconds.

In order to justify their position candidate make assumption that the price effect would be larger than the quantity effect.

What is Price?

The amount of money required to obtain a certain thing is referred to as its price. Price is a measure of value in the sense that the amount people are willing to pay for a commodity signifies its value.

Concept:

Candidate A claims that raising the sales tax from 5% to 7% will enhance revenue. This suggests that the price effect is greater than the quantity effect because when taxes rise, prices rise and quantities fall; hence, tax revenue will rise only if the price effect is more than the quantity effect.

And Candidate B claims that the tax would harm merchants and customers, slow the economy, and reduce tax revenue, but only if the quantity effect outweighed the price effect.

As a result, Candidate A believes that the price effect will be greater than the quantity effect.

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Using an exponential function, it is found that:

a) The model is: \(A(t) = 30000(1.05)^t\)

b) Her predicted profit is of $62,368.

An increasing exponential function is modeled by:

\(A(t) = A(0)(1 + r)^t\)

In which:

Item a:

Then:

\(A(t) = A(0)(1 + r)^t\)

\(A(t) = 30000(1 + 0.05)^t\)

\(A(t) = 30000(1.05)^t\)

Item b:

\(A(15) = 30000(1.05)^{15} = 62368\)

Her predicted profit is of $62,368.

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Answer: The value of x is 12

Definition of equation : In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

An equation combines two expressions connected by an equal sign (“=”). These two expressions on either side of the equals sign are called the “left-hand side” and “right-hand side” of the equation. We generally assume the right-hand side of an equation is zero. This will not reduce the generality since we can balance this by subtracting the right-hand side expression from both sides’ expressions.

EXPLANATION : Given: to solve for X:

\(x -\frac{x+7}{x - 10} = \frac{5}{x -10}\)

Solution: \(x - \frac{x+7}{x -10} = \frac{5}{x -10}\)

\(= > x^{2} -11x -7 = 5\)

\(= > x^{2} -11x-7-5=0\)

\(= > x^{2} -11x -12 =0\)

\(= > x^{2} -12x+x-12 =0\)

\(= > x(x-12) +1(x-12)= 0\)

\(= > (x-12) (x+1)=0\)

\(x =12 , x\neq -1\)

Final answer: The value of x is 12

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SOLUTION

Looking at the sequence 15, 16, 18, 21, ?, ?, ?, ?, 51, 60, 70, 81

The next number is gotten by increasing the number added by 1. That is

So, the missing numbers are 25, 30, 36, 43

Answer:

93+30=123 so e equals 123

Step-by-step explanation:

To check, do 123-30=93

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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The correct option is (A) P(X) × P(Y) = P(X ∩ Y)

What is probability and example?

 We are given to consider a situation in which X and Y are two events such that

P(X) = 4/5, P(Y) = 1/4, P(X ∩ Y) = 1/5

We are to select the statement that best describes the events X and Y

We know that

any two events A and B are said to be independent if

P(A) × P(B) = P (A ∩ B)

We have, for events X and Y,

P(X) × P(Y) = 4/5 × 1/4 = 1/5 = P (X ∩ Y)

P(X) × P(Y) = P(X ∩ Y)

Thus, X and Y are independent because P(X) × P(Y) = P(X ∩ Y)

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The complete question is -

Consider a situation in which P(X) = 4/5 and P(Y) = 1/4. If P(X and Y) is = 1/5, which best describes the events?

They are independent because P(X) x P(Y) = P(X and Y).

They are independent because P(X) + P(Y) = P(X and Y).

They are dependent because P(X) x P(Y) = P(X and Y).

They are dependent because P(X) + P(Y) = P(X and Y).

Answer: a

Step-by-step explanation:

just took the test

To bring the 2,000 kg wagon to rest, the buffer stop needs enough springs to absorb its kinetic energy. The number of springs and their stiffness can be calculated using given parameters and formulas.



To calculate the number of springs required in the buffer stop, we need to find the energy of motion that needs to be absorbed. The kinetic energy (KE) of the wagon is given by KE = (1/2)mv^2, where m is the mass (2,000 kg) and v is the velocity (0.69 m/s). The KE is 477.9 J.Next, we calculate the potential energy stored in the compressed springs. The compression distance is 15 cm, which is 0.15 m. The potential energy (PE) stored in each spring is given by PE = (1/2)kx^2, where k is the stiffness of the spring and x is the compression distance.

The total energy absorbed by all the springs is equal to the kinetic energy of the wagon. Therefore, the number of springs required is given by N = KE / PE, where N is the number of springs.To determine the stiffness of the spring, we use the formula k = (Gd^4) / (8nD^3), where G is the shear modulus (0.8 x 10^5 N/mm^2), d is the wire diameter (2 cm), n is the number of coils (15), and D is the mean diameter of the coils (20 cm).

By substituting the values into the equations, we can find the number of springs and the stiffness of each spring.

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Answer:

-1

Step-by-step explanation:

ecuacion de la pendiente está dada por:

Y-yo=m(X-xo)

donde m es la pendiente

del problema :

y-6 = - (x - 3

m=-1

Answer:

y = -1/8x - 1/2

Step-by-step explanation:

For perpendicular lines, the product of their gradient is -1

this using line 1 equation y = 8x - 3 we get the gradient of line 1 as 8

m1m2 = -1

8m2 = -1

m2 = -1/8

using the given point (4,-1) and another unknown point (X,y) we can write the equation of line 2

G = ∆y/∆x

-1/8 = y +1/x-4

we then cross multiply

8(y+1) = -(x-4)

8y + 8 = -x +4

8y = -x -4

y = -1/8x - 1/2

Answer:

Step-by-step explanation:

Since λa + ub is parallel to ha + tb, we can write:

λa + ub = k(ha + tb)

where k is some constant. We can simplify this equation by expanding both sides:

λa + ub = kha + ktb

Rearranging the terms, we get:

λa - kha = ktb - ub

Factoring out a, we get:

a(λ - kh) = b(kt - u)

Since a and b are non-parallel, they are linearly independent, which means that a and b are not multiples of each other. This also means that the only way for the left side of the equation to be equal to 0 is if λ - kh = 0, or λ = kh. Similarly, the only way for the right side of the equation to be equal to 0 is if kt - u = 0, or u/t = k/h.

Therefore, we have shown that λ/h = u/t.

Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.

Here are the details for the given frequency distribution:

Lower class limits are the least number among the pair

Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.

Upper class limits are the greater number among the pair

Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.

Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).

Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.

Class boundaries are the extreme points of the classes which are  [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.

Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1

                                     = 76

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The component form of the vector that translates A to A' is (11, -17)

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

In translation, the shape of the figure does not change but its size may change.

Other transformation processes are reflection and rotation.

The component form of the vector is governed by the rule; A' - A

so we subtract corresponding x- coordinates and corresponding y- coordinates

A' - A = (7, -9) - (-4, 8)

       = ( 7 - - 4, -9 - 8)

       -= ( 11, -17)

In conclusion, the vector that translates A to A' is ( 11, -17 )

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Answer:

Subtract both sides by x

Step-by-step explanation:

Because x is on both sides, we want x to only be on one side of the equation, so the next step should be to subtract both sides by x so x is eliminated from the right side.

3x+7=x-21

2x+7=-21

2x=-28

x=-14

And the solution becomes x=-14

Answer:

Subtract x from both sides

Step-by-step explanation:

3x+7=x-21

3x=28=x

28=-2x

28/2=14

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The distance that will be covered by the bus will be 65km.

Since his house is 325 km away from Oxford and he covered 1/5th of his journey by bus. Then, the distance that's covered by bus will be:

= 1/5 × 325km

= 65 km.

Since 227.5km is covered by train, then the distance covered by train will be: = 227.5/325 = 7/10

The distance covered by foot will be:

= 325 - (65 + 227.5 + 16.25)

= 325km - 308.75km

= 16.25km

The difference in distance covered by train and covered by bus will be:

= 227.5km - 65km

= 162.5km

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The number of pounds of copper in 120 pounds of brass is = 78 pounds of copper

The percentage of copper in the brass = 65%

Therefore the quantity of copper in the brass = 65/100= 0.65 pounds

This means that 1 pound brass contains = 0.65 pounds of copper

The quantity of copper in 120 pounds of brass = 120 * 0.65

                                                                             = 78 pounds of copper.

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Answer:

πr^2h

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

HOPE IT'S HELPFUL TO YOU

PLS MARK ABOVE GUY ANSWER AS BRAINLIEST

Answer:

2^-2

Step-by-step explanation:

When multiplying indices or exponents with the same base number, you can add the powers:

2^4 x 2³ = 2^7 (4 + 3 = 7)

2^5 x 2^4 = 2^9 (5 + 4 = 9)

When dividing indices or exponents with the same base number, you can subtract the powers:

2^7 ÷ 2^9 = 2^-2 (7 - 9 = -2)

Answer:

this is the answer I came up with hope this helps

Answer:

E. The absolute value and square root function share an x-intercept.

Step-by-step explanation:

Pre-Calc on Edge 2022

Answer:

Inequalities are used to demonstrate relationships between numbers or expressions. An inequality describes a relationship between two different values.

The notation  

a

<

b

means that  

a

is strictly smaller in size than  

b

, while the notation  

a

>

b

means that  

a

is strictly greater than  

b

.

The notion  

a

≤

b

means that  

a

is less than or equal to  

b

, while the notation  

a

≥

b

means that  

a

is greater than or equal to  

b

.

Inequalities are particularly useful for solving problems involving minimum or maximum possible values.

Step-by-step explanation:

Answer:

99$

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

-1+4=3

Answer:8+t because the value of t isn’t determined.

Answer:

3

Step-by-step explanation:

Step 1:

- 5x + 2 = - 13        Equation

Step 2:

- 5x = - 15    Subtract 2 on both sides

Step 3:

x = - 15 ÷ - 5     Divide

Answer:

x = 3

Hope This Helps :)