A map has a scale of 1cm:4km the actual distance between the two cities is 52km. What is the distance between the two cities on the map

The equation of the ellipse having foci  (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].

Given the foci of ellipse is (±2,0) and vertices (±5,0).

We are required to find the equation of ellipse having foci (±2,0) and vertices (±5,0).

Equation is the relationship between two or more variables that are expressed in equal to form. Equation of two variables looks like ax+by=c.

Equation of ellipse is as under:

[tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex],where a is the semi major axis.

We have been given that a=5, c=2.

We know that [tex]c^{2} =a^{2} -b^{2}[/tex]

We have to find the value of b.

b=[tex]\sqrt{a^{2} -c^{2} }[/tex]

=[tex]\sqrt{5^{2} -2^{2} }[/tex]

=[tex]\sqrt{25-4}[/tex]

=[tex]\sqrt{21}[/tex]

Using the values of a and b in the equation [tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex]

[tex]x^{2} /(2)^{2} +y^{2}/\sqrt{21} ^{2} =1[/tex]

[tex]x^{2} /4+y^{2} /21=1[/tex]

Hence the equation of the ellipse having foci  (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].

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Based on the given task content; the simplification of 7x - x to its simplest form is 6x.

Simplify 7x - x

7x and -x

So,

7x - x

= 6x

Therefore, 6x is the result of the simplification of 7x - x to its simplest form.

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Parabolas could Lauren be describing are:

c) y2 = x

d) y2 = 10x

F)  y2 = 5x

The intersection of a cone with a plane that is parallel to the side of the cone results in the formation of a parabola, which is a symmetrical open plane curve. Under the influence of gravity, the route taken by a projectile takes the form of a curve similar to this one.

In the question that is presented to her, Lauren gives an example of a parabola that has a positive non-zero coordinate value on focus

Generally, the equation for focus is  mathematically given as

y=a(x-h)^2+k

In conclusion

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The mpg and hp is print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))

MPG is an abbreviation for 'miles-consistent with gallon and it is used to give you an indication of the fuel financial system of a vehicle or industrial vehicle. It helps you to work out how reasonably-priced or high-priced an automobile might be to run.

As for a new vehicle, an awesome MPG is around 50 to 60. Having this stepped forward gasoline economy facilitates minimizing going for walks fees and cheaper avenue tax due to decreased CO2 emissions. consistent with What car's featured blog, here are a number of the most gasoline-green automobiles in the marketplace nowadays.

The gas economic system of a car relates to the space traveled via an automobile and the quantity of fuel fed on. intake can be expressed in terms of the volume of gasoline to travel a distance, or the gap traveled according to the unit quantity of gasoline consumed.

The car has the “best” combination of mpg and hp, where mpg and hp must be given equal weight.

#sum the scaled values of mpg and hp and add a new column called combination

myCars$combination<-scale(myCars$hp)+scale(myCars$mpg)

#Which car has the best combination of mpg and hp?

print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))

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Answer:

Let's go part by part:

14 raised to 2 = 196

-9+7x2=-9+14 = 5

196/5= 39,2 (final result)

Answer:

-3.2

Step-by-step explanation:

14 SQUARED is 196

196 - 34 = 5.7647

- 9 + 7.2 = - 1.8

5.7647 / -1.8 = -3.2

-3.2 would be your answer.

Answer:

The answer is x=2 and y=0.

Step-by-step explanation:

The given Equations are:

                    5x-2y=10      ----------------- (i)
                    4y+20=10x   ----------------- (ii)

From equation find the value of x, that is:

         5x=10+2y         (Obtained By adding 2y on both side of Equation (i))

Next divide with 5 on both side to get x:

          x=(10+2y)/5           ------------------ (iii)

Put this value of x in equation (ii):

        4y+20=10((10+2y)/5)

Simplifying the above equation:

         4y+20=2(10+2y)

         4y+20=20+4y

From the above equation the solution of y is not possible.

We can make it 0. So,
         y=0

Put this value of y in equation (iii), to get value of x:

        x=(10+2(0))/5

        x=(10+0)/5

        x=10/5

        x=2

The two possible positions of point P are:

(3, -5) and (0.6, 5.8)

We know that point P lies on the line:

y = 4 - 3*x

And that the distance between P and the origin is √34, then if the coordinates of point P are (x, y), we have that:

[tex]\sqrt{34} = \sqrt{x^2 + y^2}[/tex]

Now, we can replace "y" in the distance equation by the linear equation, and also remove the square roots:

[tex]34 = x^2 + (4 - 3x)^2[/tex]

Now we can solve the quadratic equation for x:

[tex]34 = x^2 + 9x^2 + 16 - 24x\\\\10x^2 - 24x - 18 = 0\\\\[/tex]

The solutions are:

[tex]x = \frac{24 \pm \sqrt{(-24)^2 - 4*10*(-18)} }{2*10} \\\\x = \frac{24 \pm36}{20}[/tex]

So the two solutions are:

x = (24 + 36)/20 = 3

x = (24 - 36)/20 = -0.6

To get the points, we need to evaluate y on these values:

y = 4 - 3*3 = -5   So we have P = (3, -5)

y = 4 - 3*(-0.6) = 2.2 So we have the point (0.6, 5.8)

There are the two possible positions of point P.

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A vertically opposite angle is a pair of angles formed due to the intersection of two lines, and are said to be equal. Thus the angle that is the same as <BPD is <APC.

ii. The value of x is [tex]47^{o}[/tex].

The intersection of two or more lines at a point will always produce a set of angles. Some of these angles when compared may have similar measures or properties.

Two angles can be equal with respect to their measure if they are vertically opposite. Vertically opposite angles are angles formed when two lines intersect, such that a pair of opposite angles about the point of intersection are equal.

Thus from the given question, the angle that is the same as <PBD is <APC.

i.e <BPD ≅ <APC (vertically opposite property)

Also,

x + 133 = 180 (sum of angles on a straight line)

x = 180 - 133

  = 47

x = [tex]47^{o}[/tex]

Therefore the value of x is [tex]47^{o}[/tex].

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Answer:

[tex]\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}[/tex]

Step-by-step explanation:

Both lines in the given system of inequalities are linear equations.

Slope-intercept form of a linear equation:  y = mx + b

(where m is the slope and b is the y-intercept)

Positive slope (m):  as x increases, y increases.

Negative slope (-m):  as x increases, y decreases.

When graphing inequalities:

The inequality represented by the blue line has a positive slope and shading below the line.

⇒ y ≤ mx + b

From inspection of the graph, its y-intercept is 2.

⇒ y ≤ mx + 2

The inequality represented by the yellow line has a negative slope and shading above the line.

⇒ y ≥ -mx + b

From inspection of the graph, it's y-intercept is zero.

⇒ y ≥ -mx

The only pair of inequalities that satisfies the above conditions is:

[tex]\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}[/tex]

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A quantity of 84 shingles are required to cover the surface area of 336 square feet of the first roof.

A quantity of 110 shingles are required to cover the surface area of 220 square feet of the second root.

In this question we must determine both the surface area and the number of shingles to cover two roof configurations as well. In the first case, we calculate the surface area, which is the sum of the area of rectangles:

A = 2 · (8 ft) · (12 ft) + 2 · (6 ft) · (12 ft)

A = 336 ft²

And the number of shingles required to cover the root is:

n = (336 ft²) / (4 ft²)

n = 84

A quantity of 84 shingles are required to cover the surface area of 336 square feet of the first roof.

In the second, we only need to cover the very top surface. The area and the number of shingles are, respectively:

A = 2 · (5 ft) · (22 ft)

A = 220 ft²

n = (220 ft²) / (2 ft²)

n = 110

A quantity of 110 shingles are required to cover the surface area of 220 square feet of the second root.

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Answer:

60

Step-by-step explanation:

Answer: 60

Step-by-step explanation:

The largest integers of the numbers is 406.

The sum of five consecutive positive integers is 2020.

Therefore,

let

the first positive integer = x

Hence,

x + x + 1 + x + 2 + x + 3 + x + 4 = 2020

5x + 10 = 2020

5x = 2020 - 10

5x = 2010

x = 2010 / 5

x = 402

largest integer = 402 + 4 = 406

Therefore, the largest integers of the numbers is 406.

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Answer:

=========================

We need to make a stem and leaf plot

Rearrange the data in the ascending order:

Group the data as follows:

The first two digits form a stem and the last digits form a leaf.

Make a plot:

       Stem   |  Leaf

Assumed that sides are equal

CB

Answer: 2 and 3, or 3 and 2

Step-by-step explanation:

a + b = 5 so a = 5 - b

Substitute a = 5 - b into ab = 6; (5 - b)b =  6

5b - [tex]b^{2}[/tex] = 6

[tex]b^{2}[/tex] - 5b + 6 = 0

(b - 2)(b - 3) = 0

So b is either 2 or 3

So a is either 3 or 2 depending on what b is

Answer:

x = -9

Step-by-step explanation:

-18+24 = -2(x+6) Distribute and simplify

6 = -2x-12 Add 12 to both sides

18 = -2x Divide by -2 on both sides

-9 = x Here's your answer

Hope this helps! :D

First, do -2 times x. that is -2x.  Next, do -2 times +6. That should be -12. The last steps are in order, add 18 on both sides. it should be -18+18 and -12+18. now you have 24 on the left and -2x and +6. -6 on both sides. 6-6 and 24-6. now you have 18 and -2x. so get rid of the -2x by doing -2x/-2 and on the left side 18/-2. So the answer should be -9=x.

By the use of the completing the square method, the maximum height is 3 ±√29/4 + 9 m.

The maximum height has been modeled by the use of the equation f(x)= -4x^2 +24x -29. Now we know that f(x)= h so we can write;

h = -4x^2 +24x -29

Now we have;

0 = -4x^2 +24x -29

-4x^2 +24x -29= 0

x^2 - 6x = -29/4

(x - 3)^2 = -29/4 + 3^2

(x - 3)^2 =  -29/4 + 9

x = 3 ±√29/4 + 9 m

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If (x+5) is a factor of f(x) then the condition that will be true is f(-5)=0.

Given that (x+5) is a factor the polynomial f(x) and we are required to be the condition that will be true.

Polynomial is combination of algebraic terms may be in addition, subtraction, multiplication and division. If the highest power of variable in polynomial is one then it is said to be monomial ,If the highest power of variable in polynomial is two then it is said to be binomial,If the highest power of variable in polynomial is three then it is said to be trinomial and many more polynomials.

Factors are the numbers which when multiplied gives the number whose factors they are.

It is given that (x+5) is a factor of f(x).

Put (x+5)=0

x=-5

means when we are putting x=-5 then we will get 0.

Hence if (x+5) is a factor of f(x) then the condition that will be true is f(-5)=0.

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Answer:

This is the answer of this question. Hope it helps.

The factored form of the given trinomial is (x -7)(x +1)

From the question, we are to factor the given trinomials

The given trinomial is

x² + 6x - 7

The trinomial is a quadratic expression. The trinomial/ quadratic expression can be factored as a product of two binomial. When factored, the trinomial will take the form (x + a)(x + b)

Where are a and b are integers.

Factoring the trinomial

x² + 6x - 7

To factor the trinomial, we will find two numbers such that when added, we get the middle term; and when these numbers are multiplied we get the constant term.

The numbers that satisfy this condition are +1x and -7x

x² +x -7x - 7

x (x + 1) -7(x +1)

(x -7)(x +1)

Hence, the factored form of the given trinomial is (x -7)(x +1)

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......................

The total cost that company ABC uses to produce x graphing calculators in a month is given by y = 1.5x + 150

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard form of a linear function is:

y = mx + b

Where m is the rate of change and b is the initial value of y.

Let y represent the total cost of producing x calculators in a month, hence:

y = 1.5x + 150

The total cost that company ABC uses to produce x graphing calculators in a month is given by y = 1.5x + 150

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Using the linear equation, T = 20x + 31, the total number of computers at the end of 2005 is: C. 191.

A linear equation is expressed as y = mx + b, where x is a function of y, m is the rate of change and b is the y-intercept or starting value.

In the scenario stated, we are given the linear equation for total number of laptop computers at the school after 1997 as, T = 20x + 31.

Rate of change = 20

y-intercept/starting value = 31

x = 2005 - 1997 = 8

To find the total number of laptop computers at Grove High School at the end of 2005 (T), substitute x = 8 into the equation, T = 20x + 31.

T = 20(8) + 31

T = 160 + 31

T = 191 computers.

Thus, total number of computers at the end of 2005 is: C. 191.

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According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.

Herein we have a series in rational form, whose convergence can be proved by the ratio criterion, whose defintion is shown below:

x = lim (n → ∞) |aₙ/aₙ₊₁|   (1)

The series converges if x < 0 and diverges when x > 1. If x = 1, the criterion cannot be used and another criterion must be used instead. Now we proceed to apply it on the expression behind the series:

|aₙ/aₙ₊₁| = [(2 · n + 1) · (2 · n + 2)] / [5 · (n + 1)²]

|aₙ/aₙ₊₁| = [4 · n² + 5 · n + 2] / [5 · n² + 10 · n + 5]

Then, by applying the limit property for rational equations we find that limit of the expression within the series is:

L = 4 / 5

According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.

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By the ratio test, the series diverges.

[tex]\displaystyle \lim_{k\to\infty} \left| \frac{5^{k+1} ((k+1)!)^2}{(2(k+1))!} \cdot \frac{(2k)!}{(5^k (k!)^2}\right| = 5 \lim_{k\to\infty} \frac{(k+1)^2}{(2k+2)(2k+1)} = \frac54 > 1[/tex]

The number of servings of pasta were in the dish Lois made is 31.67.

Number of servings of pasta were in the dish Lois made = Number of cups of pasta Lois made / A serving of the pasta

= 6 1/3 ÷ 0.2

= 19/3 ÷ 0.2

= 19/3 × 1/0.2

= (19×1) / (3 × 0.2)

= 19/0.6

= 31.6666666666666

Approximately,

Number of servings of pasta were in the dish Lois made is 31.67 servings

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Based on the various costs resulting from the lease terms at the local dealership, the total cash to pay at signing is $5,480

This can be found by the formula:

= Down payment + Monthly payment + Security deposit + Acquisition fee

Solving gives:

= 4,100 + 475 + 415 + 490

= $5,480

In conclusion, option A is correct.

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Answer: B. $5005

Step-by-step explanation:

Answer: D

Step-by-step explanation: The line of best fit is a straight line that passes through as many points as possible and has around the same number of points above and below it. D meets those requirements the best.

Answer:

Line D

Step-by-step explanation:

Line D is most fit because it intercepts more of the dots on the graph, if not, comes close to touching the majority of them.

A polygon is a figure that has a given number of sides.

A polygon is an n - sided figure. The number of sides in a polygon is almost infinite. Let us now match the properties with the type of polygon.

a. 12.gon - An interior angle measures 150°

The polygon that has 12 sides is called the Dodecagon.

Given that the sum of the interior angles in a dodecagon is 1800, then  each interior angle is; 1,800/12

= 150°

b. 15-gon - An exterior angle measures 24°

The polygon that contains 15 sides is called pentadecagon. Given that the sum of the exterior angles of polygon is 360 degrees and each exterior angle is  24° then;

360/ 24° = 15 sides

c. 16-gon - The sum of the interior angles is 2,520°

The polygon that contains 16 sides is called the hexadecagon. The sum of its interior angles is 2,520° hence each interior angle measures; 2,520°/16 =  157.5°

d. 18-gon - An interior angle measures 160°

A polygon that contains 18 sides is called an octadecagon .

We have;

160 = (n−2) × 180° / n

160n = 180n - 360

360 = 20n

n = 18

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Missing parts;

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match the properties to the regular polygons they describe.

An interior angle measures 150".

An exterior angle measures 24.

The sum of the interior angles is 2520°.

An interior angle measures 160".

The sum of the exterior angles is 180º.

The sum of the interior angles is 2160°.

15-gon

16-gon

12.gon

18-gon

Answer:

Step-by-step explanation:

The second store offered the better buy at the price of $92.00.

What is better buy?

Better buy refers to the lowest price out of the prices offered by the three stores.

In order to determine the lowest price, the no discount price of the first store needs to be compared to the prices of  two other stores, bearing that after-discount price is the pre-discount price multiplied by 1 minus the discount rate.

First store price=$95.00

Second store after-discount price=pre-tax discount price*(1-discount rate)

pre-discount price=$115

discount rate=20%

Second store after-discount price=$115*(1-20%)

Second store after-discount price=$92.00

Third store after-discount price=pre-tax discount price*(1-discount rate)

pre-discount price=$105

discount rate=10%

Third store after-discount price=$105*(1-10%)

Third store after-discount price=$94.50

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