Use substitution to solve the linear system of equations.

x = 4
-y = 1/2x

(4, -2)
(-2, 4)
(4, 2)
(2, -4)

The length of side walk is 500 feet

Solution:

Given that, A rectangle park measures 300 ft by 400 ft

Length = 300 feet

Width = 400 feet

A sidewalk runs diagonally from one comer to the opposite corner

We have to find the length of side walk

Which means, we have to find the length of diagonal of rectangle

The diagonal of rectangle is given by formula:

[tex]d = \sqrt{w^2+l^2}[/tex]

Where,

d is the length of diagonal

w is the width and l is the length of rectangle

Substituting the values in formula, we get

[tex]d = \sqrt{400^2+300^2}\\\\d = \sqrt{160000+90000}\\\\d = \sqrt{250000}\\\\d = 500[/tex]

Thus length of side walk is 500 feet

Answer:

original weight of the box = 15 / 16 pounds

Step-by-step explanation:

Answer:

12r+6

Step-by-step explanation:

2(6r+3)

2(6r)+2(3)

12r+6

Answer:number 1 is x<6750number 2 is $22.05 number 3 is $105

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

You have to find y in the answer

Final answer:

The volleyball court is 16 meters long, which was calculated by using the formula for the perimeter of a rectangle and the given width of 9 meters.

Explanation:

To find the length of the volleyball court, we need to use the formula for the perimeter of a rectangle which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Since we know the perimeter is 50 meters and the width is 9 meters, we can substitute these values into the formula to solve for the length l.

First, we calculate the total contribution of the width to the perimeter, which is 2w, so 2 times 9 meters = 18 meters. We then subtract this from the total perimeter to find the combined contribution of both lengths: 50 meters - 18 meters = 32 meters. Finally, we divide by 2 to find the length of one side: 32 meters / 2 = 16 meters.

Therefore, the volleyball court is 16 meters long.

Answer:

see attached picture please

Answer:

Therefore the value is

[tex]m<\dfrac{1}{9}[/tex]

Step-by-step explanation:

Given:

[tex]6m-2(7+3m)>5(2m-3)-m[/tex] ....Given

Step 1. Applying Distributive Property A(B+C)=AB+AC we get

[tex]6m-2\times7-2\times 3m>5\times 2m-5\times 3-m[/tex]

[tex]6m-14-6m>10m-15-m\\-14>9m-15[/tex]

Step 2. Add 15 both the side

[tex]-14+15>9m-15+15\\1>9m[/tex]

Step 3. Dividing both the side by 9

[tex]\dfrac{1}{9}>\dfrac{9m}{9}\\\\\dfrac{1}{9}>m[/tex]

Therefore the value is

[tex]m<\dfrac{1}{9}[/tex]

Answer:

Step-by-step explanation:

If the baby repeats this sleep pattern until she is awakened at 6 a.m., what ... We have 10 hours between 8PM and 6AM = 10 * 60 = 600 minutes ... Awake 12:15 - 12:30 ... There are 4 periods of 2 hour sleep and 1 period of 1 hour sleep = 4*2(60) + 1(60) ... So 540/600 = 54/60 = 9/10 = 90% of the time asleep.

Answer:

87.5%

Step-by-step explanation:

I am not sure how to set this up....so I am just gonna try to figure this a different way....without any formula

8 p.m - 10 pm.......awake for 15 minutes

10 pm - 12 am......awake 15 minutes

12 am - 2 am.......awake 15 minutes

2 am to 4 am.....awake 15 minutes

4 am to 6 am....awake 15 minutes

so from 8 pm to 6 am....that is a total of 10 hrs.....and in those 10 hrs, the baby was awake 5(15) = 75 minutes.....change 10 hrs to minutes.....1 hr = 60 min...so 10 hrs = (10 * 60) = 600 minutes

so in 600 minutes, the baby was awake 75 minutes.....that means the baby was asleep (600 - 75) = 525 minutes

525/600 = 0.875 = 87.5% <=== baby was asleep

or maybe this way....for every 2 hrs, the baby was awake 15 minutes....means the baby was asleep (120 - 15) = 105 minutes.

2 / 105 = 10 / x

2x = 1050

x = 1050/2

x = 525 minutes.....so the baby was asleep 525 minutes out of 600 minutes.

525/600 = 0.875 = 87.5%

I am getting the same answer either way

Answer:

I don't think you are doing anything wrong. Just ignore it and write the repeating decimal. If you're asked to do it, round it up instead.

Answer:

No you aren't doing anything wrong, it's just that the calculator is rounding the answer. So yes 1.6 repeating is correct

22 bouquets must Maria sell to break even.

bouquet costs  per unit $7

vendor  permit $150

number of bouquet need to  sell to meet break even  22 item (150/7)

22 item need to selled to meet the break even.

A sale is a deal involving two or more people when tangible or intangible commodities, services, or assets are exchanged for cash. A seller may occasionally receive assets in addition to money.

In the financial markets, a sale can also be defined as an agreement between a buyer and a seller specifying the purchase price and delivery details of a financial security.

A sale is essentially a contract between a seller of a certain good or service and a buyer who is willing to pay for that good or service, regardless of the environment.

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Answer:

12(3+4)

Step-by-step explanation:

Answer:

Etc: 12 34

Step-by-step explanation:

Answer:

Therefore NFC won 28 games and AFC won 25 games.

Step-by-step explanation:

i) let the number of Super Bowls won by NFC be x

ii) let number of Super Bowls won by AFC be y

iii) therefore it is given that  x + y = 53

iv) and also it is given that x = y + 3

v) substituting the equation in iv) into the equation in iii) we get

  (y +3) + y  =  53    ⇒  2y = 50   therefore y = 25.

vi) substituting the value of y from v) into the equation iv) we get

    x  = 25 + 3 = 28.

Therefore NFC won 28 games and AFC won 25 games.

To solve this mathematics problem, we formulate an equation based on the information that total Super Bowls were 53 and NFC won 3 more than AFC. By solving the equation, we find that NFC won 28 games and AFC won 25 games.

To solve this problem, let's start with the total number of games, which is 53. If the NFC has won 3 more Super Bowls than the AFC, that means the number of games won by both conferences adds up to 53. Let's denote the number of games won by the AFC as 'x'. So, the equation will be:

By combining like terms, we get:

Subtracting 3 from both sides, we have:

Finally, when we divide by 2, we solve for x:

This means that the AFC has won 25 games, and the NFC, having won 3 more, has won 28 games.

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The value of f(1) is 31

Solution:

Given that the sequence is defined by formula:

[tex]f(n+1) = f(n) - 3[/tex]

To find: f( 1 )

Also given that,

[tex]f(4) = 22[/tex]

So, we can say,

[tex]f(4) = f(3+1) = 22[/tex]

Substitute n = 3 in given formula

[tex]f(3+1) = f(3) - 3\\\\f(4) = f(3) - 3\\\\Substitute\ f(4) = 22\\\\22 = f(3) -3\\\\f(3) = 25[/tex]

Now we got, f(3) = 25

Use the similar steps to find for f(2)

Substitute n = 2 in given function

[tex]f(2+1) = f(2) - 3 \\\\f(3) = f(2) -3\\\\25 = f(2) - 3\\\\f(2) = 28[/tex]

Use the similar steps to find for f(1)

Substitute n = 1 in given function

[tex]f(1+1) = f(1) - 3\\\\f(2) = f(1) - 3\\\\28 = f(1) - 3\\\\f(1) = 28+3\\\\f(1) = 31[/tex]

Thus value of f(1) is 31

Answer:

Sometimes true.

Step-by-step explanation:

The statement is sometimes true and sometimes false depending on the values of x and y.

Here's an example that shows it to be true.

|x+y|=|x|+|y|

Let x = 5 and y = 6.

|x+y|=5 + 6 = 11

|x|+|y| = |5| + +|6| = 5 + 6 = 11

In this case, both sides equal 11, and the expression is true.

Here's an example that shows it to be false.

|x+y|=|x|+|y|

Let x = -5 and y = 5.

|x+y|= |-5 + 5| = |0| = 0

|x|+|y| = |-5| + |5| = 5 + 5 = 10

The left side equals 0, and the right side equals 10. The sides are different, and the expression is false.

Answer:

Anything with a numerator (top) greater then the denominater (bottom) here are some examples:

[tex] \frac{11}{2} [/tex]

[tex] \tfrac{8}{5} [/tex]

[tex] \frac{399}{7} [/tex]

[tex] \frac{6}{2} [/tex]

Hope this information helps my friend!

Answer:

Step-by-step explanation:

add all numbers together

all of them should equal 88

then divide it by how many numbers there are. so 8.

this equals 11

The median of the given data set, 11, 16, 12, 7, 23, 9, 5, 5, is 10. This is found by arranging the data in numerical order, identifying the two middle numbers, and finding their average.

The subject of this question is the calculation of the median of a given data set in mathematics. The data given is: 11, 16, 12, 7, 23, 9, 5, 5. To find the median, the data must first be arranged in numerical order from smallest to largest. Once arranged: 5, 5, 7, 9, 11, 12, 16, 23, it can be seen that this data set contains an even number of data points.

In these instances, the median is found by taking the average of the two middle numbers. Here, the middle numbers are 9 and 11. The median is found by adding these numbers together and dividing by 2. Thus, the median for this data set is 10.

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To find the percent error, calculate the absolute difference between the estimated height and the actual height, and divide it by the actual height. Finally, multiply the result by 100 to get the percentage.

To find the percent error, we need to calculate the absolute difference between the estimated height and the actual height, and then divide it by the actual height.

Finally, we multiply the result by 100 to get the percentage.

Step 1: Determine the difference between estimated and actual height.

Difference = Actual height - Estimated height

Difference = 54 inches - 50 inches

Difference = 4 inches

Step 2: Calculate the absolute value of the difference.

Absolute value of the difference = |4 inches|

Absolute value of the difference = 4 inches

Step 3: Divide the absolute difference by the actual height and multiply by 100% to get the percent error.

Percent Error = (Absolute difference / Actual height) × 100%

Percent Error = (4 inches / 54 inches) × 100%

Percent Error ≈ 7.41%

Therefore, the percent error in your estimation of your friend's height is approximately 7.41%.

Answer:

First, find the area of each side, and the just add them together. It sounds like a lot of work, but getting the question right is totally worth it.

Step-by-step explanation:

The steps to find the Surface Area of different 3D shapes is discussed below:

Surface area refers to the total area of the outer surface of a three-dimensional object.

To find the surface area of 3D shapes, you need to calculate the sum of the areas of all the individual faces of the shape.

The specific formulas for each shape vary, so let's go through some common 3D shapes and their surface area formulas:

1. Cube:

The surface area of a cube is given by the formula: SA = 6s², where s² is the area of square faces.

2. Rectangular Prism:

The surface area of a rectangular prism is given by the formula: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.

3. Cylinder:

The surface area of a cylinder is given by the formula: SA = 2πrh + 2πr², where 2πrh is area of side circular and 2πr² is Area of base.

4. Sphere:

The surface area of a sphere is given by the formula: SA = 4πr², where r is the radius of the sphere.

5. Cone:

The surface area of a cone is given by the formula: SA = πr(r + √(r² + h²)), where r is the radius of the base and h is the height of the cone.

6. Pyramid:

The surface area of a pyramid depends on the shape of its base. For example, the surface area of a square pyramid is given by the formula: SA = l² + 2lw, where l is the slant height and w is the base width.

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Answer:

14.

Step-by-step explanation:

The number of neutrons = the mass number - atomic number

= 27 - 13 = 14.

The correct answer is that Aluminium (Al), with an atomic number of 13 and a mass number of 27, has 14 neutrons.

To find the number of neutrons in an atom, one subtracts the atomic number (which is the number of protons) from the mass number (which is the sum of the number of protons and neutrons).

For Aluminium:

- The atomic number (Z) is 13, which means it has 13 protons.

- The mass number (A) is 27, which means the total number of protons and neutrons is 27.

The number of neutrons (N) can be calculated using the formula:

[tex]\[ N = A - Z \][/tex]

[tex]\[ N = 27 - 13 \][/tex]

[tex]\[ N = 14 \][/tex]

Therefore, Aluminium has 14 neutrons.

Answer:

D

Step-by-step explanation:

Given

2x(x - 4) + 7(x - 4) ← factor out (x - 4) from each term

= (x - 4)(2x + 7) → D

Answer:

Step-by-step explanation:

108 = 2*2*3*3*3=2² * 3³

120 = 2*2*2*3*5=2³*3*5

LCM = 2³*3³*5 = 8*27*5= 1080

To find the LCM of 108 and 120, first find their prime factorizations and then multiply the highest power of each prime factor.

To find the Lowest Common Multiple (LCM) of 108 and 120, we can first find their prime factorizations. The prime factorization of 108 is 2 × 2 × 3 × 3 × 3, while the prime factorization of 120 is 2 × 2 × 2 × 3 × 5. We can then find the LCM by taking the highest power of each prime factor from both numbers. So, the LCM of 108 and 120 is 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2,160.

The Lowest Common Multiple (LCM) of 108 and 120 is 1080. This is found by finding the prime factors of each number, and then multiplying together the highest power of each factor.

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Answer:

Proportional: Mike, a plumber charges $5 per hour for his service.

Non-proportional: Mike charges a initial cost of $10 plus $3 for each hours of service.

Step-by-step explanation:

Let us assume that Mike, a plumber charges $5 per hour for his service.

So, the number of hours (h) of service and the total charge (C) are proportional, which is  

C(h) = 5h ....... (1)

If the condition changes like, Mike charges an initial cost of $10 plus $3 for each hour of service.

Here, the equation that models the situation is  

C(h) = 10 + 3h .......... (2)

Now, relation (1) is non-proportional.  (Answer)

Final answer:

Real-world examples of directly proportional relationships include the relationship between distance and time at a constant speed, and cost and weight of fruit. These relationships become nonproportional when a base charge or flat fee is introduced, respectively.

Explanation:

Two real-world quantities that have a proportional linear relationship are speed and distance traveled in a given amount of time, assuming constant speed. For example, the farther you travel at a steady speed, the longer it takes. This relationship can be represented by y = kx, where y is the distance, x is the time, and k is the constant speed.

To make this relationship nonproportional, we could introduce a starting fee or base charge, making the total cost not just dependent on the distance but also an additional amount. Another example of a directly proportional relationship is the cost of fruit, where cost and weight are proportional (y = kx). By adding a flat packaging charge regardless of weight, the relationship between cost and weight becomes nonproportional.

The range of the function y = -3, graphed over the domain {x | -8 < x < 8}, is a singular value, which is y = -3.

The question asks for the range of the function y = -3 which is graphed only over the domain {x | -8 < x < 8}. This function is a horizontal line, which means that for any value of x within the domain, the value of y will always be -3.

Therefore, the range of this function is simply the single value y = -3, because no matter what x-value we have (as long as it's between -8 and 8), the y-value remains constant at -3.

Answer:

Please read the answer below.

Step-by-step explanation:

To eliminate the fractions before solving, each term can be multiplied by:

Answer:

240.3

Step-by-step explanation:

Remember SohCahToa for the trig. ratios. You always divide two sides.

'o' is opposite side. 'a' is adjacent side. 'h' is hypotenuse side.

Using alternating angles you can find the angle I marked blue (see diagram below). Because the 31° is parallel to the bottom side of the triangle, you can use alternating angles (Z pattern), where both 'insides' of the Z have the same measure.

The blue angle will be our angle of reference (angle we are talking about) represented by this symbol θ.

Since we need to find 'y', the opposite side, and we know 400ft is the adjacent side, use the tangent ratio.

tanθ = opposite / adjacent

tan31° = y / 400ft           Substitute what you know.

y = (400ft)tan31°          Isolate 'y'. Multiply 400ft and tan31°.

y = 240.344......ft      Exact answer on calculator

y ≈ 240.3ft      Answer rounded to nearest tenth

The nearest tenth is the first decimal. Since the second decimal is '4 or less', you round down, keeping the digit of the first decimal the same.

If the second digit was '5 or more', then you would round up.

The corresponding element in the range when 7 is an element  in the domain is f(5)=179/5

Step-by-step explanation:

Given that the 5 is an element in the domain of f(x)

The function f is defined by f(x)=8x-21/5

To find the corresponding element in the range:

That is put x=5 in the given function f(x)

Therefore f(x) becomes

f(5) = 8(5)-21/5

     =40-21/5

     =179/5

Therefore corresponding element in the range when 5 is an element  in the domain is f(5)=179/5

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Answer:

0.33

Step-by-step explanation:

Aight so all we do is use the formula, as shown here:

[tex]\frac{\Delta x}{\Delta y}[/tex]

[tex]x[/tex] is this amount it changed, which is 0.99. So we plug that for [tex]\Delta x[/tex]:

[tex]\frac{0.99}{\Delta y}[/tex]

Then, we find the amount of times the storm changed, and we plug that for [tex]\Delta y[/tex]:

[tex]\frac{0.99}{3}[/tex]

So, now that we have utilized the formula, we can now solve!

[tex]\frac{0.99}{3} = 0.33[/tex]

Good luck!

Answer:

0.33

Step-by-step explanation:

Answer:

Let x = the number of small boxes purchased

Let y = the number of large boxes purchased

​

​150x+400y&=1950

​x=y+2

​

The system of equations is as follows:

Equation 1: Total nails from small boxes = 150s

Equation 2: Total nails from large boxes = 400l

Equation 3: Total boxes = s + l

Equation 4: Total nails = 150s + 400l = 1950

To determine the number of small boxes and large boxes the contractor purchased, we can set up a system of equations. Let's define the variables: let "s" represent the number of small boxes and "l" represent the number of large boxes.

Now, let's break down the information given into equations:

Equation 1: The total number of nails from the small boxes is 150 times the number of small boxes, which is 150s.

Equation 2: The total number of nails from the large boxes is 400 times the number of large boxes, which is 400l.

Equation 3: The total number of boxes is the sum of small and large boxes, so the total boxes are s (number of small boxes) plus l (number of large boxes).

Given that the contractor bought 2 more small boxes than large boxes and the total number of nails purchased is 1950, we can express this as an equation:

4. Equation 4: The total number of nails purchased is 1950.

Now, we can write the system of equations:

Equation 1: 150s

Equation 2: 400l

Equation 3: s + l

Equation 4: 150s + 400l = 1950

In this system, Equation 1 represents the total number of nails from the small boxes, Equation 2 represents the total number of nails from the large boxes, Equation 3 represents the total number of boxes, and Equation 4 represents the total number of nails purchased.

To find the solution, we can solve this system of equations using various methods, such as substitution or elimination, to determine the values of "s" and "l," representing the number of small and large boxes the contractor purchased, respectively.

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Answer:

Pythagorean theorem theorem that states that the sum of the squares of the two legs is equal to the square of the hypotenuse in a right triangle