Consider the graph below representing the map of a city. Create an efficient route through the city. Your path must travel every street. List the vertices in the order that you travel them.

Answer:

  y = (-4/3)(x +4) +4

Step-by-step explanation:

Between the given points, the "rise" is -8 and the "run" is 6. The rise/run ratio is then -8/6 = -4/3. So, a version of the point-slope equation can be written:

  y = m(x -h) +k . . . . . . . line with slope m through point (h, k)

  y = (-4/3)(x +4) +4

_____

Comment on the answer

The image asks for "an equation", which seems to allow for any equation format. The equation shown above can be put into other forms.

  y -4 = -4/3(x +4) . . . . different point-slope form

  y = -4/3x -4/3 . . . . . . slope-intercept form

  4x +3y = -4 . . . . . . . . standard form

  4x +3y +4 = 0 . . . . . . general form

  x/(-1) +y/(-4/3) = 1 . . . . intercept form

Answer:

1_ scalene

2_isoscelous

Answer:

13a. scalene

13b. isosceles

13c. right

Step-by-step explanation:

i took geometry hope this helps

Answer:

3,604 books

Step-by-step explanation:

We have 2 situations:  situation A and situation B.  What we are looking for is the number of books that has situation A equal to situation B.  So the game plan is to write the equations for A and B, set them equal to each other, and then solve for the unknown number of books, x.

Situation A:  If each book costs 19.25 to produce and the number of books is x, we express that as 19.25x.  The fixed cost to use that company, regardless of the number of books it produces for you, is 22,427.  Which means it is going to charge you 22,427 whether you produce 1000000 books or no books at all.  The equation for A is:

C(A) = 19.25x + 22,427

Situation B uses the exact same reasoning, with the cost of each book being 10.50x and the flat rate cost of 53,962.  Therefore, the equation for B:

C(B) = 10.50x + 53,962

We need the number of books where A = B, so we set the equations equal to each other and solve for x:

19.25x + 22,427 = 10.50x + 53,962 so

8.75x = 31,535 and

x = 3604

Answer:

g = 28,000 - 700t

Step-by-step explanation:

This solution reads, in words,

"the amount of water remaining in the pool is equal to 28,000 gallons minus 700 gallons per hour", which is what your situation is asking you.  You start with 28,000 gallons and are pumping out (subtracting) 700 gallons per hour.

g is what remains

Answer: [tex]g=28000-700t[/tex]

Step-by-step explanation:

Given : A 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour.

i.e, Remaining gallons = 28,000- 700 × Number of hours.

Let g be the number of gallons remaining in the pool and t is the amount of time in hours the pool has been draining.

Then, the equation models this situation  will be :-

[tex]g=28000-700t[/tex]

Answer:

  A = 15t +15

Step-by-step explanation:

The amounts have a common difference of $15, so that is apparently the amount Jasmine is saving each week. Week 1, however, is $15 more than $15×1. The function ...

  A = 15t +15 . . . . dollars

seems to fit the data.

Answer:

D. 0.7611

Step-by-step explanation:

The area is:

P(z<1.60) − P(z<-0.90)

Looking up the values in a z-score table:

0.9452 − 0.1841

0.7611

Answer:

D. 0.7611

Step-by-step explanation:

We have been given a graph of a normal standard distribution curve. We are asked to find the area of the shaded region under the given standard distribution curve.

The area of the shaded region under the standard distribution curve would be area of a z-score of 1.60 minus area of a z-score of [tex]-0.90[/tex] that is [tex]P(-0.90<z<1.60)=P(z<1.60)-P(z<-0.90)[/tex]

Using normal distribution table, we will get:

[tex]P(-0.90<z<1.60)=0.94520-0.18406[/tex]

[tex]P(-0.90<z<1.60)=0.76114[/tex]

Therefore, the shaded area under the curve is 0.7611 and option D is the correct choice.

For this case we have the following equation:

[tex]\sqrt [4] {2x-8} + \sqrt [4] {2x + 8} = 0[/tex]

If we subtract both sides of the equation [tex]\sqrt [4] {2x + 8}[/tex] we have:

[tex]\sqrt [4] {2x-8} = - \sqrt [4] {2x + 8}[/tex]

To eliminate the radical we raise both sides of the equation to the fourth power:

[tex](\sqrt [4] {2x-8}) ^ 4 = (- \sqrt [4] {2x + 8}) ^ 4[/tex]

Answer:

Option D

Answer:

shortest length of fence is 8485.2 ft

Step-by-step explanation:

Given data

area =  3,000,000 square feet

to find out

shortest length of fence

let length L and width is W

so area is L × W

W = 3 × [tex]10^{6}[/tex] /L    ............1

2W = 6 × [tex]10^{6}[/tex] /L

rectangular field and then divide it in half

so fencing will be 3 × L + 2 × W

i.e.  3 L + 2W

fencing =  3 L  + 6 × [tex]10^{6}[/tex] /L

fencing minimum = 3 L  -  6 × [tex]10^{6}[/tex] /L²

fencing minimum length will be zero

3 L  -  6 × [tex]10^{6}[/tex] /L² = 0

3 L² = 6 × [tex]10^{6}[/tex]

L² =  2 × [tex]10^{6}[/tex]

L  =  1414.2

so from equation 1

W = 3 × [tex]10^{6}[/tex] /L

W = 3 × [tex]10^{6}[/tex] /1414.2

W = 2121.3

so fencing will be  3 L +2 W

so fencing =   3 × 1414.2  +2 × 2121.3

fencing =  4242.6 +4242.6

fencing =  8485.2

shortest length of fence is 8485.2 ft

The shortest length of fence the rancher can use is approximately 6104 feet. This is derived by setting up the area and perimeter equations, differentiating to find the minimum perimeter, and substituting the values back into the equation.

This problem is a basic optimization problem in mathematics. Given that the area of the field to be fenced is 3,000,000 square feet, we can use the formula for the area of a rectangle, which is length multiplied by width. Since the rancher wants to divide the field in two with a fence running parallel to one side, the total amount of fencing will be two lengths and three widths.

Let's denote the length of the rectangle as 'l' and the width as 'w'. The area is thus l*w = 3,000,000. The perimeter is defined as 2*l + 3*w. Given that the area is fixed, w can be expressed in terms of l as 3,000,000/l.

Therefore, the perimeter becomes 2*l + 3*(3,000,000/l). The minimum fence length or perimeter occurs when the derivative of this equation is zero. By differentiating and setting the equation to zero, we get l=sqrt(1,500,000), approximately 1224.74 feet. Substituting this value into the equation for w gives us w also as 1224.74 feet.

The shortest length of fence that the rancher can use is thus 2*l + 3*w = 2*1224.74 + 3*1224.74 = 6103.7 feet.

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Answer:

The x-intercept is 5.

Some people prefer you right it as a point (5,0).

Step-by-step explanation:

The x-intercept can be found by setting y=0 and solving for x.

Just like to find the y-intercept you can set x=0 and solve for y.

Let's find the x-intercept.

So we will set y=0 and solve for x:

3x-9y=15

3x-9(0)=15

3x-0    =15

3x        =15

Divide both sides by 3:

 x         =15/3

 x          =5

So the x-intercept is (5,0).

Answer:

North pacific and south pacific.

Step-by-step explanation:

D.

The Pacific Ocean's two major gyre systems are found in the North Pacific and South Pacific.

The Pacific Ocean is divided into two sets of gyres, notably in the North Pacific and South Pacific. Gyres are large systems of circulating ocean currents; the gyres in the Pacific Ocean play significant roles in influencing climate and marine life. The North Pacific Gyre, encircling the area between Asia and North America, and the South Pacific Gyre, contained mostly between Australia, South America and Antarctica, are the two main gyre systems in the Pacific Ocean.

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Answer:

The sum of the vectors is <8 , 6>

The magnitude of the resultant vector is 10

The direction of the resultant vector is 37°

The answer is the 1st answer: <8 , 6> ; 10 ; 37°

Step-by-step explanation:

* Lets explain how to solve the problem

∵ The first vector is <7 , -2>

∵ The second vector is <1 , 8>

∴ The sum of the 2 vectors = <7 , -2> + <1 , 8>

∴ Their sum = <7 + 1 , -2 + 8> = <8 , 6>

* The sum of the vectors is <8 , 6>

- The magnitude of the resultant vector = √(x² + y²)

∵ x = 8 and y = 6

∴ The magnitude of the resultant vector = √(8² + ²)

∴ The magnitude of the resultant vector = √(36 + 64) = √100 = 10

* The magnitude of the resultant vector is 10

- The direction of the vector = tan^-1 (y/x)

∵ x = 8 and y = 6

∴ The direction of the vector = tan^-1 (6/8) = 36.869 ≅ 37°

* The direction of the resultant vector is 37°

Answer:

The answer is A. ⟨8,  6⟩;  10;  37°

Answer:

The maximum area that can be obtained by the garden is 128 meters squared.

Step-by-step explanation:

A represents area and we want to know the maximum.

[tex]A(x)=-2x^2+32x[/tex] is a parabola.  To find the maximum of a parabola, you need to find it's vertex.  The y-coordinate of the vertex will give us the maximum area.

To do this we will need to first find the x-coordinate of our vertex.

[tex]x=\frac{-b}{2a}{/tex] will give us the x-coordinate of the vertex.

Compare [tex]-2x^2+32x[/tex] to [tex]ax^2+bx+c[/tex] then [tex]a=-2,b=32,c=0[tex].

So the x-coordinate is [tex]\frac{-(32)}{2(-2)}=\frac{-32}{-4}=8[/tex].

To find the y that corresponds use the equation that relates y and x.

[tex]y=-2x^2+32x[/tex]

[tex]y=-2(8)^2+32(8)[/tex]

[tex]y=-2(64)+32(8)[/tex]

[tex]y=-128+256[/tex]

[tex]y=128[/tex]

The maximum area that can be obtained by the garden is 128 meters squared.

By using the vertex formula to find the width that maximizes the area of Beth's garden, we determine that the maximum area she can enclose with 32 meters of fencing is 128 square meters when the width is set to 8 meters.

The question is about finding the maximum area that can be enclosed by Beth with 32 m of fencing for a garden, modeled by the function A(x) = -2x2 + 32x, where x is the width of the garden in meters. To find the maximum area, we need to determine the vertex of this quadratic equation since the coefficient of x2 is negative, indicating a maximum point for the area.

To find the vertex, we can use the formula x = -b / 2a, where a and b are the coefficients from the quadratic equation A(x). Thus, x = -32 / (2*(-2)) = 8 meters. Substituting x back into the function to find the maximum area, A(8) = -2(8)2 + 32(8) = -128 + 256 = 128 square meters.

This shows that the maximum area Beth can enclose with 32 meters of fencing for her garden is 128 square meters, by setting the width to 8 meters.

Answer:

102 an hour

Step-by-step explanation:

all you do is add all of them together

Answer:

  exponential: y = 2^(-x)

Step-by-step explanation:

The y-differences are not constant, and the x-y products are not constant. For each increase in x, y is divided by 2, so this is a geometric sequence that can be described by an exponential model. The common factor is 1/2.

A simple way to write the model for this is ...

  y = 2^(-x)

Assuming pure chance, on a 12 question multiple choice test with 3 options per question, it would be unusual to get 5 or more questions correct by guessing alone.

The question pertains to the probability of guessing correctly on a multiple-choice test with 3 options per question, assuming pure chance. On a 12-question test, the probability of guessing correctly on a single question is 1/3. Hence, for 12 questions, the expected number of correct guesses would be the total number of questions times the probability of getting each question right, which is 12 * 1/3 = 4. Therefore, it would be unusual to get 5 or more questions correct by guessing alone.

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In a 12-question multiple choice test with 3 possible answers for each, a student randomly guessing is expected to get roughly 4 correct answers. Getting 6 or more questions correct by random guessing would be considered unusual.

When taking a 12-question multiple choice test where each question has 3 possible answers, the probability of getting a question correct by simply guessing is 1/3. Here, we want to calculate the unusual scenario of how many or more questions correct by simply guessing.

If we apply the principle of probability, under normal circumstances where guessing is purely random, the expected number of correct answers would be the total number of questions times the probability of getting a question correct. This equates to 12 × (1/3) which is 4 correct answers. This means on average, if the student were to guess all their answers, they are likely to get around 4 correct answers.

However, getting 6 or more questions right by guessing alone would be considered unusual due to the low probability of guessing correct answers repeatedly. Keep in mind, that these calculations hold if all the guesses are random and there is no elimination of wrong answers based on known information.

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Answer:

  A.)  3

Step-by-step explanation:

In the equation g(x) = f(k·x), the factor k is a horizontal compression factor. Here the graph of g is the graph of f compressed by a factor of 3.

The point (3, 2) on the graph of f(x) becomes the point (1, 2) on the graph of g(x). The point (1, 2) is a factor of 3 closer to the y-axis than the point (3, 2).

It may be easier to think of k as the reciprocal of the horizontal expansion (dilation) factor. The function g is horizontally dilated by a factor of 1/3 from function f, so k = 1/(1/3) = 3.

To determine the value of k, we need to analyze the graphs of f(x) and g(x). By comparing the graphs, we can determine if k is greater or less than 1. The graph of g(x) is compressed horizontally, indicating that k is less than 1.

To determine the value of k, we need to analyze the relationship between the functions f(x) and g(x).

Since g(x) = f(k⋅x), we can compare the graphs of f(x) and g(x) to find the value of k.

If k is greater than 1, the graph of g(x) will be compressed horizontally compared to the graph of f(x).

If k is less than 1, the graph of g(x) will be stretched horizontally compared to the graph of f(x).

By analyzing the graphs of f(x) and g(x), we can see that the graph of g(x) is compressed horizontally, indicating that k is less than 1.

Therefore, the value of k is B.) 1/3.

Answer:

not really sure maybe 12

Answer:

8 / 12 = x / 18

8 * 18 / 12 = x

x = 12

Step-by-step explanation:

Answer:

156p

Step-by-step explanation:

13p×12

multiply the numbers

= 156p

The value of the permutation [tex]^{13}P_{12}[/tex] is 6,227,020,800.

We have,

To calculate [tex]^{13}P_{12}[/tex], we need to determine the value of 13 factorial (13!) divided by (13 - 12) factorial (1!).

The formula for factorial is n! = n * (n - 1) * (n - 2) * ... * 2 * 1.

So,

[tex]^{13}P_{12}[/tex]

= 13!/1!

= 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2

= 6,227,020,800.

Therefore,

The value of the permutation [tex]^{13}P_{12}[/tex] is 6,227,020,800.

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Answer:

Step-by-step explanation:

According to the problem

[tex]\angle N + \angle O =180\°[/tex]

[tex]\angle O + \angle P = 180\°[/tex]

[tex]\angle M + \angle P = 180\°[/tex]

Which means,

[tex]\angle N + \angle O = \angle O + \angle P\\\angle N = \angle P[/tex]

And,

[tex]\angle O + \angle P = \angle M + \angle P\\\angle O = \angle M[/tex]

Therefore, the right answer is the last choice.

Answer:

  rational: -3.786, 8/17, 8.23, 10.86731234, 0.75, √.49 = 0.7

  irrational: 3π, √11

Step-by-step explanation:

Any number that can only be represented completely using symbols, such as π or √, is an irrational number.

If the number can be expressed as the ratio of two integers, it is a rational number. Such numbers include proper and improper fractions, integers, any number you can write with a finite number of digits, and any repeating decimal, regardless of the length of the repeat.

Answer:

1.6 hours or 1 hour 36 minutes.

Step-by-step explanation:

The rate at which the trains are moving apart is 55 + 75 = 130 mph.

Speed = distance / time so:

130 = 208 / t

130t = 208

t = 1.6 hours.

Answer with Step-by-step explanation:

We are given that u and v are a basis for the two dimensional vector space.

To prove that w=u+v and x=u-v is also a basis .

By using matrix we prove w and x are basis of vector space.

We make a matrix from w and x

[tex]\left[\begin{array}{cc}1&1\\1&-1\end{array}\right][/tex]

Apply operation

[tex] R_1\rightarrow R_1-R_2[/tex]

[tex]\left[\begin{array}{cc}0&2\\1&-1\end{array}\right][/tex]

Apply [tex] R_2\rightarrow R_2-+R_1[/tex]

[tex]\left[\begin{array}{cc}0&2\\1&1\end{array}\right][/tex]

Apply [tex]R_1\rightarrow \frac{1}{2}R_1[/tex]

[tex]\left[\begin{array}{cc}0&1\\1&1\end{array}\right][/tex]

Apply [tex]R_2\rightarrow R_2-R_1[/tex]

[tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]

Rank is 2 .Therefore, row one and second row are linearly independent.

Hence, first and second row are linearly independent because, any row is not a linear combination of other row.

Therefore, w and x are formed basis of given vector space.

The value of a salary of $12,000 in 1964 would be approximately $84,000 in 2016 dollars when adjusted for inflation as measured by the Consumer Price Index.

To calculate the value of your grandfather's salary in 2016 dollars, the relative rates of Consumer Price Index (CPI) for both years need to be compared. The salary of $12,000 in 1964, adjusted for inflation through 2016, would be:

$12,000 * (219 / 31)

This formula indicates the change in CPI from 1964 to 2016 and multiplies it by the salary in 1964 dollars. Therefore, your grandfather's salary in 2016 is approximately $84,000 when accounting for inflation.

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Final answer:

The value of your grandfather's salary in 2016 dollars is approximately $84,687.10

Explanation:

The value of your grandfather's salary in 2016 dollars is approximately $84,687.10

. To calculate this, you need to adjust the 1964 salary for inflation using the Consumer Price Index (CPI) for 1964 and 2016. First, find the inflation factor by dividing the CPI of 2016 by the CPI of 1964. Then, multiply the 1964 salary by this factor to get the equivalent value in 2016 dollars.

Answer:

The third side can be any length as long as it is greater than 4 in and less than 26 in

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x ----> the length of the third side

Applying the triangle inequality theorem

1) 11+15 > x

26 > x

rewrite

x < 26 in

2) 11+x > 15

x> 15-11

x > 4 in

therefore

Aziza's claim is incomplete

The third side can be any length as long as it is greater than 4 in and less than 26 in

Answer:

Aziza’s claim is not correct. The third side must be between 4 in. and 26 in.

Step-by-step explanation:

Answer:

{2,8}

Step-by-step explanation:

This is the same thing as asking what element (in this case what number) is in all 3 sets.

0 isn't in all 3 sets because it isn't in B.

2 is in all 3 sets

3 isn't because it isn't in C

4 isn't in A.

6 isn't in C.

8 is in all 3 sets.

9 isn't in A

So the elements that are in the 3 sets are {2,8}.

Answer:

8.3

Step-by-step explanation:

Let Ao be the original amount and A the amount after t days.

Then we have the exponential function

     A = Ao(1 - x)^t or

A/Ao = (1 - x)^t

When t = 8, A/Ao = 0.5

         0.5 = (1 - x)^8

(0.5)^(1/8) = 1 - x

     0.917 = 1 - x

            x = 1 - 0.917 = 0.083 = 8.3 %

The substance decays by 8.3 % each day.

Answer: (1, -7) (11, -7)

Step-by-step explanation:

The foci of the hyperbola whose equation is (1,−7) and (11,−7).

The hyperbola is horizontal, we will count 5 spaces left and right and plot the foci there.

We need to use the formula [tex]\rm c^ 2 =a^ 2 +b^ 2[/tex] to find c.

The given equation of the hyperbola is;

[tex]\rm \dfrac{(x-6)^2}{16}-\dfrac{(y+7)^2}{9}=1[/tex]

Here a^2 is 16 and b^2 =9.

Substitute all the values in the formula

[tex]\rm c^ 2 =a^ 2 +b^ 2\\\\\rm c^ 2 16+9\\\\\rm c^2=25\\\\c^2=5^2\\\\c=5[/tex]

The center of the hyperbola is (6, -7).

The foci of the hyperbola whose equation is;

( 6 +5 , -7), (6-5, -7)

(11, -7), (1, -7)

Hence, the foci of the hyperbola whose equation is (1,−7) and (11,−7).

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Answer:

B)  Total price of cakes depend on the number of boxes.

Step-by-step explanation:

Given: Graph

To find : Based on the graph, which of the following statements is true.

Solution : We have given graph between total price of cupcakes and number of boxes.

We can see from the graph is linear graph that is straight line graph passing through the origin.

It shows the Directly relation between total price of cakes and number of boxes.

Number of boxes ∝Total price of cakes.

So, Total price of cakes depend on the number of boxes.

Therefore, B)  Total price of cakes depend on the number of boxes.

Answer:

Step-by-step explanation:

This is a combination problem from stats.  We have a total of 12 English books from which you have to 3.  The order in which you pick them doesn't matter, you only need to determine how many different combinations are available to you.  This is the combination formula, then:

₁₂C₃ = [tex]\frac{12!}{3!(12-3)!}[/tex]

I'm just going to simplify the right side and leave off the left side til the end of the algebra because it's easier.  The right side simplifies to

[tex]\frac{12*11*10*9!}{3*2*1*9!}[/tex]

The 9!'s cancel each other out, leaving you with

[tex]\frac{12*11*10}{3*2*1}=\frac{1320}{6}[/tex]

Therefore,

₁₂C₃ = 220 possible different combinations of English books from which to pick.

We'll do the same for History, which has a combination formula that looks like this:

₈C₂= [tex]\frac{8!}{2!(8-2)!}[/tex]

That right side expands to

[tex]\frac{8*7*6!}{2*1*6!}[/tex]

The 6!'s cancel each other out, leaving you with:

[tex]\frac{8*7}{2*1}=\frac{56}{2}[/tex]

Therefore,

₈C₂ = 28 possible different combinations of History books from which to pick.

You may or may not need to add those together to get the answer your teacher is looking for.

Answer:

(B)  this is not binomial function

Step-by-step explanation:

Given data

sample card n = 4 cards

total card number N =  52 cards

red card = 26

black card = 26

to find out

X be the number of cards that are red. (A) Binomial(B) Not binomial

solution

we know that 4 is selected with out replacement from 52 cards

we can say that R item is as success , here R is Red card

so that  52 - R items will be as failures

and we know

failure = 52 - 26 = 26 that is equal to 26 black card

we know this is Hyper geometric function

so this is not binomial function