two buses are driving along parallel freeways that are 8 mi apart, one heading east and the other heading west. assuming that each bus drives a constant 60 mph, find the rate (in mph) at which the distance between the buses is changing when they are 17 mi apart, heading toward each other.

The number of text messages for which the costs will be the same is of:

50 messages.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

For each plan, the slope and the intercept are given as follows:

Hence the functions are given as follows:

The costs will be the same when:

A(x) = B(x)

Hence:

30 + 0.2x = 40

0.2x = 10

x = 100/2

x = 50 messages.

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Answer:

your answer to this question is C.

The length of side XZ is 5 units and side YZ is 6 units.

A triangle is a three-sided polygon, which has three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the three angles of the triangle is equal to 180 degrees. To study about and build the world's seven sorts of triangles: equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene. The hypotenuse is the longest side of a right triangle, a "opposite" side is the one across from a given angle, and a "adjacent" side is the one close to a given angle.

Here,

XZ=3-(-2)

XZ=5 units

YZ=4-(-2)

YZ=6 units

Side XZ is 5 units long and Side YZ is 6 units long.

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Answer:

Step-by-step explanation:

The value of the vector expression 2u⋅(2u−6v) is 144.

Let's start by simplifying the expression 2u−6v. We can factor out the 2 from 2u to get:

2u−6v = 2(u−3v)

Now, we can substitute this expression back into 2u⋅(2u−6v) and get:

2u⋅(2u−6v) = 2u⋅2(u−3v)

We can use the distributive property of the dot product to expand this expression as follows:

2u⋅2(u−3v) = 4(u⋅u)−12(u⋅v)

Now, we can substitute the given values of u⋅v, ∥u∥, and ∥v∥ into this expression:

4(u⋅u)−12(u⋅v) = 4(∥u∥²)−12(9)

We are given ∥u∥, so we can substitute that into the expression:

4(∥u∥²)−12(9) = 4(6²)−12(9)

Simplifying this expression gives us:

4(6²)−12(9) = 144

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The general solution of the given homogeneous differential equation is: y/x = v = f(x^2 - ln|x|)

To solve the homogeneous differential equation (x - y) dx + x dy = 0 using an appropriate substitution, let's substitute

v = y/x. Then, y = xv and differentiate both sides with respect to x to get dy/dx = x dv/dx + v. Now, substitute y and dy/dx into the original equation:

(x - xv) dx + x(x dv/dx + v) dy = 0
(1 - v) dx + x^2 dv/dx + xv dy = 0

Now, divide the equation by x to obtain:

(1 - v) (dx/x) + x dv/dx + v dy = 0

This is now a separable differential equation. Rearrange the terms to separate the variables:

(1 - v) (dx/x) = -x dv/dx - v dy

Integrate both sides:

∫ (1 - v) (dx/x) = ∫ (-x dv - v dy)

∫ (1 - v) (1/x) dx = - ∫ x dv - ∫ v dy

ln|x| - ∫ v (1/x) dx = -xy - 1/2 y^2 + C

Now, substitute y back in terms of x and v:

ln|x| - ∫ v (1/x) (x dv) = -x(xv) - 1/2 (xv)^2 + C

Simplify and solve for v:

ln|x| - ∫ v dv = -x^2v - 1/2 x^2v^2 + C

Finally, write the general solution in terms of x and y:

y/x = v = f(x^2 - ln|x|)

where f is an arbitrary function.

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Since the slope is constant along a linear demand curve, elasticity is constant as well. - False

A linear demand curve does indeed have a constant slope, but this does not imply that it has a constant elasticity. The percentage change in the quantity required divided by the percentage change in price is the definition of elasticity. For a linear demand curve, the elasticity will change based on the slope and intercept of the curve at various places along the curve.

For example: The elasticity will be stronger in absolute terms at lower costs and smaller quantities, and smaller at higher prices and larger quantities. This is due to the fact that starting from a lower price and quantity will result in a bigger percentage change in quantity requested for a given change in price. As a result, the elasticity will change and not remain constant along the curve.

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Answer:

Step-by-step explanation:

The height of the cell-phone tower is approximately 110 feet. So the correct answer is option C: 110 ft.

We can use trigonometry to figure out how high the phone tower is. Let's use the letter h to indicate the tower's height.

The tower, Ryan's eye level, and the point where Ryan is standing all make up a right triangle in this instance. From Ryan's eye level to the top of the tower, the elevation difference is 54 degrees.

We can utilize the digression capability to relate the point of rise to the level of the pinnacle:

tan(angle) = opposite/adjacent tan(54°) = h/80 In order to find the value of "h," we can change the following equation:

h = tan(54°) * 80

Utilizing a logical mini-computer, we can work out the worth of tan(54°) as roughly 1.37638192047. Therefore:

The cell phone tower is approximately 110 feet tall because h = 1.37638192047 * 80 h  110.03.

Therefore, option C is the right response: 110 ft.

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Answer:

Step-by-step explanation:

You'll need to find a way to share the graph or graphs associated with this problem.

The period is 4.  The relationship between period and b (the coefficient of the independent variable of the cosine function) is (period) =(2π.b).  Given that the period here is 4,

       2π                          2π

4 = ---------, and so b = ------- = π/2.

                                       4

So now our y  = a*cos (bx + c) becomes

                    π

y = 10*cos (------x + 0 + 10

                     2

The horizontal center line of this cosine curve is y = 10.  The maximum value of the curve is 20, which is 10 + 10, and the minimum value is 0, which is 10 - 10.

The function that describes the given situation is \(\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10\) and this can be determined by using the properties of the trigonometric function.

Given :

The following steps can be used in order to determine the function could be the function described:

Step 1 - According to the given data, the cosine function has a period of 4.

Step 2 - Now, the independent variable of the cosine function is given by:

\(\rm 4b = 2\pi\)

\(\rm b =\dfrac{\pi}{2}\)

Step 3 - The maximum value of the cosine function is 1 and the minimum value of the cosine function is -1.

Step 4 - From the above steps, the function that described the given situation is given by:

\(\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10\)

Therefore, the correct option is C).

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Answer: 26

Step-by-step explanation:

(-4)(-2)-6(2-5)=

-(-8)-6*2-6*(-5)=

-(-8)-12-(-30)=

8-12+30=

30+8-12=

38-12=26

We witnessed that the economy has moved from its initial short-run equilibrium to a new long-run equilibrium, where the price level has stabilized despite the changes in aggregate demand and short-run supply.

Suppose the price level remains constant despite the initial shift of the AD (Aggregate Demand) curve to the right, followed by the leftward shift of the SRAS (Short-Run Aggregate Supply) curve. In that case, it suggests that the economy has experienced a change toward long-run equilibrium.

The initial shift of the AD curve to the right causes an increase in both output and the price level. However, the subsequent leftward shift of the SRAS curve indicates that in the short run, the price level has led to higher costs for businesses, potentially due to factors such as increased wages or input prices.

As a result, with a leftward shift in the SRAS curve, the output level decreases, and the price level rises further. However, if the price level remains constant after this adjustment, it suggests that the economy has reached a new equilibrium point where aggregate demand and short-run aggregate supply are once again balanced.

In short, witnessing a constant price level after the initial shifts in the AD and SRAS curves implies that the economy has moved from its initial short-run equilibrium to a new long-run equilibrium, where the price level has stabilized despite the changes in aggregate demand and short-run supply.

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If the ratio of band members in group 1 to band members in group 2 is 1 to 3, then for every 3 band members in group 2, there will be 1 band member in group 1.Therefore, group 2 will have 11 band members.

Comparing two numbers or quantities results in a ratio. Usually, it is expressed in the form "a:b" or "a/b," with a and b standing for the two quantities under comparison. Contrarily, a percentage is an equation that states that two ratios are equal. Alternatively said, a proportion is a claim that one ratio is equal to another.

For example, if the ratio of apples to oranges in a basket is 2:3, this implies that there are three oranges per each two apples. We may alternatively state that the ratio of apples to total number of fruits in the basket is 2:5, because 2 + 3 = 5. The two ratios (2:3 and 2:5) are proportionate in this instance. Also, ratio of band members in group 1 to band members in group 2 to be 1 to 3

How to solve?

If the director wants to divide 44 band members into two groups, with this ratio, then the number of band members in group 2 will be 44 / (1 + 3) = 44 / 4 = 11 band members.

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Answer:

$22,891.73

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 13.2/100

r = 0.132 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 18,800.00(1 + 0.132/12)(12)(1.5)

A = 18,800.00(1 + 0.011)(18)

A = $22,891.73

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $18,800.00 at a rate of 13.2% per year compounded 12 times per year over 1.5 years is $22,891.73.

Answer:

The options are missing, but i will answer the general statements about this type of transformation.

A transformation of the type (x, y) ----> (-x, -y) can be written in two forms:

> A rotation of 180° over the point (0, 0)

> A reflection over the line x = y.

Then the statements can be something like:

"The triangle R'S'T' is a reflection over the line x = y of the triangle RST"

Or

"The triangle R'S'T' is the rotation of 180° of the trianlgle RST about the point (0,0)"

Answer:

Option B

Step-by-step explanation:

For increasing function in the interval (a, b),

"If we draw a tangent at any point on the graph in the given interval (a, b), slope of the tangent drawn will be positive"

Given function is,

\(f(x)=\frac{1}{2}x^2+5x+6\)

In the interval (-∞, -5),

Graph is moving downwards therefore, tangents drawn at any point will have a negative slope and the function will decrease in this interval.

In the interval (-5, ∞),

In the given interval any tangent drawn at any point will have a positive slope and the function will be increasing.

Therefore, interval in which the function is increasing → (-5, ∞)

Option B is the answer.

The interval in which the function decreases is (-∞, -5).

The function decreases when, reading from left to right, the graph of the function goes downwards.

By looking at the graph, we can see that the graph goes downwards on the interval negative infinity and -5

Then we conclude that the function decreases on the interval (-∞, -5).

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If the quadratic has x-intercepts of -3 and 5 the equation would be:

y=c(x+3)(x-5)

The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, by creating one part as the mirror image of the other part.

First, we have to define the axis of symmetry.

The point right in between the two x-intercepts of a quadratic equation is called axis of symmetry.

We have x-intercepts of -3 and 5

In ordered to find the axis of symmetry we have to find their middle intercept

To find the axis of symmetry:

-3+5/2=2/2=1

So the axis of symmetry is x = 1

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Answer:

b

c

a

d

Step-by-step explanation:

sum=addition

difference=subtraction

groups=hints multiplication

split into=division

Answer:

Hope this helps!

Answer:

2.6 hours

Step-by-step explanation:

use distance formula:  d = r * t

                                     83 = 32t

                                     83/32 = t

                                       2.6 = t

2.6 hours is 2 hours, 36 minutes

Using the given digits only once , the four 2 digit prime numbers are 23 , 41 , 59 , 67  and the the sum of the 4 prime numbers is 190 .

Prime Numbers can be defined as numbers that is greater than 1 and whose only factors are 1 and itself .

For Example : 2 is prime number , 11 is a prime number .

In the question ,

9 digits are given as 1, 2, 3, 4, 5, 6, 7, and 9  

we have to form 4 two - digit prime numbers , using each digit only once ,

So , the prime numbers using the given digits using the digits only once is

(i) 23

(ii) 41

(iii) 59

(iv) 67

and the sum of the 4 prime numbers is = 23 + 41 + 59 + 67

= 190

Therefore , the 4 prime numbers are 23 , 41 , 59 , 67 and their sum is 190 .

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The symmetric difference of two sets is the set of elements that are in either of the sets, but not in their intersection. In this case, the intersection of {1, 3, 5} and {1, 2, 3} is {1, 3}, so the symmetric difference is the set of elements that are in either {1, 3, 5} or {1, 2, 3}, but not in {1, 3}. This set is {2, 5}, since 2 is in {1, 2, 3} but not in {1, 3, 5}, and 5 is in {1, 3, 5} but not in {1, 2, 3}. Therefore, the symmetric difference of {1, 3, 5} and {1, 2, 3} is {2, 5}.

Step 1: Identify the two sets.
Set A = {1, 3, 5}
Set B = {1, 2, 3}

Step 2: Find the difference between the two sets.
A - B = {5} (elements in A that are not in B)
B - A = {2} (elements in B that are not in A)

Step 3: Combine the two differences to find the symmetric difference.
Symmetric Difference = A - B ∪ B - A

Your answer: The symmetric difference of {1, 3, 5} and {1, 2, 3} is {2, 5}.

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Answer:

C. The relationship is linear; y – 5 = 2(x + 7).

Step-by-step explanation:

The correct answer is:

The relationship is linear, and the equation is  

y-5 = 2(x+7).

Explanation:

To determine if the relationship is linear, we find the slope between each pair of points.  Slope is given by the formula:

The slope between the first two points is given by:

The slope between the second pair of points is given by:

The slope between the third pair of points is given by:

Since the slope is the same throughout the data, the relationship is linear and the slope is 2.

To write the equation, we use point-slope form, which is:

y-y₁ = m(x-x₁)

Using the first point, we have:

y-5 = 2(x--7)

y-5 = 2(x+7)

The answer is The relationship is linear; y - 5 = 2(x + 7).

Answer:

Below

Step-by-step explanation:

Using   162 km = 162000m   and  1 hour = 3600 s

162000 m / 3600s = 45 m/s

At constant 45 m/s :

  rate * time = distance

    45 m/s * 15 s = 675 m   in 15 seconds

Answer:

2x=20  and x=10

Step-by-step explanation:

Answer:x =10

Step-by-step explanation:

2x -7=13

2x =13 +7

2x = 20

X= 20/2

X= 10