Write an equation of a parabola with vertex at the origin and the given focus.
focus at (-1,0)

Area of hexagon is 93.531cm².

In the given statement is:

A regular hexagon is inscribed in a circle with a diameter of 12 centimeters.

Diameter of a circle = 12 cm.

⇒Radius of a circle = 6cm.

Length of side of hexagon = 6cm

Area of regular hexagon = (3/2) × √3 × (side)²

⇒Area of regular  hexagon =  (3/2) × √3 × (6)²

                                              = (3/2) × √3 ×36

                                              = 54 × √3

                                              = 93.531cm².

Hence, area of hexagon is 93.531cm².

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By combining the like terms, the simplified form of the expression 6r+3s+2s+4r is 10r+5s

Given,

The expression = 6r+3s+2s+4r

Rearrange the terms

6r+4r+3s+2s

Combine the like terms

6r+4r+3s+2s=(6+4)r+(3+2)s

=10r+5s

Hence, By combining the like terms, the simplified form of the expression 6r+3s+2s+4r is 10r+5s.

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2 and -2 both are the solution of the equation x/2 = 2/x.

According to the given question.

We have an equation 2/x = x/2.

As we know that, as we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.

Therefore, the solution of the equation 2/x = x/2 is given by

2/x = x/2

⇒ 2  = (x/2)x    (multiplying both the sides by x)

⇒ 2 = x^2/2

⇒ 2(2) = x^2  (multiplying by 2 both the sides by 2)

⇒ 4 = x^2

⇒ x^2 = 4

⇒ x = √4

⇒ x = ±2

⇒ x = 2 or -2

Now we will check 2 is the solution of the given equation or not.

Therefore,

LHS = 2/2 = 1

RHS = 2/2 = 1

Here, LHS = RHS. Therefore, 2 is the solution of the given equation.

Similarly, for -2

LHS = 2/-2 = -1

RHS = -2/2 = -1

Here. RHS = LHS. Therefore, -2 is also the solution of the given equation.

Hence, 2 and -2 both are the solution of the equation x/2 = 2/x.

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Given that the two angles form a linear pair, the measure of each angle is 40° and 140°.

The sum of angles of a linear pair is always equal to 180°.

Given the data the data in the question;

Let x represent the measure of the first angle.

Since the sum of angles of a linear pair is always equal to 180°.

m∠1 + m∠2 = 180

x + 3.5x = 180

Solve for x

4.5 = 180

x = 180/4.5

x = 40

Hence,

Measure of angle 1 = x = 40°

Measure of angle 2 = 3.5x = 3.5(40) = 140°

Given that the two angles form a linear pair, the measure of each angle is 40° and 140°.

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The pilot's distance is increasing.

In the graph, we can see distance on y axis and time on x axis. It is clearly visible that at 2 minutes, the distance covered is 0.4 miles. Further, at 4 minutes, the distance covered increases to 0.8 miles. At 6 minutes, the distance covered again increases by 0.4 miles and is 1.2 miles. At 8 minutes, the distance covered in 1.6 miles, which again increases by 0.4.

Now, it is evident that distance is increasing.

We can further calculate the speed using given information -

Speed = distance/time

Total distance = 1.6 - 0.0

Total distance = 1.6 miles

Total time = 8 - 0

Total time = 8 minutes

Speed = 1.6/8

Speed = 0.2 miles per minute.

Hence, the distance of pilot is increasing at constant rate or speed of 0.2 miles per minute.

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The complete question and figure is attached -

The graph below represents the distance a pilot is from the home airport during a period of time. A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0.0, 0.4, 0.8, 1.2, 1.6. Which describes the pilot’s distance in section I? zero constant decreasing increasing

Answer:

x = 0

Step-by-step explanation:

Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function

For f(x) set the denominator = 0 and solve for x

For [tex]\frac{1}{x^2}[/tex]

set x² = 0

x = √0  = 0 which is the vertical asymptote

Answer:

x = 0

Step-by-step explanation:

The Vertical asymptotes are vertical lines which correspond to zeroes of denominators.

For f(x) set the denominator = 0 and solve for x

For \fract {1}{x^2}

you set x² = 0

x = √0 = 0 which is the vertical asymptote

Answer:

0.0000002702

Step-by-step explanation:

2.702 * 10^-7

The seventh term of the given geometric sequence is: [tex]\frac{4}{625}[/tex].

Given: 100, 20, 4, ....

Here, a₁ = 100, r = [tex]\frac{100}{20}=\frac{20}{4}=\frac{1}{5}[/tex], for the given geometric progression.

In the formula: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 7, a₇ = 100 ([tex](\frac{1}{5})^{7-1}[/tex]

=> a₇ = 100 [tex](\frac{1}{5})^6[/tex]

=> a₇ = 4([tex]\frac{1}{625}[/tex])

Hence, The seventh term of the given geometric sequence is: [tex]\frac{4}{625}[/tex].

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The equation of the line in point-slope form, which passes through the pair of points located at (0 , 0) and (-4 , -5), is y + 5 = 5/4(x + 4).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (0 , 0) and (-4 , -5)

m = (y2 - y1)/(x2 - x1)

m = (-5 - 0)/(-4 - 0)

m = -5/-4

m = 5/4

Using the point slope form, plug in the values of the slope and Point A to set up the equation.

(y - y1) = m(x - x1)

where m = 5/4 and (x1 , y1) = (-4 , -5)

(y - -5) = 5/4(x - -4)

y + 5 = 5/4(x + 4)

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Answer:

Not possible without knowing what the spinners are

The probability that the camper is heading in the N to NE direction when a camper lost in the woods points his compass in a random direction is 1/8.

As given,

Compass is divided into 8 sectors N→NE→E→SE→S→SW→W→NW→N

Whole compass represents the circle with area 360 degrees

Area of each sector is equal to 45 degrees

Probability that the camper is heading in the N to NE direction

=45/360

=1/8

Therefore, the probability that the camper is heading in the N to NE direction when a camper lost in the woods points his compass in a random direction is 1/8.

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Step-by-step explanation:

35×35 may be ?? ..........

The slope of the line that contains the given points E(6,3) and, F(-6,3) is 0.

It is given in the question that the line contains the points E(6,3) and F(-6,3).

We know that:-

The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-

m = (d-b)/(c-a)

Here, we have

m = slope of the line

(a,b) = (6,3)

(c,d) = (-6,3)

Hence, putting the values of (a,b) and (c,d) , we get

Slope of the line that contains the given points E(6,3) and, F(-6,3) is given by:-

(3-3)/(-6-6) = 0/-12= 0

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Answer:

I hope it's helpful.........

The mean temperature change between the two cold seasons is (b) went up by 0.3°

The given parameters are:

2011-2012:

2012-2013:

The mean is calculated as

Mean = Sum/Count

So, we have

2011 - 2012 mean = (61.1 + 51.9 + 53.6 + 56.5)/4

Evaluate

2011 - 2012 mean = 55.8

Also, we have

2012 - 2013 mean = (64.2 + 56.8 + 48.3 + 55.1)/4

Evaluate

2012 - 2013 mean = 56.1

The difference in these mean values are

Difference = 56.1 - 55.8

Evaluate

Difference = 0.3

Hence, the mean temperature change between the two cold seasons is (b) went up by 0.3°

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Answer: C

Step-by-step explanation:

6 planes

Answer: C, 6)

Step-by-step explanation: Area of square = a2 Square units, where a is the side length of square.

Area of rectangle = l × b Square units, where l is the length, b is the breadth.

Area of circle = π × r2 Square units, where r is the radius of a circle.

Step-by-step explanation:

In order to get answer of this question, we should use the distance formula. So, what is that formula? let us see the formula and simplify to get the answer :)

[tex]{ \red{ \tt{given}}}[/tex]

[tex]{ \orange{ \tt{(1, - 1)}}} = { \green{ \tt{(x1,y1)}}}[/tex]

[tex]{ \orange{ \tt{(7,8)}}} = { \green{ \tt{(x2,y2)}}}[/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{ {(x1 - x2)}^{2} + ( {y1 - y2)}^{2}}}}}[/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt \sqrt{ {(1 - 7)}^{2} + { (- 1 - 8)}^{2}}}}[/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{ {(6)}^{2} + {( - 9)}^{2}}}}} [/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{36 + 81}}}}[/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{117}}}} [/tex]units.

Answer: x=-20/3

Step-by-step explanation:

6(x + 1) = 3x - 14

6x+6 = 3x - 14

6x-3x+6 = 3x-3x - 14

3x+6 = -14

3x+6-6=-6-14

3x=-20

x=-20/3

Answer:0-ounce package of cashews costs $8.11 is better then a 16-ounce package of cashews costs $12 , because cost per ounce for the 10-ounce package of cashews = $ is greater then cost per ounce for the 16-ounce package of cashews = $

Step-by-step explanation:

In order to get standard deviation of 15. Subtract 68 from everybody's score, then divide these values by 15.

The square root of the variance is used to determine the standard deviation. An alternative method of calculating it is to identify the mean of a data set, compare each data point to the mean, square the differences, add them all together, divide by the number of points in the data set minus 1, and then compute the square root.

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Mr. Olsen uses an unusual grading system in his class. After each test, he transforms the scores to have a mean of 0 and a standard deviation of 1. Mr. Olsen then assigns a grade to each student based on the transformed score. On his most recent test, the class's scores had a mean of 68 and a standard deviation of 15. What transformations should he apply to each test score? Explain.

The required linear equation is of the form 54.5 + 5 g = 74 , and Caroline can use 3.9 gigabytes of data to stay within budget.

There are about one or two variables in a simple linear equation. In a linear equation, no variable can be multiplied by a numerical  value that is greater than one used as the fraction 's denominator.

Let us consider that Caroline uses g gigabytes of data for the month.

Therefore total cost incurred by her in one month = 54.5 + 5g

She wants to keep the value of her monthly bill at $ 74.

Therefore we can write a linear equation to solve this problem:

    54.5 + 5 g = 74

or, 5 g = 74 - 54.5

or, g = 19.5 ÷ 5

or, g = 3.9

Therefore Caroline can get maximum of 3 gigabytes of data if she wants to keep the budget below $74 .

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Answer:

c

Step-by-step explanation:

If you look at the two points on the graph you can see that the point that crosses the y axis is at -4

If you use the two points and count the slope you see that it is down 5 over 6 which gives it a slope of -5/6

Answer:

The flud dram (or flud drahm in British speling) is defined as 1⁄8 of a flud ones is is british words cop to nuber of a flud, and is ecactly ewelual to 3696691 ml in the U.S. cutomary 3.551632 ml in the British can of fluding can keep it from fluding over are heads and keep it safe from fluding but 3696691 is the number that you haft to use  it  order to keep it up you haft to put it in the same order

Number of Fluid Drams 88888

Number of Fluid Ounces 1 2 3 4 5

Number of Fluid Drams 8 9 10 11 12 A fluid dram is a unit of capacity. One fluid ounce is equivalent to eight fluid drams. Which table represents the relationship between number of fluid ounces a...

0.00

0 votes

0

In the apothecary system, the symbol fl ℥ represents a/an A. pound. B. grain. C. fluid ounce. D. dram

The expression that is a difference between two terms is:

5y - 7

An algebraic expression should have at least one variable, and here we know that we should find a difference (remember that a difference is a subtraction).

And it must have two terms, then the expression is something like:

A - B

Such that A or B depend on the variable.

With this in mind, we can see that the correct option (the only subtraction with two terms) is the first one:

5y - 7

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The coordinate of C=(4,0).

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Given:

ΔABC with

A(3, 0), B(7, 3)

let the coordinate of c(x, y)

Also, Perimeter of triangle = 2 * Area of triangle

Area of triangle=1/2 * b * h

Area=1/2 * 4 * 3

Area=1/2 * 12

Area=6 units

Perimeter= AB + BC + CA

Now,

Now, using distance formula

AB = √(7-3)² + (3-0)²

AB = √16+9

AB= 5 units

Perimeter of triangle=5+4+3

Perimeter =12

So, the coordinate of C=(0+4,0)

C=(4, 3-3)

C=(4,0)

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Using different mathematical operations, the price of a slice that is all vegie is calculated to be $1.25.

What are arithmetic operations?

Arithmetic operations are a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics.

Given, Cost of the pizza = $10

and number of slices = 8 (half pepperoni and half veggie)

So, number of slices containing veggies = 8/2 = 4

and cost of 4 slices containing all veggie= 10/2 = $5

Therefore, value of a slice containing all veggie = 5/4 = $1.25

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The recursive formula for the arithmetic sequence [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d

A recursive formula is a sequence in which terms are defined using one or more previous terms which are given. If we know the nth term of an arithmetic sequence and you know a common difference, d, we can find the (n+1)th term using the recursive formula.

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d

The sequence -2, 7, 16, 25,.... is in arithmetic sequence and its common difference is 7 - (-2) = (16-7)= 9 .

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