-5x+7y=11
-5x+3y=19
Elimination

Final answer:

The jogger runs a total distance of 224 meters, which includes running along the width and length of the park and taking a shortcut diagonally across the park.

Explanation:

To calculate the total distance the jogger runs, we must add the distances from each leg of the jogger's path. Starting from the southeast corner, the jogger runs the width of the park (28 meters) to the west, and then the length of the park (96 meters) to the north, reaching the northwest corner. The shortcut from the northwest corner directly back to the southeast corner, where her car is parked, is the hypotenuse of the resulting right-angled triangle. To find the length of this hypotenuse, we use the Pythagorean theorem (a² + b² = c²), where the sides of the rectangle serve as 'a' and 'b'.

Let's calculate the hypotenuse:

a = 28 m (width)

b = 96 m (length)

c = √(a² + b²) = √(28² + 96²)

c = √(784 + 9216)

c = √10000

c = 100 m

Now, we sum up all the distances:

28 m (west along the width)

96 m (north along the length)

100 m (shortcut diagonally)

Total distance = 28 m + 96 m + 100 m = 224 meters

Answer: 5

Step-by-step explanation:

Let x represent the number, then

x² + x = 30

x² + x - 30 = 0      

(x + 6) (x - 5) = 0

x + 6 = 0   x - 5 = 0

 x = -6        x = 5

    ↓

not valid since the restriction is that x > 0 (a positive number)

So, x = 5

Answer:

400/500

48 to 60

both  are correct

Step-by-step explanation:

4/ 5

Multiply top and bottom by 100

4*100/ 5* 100 =400/500

400:500

4/5  

Multiply top and bottom by 12

4/5 * 12/12 = 48/60

we can rewrite as 48:60

Answer:

In quadrant I   x is positive , y is positive

In quadrant II   x is negative , y is positive

In quadrant III   x is negative , y is negative

In quadrant IV  x is positive , y is negative

Step-by-step explanation:

In quadrant I   x is positive , y is positive

In quadrant II   x is negative , y is positive

In quadrant III   x is negative , y is negative

In quadrant IV  x is positive , y is negative

How I remember, I and II quads have a positive y

                             I and IV quads have a positive x

Answer:

Third choice "The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4." is the correct answer.

Step-by-step explanation:

We know that partitioning a directed line segment into a ratio of 1:3 means that we are dividing the given line segment into two parts whose first part is 1 times the of some quantity while the another part is 3 times of the same quantity. So basically we are comparing part to part in by ratio. And total number of parts in the whole will be just sum of both so we get 1+3=4

Hence choice (3) is correct answer.

"The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4."

Answer:

it is C

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4." is the correct answer.

Answer:

$780

Step-by-step explanation:

The initial sum of money borrowed was $750

at a simple interest rate of 8%

Dan pays the money back in 6 months

The amount of money Dan has to pay back his brother including the interest in 6 months' time.

The total amount accrued, principal plus interest, from simple interest on a principal of $750 at a rate of 8% per year for 6 months is $780.

The total interest that is to be paid back can be calculated using the formula

where P is the prinicipal amount of money we begin with (in this case $750), r is the rate of interest (in this case 8%) and t is the time period (in this case, 6 months or 1/2 of a year).

(Note that we must take the value of t in years if the interest is annual interest and that is why we use t = 1/2 = 0.5 instead of t = 6).

So, by simple calculation we can find interest to be paid as

the interest accrued is $30

To find the total sum to be paid back, we add the initial sum or pricipal amount to the interest we have calculated above i.e.,

the total amount accrued, principal plus interest, from simple interest on a principal of $750 at a rate of 8% per year for 6 months is $780.

Answer:

16/12 = 1 4/12 or 1 2/6

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Since this is an isosceles triangle, sides AB and sides AC are equal

AB=AC

8x-4 = 5x+11

Subtract 5x from each side

8x-5x-4 = 5x-5x+11

3x-4 = 11

Add 4 to each side

3x-4+4 = 11+4

3x=15

Divide by 3

3x/3 =15/3

x=5

We want to find BC

BC= 4x-2

Since x=5

BC = 4(5) -2

BC = 20-2

BC =18

Answer:

x = 9

Step-by-step explanation:

12^2 + a^2 = 54^2

a^2 = 54^2 - 12^2

a = sqrt (54^2 - 12^2) = 6 * sqrt(77)

Then calculate it for another triangle, where each side is 6 times shorter (as 12/2 = 6):

2^2 + (sqrt(77))^2 = x^2

x^2 = 81

x = 9

Answer: 9(3 + 2r)

Step-by-step explanation:

      27                     18r

       ∧                       ∧

    3  9                    2  9r

         ∧                         ∧

        3  3                     3 3r

27: 3 * 3 * 3

18r: 2 * 3 * 3 * r

Common Factors are 3 * 3 = 9

27: 9 * 3

18: 9 * 2r

27 + 18r  =  9(3 + 2r)

Answer:2.6

Step-by-step explanation:

Use your graphing calculator of you have one and if you don't you can find one online and plug in the equation and find the intersection . If you get 2.5571 round it to the nearest tenth and you should get 2.6

Answer:2.6

Step-by-step explanation:

Use your graphing calculator of you have one and if you don't you can find one online and plug in the equation and find the intersection . If you get 2.5571 round it to the nearest tenth and you should get 2.6

The mechanical advantage is found by dividing Rw by Ra:

Mechanical advantage = 18 / 2 = 9

Answer:

Step-by-step explanation:

so it is basically nine

Answer:

b

Step-by-step explanation:

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

Initial value of the property = P

Rate of growth = 275%

So, we need to find the property's current value:

We will use "compound interest ":

Answer:

D. 7

Step-by-step explanation:

In synthetic division, the first # in the division bracket (2)  is dropped, and the number outside the bracket is multiplied with it to find 4. Then, -2 and 4 are added to get 2. Again, 2 x 2=4. 3+4=7.

Simplified version: Drop, multiply, add, multiply, add till you reach the last term.

The synthetic division problem hasn't been stated in this query, making it impossible to ascertain the missing number. Synthetic division is a mathematical methodology used to simplify polynomial division by binomial. The correct problem should be offered for accurate guidance.

Unfortunately, the provided synthetic division problem was not included in your question so I'm unable to solve for the missing number. In general, synthetic division is a method used in algebra to divide a polynomial by a binomial. I would suggest you to verify the problem and restate your question providing all necessary details. Then I would gladly help you solve the missing number in the synthetic division.

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Answer:

Domain: {2,3,4,6,7}

Range: { -7,-5,2,3,9}

Step-by-step explanation:

The domain is the input, or x, values.

The range is the output, or y, values.

They are normally written from least to greatest.

Answer:

Domain: 2,3,4,6,7

Range: -7,-5,2,3,9

Step-by-step explanation:

hope this helps :)

Answer:

Amount of gas that can be hold by Joe's tank = 16 gallons.

Step-by-step explanation:

Given that Joe's gas tank is 1/4 full. After he buys 6 gallons of gas, it is 5/8 full. Now we need to find about how many gallons can Joe's tank hold.

So let's find change that happened after filling the gas.

Change = (5/8 full) - (1/4 full)

Change = (5/8 - 1/4)  full

Change = (5/8 - 2/8)  full

Change = (5 - 2)/8  full

Change = 3/8  full

So that means 3/8 full happens in 6 gallons

then 1 full will happen in 6/(3/8) gallons = 6*(8/3) gallons = 48/3 gallons = 16 gallons

So the amount of gas that can be hold by Joe's tank = 16 gallons.

Answer:

Eliza travels 54 minutes.

Step-by-step explanation:

Let's use the variable r to represent the number of minutes Ricky travles to school.

Eliza travels 6 times as many minutes as Ricky, so Eliza travels 6r minutes.

Altogether, they travel r + 6r minutes, or 7r minutes.

We are told they travel 63 minutes altogether, so 7r must equal 63.

7r = 63

Divide both sides by 7.

7r/7 = 63/7

r = 9

Ricky travels 9 minutes.

Eliza travels 6r minutes.

6r = 6 * 9 minutes = 54 minutes

Eliza travels 54 minutes.

Answer:

5 pages

Step-by-step explanation:

30 sticker and 6 stickers on each page

30 divided by 6 = 5

Answer:

He puts stickers on 5 pages.

Answer:

Proof

Step-by-step explanation:

Recall the identity [tex]\sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b)[/tex].

Consider [tex]\sin(a + b) = k\sin(a - b)[/tex]. We firstly apply the above identity to reach

[tex]\sin(a)\cos(b) + \cos(a)\sin(b) = k(\sin(a)\cos(b) - \cos(a)\sin(b))[/tex].

By expanding the bracket on the right we obtain

[tex]\sin(a)\cos(b) + \cos(a)\sin(b) = k\sin(a)\cos(b) - k\cos(a)\sin(b)[/tex] and so

[tex]\cos(a)\sin(b) + k\cos(a)\sin(b) = k\sin(a)\cos(b) - \sin(a)\cos(b)[/tex] and so

[tex](1+k)\cos(a)\sin(b) = (k-1)\sin(a)\cos(b)[/tex] and so

[tex](k+1)\frac{\cos(a)}{\sin(a)}= (k-1)\frac{\cos(b)}{\sin(b)}[/tex] and finally

[tex](k+1)\cot(a)= (k-1)\cot(b)[/tex].

Final answer:

Using the sum and difference identities for sine, we can manipulate the equation sin(a+b) = k sin(a-b) to prove the trigonometric identity (k-1)cotb = (k+1)cota as required.

Explanation:

To solve the given trigonometric identity, we must show that if sin(a+b) = k sin(a-b), then (k-1)cotb = (k+1)cota. First, let's utilize the sum and difference identities for sine:

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

Substitute these into the original equation:

sin(a)cos(b) + cos(a)sin(b) = k(sin(a)cos(b) - cos(a)sin(b))

Now, distribute the k on the right side and arrange terms:

sin(a)cos(b)(1-k) = cos(a)sin(b)(1+k)

Divide both sides by sin(b)cos(b) to isolate cot(a) and cot(b):

(1-k) cot(b) = (1+k) cot(a)

This proves the identity as required. Notice that the cotangent function is the reciprocal of the tangent function, which is the ratio of sine to cosine.

Answer:

3.10 miles

Step-by-step explanation:

1k = 0.62 miles

5x.62= 3.10

Kyle will run approximately 3.11 miles in a 5K marathon. This calculation is performed by first converting the 5K race distance into meters and then into miles, rounding the result to the nearest hundredth place.

The subject of this question is conversions between different units of distance, specifically kilometers to miles. To help Kyle with this, first, we need to convert the kilometers into meters. Since 1 kilometer equals 1000 meters, therefore, 5 kilometers will be 5000 meters.

Then, remembering that 1 mile is approximately 1609.34 meters, we can divide the total meters by the conversion factor for meters to miles. Therefore, the conversion from meters to miles is as follows: 5000 meters / 1609.34 meters/mile = 3.11 miles.

So, if Kyle is running a 5K marathon, he will be running approximately 3.11 miles. This answer has been rounded to the nearest hundredth place as per your instructions.

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Answer:

1/6 = 3/18

1/9 = 2/18

Step-by-step explanation:

The common denominator for 6 and 9 is the smallest number that they both go into, which is 18.  We need to multiply 6 by 3 to get 18 and multiply 9 by 2 to get 18

1/6 *3/3 = 3/18

1/9 *2/2 = 2/18

Answer:

the pair would be 3/18 and 2/18

Answer:

0.1

Step-by-step explanation:

Answer:

FOIL IT:

First multiply the first terms in each parenthesis.

Outside is next. You multiply the terms on the outer edges of each parenthesis.

Inside is next. Multiply the terms on the inside edge of each parenthesis.

Last: Multiply last terms in each parenthesis.

YOU GET:

3x^2 - 2x - 8

Answer:

25% of 1000 > 15% of 1500

Step-by-step explanation:

Lets calculate how much money you could receive

15% of 1500

.15 * 1500 = 225

25% of 1000

.25*1000 = 250

250>225

Final answer:

After calculating 15% of $1,500 and 25% of $1,000, it is evident that choosing the latter provides more money, amounting to $250 compared to $225 from the former option.

Explanation:

Choosing between percentages of different amounts involves straightforward arithmetic. To determine which option gives you more money, calculate the numerical value of each percentage. Option one is 15% of $1,500, which can be calculated as follows:

Convert the percentage to a decimal: 15% = 0.15.

Multiply the decimal by the total amount: 0.15 x $1,500 = $225.

Option two is 25% of $1,000:

Convert the percentage to a decimal: 25% = 0.25.

Multiply the decimal by the total amount: 0.25 x $1,000 = $250.

Now, compare the two amounts: $225 from the first option and $250 from the second option. It is clear that you would receive more money by choosing the 25% of $1,000, as it gives you a total of $250 compared to the $225 from the first option.

Answer:

x = -11, -11/5, -1, -1/5, 1/5, 1, 11/5,11

Step-by-step explanation:

The general formula for a third-degree polynomial is

f(x) = ax³ + bx² + cx + d

Your polynomial is  

f(x) = 5x³ + 7x + 11

a = 5; d = 11

p/q = Factors of d/Factors of a

Factors of d = ±1, ±11

Factors of a = ±1, ±5

Potential roots are x = ±1/1, ±1/5, ±11/1, ±11/5

Putting them in order, we get the potential roots

x = -11, -11/5, -1, -1/5, 1/5, 1, 11/5, 11

(There are no rational roots. There is one irrational root and two imaginary roots.)

Answer:

18

Step-by-step explanation:

The total number of scoops of ice cream that Richard got from the tub is,

  (234 regular cones) x (2 scoops / 1 regular cone) + (156 large cones) x (2 scoops / 1 large cone) = 936 scoops

Given that each scoop weighs 3 ounces, the total weight of the ice cream is 2808 ounces. For the number of tubs,

         (2808 ounces) x (1 lb / 16 ounces) x (1 tub /10 lb) = 17.55

Thus, the answer is 18. 

Hope this helped!

Answer:

0 And 12

Step-by-step explanation:

0 + 12 = 12

But 0 is 12 away from 12. hope i helped :)

Answer:

0 and 12

Step-by-step explanation:

0+12=12

12-0=12