Dale travels from city A to city B to city C and back to city A. Each city is exactly 120 miles from the other two. His average rate from city A to city B is 60 mph. His average rate from city B to city C is 40 mph. His average rate from city C to city A is 24 mph. What is Dale's average rate for the entire trip, in miles per hour?

Answer:

Step by-step explanation:

Speed v = 12km/h = 12/60km/min

Time t = 75min =

Distance d = ?

V = d/t

12/60 = d/75

Cross multiply

60d = 75 × 12

60d = 900

d = 900/60

d = 15km

To find the values of x and y requires solving equations, refining the solution through iterative methods like the extended Newton-Raphson technique, and validating results with approximation checks.

In answering this mathematical question, we are attempting to find specific values for the variables x and y. To solve for these variables, we employ various mathematical methods such as the Newton-Raphson technique for refinement.

Keeping the referenced data in consideration, the equations provided reveal that we manipulate these equations to gradually reach a more accurate result. For instance, taking the quadratic equation y²-0.30068y +0.022500 = 0 and using the quadratic formula y = 0.30068 ± √(0.30068)² – (4)(1)(0.022500) allows us to find the value for y, and an iterative process enhances the precision of x and y.

Remember to always retain a few extra significant figures to minimize rounding errors in the computational process. Additionally, entering our data into a calculator or a computer program will help in writing the linear equation, which needs to be rounded to an appropriate number of decimal places for accuracy. Examples mentioned illustrate evaluating the coordinates of a point, substituting values into equations, and analyzing the relation between variables through a graphical approach.

To validate our results, we compare the approximation to the actual value to ensure that our error margin is acceptable, especially when dealing with extrapolations from implicit differentiation in calculus contexts.

Answer:

  1/16

Step-by-step explanation:

Area is the product of linear dimensions.

Suppose the area of the triangle is the product of two dimensions p and q*:

  A = pq

Then the smaller triangle will have an area that is ...

  A = (1/4p)(1/4q) = (1/4)²pq = (1/16)pq . . . . . . 1/16 of the original area

__

If each of the linear dimensions of the triangle is multiplied by 1/4, the area will be multiplied by (1/4)² = 1/16.

_____

* No doubt, you have learned the area formula for a triangle is ...

  A = (1/2)bh

In the above, we might have p=1/2b and q=h. Or, there could be some other relationship between triangle dimensions and p and q.

Answer:

[tex]Give\ Two\ expressions\ are\ equivalent.[/tex]

Step-by-step explanation:

[tex]First\ expression=7^2+4x\\\\At\ x=2,\ value\ of\ first\ expression=7^2+4\times 2=49+8=57\\\\Second\ expression=4x+(7\times 7)\\\\Second\ expression=4x+7^2\ \ \ \ \ \ \ \ \ \ \ as\ m\times m=m^2\\\\Second\ expression=7^2+4x\ \ \ \ \ \ \ \ using\ commutative\ property\ of\ addition\\\\At\ x=2,\ value\ of\ second\ expression=7^2+4\times 2=49+8=57\\\\Hence\ these\ two\ expressions\ are\ equivalent.[/tex]

Answer:

  $2.40

Step-by-step explanation:

You have ...

  finance charge = 1.2% × unpaid balance

     = 0.012 × $200 . . . . . fill in the value of unpaid balance

  finance charge = $2.40

Answer:

Therefore the area of the quadrilateral =35 cm²

Step-by-step explanation:

Given, the length of one of diagonal of quadrilateral is 10 cm and perpendicular drawn from the opposite vertices to this diagonal are the length of 2.8 cm and 4.2 cm.

A diagonal divided a quadrilateral into two triangle.

Therefore the area of the quadrilateral

= sum of the area of the triangles

[tex]=(\frac{1}{2}\times 10\times 2.8+ \frac{1}{2}\times 10\times 4.2)[/tex]cm²      [ area of a triangle[tex]= \frac{1}{2}\times base\times height[/tex]]

=35 cm²

The area of flying disk is 452.16 square centimeters

Step-by-step explanation:

The disc is in circular shape so we will use the formulas for circle in this question.

Given

Circumference = C = 75.36 centimeters

We have to find the area of the disc for which we have to find the radius first.

Let r be the radius

Then

Circumference is given by:

[tex]C=2\pi r[/tex]

putting the values

[tex]75.36 = 2*3.14*r\\75.36 = 6.28r[/tex]

Dividing both sides by 6.28

[tex]\frac{6.28r}{6.28} = \frac{75.36}{6.28}\\r = 12\ cm[/tex]

The area of circle is given by:

[tex]A = \pi r^2[/tex]

Putting the values

[tex]A = 3.14 * (12)^2\\A = 3.14*144\\A =452.16\ cm^2[/tex]

Hence,

The area of flying disk is 452.16 square centimeters

Keywords: Circle, area

Learn more about circle at:

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Answer:D

Step-by-step explanation:

Multiply the cost of the house by 0.18.

Answer:

[tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Slope = [tex]\frac{4-(-1)}{3-0} =\frac{5}{3}[/tex]

Answer:

This is Equivalence system of equations. The first equation in B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2

Yo sup??

Equation of the given line is

y=12 - 0.5x

on the y axis the x coordinate will be , therefore at x=0 we get

y=12 - 0.5*0

y=12

Therefore the coordinates of the y intercept are (0,12).

Hope this helps.

Final answer:

The y-intercept for the equation y = 12 - 0.5x is found by setting x to 0, resulting in y = 12, giving us the coordinates of the y-intercept as (0, 12).

Explanation:

The equation of a straight line is given by y = mx + b, where m represents the slope of the line, and b is the y-intercept. In your case, the equation is y = 12 - 0.5x. To find the coordinates of the intercept on the y-axis, we set x to 0 and solve for y. This gives us the y-intercept directly from the equation without needing to graph it.

For the equation y = 12 - 0.5x, when x = 0:

y = 12 - 0.5(0)

y = 12 - 0

y = 12

Therefore, the coordinates of the intercept on the y-axis are (0, 12).

Answer:

$36.94

Step-by-step explanation:

Okay, so. This is what we do. There is two magazines and they cost 9.95 each multiply 9.95 times 2

9.95 x 2 = 19.90

Okay, then he buys a book for 14.95 we add 19.9. and 14.95

19.90 + 14.95 = 34.85

Then we have a sales tax of 6% we would multiply 34.85 time 6%

34.85 x 6% = 2.09

Then we would add. 34.85 + 2.09

34.85 + 2.09 = 36.94

Therefore your answer is $36.94

Hope this helps!!!

The answer is $36.94. You add up the total purchases, multiply them by .06, then add that number to you total purchases.

Answer:

x+y>1

Step-by-step explanation:

96 m

2 m/sec²

Step-by-step explanation:

Step 1:

In a velocity and time graph , the area which is under the plotted line represents the distance traveled

In the given graph , the plotted line from t=0 to t=4 ( for the first 4 secs) is a   triangle with base = 4 and height = 8

Area of this triangle is (1/2) * b * h = (1/2)* 4*8 = 16 m

Step 2 :

The plotted line from t = 4 to t = 14 is a rectangle with length equal to 10 and breadth equal to 8

Hence its area = length * breadth = 10 * 8 = 80 m

Step 3 :

Total  distance traveled is 80 + 16 = 96 m

Step 4 :

In the velocity time graph , slope denotes the acceleration at any given time. Since we want the acceleration for the first 4 secs, we need to find  slope of  line in from t = 0 to t= 4

when t = 0, v =0 and t= 4, v = 8

Slope = 8-0/4-0 =2 m/sec²

Answer:

The quotient is 345.5

Step-by-step explanation:

Check image

Final answer:

To find the quotient of 1,382 divided by 4, divide each place value separately. The quotient is 343 with a remainder of 2.

Explanation:

To find the quotient of 1,382 divided by 4, we divide the thousands, hundreds, tens, and ones place separately. Starting from the leftmost digit, we divide 1,382 by 4.

4 divided by 1 is 0 with a remainder of 4. Bring down the next digit 3. So, we have 43. Next, divide 43 by 4. 4 divided by 43 is 10 with a remainder of 3. Bring down the next digit 8. So, we have 38. Finally, divide 38 by 4. 4 divided by 38 is 9 with a remainder of 2.

Therefore, the quotient of 1,382 divided by 4 is 343 remainder 2.

Answer:

Slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].

Step-by-step explanation:

The slope of the line can be determined by simplifying the given equation to its standard form.

In the standard form, y =  mx + c, m represents the slope of the line.

We are given: [tex]$ y - 2 = - \frac{2}{3}(x + 1) $[/tex]

[tex]$ \implies y = -\frac{2}{3}x - \frac{2}{3} + 2 $[/tex]

[tex]$ \implies y = - \frac{2}{3}x + \frac{(-2 + 6)}{3} $[/tex]

[tex]$ \implies y = -\frac{2}{3}x + \frac{4}{3} $[/tex]

Comparing it with the standard equation, we can see that the slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].

Hence, the answer.

[tex]\text{Hey there!}[/tex]

[tex]\bf{What\ is\ greater: \dfrac{3}{10}, \dfrac{1}{2},\&\dfrac{2}{5}?}[/tex]

[tex]\bf{Well, let's\ turn\ our\ fractions\ into\ decimals\downarrow}[/tex]

[tex]\bullet\ \bf{\dfrac{3}{10}=0.30(also\ known\ as\ 0.3)}\\\\\bullet \ \bf{\dfrac{1}{2}=0.50(also\ known\ as\ 0.5)}\\\\\bullet \ \bf{\dfrac{2}{5}=0.40(also\ known\ as\ 0.4)}[/tex]

[tex]\bf{The\ fractions\ in\ percentages\downarrow}[/tex]

[tex]\bullet \ \mathsf{\dfrac{3}{10}=30\%}\\\\\bullet \ \mathsf{\dfrac{1}{2}=50\%}\\\\\bullet \ \mathsf{\dfrac{2}{5}=40\%}[/tex]

[tex]\text{Now that we have that out the way. Let's solve for your answer!}[/tex]

[tex]\bf{\dfrac{1}{2}}\rightarrow\dfrac{2}{5}\rightarrow\dfrac{3}{10}}}} \leftarrow( that's\ for\ GREATEST\ to\ LEAST)[/tex]

[tex]\boxed{{\bf{Answer: \dfrac{1}{2}\ would\ be\ your\ GREATEST\ or \ BIGGEST\ one}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

5 + 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Multiply top and bottom by sqrt(3) + sqrt(2)

Top = (sqrt (3) + sqrt(2)) * (sqrt(3) + sqrt(2))

Top = 3 + sqrt(6) + sqrt(6) + 2

Top = 5 + 2sqrt(6)

Bottom = (sqrt (3) - sqrt(2)) * (sqrt(3) + sqrt(2))

Bottom = (3 - sqrt(6) + sqrt(6) - 2)

Bottom = 1

So, the answer is 5 + 2[tex]\sqrt{6\\}[/tex]

Answer: 5+2√6

Step-by-step explanation: attachment

Answer: 4)

Step-by-step explanation:

Answer:

1st one is 3, 2nd is 4

Step-by-step explanation:

Final answer:

The volume of a pyramid with a height of 215 units and a square base of 339 units on each side is calculated using the formula V = (1/3)Bh, resulting in a volume of 1,304,688.67 cubic units.

Explanation:

To find the volume of a pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. If the base is a square with each side being 339 units, then the area of the base (B) can be calculated as 339×339 square units. Given the height (h) of the pyramid is 215 units, the volume can then be calculated.

First, calculate the area of the base:
B = 339×339 = 114921 square units.

Then, use the volume formula by plugging in B and h:
V = (1/3)×114921×215 = 1,304,688.67 cubic units.

Therefore, the volume of the pyramid is 1,304,688.67 cubic units.

The value of expression when n = 3 is 22

Solution:

Given expression is:

[tex]\frac{6(n^2 + 2)}{n}[/tex]

We have to find the value of expression when n = 3

Substitute n = 3 in given expression

[tex]\rightarrow \frac{6(3^2 + 2)}{3}\\\\Simplify\ the\ above\ expression\\\\\rightarrow \frac{6(9+2)}{3}\\\\Solve\ the\ terms\ inside\ the\ bracket\\\\\rightarrow \frac{6(11)}{3}\\\\Divide\ 6\ by\ 3 \\\\\rightarrow 2 \times 11 = 22[/tex]

Thus the value of expression when n = 3 is 22

Answer:

22

Step-by-step explanation:

Following the slope of the line at x= 0 the line is at y =1 , at x=, it is at Y = 1.5, so the slope is 1/2

The y intercept is where the line crosses the y a is at x =0 which is 1

The equation would be y = 1/2x+ 1

Answer:

y = 1/2x+ 1

Step-by-step explanation:

The result of the given expression 12 5/6x - 14x + 1/6x  is -x

Given the expression

12 5/6x - 14x + 1/6x

Convert the mixed fractions into improper fractions as shown:

[tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]

Collect the like terms;

[tex]= \frac{77}{6} x+\frac{1}{6}x - 14x\\= \frac{77x+x}{6} - 14x\\= \frac{78x}{6} - 14x\\= 13x - 14x\\= -x[/tex]

Hence the result of the given expression is -x

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The simplified form of the expression is -x .

Given, expression [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex] .

Expression:  [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex]

Firstly solve the mixed fraction.

[tex]12\frac{5}{6} x\\= \frac{77}{6}x[/tex]

Rewriting the expression :

= [tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]

Solve the terms with common denominator.

= [tex]\frac{77+1}{6} x[/tex]

= [tex]13x[/tex]

Solve the like terms,

[tex]= 13x - 14x\\\\=- x[/tex]

Hence the simplified form of expression is -x .

Know more about expressions,

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63 divided by 9 is 7, so -7+7 is 0

Hope this helped

Answer:

0

Step-by-step explanation:

using PEMDAS

63/9 = 7

-7 + 7 = 0

f(x) = 2([tex]2^{x}[/tex])

Step-by-step explanation:

Step 1 :

Given

When  x =0, f(x) = 2

x =1, f(x) = 4

x =2, f(x) = 8

x =3, f(x) = 16

Step 2 :

Substituting for x in the function f(x) = 2([tex]2^{x}[/tex]) we get,

When  x =0, f(x) = 2

x =1, f(x) = 4

x =2, f(x) = 8

x =3, f(x) = 16

This matches the given sequence and this shows that the function represents the given sequence .

Final answer:

The function rule for the given sequence 2, 4, 8, 16, ... is [tex]f(x) = 2^x[/tex], representing the sequence's exponential growth pattern where each term is double the previous term.

Explanation:

The given sequence is 2, 4, 8, 16, ..., which is a geometric sequence where each term is multiplied by 2 to get the next term. This pattern corresponds to an exponential function where the base is 2 and the exponent is the position of the term, which can also be thought of as the function's input, x. Therefore, the function that represents this sequence is f(x) = 2x.

The other function choices given, such as f(x) = 2x + 2 or f(x) = 2, do not correctly represent the pattern observed in the sequence. The correct function rule for the given sequence is f(x) = 2x which fits the pattern where when x is substituted for each term's position (starting from 0), the function provides the corresponding term of the sequence.

area = sum of parallel sides . height/2

= (5.9 + 16.3) 4.6/2

= 22.2 . 2.3

= 51.06 m²

so the answer is A

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by  

3

gives the next term. In other words,  

a

n

=

a

1

⋅

r

n

−

1

.

Geometric Sequence:  

r

=

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of  

a

1

=

5

and  

r

=

3

.

a

n

=

(

5

)

⋅

(

3

)

n

−

1

Remove parentheses.

a

n

=

5

⋅

3

n

−

1

Answer:

A (5x + 3)(5x – 3)

B (7x + 4)(7x + 4)

E (x – 9)(x – 9)  

F (–3x – 6)(–3x + 6)

in other words, A,B,E, and F on edge-nuity. just completed with 100%

Step-by-step explanation:

Answer:

y = 38°

Step-by-step explanation:

If Angle x and angle y are complementary, then x + y = 90°

Also, if angle x is supplementary to a 128 angle, then x + 128° = 180°.

Solving the latter equation for x, we get x = 52°.

Therefore, by the first equation, x + y = 90° becomes 52° + y = 90°, yielding

y = 38°

Answer:

[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]

[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for the measures of angles x and y.}[/tex]

[tex]\textsf{First, x is supplementary to an angle that equals 128}^{\circ}.[/tex]

[tex]\Large\underline{\textsf{What are Supplementary Angles?}}[/tex]

[tex]\textsf{Supplementary angles are 2 or more angles that add up to \underline{180}}^{\circ}.[/tex]

[tex]\large\underline{\textsf{This means that;}}[/tex]

[tex]\mathtt{x+128^{\circ}=180^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Subtract 128 from both sides for x:}}[/tex]

[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]

[tex]\Large\underline{\textsf{What are Complementary Angles?}}[/tex]

[tex]\textsf{Complementary angles are 2 or more angles that add up to \underline{90}}^{\circ}.[/tex]

[tex]\large\underline{\textsf{This means that;}}[/tex]

[tex]\mathtt{x+y=90^{\circ}.}[/tex]

[tex]\textsf{Because we know x, we can solve for y.}[/tex]

[tex]\large\underline{\textsf{Substitute:}}[/tex]

[tex]\mathtt{52^{\circ}+y=90^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Subtract 52 from both sides for y:}}[/tex]

[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]