-24 ≤ 2x-10 <-6 how to solve for x

The area, in square units, of the region where the two triangles overlap is found as 1 square units.

We can determine the equation for each line with in diagram using its coordinates.

We can determine the coordinates for each point. (1/4,3/4) is one of the intersections.

d² = 2² + 2² = 8

A₁ = (1/3d + 1/6d )/2 * 1/4d

A₁ = 1/4d * 1/4d

A₁ = 1/ 16 d²

Now,

A = 2A₁

A = 2.(1/16)d²

A = 1/8d²

A = 1/8 *8

A  = 1

Thus, the area, in square units, of the region where the two triangles overlap is found as 1 square units.

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Answer:

1 square unit

Step-by-step explanation:

Using a system of equations, it is found that the meter contains 20 dimes and 10 quarters.

For the system, the variables are:

A dime is worth $0.1 and a quarter is worth $0.25. In total, the parking meter is filled with $4.50, hence:

\(0.1x + 0.25y = 4.5\)

There are twice as many dimes as quarters, hence:

\(x = 2y\)

Then:

\(0.1x + 0.25y = 4.5\)

\(0.1(2y) + 0.25y = 4.5\)

\(0.2y + 0.25y = 4.5\)

\(0.45y = 4.5\)

\(y = \frac{4.5}{0.45}\)

\(y = 10\)

\(x = 2y = 2(10) = 20\)

There are 20 dimes and 10 quarters in the parking meter.

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The result is the same as the dividend 6x³ - 9x² + 8x + 3, which confirms that our quotient and remainder are correct.

To divide the polynomial 6x³ - 9x² + 8x + 3 by 2x³ - 1, we can use polynomial long division.

            3x² - 3x - 15

       ____________________

2x³ - 1 | 6x³ - 9x² + 8x + 3

          - (6x³ - 3x²)

          _______________

                   -6x² + 8x + 3

                  - (-6x² + 3)

                  ______________

                            5x + 3

                           - (5x + 5)

                           ___________

                                   -2

The quotient is 3x² - 3x - 15, and the remainder is -2.

To verify our work, we can check if (Quotient)(Divisor) + Remainder equals the Dividend:

(3x² - 3x - 15)(2x³ - 1) - 2

Expanding the product:

6x⁵ - 3x² - 30x³ + 3x² - 15x - 6x³ + 3x + 15 - 2

Simplifying the terms:

6x⁵ - 6x³ - 30x³ - 15x + 3x + 15 - 2

Combining like terms:

6x⁵ - 36x³ - 12x + 13

The result is the same as the dividend 6x³ - 9x² + 8x + 3, which confirms that our quotient and remainder are correct.

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Answer:

The Circle on the Top right doesn't belong since every other circle has a green quadrant, whereas on the other hand the circle on top right is missing the green quadrant

Hope this helps!

The record that represents an outlier in this data set is John's weight.

An outlier is a data point that differs significantly from other observations.

In other words, an outlier is a value or point that differs substantially from the rest of the data.

Therefore, the record that represents an outlier in this data set is  John's weight. This is because it is on the

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By using the concept of power and energy, it can be inferred that

0.76 calories were delivered to the food

What is energy and power?

Capacity of doing work is called energy

Rate of doing work is called power

There is a relationship between power and energy.

\(Power = \frac{Energy}{Time}\)

Power of a microwave oven = 1250 W

Time = 6.5 minutes

Energy delivered to the food = \(\frac{1250}{6.5 \times 60}\)

                                                 = 3.2 J

                                                 = \(\frac{3.2}{4.2}\) Calorie

                                                 = 0.76 Calorie

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The annual investment amount required to accumulate a reserve fund of $50,000 in 10 years, assuming an annual return of 5%, is approximately $3,720.

To calculate this, we can use the formula for the future value of an ordinary annuity: \[FV = P \times \left( \frac{{(1 + r)^n - 1}}{r} \right),\] where \(FV\) is the future value (desired reserve fund amount), \(P\) is the annual investment amount, \(r\) is the annual interest rate (in decimal form), and \(n\) is the number of years. Rearranging the formula to solve for \(P\), we have: \[P = \frac{{FV \times r}}{{(1 + r)^n - 1}}.\]Substituting the given values into the formula, we get: \[P = \frac{{50000 \times 0.05}}{{(1 + 0.05)^{10} - 1}} \approx 3720.\]Therefore, the business owner would need to invest approximately $3,720 annually to accumulate a reserve fund of $50,000 at the end of 10 years, assuming a 5% annual return.

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By simplifying and solving the equation 3/5(4x+1)=3(2-4)+9 using the order of operations, the solution is x=1, which can be verified by substitution.

let me explain step by step how we solved the equation:

\(3/5(4x+1)=3(2-4)+9\)

Step 1: Simplify both sides using the order of operations (PEMDAS).

On the left-hand side, we use the distributive property to multiply 3/5 by 4x and 3/5 by 1. This gives us:

\(3/5(4x) + 3/5(1) = (12/5)x + 3/5\)

On the right-hand side, we simplify 3(2-4) to get:

3(-2) = -6

Then we add 9 to get:

3(-2) + 9 = 3

So the original equation simplifies to:

(12/5)x + 3/5 = 3

Step 2: Isolate x on one side of the equation.

We want to solve for x, so we need to get rid of the 3/5 on the left-hand side. We can do this by subtracting 3/5 from both sides of the equation:

(12/5)x = 3 - 3/5

To simplify the right-hand side, we need to get a common denominator:

(15/5) - (3/5) = 12/5

So the equation becomes:

(12/5)x = 12/5

To solve for x, we divide both sides of the equation by 12/5:

x = (12/5)/(12/5) = 1

As a result, the equation's answer is x = 1.

Step 3: Check the solution.

To check if our solution is correct, we substitute x = 1 back into the original equation:

\(3/5(4x+1)=3(2-4)+9\)

\(3/5(4(1)+1)=3(2-4)+9\)

\(3/5(5)=3(-2)+9\)

3=3

Since both sides of the equation are equal when x = 1, we know that the solution is correct.

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The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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In the topical method, we focus on discussing different topics or subjects by considering various aspects and details related to them. This approach allows us to think about and communicate more effectively by addressing both general and specific points that might be relevant to the conversation.

The method of communication that involves reviewing possible things (both general and specific) that might be said. The correct answer is: e. Topical.

The method described in the question is a form of "topical" communication. This approach involves considering different topics or subjects that may need to be discussed and organizing thoughts and information around them. By reviewing possible things that may be said on each topic, one can prepare for a more effective and focused communication.

                             This method can be especially helpful in situations where there are multiple topics to cover or when discussing complex information that requires careful organization and planning.

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The percentage of the beads were green is 20% .

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.

Given that

Total number of beads = 35

In which Number of green beads = 7

Find out  What percentage of the beads were green?

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

So here total value = 35

Value = 7

Put the values in the formula

(value/total value)100%

= (7/35) × 100 %

= 1/5 × 100 %

= 100 / 5 %

= 20 %

Hence , Twenty percent (20%) of the beads were green.

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Answer:

Wasim has enough money.

Step-by-step explanation:

1. find the area of the garden path:

600 cm x 120 cm = 72,000 sq. cm

2. find the area of each stone:

it is a square of 30 cm by 30 cm, so:

30 cm x 30 cm = 900 sq. cm

3. find how many stones can fit in the path:

72,000 / 900 = 80 stones

4. multiply that by the price of each stone:

80 stones x $2.50 = $200

Wasim's budget is $220 and the stones will only cost $200, so it is within the budget

The given region R is bounded by the ellipse 9x² + 4y² = 36. Using the transformation of variables x = 2M and y = 3V, we can integrate over the transformed region S defined by the equation M² + V² = 1.

To integrate over the region R bounded by the ellipse 9x² + 4y² = 36, we perform the transformation of variables x = 2M and y = 3V. Substituting these values into the equation of the ellipse, we get:

9(2M)² + 4(3V)² = 36

36M² + 36V² = 36

M² + V² = 1

This equation represents the unit circle centered at the origin, which is the transformed region S. By transforming the variables, we have effectively changed the integration bounds to the unit circle. Thus, we can integrate over the transformed region S defined by M² + V² = 1 to evaluate the desired integral over the original region R.

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Answer:

900 cubic feet

Step-by-step explanation:

Volume = length x width x height

= 10 x 20 x 4.5

= 900

Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

Answer:

Step-by-step explanation:

We cannot determine whether f(2)+f(3) is equal to f(5) or not without any information about the function f.

For example, if f(x) = x, then f(2) + f(3) = 2 + 3 = 5, and f(5) = 5, so f(2)+f(3) = f(5).

However, if f(x) = x^2, then f(2) + f(3) = 2^2 + 3^2 = 4 + 9 = 13, and f(5) = 5^2 = 25, so f(2)+f(3) ≠ f(5).

Therefore, the relationship between f(2)+f(3) and f(5) depends on the specific function f, and cannot be determined without knowing the functional form of f.

Answer:

Reflection over the y-axis

Step-by-step explanation:

Answer:

51.68 miles per hr

Step-by-step explanation:

To find the average rate, divide the total miles traveled by the total amount of time.

325 miles / 6 1/4 hours = 51.68 miles per hr

The graph of a proportional relationship is a line through the origin or a ray whose endpoint is the origin

3. No because it's a line that doesn't go through the origin

4. Yes because it's a line through the origin

5. Yes because 1/3 = 2/6 = 3/9 = 4/12

6. No because 4/2 isn't equal to 8/5

7. Draw a graph just like 4., but change the y-axis

8. a. Let the equation be y = ax. 27 = 3a. a = 9. Therefore the equation is y = 9x.

8. b. 9

8. c. 9 * 5 = 45

9. a. The car travels 25 (> 18) miles per gallon of gasoline.

9. b. 25 * 8 - 18 * 8 = 7 * 8 = 56

Answer:

11.855762

Step-by-step explanation:

Answer:

11.856 miles

Step-by-step explanation:

I just know

Answer:

5,7

Step-by-step explanation:

4+6/2=5 (x coordinate), and for the y coordinate 5+9/2=7

5,7 is the final point

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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The relation's graph can be seen in the graphic at the bottom, where it is clear that it is   function.

The actual function can be specified using this "mapping" notation. Writing f:(x,y)x+y would allow us to define the above f(x, y). Real numbers are referred to as scalars to distinguish them from vectors. Each input is translated into a single output in a relation known as a function (input, output).

The horizontal axis is used for inputs, and the vertical axis is used for outputs. Here, we have the relationship shown below:

(-5,-1), (-4,1), (-3,3), (-1,5), (1,7) (1,7)

The figure below shows the graph of these points. Since there are no two points on the same vertical line, the relation is a function, as you can see.

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Answer:

A. a net

Step-by-step explanation:

I did the test

The increase in the minimum wage to $8.00 per hour could potentially lead to an increased demand for clothes due to higher purchasing power and potential shifts in consumer preferences.

We have,

Increasing the minimum wage to $8.00 per hour can have some impact on the demand for clothes.

Here are a few potential effects to consider:

Increased purchasing power:

When the minimum wage is increased, low-wage workers have more disposable income. This extra income can lead to increased consumer spending, including on clothing.

As a result, there could be a boost in the demand for clothes as more people can afford to purchase new clothing items.

A shift in consumer preferences:

With a higher minimum wage, individuals who previously had limited resources may now have the ability to choose higher-quality clothing or purchase from more expensive brands.

This shift in consumer preferences could lead to changes in the demand for different types of clothes and potentially result in an increase in demand for higher-end or premium clothing.

Price sensitivity:

While an increase in the minimum wage may provide workers with more spending power, some individuals may still be price-sensitive and prefer more affordable clothing options.

As a result, there may be continued demand for lower-priced clothing items or a preference for sales and discounts.

Employment and production costs:

An increase in the minimum wage could potentially lead to higher labor costs for clothing manufacturers and retailers.

To mitigate these increased costs, businesses may take steps such as adjusting their pricing strategies, implementing cost-saving measures, or exploring more efficient production methods.

These factors could impact the overall supply of clothes and potentially influence prices.

Thus,

The increase in the minimum wage to $8.00 per hour could potentially lead to an increased demand for clothes due to higher purchasing power and potential shifts in consumer preferences.

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The probability that Rosa's mom chooses sausage and onion is: 1/8C₂.

Probability refers to the chance of an event occurring. It is given by the formula: number of favorable outcomes/number of total outcomes. The total number of groups from which Rosa's mom can make her choice is 1 and this is the number of favorable outcomes.

But, the total number of outcomes that Rosa can hope to expect are 2 two toppings(sausage or onions) out of 8. So, the selected answer is the representation of the probability.

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cos s = 2/3 , s is in quadrant I, value of sin s, other related trigonometric functions using Pythagorean identity sin s = √(5/9) = √5/3,  tan s = √5/2 ,cot s = 1 / tan s = 1 / (√5/2) = 2 / √5 = (2√5) / 5, cot s = (2√5) / 5.

We are given cos s = 2/3. Since s is in quadrant I, we know that all trigonometric functions will be positive in this quadrant.

Let's find sin s using the Pythagorean identity: sin^2 s + cos^2 s = 1.

sin^2 s + (2/3)^2 = 1

sin^2 s + 4/9 = 1

sin^2 s = 1 - 4/9

sin^2 s = 5/9

Taking the square root of both sides, we get:

sin s = √(5/9) = √5/3

Now, let's find the value of tan s using the relationship: tan s = sin s / cos s.

tan s = (√5/3) / (2/3)

tan s = √5/2

Similarly, we can find the values of other trigonometric functions using the relationships:

sec s = 1 / cos s = 1 / (2/3) = 3/2

csc s = 1 / sin s = 1 / (√5/3) = 3/√5 = (3√5) / 5

cot s = 1 / tan s = 1 / (√5/2) = 2 / √5 = (2√5) / 5

Therefore, for the given condition cos s = 2/3 and s is in quadrant I, we have:

sin s = √5/3

tan s = √5/2

sec s = 3/2

csc s = (3√5) / 5

cot s = (2√5) / 5

Please note that the values of the trigonometric functions have been simplified and the square root values have not been rationalized.

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Cos s = 2/3 , s is in quadrant I, value of sin s, other related trigonometric functions using Pythagorean identity sin s = √(5/9) = √5/3,  tan s = √5/2 ,cot s = 1 / tan s = 1 / (√5/2) = 2 / √5 = (2√5) / 5, cot s = (2√5) / 5.

We are given cos s = 2/3. Since s is in quadrant I, we know that all trigonometric functions will be positive in this quadrant.

Let's find sin s using the Pythagorean identity: sin^2 s + cos^2 s = 1.

sin^2 s + (2/3)^2 = 1

sin^2 s + 4/9 = 1

sin^2 s = 1 - 4/9

sin^2 s = 5/9

Taking the square root of both sides, we get:

sin s = √(5/9) = √5/3

Now, let's find the value of tan s using the relationship: tan s = sin s / cos s.

tan s = (√5/3) / (2/3)

tan s = √5/2

Similarly, we can find the values of other trigonometric functions using the relationships:

sec s = 1 / cos s = 1 / (2/3) = 3/2

csc s = 1 / sin s = 1 / (√5/3) = 3/√5 = (3√5) / 5

cot s = 1 / tan s = 1 / (√5/2) = 2 / √5 = (2√5) / 5

Therefore, for the given condition cos s = 2/3 and s is in quadrant I, we have:

sin s = √5/3

tan s = √5/2

sec s = 3/2

csc s = (3√5) / 5

cot s = (2√5) / 5

Please note that the values of the trigonometric functions have been simplified and the square root values have not been rationalized.

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Answer:

\(-65\)

Step-by-step explanation:

\((5d-7)(5d-6)\)

\(5d(5d)+5d(-6)-7(5d)-7(-6)\)

\(25d^2+-30d+-35d+42\)

\(25d^2+-65d+42\)

The missing coefficient of \(d\) is \(-65\).

Answer:

25d^2 -65d +42

Step-by-step explanation:

(5d-7)(5d-6)=25d^2+__d+42

FOIL

(5d-7)(5d-6)=

First  5d*5d = 25d^2

Outer  5d*-6 = -30d

Inner  -7*5d = -35d

Last = -7*-6 = 42

Add them together

25d^2 -30d -35d +42

25d^2 -65d +42