Harry and Selma start driving from the same location. Harry drives 42 miles north and Selma drives 144 mies east. How far apart are Harry and Selma when they stop?

Answer:

y = -2/3x - 11

Step-by-step explanation:

Steps to find the perpendicular bisector:

1) Find the midpoint of line PQ

Midpoint formula: (\(\frac{x_{1} + x_{2} }{2} \\\), \(\frac{y_{1} + y_{2}}{2}\))

Midpoint of line PQ = (6, -2)

2) Find the slope of line PQ

Slope formula: \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

Slope of line PQ = 3/2

3) Find the negative reciprocal of the slope of PQ

To find the negative reciprocal just swap the numerator and denominator and add a negative sign. If it is already negative it will become positive.

In this case it will be -2/3

4) Write the equation of line PQ in slop-intercept form.

Slope-intercept form: y = mx + b

This is what it will look like for line PQ: y = \(\frac{3}{2}\)x + b

5) Plug the points of the midpoint into the line and solve for the intercept (b)

This is what it will look like: -2 = \(\frac{3}{2}\)(6) + b

-2 = 18/2 + b

-2 = 9 + b

-11 = b

6) Write the equation of the perpendicular bisector

m = the negative reciprocal of the slope of PQ = -2/3

This is what the equation will look like: y = -2/3x - 11

Hope this helped! Please give Brainliest!

The linear equation formed from the  perpendicular bisector of PQ is y = -2/3 x + 2

The standard equation of a line is expressed as y = mx + b

m is the slope

b is the y-intercept

Given the coordinate points P(10,4 ) and Q(2,-8), find the slope of the line passing through the points.

m = -8-4/2-10

m = -12/-8

m = 3/2

The slope of the perpendicular bisector will be -2/3

Get the y-intercept.

Using the midpoint of the coordinates P(10,4 ) and Q(2,-8) and m = -2/3 into the formula y = mx + b

\(m = (\frac{10+2}{2},\frac{4-8}{2} )\\m=(6, -2)\)

-2 = -2/3(6) + b

-2 = -4 + b

b = 2

Hence the linear equation formed from the  perpendicular bisector of PQ is y = -2/3 x + 2

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Answer:

The first one (4cm for height and 3cm for base)

Step-by-step explanation:

the original height is 16cm and base is 12cm

if you multiply them both by 1/4 or 0.25 you get 4 and 3

(16*0.25=4 and 12*0.25=3)

Another way you could do it is to divide 16 and 12 by four and you still get 4 and 3

(16/4=4 and 12/4=3)

Answer:

Is A.

Step-by-step explanation:

The sides of the triangle include numbers 4 and 3 in option A. Mathematically in scale factor form, 16 cm 12 cm divide or multiply evenly into the scale factor of 1/4.

Answer:

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)

Step-by-step explanation:

By the rule of Integer multiplications,

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)

                                                      \(= [2] \times [12] \times (-5)\)

                                                      \(= -120\)

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Answer:

x=-1

Step-by-step explanation:

12x+28=16

-28 on both sides

12x=-12

x=-1

Answer:

10 minutes

Step-by-step explanation:

Mario can eat e21 hot dog in 6 minutes

Let 35 hot dog  eats in x minutes :

\(\frac{35}{x} =\frac{21}{6} \\x=\frac{35(6)}{21} \\x=10 min\)

Therefore, mario would eat 35 dogs in 10 min.

This can be done by finding the CPI or another price index for the same period. Once you have the GDP deflator, you can use the formula above to calculate the real GDP.

If you only know the nominal GDP, you cannot determine the real GDP. In order to determine the real GDP, you need to take into account inflation. This is done by adjusting the nominal GDP for inflation using a price index, such as the Consumer Price Index (CPI).The formula for calculating real GDP is:Real GDP = Nominal GDP / GDP DeflatorThe GDP deflator is a measure of inflation that takes into account changes in the prices of all goods and services produced in an economy. It is calculated by dividing nominal GDP by real GDP and multiplying by 100. This gives us a ratio of the current price level to the base year price level.

The base year price level is assigned a value of 100.Using this formula, we can see that if we know the nominal GDP and the GDP deflator, we can calculate the real GDP. For example, if the nominal GDP is $10 trillion and the GDP deflator is 120, the real GDP would be:Real GDP = $10 trillion / 1.2 = $8.33 trillionTherefore, in order to determine the real GDP if you only know the nominal GDP, you need to obtain the GDP deflator.

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Answer:

Step-by-step explanation:

Add up the 3 equations and solve for s:

The two ratios that are equivalent to 15/36 are expressed as: B.) 5/12 and 30/72.

If two ratios are said to be equivalent, it means that they will have the same value when simplified or expressed in their simplest form.

Given the ratio, 15/36, simplify in its simplest form:

15/36 = 5 * 3 / 12 * 3 = 5/12

So also, we have:

30/72 = 5 * 6 / 6 * 12 = 5/12

Therefore, 5/12 and 30/72 are equivalent to the ratio, 15/36.

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There are 792 different ways a group of 5 guitars is selected.

What is the combination?

A combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

Here, we have

Given: A guitar shop owner has 12 guitars in his main shop display. The owner wishes to select 5 of them to display at a special show.

We have to find how many different ways can a group of 5 guitars be selected.

Total guitars = 12

No of guitars to be selected = 5

No of different ways they can be selected = ¹²C₅

= 12!/((12-5)!x5!)

= 12!/(7!x5!)

= 479001600/(5040x120)

= 479001600/604800

= 792 different ways

Hence, there are 792 different ways a group of 5 guitars is selected.

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A strategy canvas is a visual framework used to analyze and compare the strategic positioning of different companies or products within an industry.

It is a tool developed by W. Chan Kim and Renée Mauborgne, the creators of the Blue Ocean Strategy, to help organizations identify and create new market spaces by differentiating their offerings.

The strategy canvas consists of two axes: the horizontal axis represents the key factors that the industry competes on, and the vertical axis represents the offering level or degree of offering provided for each factor. By plotting the current state of competing products or companies on the canvas, organizations can gain insights into the competitive landscape and identify areas of opportunity for innovation and differentiation.

The strategy canvas helps visualize the competitive factors that are driving the industry and highlights areas of convergence or similarity among existing offerings. It allows organizations to identify untapped market spaces where they can create unique value propositions and redefine the competitive boundaries.

To use a strategy canvas effectively, organizations need to analyze the key factors that customers value in the industry and assess the relative performance of their offerings compared to competitors. By identifying the factors where they are underperforming and overperforming, organizations can focus on enhancing their value proposition by reallocating resources, investing in areas of differentiation, and eliminating or reducing elements that do not create significant customer value.

A strategy canvas is a powerful tool for strategic analysis and innovation. It helps organizations visualize the competitive landscape, identify areas for differentiation, and create new market spaces by providing a clear understanding of customer preferences and the competitive factors that drive industry success.

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Random variables that are continuous are A and B, random variables that are discrete are C and D.

Probability is a measure of the likelihood or chance of an event occurring. It is a fundamental concept in mathematics, statistics, and many other fields, and it is used to model and analyze uncertainty and randomness.

The probability of an event is a number between 0 and 1, where 0 represents impossibility and 1 represents certainty. If an event has a probability of 0.5, for example, it means that there is a 50% chance of the event occurring and a 50% chance of it not occurring.

The random variables that are continuous are:

The random variables that are discrete are:

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The system of equations that model the situation is:

4c + 2s+ 3b == $29.51

c + 4s + 2b = $21.83

2c + 5s = $21.93

Simultaneous equations are more than one equation that would have to be solved jointlu in order to determine the required values.

Methods of solving simultaneous equations are:

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Answer:

I would say pretty fast lol It would be traveling about somewhere beetween 30 to 50 mph because it would have hit terminal velocity at that point.

Answer:

Step-by-step explanation:

1. Notice that these angles are vertical angles which are angles opposite each other when two lines cross, they share the same vertex. Vertical angles are congruent angles.

Therefore,

2. In this case, the angles shown are complementary, which mean they must add up 90 degrees:

Answer:

what grade are you in? Maybe i can help :)

Answer:

a=750

Step-by-step explanation:

If the cost varies directly with the number of minutes Jalen talks on the phone, we can use the equation y = kx, where y represents the cost, x represents the number of minutes, and k is the constant of variation.

To determine the value of k, we can choose any of the given data points to substitute into the equation.

Let's use the first data point: Number of minutes, x = 150 and Cost, y = $7.50.

Substituting these values into the equation, we have:

$7.50 = k * 150

To solve for k, we divide both sides of the equation by 150:

k = $7.50 / 150

k = 0.05

Therefore, the equation that represents the variation is y = 0.05x.

Out of the given options, the equation y = 0.05x is the correct representation of the variation between the cost and the number of minutes Jalen talks on his mobile phone.

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Answer:

She will save 1.24

Step-by-step explanation:

2.65 x 4 10 .60 plus .53 x 4 equals 12.72

6.48 x 2 equals 13.96

The values of ∠PQR = 45° and ∠POR = 90°.

The circumference of a circle is defined as its linear distance around it. In other words, if a circle is opened to form a straight line, the length of that line equals the circumference of the circle.

The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually denoted by the letters 'R' or 'r'.

Given that

O is the center of the circle, if ∠OPQ = 25° &∠ORQ = 20°

We have to determine the values of ∠PQR and ∠POR

Sol. OP = OQ

⇒∠OQP = ∠OPQ = 25° [Radii of the same circle]

Similarly, ∠OQR = 20°

∠PQR = 25° + 20°

∠PQR = 45°

Furthermore ∠POR = 2 ∠PQR [the angle at the centre is twice the angle at the circumference].

⇒∠POR = 2 × 45°

∠POR = 90°.

Therefore the values of ∠PQR = 45° and ∠POR = 90°.

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The solution for the value of x is 55.

Since the segments of the secant segment and the tangent segment share an endpoint outside of the circle.

According to Tangent-Secant Theorem, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment. That is:

x² = 5 * (5 + 6)

x = 5 * 11

x = 55

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m<1 =163 degrees

163,17,163,17 (all in degrees)

163,17,163,17  (all in degrees)

I have reproduced and attached a diagram (in figure 1) of the problem.

For ease of understanding, I have attached a second diagram which is labelled.

On line a

17+<CBE=180 (Linear Pair Postulate)

m<2=<CBE=180-17=163 degrees

<ABG=<CBE=163 degrees (Vertically Opposite Angles)

<ABE=<GBC= 17 degrees(Vertically Opposite Angles)

On line b

m<1=<DEB=<ABG=163 degrees (Corresponding Angles)

<BEF=<GBC= 17 degrees (Corresponding Angles)

<HEF=<DEB=163 degrees  (Vertically Opposite Angles)

<DEH=<BEF=17 degrees (Vertically Opposite Angles)

Therefore:

m<1 =163 degrees

Clockwise from top left, the angles formed with line a are: 163 degrees, 17 degrees, m<2=163 degrees and 17 degrees.

Clockwise from top left, the angles formed with line b are: m<1=163 degrees, 17 degrees, 163 degrees, and 17 degrees.

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The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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The answer is 231 inches.

To understand how we arrive at this answer, let's break down the given measurement step by step. We have 6 yards, 3 feet, and 7 inches.

Starting with yards, we know that 1 yard is equal to 3 feet, so 6 yards would be equivalent to 6 * 3 = 18 feet. Adding the 3 feet given, we have a total of 18 + 3 = 21 feet.

Moving on to inches, we know that 1 foot is equal to 12 inches. So, the 21 feet we calculated earlier would be equal to 21 * 12 = 252 inches. Finally, adding the 7 inches given, we get a total of 252 + 7 = 259 inches.

Therefore, 6 yards 3 feet 7 inches is equal to 259 inches.

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The statement that "when dealing with fixed effects, a de-meaned model approach is superior to the lsdv approach because the de-meaned model gives us more accurate coefficient estimates" is true.

Fixed effects are a type of regression technique used to understand the effect of a single variable across different groups (such as across countries, across states, across individuals, etc.) by comparing the variance of the variable within each group to the variance of the variable across all groups.

When conducting a fixed effects regression, researchers must choose between the least squares dummy variable (LSDV) and de-meaned model approaches.Both models produce unbiased estimates of the coefficients, but the LSDV model has an advantage in that it provides more flexibility when dealing with interactions between fixed effects and time-varying covariates. On the other hand, the de-meaned model is preferred for reasons of computational efficiency and it can handle certain types of data that the LSDV model cannot (such as panel data with a small number of time periods).

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Answer:

ok i think its  D

Step-by-step explanation:

2,4; x= 3

i am not 100% but like i looked up examples and that seems to be the only one that looks right

Answer:

d.   zeros: 2, 4           axis of symmetry: x = 3

Step-by-step explanation:

The zeros are the values of x where the graph crosses the x-axis

zeros = 2, 4

The axis of symmetry is the vertical line thru the vertex of the parabola

The vertex is (3, -1), so x = 3 is the axis of symmetry

At the point P(1,1,1), the function f(x,y,z)=ln(xy) + ln(yz) + ln(xz) has a saddle point, with directions of maximum and minimum decrease given by [1, −1, 0] and [0, 0, 1], respectively. The function increases most rapidly in the direction [0, 0, 1], with a derivative of 2, and decreases most rapidly in the direction [1, −1, 0], with a derivative of 0.

To find the directions in which the function f(x,y,z)=ln(xy) + ln(yz) + ln(xz) increases and decreases most rapidly at P(1,1,1), we need to compute the gradient of f at P and then evaluate it at P.

The gradient of f is given by:

grad f(x,y,z) = (∂f/∂x, ∂f/∂y, ∂f/∂z) = (1/x + 1/z, 1/x + 1/y, 1/y + 1/z)

At P(1,1,1), the gradient is (2,2,2).

To find the directions of maximum and minimum increase, we need to find the eigenvectors of the Hessian matrix of f at P. The Hessian matrix is given by:

H(f) = [∂²f/∂x², ∂²f/∂x∂y, ∂²f/∂x∂z;

∂²f/∂y∂x, ∂²f/∂y², ∂²f/∂y∂z;

∂²f/∂z∂x, ∂²f/∂z∂y, ∂²f/∂z²]

Evaluating the Hessian at P(1,1,1), we get:

H(f)(P) = [−1, −1, 0;

−1, −1, 0;

0, 0, −1]

The eigenvalues of H(f)(P) are −1 and −1 (with multiplicity 2), indicating that the function f has a saddle point at P(1,1,1).

The corresponding eigenvectors are [1, −1, 0] and [0, 0, 1], which indicate the directions of maximum and minimum decrease, respectively. To find the derivatives of f in these directions, we need to compute the directional derivatives of f at P along these eigenvectors.

For the direction [1, −1, 0], the directional derivative of f at P in this direction is given by:

D[1,-1,0]f(P) = ∇f(P) · [1, −1, 0] = 2(1) + 2(−1) + 0 = 0

For the direction [0, 0, 1], the directional derivative of f at P in this direction is given by:

D[0,0,1]f(P) = ∇f(P) · [0, 0, 1] = 2(1) + 2(1) + 2(−1) = 2

Thus, the function f decreases most rapidly in the direction [1, −1, 0], and increases most rapidly in the direction [0, 0, 1]. The derivatives of f in these directions are 0 and 2, respectively.

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The period of a function is the horizontal distance between two consecutive points on the graph that have the same value.

It represents the length of one complete cycle or repetition of the function. To find the period of a function, we need to identify the portion of the function that repeats itself.

To identify the period of the function, we need to determine if there is a pattern in the function or if it resembles any standard periodic functions such as sine or cosine.

Once we identify the pattern, we can determine the period.

Asymptotes are imaginary lines that the graph of a function approaches but never crosses. They can be vertical, horizontal, or slant.

To identify the asymptotes of a function, we need to determine the behavior of the function as it approaches infinity or negative infinity. If the function approaches a certain value or line as the input increases or decreases without bound, that value or line is an asymptote.

It's important to note that not all functions have asymptotes. Some functions have vertical asymptotes, horizontal asymptotes, or both.

Let's consider an example to illustrate these concepts:

Example:
Given the function f(x) = 2sin(3x), let's identify the period and the asymptotes.

The function f(x) = 2sin(3x) represents a sine function with an amplitude of 2 and a frequency of 3.

To find the period, we can use the formula: period = 2π/|b|, where b is the coefficient of x in the function.

In this case, the coefficient of x is 3. Therefore, the period is: period = 2π/|3| = 2π/3.

So, the period of the function f(x) = 2sin(3x) is 2π/3.

As for the asymptotes, since this is a sine function, it does not have any vertical asymptotes. However, if we had a function involving a rational expression, we would need to check for vertical asymptotes by setting the denominator equal to zero and solving for x.

In terms of horizontal asymptotes, a sine function does not have any horizontal asymptotes either.

In conclusion, the function f(x) = 2sin(3x) has a period of 2π/3 and does not have any asymptotes.

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Answer:

For the regular tax in Pennsylvania, it would be 12 cents or $0.12. For Philadelphia, it would be 4 cents or $0.04. I got these two amounts by multiplying 2 times 6 or 2 percent, aka 0.06 and 0.02. If you added the two together, you would get, $0.16 or 16 cents. You would then add that to the two dollars and end up with $2.16 or two dollars and sixteen cents. I hope this helps.

Step-by-step explanation:

\(\dag\bf\:P(x_1,y_1)=(3,0)\)

\(\dag\bf\:Q(x_2,y_2)=(-1,3)\)

\(\dag\bf\:R(x_3,y_3)=(11,6)\)

❅ Distance between P and Q :

\(\sf\:PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\sf\:PQ=\sqrt{(-1-3)^2+(3-0)^2}\)

\(\sf\:PQ=\sqrt{(-4)^2+(3)^2}\)

\(\sf\:PQ=\sqrt{16+9}\)

\(\sf\:PQ=\sqrt{25}\)

\(\bf\:PQ=5\:unit\)

❅ Distance between Q and R :

\(\sf\:QR=\sqrt{(x_3-x_2)^2+(y_3-y_2)^2}\)

\(\sf\:QR=\sqrt{(11-(-1))^2+(6-3)^2}\)

\(\sf\:QR=\sqrt{(12)^2+(3)^2}\)

\(\sf\:QR=\sqrt{144+9}\)

\(\sf\:QR=\sqrt{153}\)

\(\bf\:QR=12.37\:unit\)

❅ Distance between P and R :

\(\sf\:PR=\sqrt{(x_1-x_3)^2+(y_1-y_3)^2}\)

\(\sf\:PR=\sqrt{(3-11)^2+(0-6)^2}\)

\(\sf\:PR=\sqrt{(-8)^2+(-6)^2}\)

\(\sf\:PR=\sqrt{64+36}\)

\(\sf\:PR=\sqrt{100}\)

\(\bf\:PR=10\:unit\)

◈ Perimeter of Triangle :

➝ perimeter = PQ + QR + PR

➝ perimeter = 5 + 12.37 + 10

➝ Perimeter = 27.37 unit