The perimeter of a rectangle is 34 units. Its width is 6.5 units.

Write an equation to determine the length of the rectangle

Answer:

a) Comparing: Comparing means evaluating the similarity or difference between two or more objects, values, or variables. It is a process of identifying and highlighting the similarities and differences among objects, values, or variables based on specific criteria.

b) Non-standard units of measurement: Non-standard units of measurement are those that are not part of the International System of Units (SI) and are often created for specific purposes or contexts. These units may be used to measure variables such as time, distance, weight, or volume, but they are not universally recognized or standardized.

c) Standardized units of measurement: Standardized units of measurement are those that are part of the International System of Units (SI) and are universally recognized and accepted. These units provide a standard framework for measuring variables such as time, distance, weight, or volume, making it possible to compare and communicate measurements accurately across different contexts and languages. Some examples of standardized units of measurement include seconds, meters, kilograms, and liters.

Answer: Circumference, C = 15.71 miles

Step-by-step explanation:

The formula for the circumference of a circle is C = 2*pi*r, where C is the circumference and r is the radius. (Value of pi = 3.1415)

In this case, the diameter, d = 5 miles = 2*r, so we can substitute that into the formula:

C = pi*d = 3.1415*5

C = 15.7079 miles

Therefore, the circumference of the circle is approximately 15.71 miles, if we round to two decimal places.

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answer: x= 20x

Step-by-step explanation: 2+2 is 4, 4+4 is 8, quick maths

Therefore , the solution of the given problem of angles comes out to be  M∠R measured at 45.4 degrees, to the closest tenth.

The intersection of the lines that form a skew's ends determines the size of its biggest and smallest walls. There's a possibility that two paths will intersect at a junction. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.

Here,

To determine the size of angle R in triangular PQR, we can apply the Law of Cosines:

=> cos(R) = (PQ₂ + PR₂ - QR₂) / (2 * PQ * PR)

=>  cos(R) = (5.4₂ + 6.2₂ - 3.6₂) / (2 * 5.4 * 6.2)

=>  cos(R) = 0.6960917

When we calculate the inverse cosine of both sides, we obtain:

=>  R = cos⁻¹(0.6960917)

=>  R equals 45.4 degrees

Angle R in triangle PQR is therefore measured at 45.4 degrees, to the closest tenth.

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We have shown that ΔABC ~ ΔDBE because the corresponding angles are congruent and the corresponding sides are proportional.

The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well.

We must demonstrate that the respective angles of the two triangles are congruent and the corresponding sides are proportionate in order to demonstrate that ABC DBE.

To begin with, we can relate the sides of the two triangles using the following equation AB BE = CB BD. Let x, y, and z all be equal to AB. Next, we have:

x · BE = y · z (substituting the given values)

y/x = BE/BD (dividing both sides by BD and then by x)

Now, we can utilise the knowledge that a triangle's angles sum to 180 degrees to get the length of ABC:

ACB - 180° = ABC (from the given triangle ABC)

ABC = 180 degrees - BDE (corresponding angles)

The measure of BDE can then be determined using the connection between the sides that we discovered earlier:

y/x = BE/BD (from above)

BE/DE = y/(x+z) (substituting z = BD)

BDE is equal to tan(y/(x+z)) Inverse tangent is used.

Now, we can use the fact that a triangle's angles sum to 180 degrees to determine the size of the DBE:

DBE = 180°, BDE, and BED

DBE is equal to 180 - tan(y/(x+z)) - ∠BED (substituting the angle measure we just found) (substituting the angle measure we just found)

DBE is equal to 180° - tan(y/(x+z)) - tan(y/z) (using inverse tangent again)

tan(z(y+x)/(xz-yz)) = DBE (using the tangent of the sum formula)

In order to demonstrate that the sides of the two triangles are proportional, we can once more use the relationship between the sides:

BE/BD = AB/CB (from the given equation and simplification)

Y/x = AB/CB (from the relationship between the sides)

As a result, we have demonstrated that ABC DBE since the associated angles and sides are congruent and proportionate, respectively.

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Answer:

The Answer is x=2

Step-by-step explanation:

Hope this helps!!!!

Answer:

x=2  

Step-by-step explanation:

4x+3=11

4x=11-3      ( subtract 3 on both sides)

4x=8

x=2            ( divide 4 on both sides)

Answer:

Step-by-step explanation:

You want to know which set of equations could be combined in such a way as to result in the equation 3x = 18.

To obtain a term of 3x, the second equation must be subtracted from the first. That will result in 3x +2y = 18, not the equation of interest.

A term of 3x can be obtained by adding twice the first equation to the second:

  2(x +y) +(x -2y) = 2(4) +(10)

  3x = 18 . . . . . as required

A term of 3x can be obtained by subtracting the second equation from the first. That will result in 3x +2y = 18, not the equation of interest.

These equations are dependent. The second is the opposite of the first. They have an infinite number of solutions, not the single solution of the system of equations of interest.

Answer:

5 eggs.

Step-by-step explanation:

Since two eggs are needed for 24 cookies, we know by dividing both numbers by two that the rate is one egg for 12 cookies. 60/12 = 5. Multiply both numbers by 5 to get the answer. So, the answer is 5 eggs.

Answer:

$42

Step-by-step explanation:

75%=(3/4) so you do (3/4)*24=18

18+24=$42

Answer:

Step-by-step explanation:

To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.

ax² - (a² + ab)x + a²b can be factored as:

ax² - (a² + ab)x + a²b = a(x - b)(x - a)

bx² - (b² + bc)x + b²c can be factored as:

bx² - (b² + bc)x + b²c = b(x - c)(x - b)

cx² - (c² + ac)x + c²a can be factored as:

cx² - (c² + ac)x + c²a = c(x - a)(x - c)

Now, the LCM is the product of the highest powers of all the factors.

The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:

LCM = a²b²c²(x - a)(x - b)(x - c)

Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).

Answer:

Step-by-step explanation:

To calculate this, we need to use the formula for future value of an annuity:

FV = PMT x ((1+i)^n - 1)/i

Where:

PMT = the periodic payment (or deposit)

i = the interest rate per period

n = the number of periods

In this case, there are three deposits:

- R3,600 deposited one year ago

- R5,000 deposited today

- R7,500 to be deposited next year

We can calculate the future value of each of these deposits separately, and then add them together to get the total future value:

Future value of R3,600 deposited one year ago:

n = 4 (4 years until the equipment purchase)

i = 7% per year

PMT = R3,600

FV = R3,600 x ((1+0.07)^4 - 1)/0.07 = R4,661.07

Future value of R5,000 deposited today:

n = 3 (3 years until the equipment purchase)

i = 7% per year

PMT = R5,000

FV = R5,000 x ((1+0.07)^3 - 1)/0.07 = R6,885.02

Future value of R7,500 to be deposited next year:

n = 2 (2 years until the equipment purchase)

i = 7% per year

PMT = R7,500

FV = R7,500 x ((1+0.07)^2 - 1)/0.07 = R8,733.63

Total future value = R4,661.07 + R6,885.02 + R8,733.63 = R20,279.72

Therefore, there will be R20,279.72 available when the family is ready to buy the equipment, assuming a 7% rate of return on the investment.

There is a significant linear correlation (r=0.80) between the heights of winning candidates and runners-up in recent US presidential elections.

Using the data from the table, here are the steps to determine the correlation coefficient and test for a linear correlation:

Calculate the correlation coefficient (r) using the formula: r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)], where n is the sample size, X and Y are the two variables (heights of candidates who won and runners-up), Σ denotes the sum of the values, and sqrt is the square root function.

Using a spreadsheet, we get r = 0.80.

Using the formula: df = n - 2.

The sample size (n) is 10, so df = 10 - 2 = 8.

Find the critical values of r using a table or calculator based on the degrees of freedom and the desired level of significance (0.05).

For a two-tailed test with df = 8 and α = 0.05, the critical values are ±0.632.

Since |0.80| > 0.632, we can conclude that there is a significant linear correlation between the heights of winning candidates and runners-up.

Therefore, the correlation coefficient is 0.80, and the critical values are ±0.632. There is a significant linear correlation between the heights of winning candidates and runners-up in recent presidential elections.

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Answer:

To find all values of x for which f(x) = 26, we can set up the equation:

8x + 15/x = 26

Multiplying both sides by x, we get:

8x^2 + 15 = 26x

Bringing all the terms to one side, we get:

8x^2 - 26x + 15 = 0

We can factor this quadratic equation using the factoring method or by using the quadratic formula. Here, we will use the factoring method:

8x^2 - 26x + 15 = 0

(4x - 3)(2x - 5) = 0

Setting each factor equal to zero and solving for x, we get:

4x - 3 = 0 OR 2x - 5 = 0

4x = 3 OR 2x = 5

x = 3/4 OR x = 5/2

Therefore, the values of x for which f(x) = 26 are x = 3/4 or x = 5/2.

Answer:

we will do TanA = perpendicular / Base

A = 35°

Tan 35° = 217 / W

value of Tan 35° is approx = 0.7

0.7 = 217/ W

W = 217 / 0.7

W = 310

Answer:

12

Step-by-step explanation:

Mean = 3+22+0+15+9+23=72

72÷6 =12

Answer:

1250/500

=2.5

Multiplied by interest rate (30)

2.5 times 30

= $75.00

Step-by-step explanation:

Hope I helped.

Roderick earns an interest of $30 per year for every $500 deposited in his savings account. This means that the interest rate per $500 deposit is:Interest rate per $500 = $30/$500 = 0.06 or 6%To calculate the interest earned on Roderick's savings account, we first need to determine how many $500 deposits he has. We can do this by dividing his total savings by $500:Number of $500 deposits = $1,250/$500 = 2.5

Answer:

D. 1519.8

Step-by-step explanation:

The measure of the angle A in the given right angled triangle is found as: A = 64.82°

Applying the sin function in the given right angled triangle.

Sin A = 77/85

Sin A = 0.905

A = Sin⁻¹ (0.905)

A = 64.82°

Thus, the measure of the angle A in the given right angled triangle is found as: A = 64.82°

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The answer of the given question based on the graph and the function the answer are,

a) Demi's speed is decreasing over time.

b) Demi's speed decreases  from approximately 8.5 miles per hour to 5 miles per hour and  Demi's speed decreases from approximately 6 miles per hour to 3 miles per hour.

Speed is measure of how fast object is moving, or  rate at which it covers  certain distance over time. Mathematically, speed is calculated as distance traveled divided by time it takes to travel that distance.

a. When the function is decreasing, Demi's speed is decreasing over time. This means that she is running more slowly as time goes on. On the graph, this will be shown as a downward slope or a negative slope. The steeper the slope, the faster her speed is decreasing.

b. From the graph, we can see that the function is decreasing in two intervals. The first interval is from 0 to 5 minutes, where Demi's speed decreases from approximately 8.5 miles per hour to 5 miles per hour. The second interval is from 10 to 15 minutes, where Demi's speed decreases from approximately 6 miles per hour to 3 miles per hour.

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Demi went for a run in the park. The graph shows her speed during the run.

a. Describe the graph when the function is decreasing.

b. In how many intervals is the function decreasing?

not to sure about that try researching that

depends on ur teacher for me its really hard but the material wouldnt be too bad if you have a good teacher. it contains a lot of logistics and specific wording but memorization is key

Answer:

(6,3)

(-6,3)

Step-by-step explanation:

Answer:

Vertex: (0,0)

Step-by-step explanation:

Two points on the left: (-10,25), (-20,100)

Two points on the right: (10,25), (20,100)

Answer:

3n + 5n = 8n = 95

n = 11

$95 - $88 = $7

(11 paint brushes, 11 boxes of colored pencils)

A triangle must have a third side that is bigger than the sum of any two of its sides. There cannot be a triangle with these side lengths because in this instance, 5 + 15 = 20 is not greater than 250.

To check whether the given lengths can form the sides of a right triangle, we need to check if they satisfy the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the sides of the triangle as a, b, and c, where c is the hypotenuse. Then, the Pythagorean theorem can be written as:

a^2 + b^2 = c^2

Plugging in the given values, we get:

5^2 + 15^2 = (√250)^2

Simplifying the left-hand side, we get:

25 + 225 = 250

This is not true, since 25 + 225 = 250 does not hold. Therefore, the given lengths cannot form the sides of a right triangle.

In fact, we can see that the given lengths violate the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. In this case, 5 + 15 = 20 is not greater than √250, so a triangle with these side lengths cannot exist.

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The total area of the tiles that Felix needs to buy would be = 80cm²

The quantity of black tiles needed by Felix = 5

The quantity of white tiles needed by Felix = 5

The cost of each tile = $0.50 per cm².

The area of a tile = area of parallelogram = base×height.

base = 4cm

height = 2cm

area = 2×4 = 8cm²

For the 10 tiles = 8×10 = 80cm²

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Answer:

Step-by-step explanation:

If x=8, y = 4(8) - 7 = 25

If x=3, y = 4(3) - 7 = 5

If x=3, y = 2(3^2) = 18

If x=5, y = 2(5^2) = 50

If x=1, y = (2+1)^2 = 9

If x=3.5, y = (2+3.5)^2 = 30.25

2.4 < 2.8

53 > 1.666…

1.43 > .296

92 > 4.500

5.62 > 5.602

0.32 > 0.032

314 < 318

3437 > 3435

There is no table provided to reference, but the equation that represents a linear relationship between X and Y is:

y = mx + b

where m is the slope of the line and b is the y-intercept. The equation can also be written as:

y = b + mx

where b is the y-intercept and m is the slope. The equation represents a straight line on a graph, where the slope determines the steepness of the line, and the y-intercept is the point where the line crosses the y-axis. To write the equation for the table of X and Y values, we need to determine the slope and y-intercept from the given data.

Answer:

 in a right triangle, the square of the length of the hypotenuse (the side across from the right angle) is equal to the sum of the squares of the other two sides. So if the length of the hypotenuse is c and the lengths of the other two sides are a and b, then c^2 = a^2 + b^2.Apr 24, 2017

The calculated value of the force of the resistance is 15.62 N

We can use Newton's Second Law of Motion to solve this problem. The formula is:

F = m*a

where F is the net force, m is the mass of the object, and a is the acceleration.

In this case, the brick is falling through water, so there are two forces acting on it:

The net force is the difference between these two forces:

F_net = F_gravity - F_resistance

The weight of the object is:

F_gravity = m*g

So, we have

F_gravity = 2 kg * 9.81 m/s^2 = 19.62 N

Now we can use the formula for net force to find the force of water resistance:

F_net = F_gravity - F_resistance

F_resistance = F_gravity - F_net

F_resistance = 19.62 N - m*a

This gives

F_resistance = 19.62 N - 2 kg * 2 m/s^2 = 15.62 N

Therefore, the force of water resistance is 15.62 N.

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The mass of the individual can be up to 87.27 kg for the hot-weather training strategy to be appropriate.

Given that the training strategy is appropriate for a BSA less than 2.0, we need to find the maximum mass (M) for the individual with a height (H) of 165 cm. The equation for BSA is:

BSA = √(H x M) / 3600

We can rearrange the equation to solve for M:

M = (BSA^2 x 3600) / H

Since we want the maximum mass for a BSA less than 2.0, we can use BSA = 2.0 as the upper limit:

M = (2.0^2 x 3600) / 165

M = (4 x 3600) / 165

M = 87.27 kg

The above question is in response to the full question as seen in the image;

A sports medicine specialist determines that a hot-weather training strategy is appropriate for a 165 cm tall individual whose BSA is less

than 2.0. To the nearest hundredth, what can the mass of the individual be for the training strategy to be appropriate?

The equation for BSA is BSA = √(H x M)/3600

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