hiking up a mountain,you notice that the air temperature drops 10°c for every 1,000 meters increase in elevation to represent the decrease in temperature if you hike up the mountain 2,000 meters. Then evaluate the expression and explain it's meaning

Answer : option B

This graph shows the solutions to the inequalities

system of inequalities y>3x+14 and y<3x+2

the system of inequalities have solutions only when the shaded part satisfies the given inequalities

We are given with the graph of inequalities . The given inequalities have 'and' in between.

so we look at the graph where both inequalities intersects

From the graph we can see that there is no intersection part of both  shaded portions

So , we conclude that there is no solution.

Answer:

Step-by-step explanation:

There is no solution

Answer:

The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).

D=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√

D=(x2−x1)2+(y2−y1)2

Example

Find the distance between (-1, 1) and (3, 4).

This problem is solved simply by plugging our x- and y-values into the distance formula:

D=(3−(−1))2+(4−1)2−−−−−−−−−−−−−−−−−√=

D=(3−(−1))2+(4−1)2=

=16+9−−−−−√=25−−√=5

=16+9=25=5

Sometimes you need to find the point that is exactly between two other points. This middle point is called the "midpoint". By definition, a midpoint of a line segment is the point on that line segment that divides the segment in two congruent segments.

If the end points of a line segment is (x1, y1) and (x2, y2) then the midpoint of the line segment has the coordinates:

(x1+x22,y1+y22)

(x1+x22,y1+y22)

Step-by-step explanation:

To find the endpoint B given midpoint M and endpoint A, we use the coordinates of the midpoint formula and solve for the unknown values. Plugging the given values into the formula, we solve for B and find that the coordinates of B are (-5, 7).

In this particular instance, we are working with the concept of midpoints on a coordinate plane. Given that the point M(-3,5) is the midpoint of the segment AB and A(-1,3) is one endpoint, we are tasked to find the coordinates of point B, the other endpoint.

The formula for the coordinates of the midpoint is [(x1+x2)/2 , (y1+y2)/2]. This finds the average of the x-coordinates and y-coordinates of the two endpoints to find the point exactly in between, or the midpoint.

Since we are given one endpoint A(-1,3) and the midpoint M(-3,5) and are asked to find the other endpoint B, we should set up the equation using the known values and solve for the unknown values. We know that (-3,5) should equal [(-1+x2)/2 , (3+y2)/2]. Solving for x2 (x-coordinate of B) gives us x2 = -3*2 + 1 = -5. Solving for y2 (y-coordinate of B) gives us y2 = 5*2 - 3 = 7. Therefore, the coordinates of B are (-5, 7).

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Answer:

Duration of the tour he planned first is 8 days.

Step-by-step explanation:

Given that a person has 12000 rupees for his daily expenses.

Let x be the number of days.

Then daily expenses per day [tex]=\frac{12000}{x}[/tex]

Given that number of day is increased by 2 more days, that is number of days is x+2.

New daily expense per day [tex]\frac{12000}{x+2}[/tex]

Given that this new daily expenses are 300 less than original.

That is [tex]\frac{12000}{x}-\frac{12000}{x+2}=300[/tex]

              [tex]\frac{12000(x+2)-12000x}{x(x+2)}=300[/tex]

                  [tex]\frac{24000}{x(x+2)}=300[/tex]

                  [tex]x(x+2)=\frac{24000}{300}[/tex]

                    [tex]x^{2}+2x-80=0[/tex]

                    (x-8)(x+10)=0

                     x=8 or -10.

Since number of days cannot be negative, duration of the tour planned=8.

Answer:

468

Step-by-step explanation:

If the first term of a geometric series and the common ratio are known, then the sum of the infinite series is

                a

s      = --------------

               1 - r

In this particular case we have:

               156

s      = -------------- = 156/(1/3) = 468

               1 - 2/3

The sum of an infinite geometric series with a first term of 156 and a common ratio of 2⁄3 is 468. This is computed using the formula [tex]S = a / (1 - r).[/tex]

The sum of an infinite geometric series can be found by using the formula [tex]S = a / (1 - r)[/tex], where 'S' is the sum of the series, 'a' is the first term of the series, and 'r' is the common ratio. In this case, the first term 'a' is 156 and the common ratio 'r' is 2⁄3.

Substituting these numbers into the formula, we get: S = 156 / (1 - 2/3) . After calculating this expression, we find the sum of the series to be 468. Therefore, the sum of the infinite geometric series with a first term of 156 and a common ratio of 2⁄3 is 468.

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The square root of 300 is approximately 17.32, placing it between the integers 17 and 18. The square of 17 is 289, and 18 is 324, confirming this placement.

The square root of 300 falls between two consecutive integers. To find the closest integers, we can estimate the square root's value. The square root of 300 is approximately 17.32, as 17 squared is 289 and 18 squared is 324. Therefore, the square root of 300 is greater than 17 but less than 18.

In terms of integers, the square root of 300 is between 17 and 18. These are the closest integers that the square root of 300 falls between.

To further validate this, we can square both 17 and 18. The square of 17 is 289 (less than 300), and the square of 18 is 324 (greater than 300). This confirms that the square root of 300 indeed lies between 17 and 18.

In summary, the closest integers that the square root of 300 falls between are 17 and 18.

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The easy way to do this is:

Since the radius of the second circle is exactly 6 times the radius of the first circle, you could just multiply the circumference by 6:

9.42 x 6 = 56.52!  But let's double-check.

9 x 2 = 18    So, the diameter is 18.

18 x 3.14 = 56.52!     So, 56.52 is the correct answer!

Remark

The formula you should be using is

C = k*r because this is a variation question. There are ways of doing this without solving for k, but it is a good idea to solve for k first.

Givens

C = 9.42

r = 1.5

k = ??

K =

C = k*r

9.42 = k * 1.5

k = 9.42/1.5

k = 6.28 which is what it should be given that pi = 3.14. But you must check.

r = 9

C = k*r

C = 6.28 * 9

C = 56.52 which rounded = 57 to the nearest inch

57 Answer

22, 76, 238, 724, 2182

to generate the terms substitute n = 0, 1, 2, 3, 4 into the recursive function

[tex]a_{1}[/tex] = 3[tex]a_{0}[/tex] + 10 = ( 3 × 4 ) + 10 = 22

[tex]a_{2}[/tex] = 3[tex]a_{1}[/tex] + 10 = (3 × 22)+ 10 = 76

[tex]a_{3}[/tex] = 3[tex]a_{2}[/tex] + 10 = ( 3× 76) + 10 = 238

[tex]a_{4}[/tex] = 3[tex]a_{3}[/tex] + 10 = ( 3 × 238) + 10 = 724

[tex]a_{5}[/tex] = 3[tex]a_{4}[/tex] + 10 = (3 × 724) + 10 = 2182

Lets go through the steps

1) 1.22 + .89 = 2.11

2) 2.34 - 2.11 = .23

Jenny's frog jumped .23 meters further than Christina's frog.

I hope this helped!

Have a fantastic day!

Jenny's: 2.34

Chistina's: 1.22+0.89

The first thing you want to do is add 1.22 and 0.89 which is 2.11

Then too find how much further Jenny's frog jumped you subtract 2.34 and 2.11 which is 0.23.

Therefore your answer would be:0.23

First, we start with the product

so _________ * _________

Now, the first part of the product is 3+ (a number), n

so (3+n)*___________

And the other side is 8

(3+n)*8

or 8(3+n) =14

Let the number is x

Three more than a number: x  + 3

so the product of three more than a number and eight : 8(x + 3)

Now you can write he equation of the product of three more than a number and eight is fourteen

8 (x + 3) = 14

Hope that helps

The surface area of a cylinder with a radius of 6.8 inches and a height of 14.2 inches can be estimated by using the formula including both the curved surface area and the area of the bases, then rounding to compare with provided options.

The surface area of a cylinder can be calculated using the formula S = 2πr(height) + 2πr². Substituting the given radius r = 6.8 inches and height L = 14.2 inches, and using π = 3.14, we estimate the surface area as follows:

S = 2πrL + 2πr² = 2(3.14)(6.8)(14.2) + 2(3.14)(6.8)²

The first term accounts for the curved surface area of the cylinder and the second term accounts for the two circular bases. Calculate each part and sum them to estimate the total surface area. To compare to the provided options, we can round to the nearest whole number.

.1 Option D) Surface area of cylinder 923 in².2 Option (B)√41 3.Option (D) 5/13 4.Option (D) 4. 5Option (c)y = 2x + 1.  6 Option (c)53/72

To find the surface area of a cylinder with radius r = 6.8 inches and height h = 14.2 inches, we use the formula for the surface area of a cylinder:

Surface Area = 2πr(h + r)

First, calculate the lateral surface area:

Lateral Surface Area = 2πrh = 2 * 3.14 * 6.8 * 14.2

Lateral Surface Area ≈ 607.04 square inches

Next, calculate the area of the two circular bases:

Area of bases = 2πr² = 2 * 3.14 * (6.8)^2

Area of bases ≈ 290.66 square inches

Now, add the lateral surface area and the area of the bases to get the total surface area:

Total Surface Area ≈ 607.04 + 290.66 ≈ 897.7 square inches

Comparing this with the given options, the closest estimate is:

D) 923 in²

Using the Pythagorean Theorem

To find the distance between points A and B, assuming a right triangle with legs of length 2 and 3:

Distance = √(2² + 3²) = √(4 + 9) = √13

Thus, the best estimate for the distance is:

B) √41

Fraction between 5/12 and 5/11

To find a fraction between 5/12 and 5/11, first convert these fractions to a common denominator:

Common denominator is 132:

5/12 = 55/132

5/11 = 60/132

Between 55/132 and 60/132, the fraction closest to these is:

D) 5/13

Probability of picking an orange marble

If you pick a marble at random and replace it each time over 4 attempts, the best prediction for the number of times you will pick an orange marble will depend on the probability of picking an orange marble once. If the probability is uniform, then:

D) 4

Choosing the correct rule for the graph

Based on given options and typical linear functions, if a graph shows a line increasing with a slope of 2 and a y-intercept of 1:

C) y = 2x + 1

Rational number between 7/8 and 6/9

Convert to a common denominator to find a fraction that fits:

7/8 = 21/24, 6/9 = 16/24

The fraction closest to these is:

C) 53/72

4.3 you can't expand a number, only an equation

The expanded form of a number shows the value of each digit. Meaning you must separate each digit by its placement.

4 is in the ones, therefore it just remains as 4

.3 is in the tenths, and therefore turns into 0.3

Now combine the two terms. The expression would be the answer:

4 + 0.3

Answer:

The correct answer would be 4. Explanation below

Step-by-step explanation:

-6x-11x = 68

-6x-11x = -17x

-17x = 68

68/-17 = 4

Hope this helps!

~Starr

Answer:

Hey there! The correct answer would be x=-4.

Step-by-step explanation:

To start, you would first need to combine your like terms, terms that are not only raised to the same power but also have the same exact variables. In this case, your like terms are -6x and -11x:

-6x-11x=68 --> -17x=68

Now, divide both sides by -17 in order to isolate your variable term:

-17x/-17 = 68/-17

x=-4

Therefore, your answer would be x=-4.

To check to make sure this answer is right, plug -4 in for x and see if the result is 68=68:

-6(-4)-11(-4)=68

24+44=68

68=68

Hope this helps! :)

Answer-

Set of constraints to model the problem are,

[tex]12x+9y\geq 510[/tex]

[tex]y \leq 2x[/tex]

[tex]y \geq 25[/tex]

Solution-

x = the number of lawns weeded by Gwen,

y = the number of dogs walked by Fabio.

1.

As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,

[tex]\text{Earnings of Gwen} = 12x[/tex]

[tex]\text{Earnings of Fabio} = 9y[/tex]

[tex]\text{Total earning} = 12x+9y[/tex]

They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.

The equation for this is,

[tex]12x+9y\geq 510[/tex]

2.

The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means

y must be less than or equal to 2x.

The equation for this is,

[tex]y \leq 2x[/tex]

3.

Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.

The equation for this is,

[tex]y \geq 25[/tex]

Explanation:

Lets break the problem into steps and observe the constraints:

So Fabio and Gwen they are trying to save money and altogether they need at least $510.00.

Gwen charges $12.00 each time she weeds a yard.

Fabio charges $9.00 each time he walks a dog.

Fabio will walk at least 25 dogs. Here, 'x' represents the number of lawns weeded and 'y' represents the number of dogs walked.

Now talking about constraints:

Fabio will walk at least 25 dogs, so that implies:

[tex]y>25[/tex]

Also, the number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, that implies:

[tex]y<2x[/tex]

The total money that they need after doing all the work should be at least $510.00.

[tex]12x+9y>510[/tex]

The absolute value inequality which illustrates the information on the number line is 1 ≤ X ≤ 11

Therefore, the expression depicted by the absolute value graph is 1 ≤ X ≤ 11

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Remember the formula for time is distance/speed

So 60 would be the distance, or 60m.

Answer:

60 represents the distance

Step-by-step explanation:

Given : y is the time in hours that it takes Micheal to travel to his grandparents house,

            x is his average speed in miles per hour.

To Find: What does the number 60 represents

Solution :

Time= y

x = speed

So, To find distance we will use formula :

[tex]Time = \frac{Distance}{Speed}[/tex]

[tex]y = \frac{Distance}{x}[/tex]  -- A

Given function: [tex]y = \frac{60}{x}[/tex] --B

On comparing A and B

Distance = 60 miles

So, 60 represents the distance .

The answer is $8, sense 12÷3×2=4×2=8.

To find the cost of the store brand cough medicine, which is 2/3 the cost of the national brand priced at $12, you multiply $12 by 2/3, resulting in the store brand costing $8.

The question asks: If one bottle of the national brand of cough medicine costs $12, what is the cost of a bottle of the store brand if it's 2/3 of the national brand? To find the answer, you multiply the cost of the national brand by 2/3, since the store brand costs 2/3 of the national brand's price.

Here's the calculation:

Therefore, the cost of a bottle of the store brand cough medicine is $8.

Answer:

20 students do NOT prefer math over lunch.

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

If nine out of ten students ([tex]\frac{9}{10}[/tex]) prefer math class over lunch, then we can infer that one out of ten students ([tex]\frac{1}{10}[/tex]) do not.

[tex]\frac{1}{10} = 0.10[/tex] or 10%

As we can see, this equals a 10% of the students that were asked. If 200 students were asked, we would need to find what 10% of 200 would be. We can do this by multiplying 200 by the decimal form of 10% like so,

[tex]200 * 0.10 = 20 students[/tex]

So we can see that 20 students do NOT prefer math over lunch.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

A little more specific? So i could help out, thanks

From the fact that the two horizontal lines are parallel, you can deduce <A=<B

so you can equate the two right-hand sides of the equations:

6x+12=3x+63 and solve for x

3x = 51

x= 17 degrees is the measure <A (and <B as well)

The values for each of the 7s in 74,877 can be expressed as ;

The rank or position of a digit in a huge number is one tens hundred thousand. It establishes the place value where the digit is located. The value a digit in a number represents based on where it is in the number is known as place value.

For instance, 700 is the place value of 7 in 3,743. Nevertheless, 7,000 or 7,000 is the place value of 7 in 7,432.

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It is 192.

75 is 100%  so we can write it down as 75=100%.

75=100%  x=256%

CROSS MULTIPLY, proportions.

75/100     X/256

19200/100 equals 192

Answer:

Step-by-step explanation:

TO prove this we have to prove one of following.

SSS ( all three sides are equal )

SAS ( two sides and their middle angle is equal )

ASA ( two angles and their middle side are equal )

I am proving both triangles equal by ASA method.

The complete proof and explanation is given in attachment below.

The system of equations satisfied by the solution shown in the graph are:

x + y = 6 and x − y = -10.

Option D is the correct answer.

We have,

To check which system of equations is satisfied by the solution (-2, 8), we substitute the values x = -2 and y = 8 into each equation of the given systems.

A.

x + 2y = 6

(-2) + 2(8) = 6

-2 + 16 = 6

14 ≠ 6

B.

x + y = 6

(-2) + 8 = 6

6 = 6

x − 2y = 10

(-2) − 2(8) = 10

-2 - 16 = 10

-18 ≠ 10

C.

x + 2y = 10

(-2) + 2(8) = 10

-2 + 16 = 10

14 ≠ 10

x − y = 6

(-2) − 8 = 6

-10 ≠ 6

D.

x + y = 6

(-2) + 8 = 6

6 = 6

x − y = -10

(-2) − 8 = -10

-10 = -10

From the above calculations, we can see that the solution (-2, 8) satisfies the equations in x + y = 6 and x − y = -10.

Therefore,

The system of equations satisfied by the solution shown in the graph are:

x + y = 6 and x − y = -10.

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3(y − 2) + 6(x + 1) − 2 = 0

3y - 6 + 6x + 6 - 2 = 0

3y + 6x - 2 = 0

3y = -6x + 2

 y = -2x + 2/3

 Slope = - 2

Y intercept = b - 2/3

Answer

A. slope = -2, y-intercept = B

slope = -2

Y-intercept= 2/3

You dont have the Y-intercept numbers so i cant say if its A,B,C, or D.

(a) Let x be the cost of one of Brian's items, then cost of all 4 items bought by Brian will be 4x.

We have been given that Chris bought 3 items that each cost $2.50 more than Brian’s items each cost. The price of each item bought by Chris will be x+2.5. Therefore, the cost of all 3 items bought by Chris will be [tex]3(x+2.5)[/tex].

(b) We are told that Brian and Chris both paid the same amount of money, so we can equate costs of Brian's 4 items and Chris's 3 items as:

[tex]4x=3(x+2.5)[/tex]

Now let us solve for x by distributing 3.

[tex]4x=3x+7.5[/tex]

[tex]4x-3x=7.5[/tex]

[tex]x=7.5[/tex]

Therefore, cost of Brian's each item is $7.5.

Now let us find price of Chris's each item.

[tex]\text{Cost of Chris's each item}=x+2.5=7.5+2.5=10[/tex]

Therefore, cost of Chris's each item is $10.

(c) Now let us check our solution by substituting x=7.5 in [tex]4x=3(x+2.5)[/tex].

[tex]4(7.5)=3(7.5+2.5)[/tex]

[tex]4(7.5)=3(10)[/tex]

[tex]30=30[/tex]

We can see that both Brian and Chris spent equal amount of money that is $30, therefore, our solution is correct.

1) 36

2)8

3)14

4a) 21 4b) 42 4c) 56

5a)22 5b)40 5c)52

6a) 15.5 6b) 17 6c)18

7a)9 7b)18 7c)24

8) 3x +5

3  x 4 +5

=17