8x= -14 Give your answer as an improper fraction in its simplest form. please help its due now! AWARD = BRAINLIEST!!!

Answer:

ok no

Step-by-step explanation:

i am big brain

Answer:

\(x^{4}\) - 6x³ + 35x² - 150x + 250

Step-by-step explanation:

note that i² = - 1

(x + 5i)(x - 5i)(x - 3 - i)(x - 3 + i) ← expand the first pair of factors using FOIL

= ( x² - 5ix + 5ix - 25i²)((x - 3) - i)((x - 3) + i) ← expand second pair using FOIL

= (x² - 25(- 1))((x - 3)²+ i(x - 3) - i(x - 3) - i²)

= (x² + 25)(x² - 6x + 9 - (- 1))

= (x² + 25)(x² - 6x + 9 + 1)

= (x² + 25)(x² - 6x + 10)

each term in the second factor is multiplied by each term in the first factor

= x²(x² - 6x + 10) + 25(x² - 6x + 10) ← distribute parenthesis

= \(x^{4}\) - 6x³ + 10x² + 25x² - 150x + 250 ← collect like terms

= \(x^{4}\) - 6x³ + 35x² - 150x + 250

Answer:

53 (seconds)

Step-by-step explanation:

Let's calculate each of the boy's time to reach the destination and subtract them from each other to get our answer.

Bill:
Using the Pythagorean Theorem, a^2 + b^2 = c^2
Plugging in:
300^2 + (500+150)^2 = c^2

90000 + 650^2 = c^2 (you're gonna want a calculator)

90000 + 422500 = c^2
512500= c^2

Take the square root of both sides, isolating the variable c:
c= 715.891053 m
round it off: 716 m
c stands for the distance that Bill has to walk. If he is walking at 3 meters per second, we can divide to get the number of seconds:

716 / 3 = 238.666667 seconds to get to the playground
round it off: 239

Ted:
Using the Pythagorean Theorem, a^2 + b^2 = c^2
Plugging in:
300^2 + 500^2 = c^2

90000 + 250000 = c^2

340000=c^2

Take the square root of both sides, isolating the variable c:
c= 583.095189 m
round it off: 583 m
c stands for the distance that Ted has to walk. If he is walking at 2 meters per second, we can divide to get the number of seconds:

583 / 2 = 291.5 seconds to get to the playground
round it off: 292

Lastly, subtract the number of seconds it took Ted to the number of seconds it took Bill because Ted took a longer amount of time, and that will be your answer:
292-239= 53

The shorter route 53 seconds faster

Answer: A

Step-by-step explanation:

A) The third relation is not a function.

B) evaluating the function we can see that f(-3) = -7

A relation is not a function if we can see that one input is mapped into two different outputs.

With that in mind, we can see that relation 4 has the input x = 2 mapped into two different outputs, A and B, then it is not a function.

b) Here we need to evaluate the given function, we know that:

f(x) = 4x + 5

We want to find f(-3), to get it, just replace x by the number -3 in the equation above:

f(-3) = 4*-3 + 5

      = -12 + 5

       = -7

The correct option is 2.

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Answer:

12 is the answer 12 I think but I'm not sure

Answer:

Step-by-step explanation:

Given the profit function P(x) = -6x² +288x -3162, you want to find the value of x and the value of P(x) corresponding to maximum profit.

The vertex of the parabola described by ax²+bx+c lies on the line of symmetry:

  x = -b/(2a)

This will be the value of x that is a maximum when a < 0.

The value of the function at that point can be found by evaluating the quadratic expression for the value of x just found.

Maximum profit is had when ...

  x = -(288)/(2(-6)) = 24

That maximum profit is ...

  P(24) = (-6(24) +288)(24) -3162 = 144(24) -3162 = 294

For maximum profit, 24 tables should be made per day. The maximum profit is $294 per day.

c)  It will have less variation.

Decreasing the sample size will generally result in more variation in the distribution of sample means. This is because with a smaller sample size, there is less information available to estimate the population mean, which means that the sample mean will be less precise and will vary more from one sample to the next.

For example, if you take a sample of 10 individuals from a population and calculate the mean of their heights, the sample mean will likely be a good estimate of the population mean height. However, if you take a sample of just 2 individuals and calculate the mean of their heights, the sample mean will be less precise and will be a less reliable estimate of the population mean height. This is because the sample of 2 individuals may not be representative of the overall population, and the sample mean will be more influenced by extreme values or outliers.

In general, as the sample size decreases, the distribution of sample means will become more spread out and will have more variation. This is because with a smaller sample size, there is more uncertainty about the population mean, and the sample means will be more likely to deviate from the true population mean.

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The answer is,

\(5 - \frac{4(2.5n - 2)}{5} \)

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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The domain and range of F is F={(x, y) Ix+y=10] is: 3. Domain: All Real Numbers Range: All Real Numbers

The given set F={(x, y) | x+y=10} represents a linear equation where the sum of x and y is always equal to 10.

To determine the domain and range of F, we need to consider the

possible values of x and y that satisfy the equation.

Domain: The domain represents the set of all possible values for the independent variable, which in this case is x. Since there are no restrictions on the value of x, the domain is All Real Numbers.

Range: The range represents the set of all possible values for the dependent variable, which in this case is y. By rearranging the equation x+y=10, we can solve for y to get y=10-x. Since x can take any real value, y can also take any real value. Therefore, the range is also All Real Numbers.

The correct answer is: 3. Domain: All Real Numbers Range: All Real Numbers

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Given

let the value of geometric mean be a and b

a=12

b=7

we know that,

Geometic mean(G.M)=√ab

=√12×7

=√84

=9.16

the geometric mean of 12 and 7 is 9.16

Assume that the linear system \(Ax = b\) has more than one solution, and let \(x1\) and \(x2\) be two distinct solutions. Let \(x3 := ux1+7x2\), where µ, \(7 E IR\) with the property that \(u+n = 1.\)

Then we have: \(Ax1 = b and Ax2 = b\) since x1 and x2 are solutions.

Subtracting the second equation from the first, we get: \(A(x1 - x2) = 0.\)

Since \(x1\) and \(x2\)are distinct solutions, we know that \(x1 - x2 ≠ 0\).

Therefore,\(A(x1 - x2) = 0\) this implies that the columns of A are linearly dependent. That is, there exist scalars \(c1, c2, ..., cn\) (not all zero) such that

\(c1a1 + c2a2 + ... + cnan = 0,\)

where \(a1, a2, ...,\)and an are the columns of A.

Let x be any solution of Ax = b. Then we have:\(A(x + tx3) = Ax + tAx3 = b + tAx3\)

where t is any scalar. But we know that \(Ax3 = A(ux1 + 7x2) = uAx1 + 7Ax2 = ub + 7b = 8b,\) since \(Ax1 = Ax2 = b.\)

Therefore, we have: \(A(x + tx3) = b + t(8b) = (1 + 8t)b.\)

Thus, \(x + tx3\) is a solution of \(Ax = b\) for any scalar t.

In particular, if we take \(t = 1/n,\) where n is any nonzero integer, we get:

\(x + (1/n)x3 = (1 - 1/n)x + (1/n)ux1 + (7/n)x2.\)

Since \(u + 7 = 1,\) we have:\((1/n)ux1 + (7/n)x2 = (1/n)((1 - u)x1 + ux1 + 7x2) = (1/n)x1 + (7/n)x2.\)

Therefore, we can write:\(x + (1/n)x3 = (1 - 1/n)x + (1/n)x1 + (7/n)x2.\)

This shows that \(x + (1/n)x3\) is another solution of Ax = b for any nonzero integer n. Since we can find infinitely many integers n such that 1/n is nonzero, we conclude that there are infinitely many solutions of .

Therefore, if the linear system \(Ax = b\) has more than one solution, then it must have infinitely many solutions.

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Complex sums arrangement:

0, +an, 2n, 4", 5n²+7n, 8n+12, n 5/2, Nnan, e", 10"+n20, (In n)2, (log n)!, (log n)!, (log n!), 5logs, n!

Arranging the complex functions in the form of complex sums involves organizing them in a specific order that highlights their similarities and patterns. In the given list of complex functions, we can arrange them as follows:

0, +an, 2n, 4", 5n²+7n, 8n+12, n 5/2, Nnan, e", 10"+n20, (In n)2, (log n)!, (log n)!, (log n!), 5logs, n!

This arrangement groups similar terms together and showcases the various expressions in a systematic manner. Starting with 0, which represents the constant term, we then have +an, which represents linear terms with coefficients. Next, we have the terms involving powers of n, such as 2n, n 5/2, Nnan, and (In n)2.

The arrangement continues with exponential terms, such as e" and 10"+n20, followed by expressions involving logarithmic functions, including (log n)!, (log n)!, (log n!), and 5logs. Finally, we have the factorial term n!.

This order allows for a clear understanding of the different types of complex functions present and makes it easier to identify common characteristics or evaluate them in a structured manner

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Yes, the base angles of an isosceles triangle are equal to each other.

The base angles of an isosceles triangle are equal because of the symmetry of the triangle. In an isosceles triangle, the two sides that are opposite the congruent angles are also congruent in length. This means that the triangle has a line of symmetry, or a line that divides it into two congruent halves. Since the triangle is symmetrical, the base angles are equal in measure.

Another way to understand why the base angles of an isosceles triangle are equal is to consider the definition of an isosceles triangle. An isosceles triangle is defined as a triangle with at least two congruent sides. Since the base angles are opposite the congruent sides, they must also be congruent. Therefore, the base angles of an isosceles triangle are equal.

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yes , base angles of isosceles triangle are equal 1 because An isosceles triangle is a triangle with two sides of equal length and the base angles of the isosceles triangle are equal in length.

The sides of equal length are called the legs of the triangle, and the third side is called the base. The base angles of an isosceles triangle are the angles formed by the base and the legs of the triangle. Since the base angles are formed by the base and the legs of the triangle, which are both congruent (i.e., have the same length), the base angles must also be congruent. In other words, the base angles of an isosceles triangle are equal.

The vertex angle of an isosceles triangle is the angle formed by the two legs at the apex of the triangle. This angle is always larger than the base angles, and its measure is equal to the sum of the measures of the base angles. For example, if the base angles of an isosceles triangle have a measure of 45 degrees each, the vertex angle will have a measure of 90 degrees (45 + 45). In summary, the base angles of an isosceles triangle are congruent and equal, and the vertex angle is larger than the base angles and is equal to the sum of the measures of the base angles.

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Answer:

C

Step-by-step explanation:

y=mx+b m=slope b=y-intercept, y-int: 4 slope: 3/1 but can just be put as 3. y=3x+4 bc it's a positive slope with a positive y-int.

Sine function relates side lengths of a right triangle to an acute angle.

In a right triangle, the side lengths are related to the acute angles through the trigonometric functions. The side opposite the acute angle is related to the angle through the sine function, the side adjacent to the acute angle is related to the angle through the cosine function, and the hypotenuse is related to the angle through the tangent function.

More specifically, if θ is an acute angle in a right triangle and a and b are the lengths of the side opposite and adjacent to the angle respectively, and c is the length of the hypotenuse, we have:

sin(θ) = a/c

cos(θ) = b/c

tan(θ) = a/b

Thus, we can use these functions to find the length of any side of the right triangle if we know the measure of one of the acute angles and the length of one of the other sides.

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Answer:

System of equation : 14x+23y = 213 and y = x-2

The cost of regular tickets is $7 and the cost of tickets with donation is $5.

Step-by-step explanation:

Let regular ticket's cost be x and tickets with donation's cost be y.

14x+23y = 213

y = x-2

Now,

14x+23y = 213

or, 14x+23(x-2) = 213

or, 14x + 23x - 46 = 213

or, 37x = 259

so, x = 7

again,

y = x-2

or, y = 7-2

so, y = 5

The probability that something other than between 1 and 5 seconds will elapse between arrivals is 0.917.

There are three parts to this question. First, you need to know the arrival rate which is 15 cars per minute. Second, you need to know the probability of a car arriving between 1 and 5 seconds which is 0.083.

Third, you need to know the probability that something other than between 1 and 5 seconds will elapse between arrivals which can be calculated as follows:

P (something other than 1 to 5 seconds elapse) = 1 - P (1 to 5 seconds elapse)

P (1 to 5 seconds elapse) = 0.083

P (something other than 1 to 5 seconds elapse) = 1 - 0.083 = 0.917

Therefore, the probability that something other than between 1 and 5 seconds will elapse between arrivals is 0.917 .

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Answer:

y ≥ 2

x ≥ -1

y ≤ -x+6

Step-by-step explanation:

The solid line means ≤ or ≥

The dashed line means < or >

y ≥ 2

x ≥ -1

y ≤ -x+6

The  equation for inequalities are x + y ≤ 6, x ≥ -1 and y ≥ 2.

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠), can take the place of the equal sign "=" in this expression. Polynomial inequality, rational inequality, and absolute value inequality are the various kinds of mathematical inequalities.

Given graph is made with three inequalities

graph shows the straight line which passes from (0, 6) and (6, 0)

the equation is x + y = 6

but the shaded region is under the line which means no more than 6,

x + y ≤ 6,

the second line is parallel to x axis at (0, 2)

here y = 2 and shaded region is above the line means more that 2

y ≥ 2,

and third line is parallel to y axis at (-1, 0)

equation is x = -1 and shade region is on right side of -1 equation is

x ≥ -1

Hence the equations are x + y ≤ 6, x ≥ -1 and y ≥ 2.

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The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.

To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).

Rationalizing the denominator

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)

Note that multiplying the conjugate of the denominator is like squaring a binomial:

This simplifies to:

(-6√(5y))/(√(5y) * √(5y))

The denominator simplifies to:

√(5y) * √(5y) = √(5y)^2 = 5y

So, the expression becomes:

(-6√(5y))/(5y)

Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).

\($(a-b)(a+b)=a^2-b^2$\)

This is what we will do to rationalize the denominator in this problem.

We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).

Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)

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Answer:

you did this to me too lol

Step-by-step explanation:

jjdfksljdkfj JFKLJSDK djfa

Answer:

\(\frac{100}{w}\)

Step-by-step explanation:

When it asks for the quotient you are dividing/ putting it in a fraction.

Answer:

(300,15) \(\frac{y}{x}\)=15/300=1/20

Step-by-step explanation:

How much money does Clare make after stuffing 1,500 envelopes?

Clare: y=1/10x=1/10(1500)=$150

How much money does Han make after stuffing 1,500 envelopes?

Han: y=1/20x=1/20(1500)=$75

What is Clare's rate of change?

1/10 means $1 for 10 envelopes

What is Han's Rate of change?

1/20 means $1 for 20 envelopes

Who gets paid more?

Clare gets paid more

The expression used  to calculate the surface area of the rectangular prism is given by option b. 2×6 + 2×10 + 2×15.

Let us consider 'l' be the length of the rectangular prism.

'w' be the width of the rectangular prism .

'h' be the height of the rectangular prism.

From the attached figure we have,

Length of the rectangular prism l = 3 units

Width of the rectangular prism w = 2 units

Height of the rectangular prism h = 5 units

Surface of the rectangular prism = 2(lw + wh + hl )

Substitute the values in the formula we get,

⇒Surface of the rectangular prism = 2 (3×2 + 2×5 + 5×3 )

⇒Surface of the rectangular prism = 2 ( 6 + 10 + 15)

⇒Surface of the rectangular prism = 2×6 + 2×10 + 2×15

Therefore, the surface area of the rectangular prism with given dimensions is equal to option b. 2×6 + 2×10 + 2×15.

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The above question is incomplete, the complete question is:

Which expression can be used to find the surface area of the following rectangular prism?

Attached figure.

Answer:

PAGE 1

8.) d

9.) b

PAGE 2

6.) b

7.) d

PAGE 3

4.) c

5.) a

PAGE 4

1.) c

2.) c

3.) a

PAGE 5

10.) b

11.) d

Step-by-step explanation:

PAGE 1

8.) x - 20 + x + 10 = 180 (collect like terms)

2x - 10 = 180 (add 10 on both sides)

2x = 190 (divide by 2 on both sides)

x = 95

9.) 2y + y = 180 (collect like terms)

3y = 180 (divide by 3 on both sides)

y = 60

x = y ----> x = 60

PAGE 2

6.)  16x - 6 = 90 (add 6 on both sides)

16x = 96 (divide by 16 on both sides)

x = 6

7.) 5x + 30 = 7x (subtract 5x on both sides)

30 = 2x (divide by 2 on both sides)

15 = x

PAGE 3

4.) <8 and <16 are corresponding angles

5.) 180 - 130 = 50

PAGE 4

1.)  HD and GE are skew lines

2.) AC, EG, and BD are parallel to FH

3.) EF, GH, and BF are perpendicular to FH

PAGE 5

10.) | and || only are the only ones correct

11.) l || m, by the Converse of the Consecutive Interior Angles Theorem.

b/c the two angles equal 180 together and one angle is on line l and the other is on line m. This shows they're parallel.

Hope this helps ya!!

Answer:

The northern lighthouse is approximately \(24.4\; \rm mi\) closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as \(\rm N\), the southern lighthouse as \(\rm S\), and the boat as \(\rm B\). These three points would form a triangle.

It is given that two of the angles of this triangle measure \(40^{\circ}\) (northern lighthouse, \(\angle {\rm N}\)) and \(21^{\circ}\) (southern lighthouse \(\angle {\rm S}\)), respectively. The three angles of any triangle add up to \(180^{\circ}\). Therefore, the third angle of this triangle would measure \(180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}\) (boat \(\angle {\rm B}\).)

It is also given that the length between the two lighthouses (length of \(\rm NS\)) is \(75\; \rm mi\).

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, \(\angle {\rm B}\) is opposite to side \(\rm NS\), whereas \(\angle {\rm S}\) is opposite to side \({\rm NB}\). Therefore:

\(\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}\).

Substitute in the known measurements:

\(\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}\).

Rearrange and solve for the length of \(\rm NB\):

\(\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}\).

(Round to at least one more decimal places than the values in the choices.)

Likewise, with \(\angle {\rm N}\) is opposite to side \({\rm SB}\), the following would also hold:

\(\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}\).

\(\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}\).

\(\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}\).

In other words, the distance between the northern lighthouse and the boat is approximately \(30.73\; \rm mi\), whereas the distance between the southern lighthouse and the boat is approximately \(55.12\; \rm mi\). Hence the conclusion.

Answer:

Last Option: y=2x-2

Answer: 4z + 3

Step-by-step explanation:

Number of books read by Zeke = z

Michelle read twice as many book as Zeke. This will be: = 2 × z = 2z

Tay read 3 more books than Zeke. This will be: = z + 3

The expression that represents the total number of books read over the summer by Zeke, Michelle and Tay would be the addition of the books read by each person. This will be:

= z + 2z + z + 3

= 4z + 3

The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

Hence, The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

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