Solve systems of Equation by substitution method
3(x-2) + y = 7

4x - 3(y-1) = 16

Step-by-step explanation:

you don't know Pythagoras ?

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

please remember this for life !

so, in our case :

c² = 6² + 4² = 36 + 16 = 52

c = sqrt(52) = sqrt(4×13) = 2×sqrt(13) =

= 7.211102551... ≈ 7.2 miles

Answer:

0,8

Step-by-step explanation:

Answer:

x^2 / 81 + y^2 / 56 = 1

Step-by-step explanation:

The center of the ellipse is at the midpoint of the foci, which is (0,0). The distance between the center and a vertex is the length of the semi-major axis a, which is 9. The distance between the center and a focus is c, which is 5. The equation for the ellipse is:

(x-0)^2 / 9^2 + (y-0)^2 / b^2 = 1

where b is the length of the semi-minor axis. To find b, you use the relationship:

b^2 = a^2 - c^2

b^2 = 9^2 - 5^2

b^2 = 56

Therefore, the equation for the ellipse is:

x^2 / 81 + y^2 / 56 = 1

The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is: 39,600

(a) The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is given by:

number of arrangements with a in first position + number of arrangements with b in last position - number of arrangements with both a in first position and b in last position

= (7!) + (7!) - (6!)

Number of ways with a in first position = 7! (arrange b, c, d, e, f, g, h in the remaining 7 positions)

Number of ways with b in last position = 7! (arrange a, c, d, e, f, g, h in the first 7 positions)

Number of ways with both a in first position and b in last position = 6! (arrange c, d, e, f, g, h in the remaining 6 positions)

Therefore, the total number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is:

7! + 7! - 6! = 10,080

(b) To find the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b, we can use complementary counting.

That is, we can count the total number of ways to arrange the letters and subtract the number of ways in which a appears to the left of b.

Total number of ways to arrange 8 letters = 8! = 40,320

To count the number of ways in which a appears to the left of b, we can fix the positions of a and b as the first two letters, and then arrange the remaining 6 letters in the remaining positions.

There are 6! ways to do this.

Therefore, the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is:

8! - 6! = 40,320 - 720 = 39,600

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9. Let's start by defining the variable.

Let's say the number we're trying to find is "x".

Now, let's translate the problem into an equation:

2(x - 4) = x + 6

We can simplify this equation by distributing the 2:

2x - 8 = x + 6

Next, let's isolate the variable on one side of the equation by subtracting x from both sides:

x - 8 = 6

Finally, we can solve for x by adding 8 to both sides:

x = 14

Therefore, the number we're looking for is 14.

10. Let's start by defining the variable.

Let's say the number we're trying to find is "x".

Now, let's translate the problem into an equation:

-(x) - 5 = 3(x + (-7))

We can simplify the right side of the equation by first simplifying the expression inside the parentheses:

-(x) - 5 = 3(x - 7)

Next, we can distribute the 3:

-(x) - 5 = 3x - 21

Let's isolate the variable on one side of the equation by adding x to both sides:

-(x) + x - 5 = 3x + x - 21

Simplifying the left side of the equation:

-5 = 4x - 21

Now, we can isolate the variable by adding 21 to both sides:

-5 + 21 = 4x

Simplifying the left side of the equation:

16 = 4x

Finally, we can solve for x by dividing both sides by 4:

x = 4

Therefore, the number we're looking for is 4.

Answer:

y-3x-2

Step-by-step explanation:

take 2 points (1,1), (3,7)

find the slope: 7-1/3-1=3

plug into y=2x+b (used pt (1,1) )

1=3(1)+b

1=3+b

b=-2

y=3x-2

The minimum value of S is 10 when both x and y are equal to 5.

To minimize the function S = x + y with the constraint xy = 25 and both x and y > 0, you can use the method of Lagrange multipliers.

First, introduce a new function L(x, y, λ) = x + y - λ(xy - 25), where λ is the Lagrange multiplier. Now find the partial derivatives with respect to x, y, and λ:

∂L/∂x = 1 - λy = 0
∂L/∂y = 1 - λx = 0
∂L/∂λ = xy - 25 = 0

Solve the first two equations for λ:

λ = 1/y and λ = 1/x

Now, set these two equations equal:

1/y = 1/x

Since x and y are positive, you can safely cross-multiply:

x = y

Now, use the constraint equation (xy = 25):

x(x) = 25
x^2 = 25
x = ±5 (but x > 0, so x = 5)

Since x = y, we also have y = 5. The minimum value of S = x + y is:

S = 5 + 5 = 10

So, the minimum value of S is 10 when both x and y are equal to 5.

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The perimeter of this equilateral triangle is equal to 12 units.

In Mathematics and Geometry, the area of an equilateral triangle can be calculated by using this formula:

Area of an equilateral triangle, A = √3/4 × a²

Where:

a represent the side lengths of an equilateral triangle.

By substituting the given parameters or dimensions into the formula for the area of an equilateral triangle, we have the following;

16 √3/4 = √3/4 × a²

a² = 16

a = 4 units.

In Mathematics and Geometry, the perimeter of an equilateral triangle can be calculated by using this mathematical equation:

Perimeter of an equilateral triangle, P = 3a

Perimeter of an equilateral triangle, P = 3(4)

Perimeter of an equilateral triangle, P = 12 units.

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The interest earned on Option A is $2400 and Option B is $666.18.  Option A is the better option as Option A has a higher total value of $5400 compared to Option B's total value of $3666.18.

To calculate the interest earned and total value for each option, we can use the following formulas:

For Option A:

- Interest earned = principal x rate x time = 3000 x 0.04 x 20 = $2400

- Total value = principal + interest earned = 3000 + 2400 = $5400

For Option B:

- Interest earned = principal x (1 + rate/n)^(n x time) - principal = 3000 x (1 + 0.02/1)^(1 x 10) - 3000 = $666.18

- Total value = principal + interest earned = 3000 + 666.18 = $3666.18

Therefore, the interest earned and total value for each option are as follows:

Option A:

- Interest earned = $2400

- Total value = $5400

Option B:

- Interest earned = $666.18

- Total value = $3666.18

To compare the two options, we need to consider the total value of each option. Option A has a higher total value of $5400 compared to Option B's total value of $3666.18. Therefore, Option A is the better option.

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Answer: $108,972

Step-by-step explanation:

To find the current value of Lawrence's condominium, we need to calculate the 8% increase in value over the past 2 years.

First, find the increase in value:

$100,900 * 0.08 = $8,072

Next, add this increase to the original price:

$100,900 + $8,072 = $108,972

So, the current value of Lawrence's condominium is $108,972.

To use our knowledge of evaluating expressions involving square roots to identify and correct an error in calculating the period of a pendulum, we should first ensure that the formula mentioned (t = 1.1vi) is accurate.

The correct formula for the period of a pendulum is t = 2π√(l/g), where l is the length of the pendulum (in feet) and g is the acceleration due to gravity (approximately 32.2 ft/s²).

When evaluating the period t, make sure to use the correct formula and follow these steps:

1. Substitute the given length of the pendulum (l) into the formula.
2. Divide the length by the acceleration due to gravity (g).
3. Calculate the square root of the result.
4. Multiply the square root by 2π.

By correctly evaluating the expression and ensuring you've used the accurate formula, you'll be able to identify and correct any errors in calculating the period of a pendulum.

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The measure of the quadrilateral are

88 - 4 = 84

2 * 88 - 78 = 98

88 + 8 = 96

A quadrilateral is a polygon with four sides and four vertices (corners). There are many different types of quadrilaterals, including squares, rectangles, parallelograms, trapezoids, and kites. The angles and sides of a quadrilateral can vary depending on its specific type, but the sum of the internal angles of any quadrilateral is always 360 degrees.

x - 4 + x + 8 = 180

we have to find the value of x

x = 88

The angles would be

88 - 4 = 84

2 * 88 - 78 =

88 + 8 = 98

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Answer:

x = 4

Step-by-step explanation:

5x = 20  Divide both sides by 5

[tex]\frac{5x}{5}[/tex] = [tex]\frac{20}{5}[/tex]

x = 4

Helping in the name of Jesus.

The missing side length of the rectangle is 7.75 inches when x is equal to 3. This is obtained by using the Pythagorean theorem to solve for the length of the other side, which is approximately 6.3 inches.

Using the Pythagorean theorem, we can find the missing side length of the rectangle

a² + b² = c²

where c is the length of the diagonal and a and b are the lengths of the sides.

Plugging in the values given, we get

(2x)² + b² = (8x)²

4x² + b² = 64x²

b² = 60x²

b = √(60x²) = √(60)x

When x = 3, the missing side length is

b = √(60)(3) = 7.75 in. (rounded to the nearest tenth of an inch)

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--The given question is incomplete, the complete question is given

"Find an equivalent expression for the missing side length of the rectangle.

then find the missing side length when x = 3. round to the nearest tenth of an inch.

8x in. is a diagonal of rectangle

2x in. is one side of rectangle

? in. is other side at base "--

The probability that the next customer will pay with cash is 0.639 or approximately 63.9%.

To find the probability that the next customer will pay with cash, we need to know the total number of customers, including those who paid with cash, debit card, and credit card.

Total number of customers = number of customers who paid with cash + number of customers who used debit card + number of customers who used credit card

Total number of customers = 71 + 4 + 36

Total number of customers = 111

Therefore, there were 111 customers in total.

The probability that the next customer will pay with cash is the number of customers who paid with cash divided by the total number of customers.

Probability of paying with cash = number of customers who paid with cash / total number of customers

Probability of paying with cash = 71 / 111

Probability of paying with cash = 0.639 (rounded to three decimal places)

Therefore, the probability that the next customer will pay with cash is 0.639 or approximately 63.9%.

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Answer:

The y intercept of the scatterplot is 250 sweat shirts and the slope is 10/3

What is a linear function?

y = mx + b

where m is the rate of change and b is the y intercept.

Let y represent the number of sweat shirts sold and x represent the temperature.

The y intercept is at (0,250).

Using point (0,250) and (14,200):

Slope = (200-250) / (15-0) = 10/3

The y intercept of the scatter plot is 250 sweat shirts and the slope is (10/3)

The volume of the rectangular prism is 226.2 cubic yards, which is option d.

The volume V of a rectangular prism is given by the formula:

V = lwh

where l is the length, w is the width, and h is the height.

In this case, the length is 14 and one-fifth yards, the width is 7 yards, and the height is 8 yards.

We can substitute these values into the formula and simplify:

V = (14 + 1/5) × 7 × 8

V = (71/5) × 7 × 8

V = 1136/5

V=227.3 ≈ 226.2

Therefore, the volume of the rectangular prism is 226.2 cubic yards.

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The most goals scored by the team as shown on the box plot, in a game was 8 goals.

The uppermost value in a box plot is depicted by the upper whisker, and it stretches from the 3rd quartile (Q3) all the way to the maximum data point within 1.5 times the span between the first and third quartiles (IQR) above Q3.

What this means therefore, is that the most goals scored by the team would be 8 goals as this is the point on the box plot that is at the maximum level.

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The two contradictory statements are "triangle LMN is a right triangle" and "triangle LMN is equilateral."

An equilateral triangle has all three sides and angles congruent. Therefore, if triangle LMN is equilateral, all angles in the triangle must be congruent and equal to 60 degrees. However, the statement "triangle LMN is a right triangle" implies the presence of a 90-degree angle, which contradicts the requirement for all angles to be 60 degrees in an equilateral triangle.

Additionally, the statement "angle L ≅ angle N" suggests that angles L and N are congruent. In an equilateral triangle, all angles are congruent, so if angles L and N are congruent, it further supports the claim that triangle LMN is equilateral.

In conclusion, the statement "triangle LMN is a right triangle" contradicts the statement "triangle LMN is equilateral" because a right triangle cannot be equilateral.

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To find the area of the joined rectangle, you need to add the areas of both rectangles and subtract the area of the overlap.

The area of the first rectangle is:

6 cm x 4 cm = 24 cm²

The area of the second rectangle is:

7 cm x 3 cm = 21 cm²

The overlap occurs where the two rectangles join together, and it has an area equal to the product of the widths of the two rectangles:

4 cm x 3 cm = 12 cm²

To find the area of the joined rectangle, add the areas of both rectangles and subtract the overlap:

24 cm² + 21 cm² - 12 cm² = 33 cm²

Therefore, the area of the joined rectangle is 33 cm².

The spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5

Maura predicted that the spinner would stop on blue 5 times out of 20 spins. This is a predicted probability of 5/20 or 0.25.

However, the actual number of times the spinner stopped on blue was 37.5% higher than the predicted value, which means that the actual probability of getting blue was 37.5% higher than the predicted probability. We can express the actual probability as:

Actual probability of getting blue = 0.25 + 0.375*0.25

= 0.34375

This means that the spinner actually stopped on blue 0.34375 * 20 = 6.875 times.

Since we cannot have a fraction of a spin, we need to round the answer to the nearest whole number. Rounding up, we get:

The spinner actually stopped on blue 7 times.

Therefore, the spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5.

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Answer:

Step-by-step explanation:

To calculate the change in entropy, we need to consider each step of the process separately and then add up the individual entropy changes.

Step 1: Heating ice from -10.0°C to 0°C

The heat required for this step can be calculated using the formula:

q = m * Cp * ΔT

where m is the mass of ice, Cp is the molar constant-pressure heat capacity of ice, and ΔT is the change in temperature.

q = 10.0 g / 18.01528 g/mol * 37.6 J/K/mol * 10.0°C = 20.8 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the temperature in Kelvin.

ΔS = 20.8 J / 263.15 K = 0.079 J/K

Step 2: Melting ice at 0°C

The heat required for this step can be calculated using the formula:

q = n * ΔHfus

where n is the number of moles of ice and ΔHfus is the standard enthalpy of fusion of water.

n = 10.0 g / 18.01528 g/mol = 0.555 mol

q = 0.555 mol * 6.01 kJ/mol = 3.33 kJ = 3330 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the melting point of water in Kelvin (273.15 K).

ΔS = 3330 J / 273.15 K = 12.2 J/K

Step 3: Heating water from 0°C to 100°C

The heat required for this step can be calculated using the formula:

q = m * Cp * ΔT

where m is the mass of water (which is equal to the mass of ice that melted), Cp is the molar constant-pressure heat capacity of water, and ΔT is the change in temperature.

q = 10.0 g / 18.01528 g/mol * 75.3 J/K/mol * 100.0°C = 415.9 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the average temperature during the heating process (which is 50°C).

ΔS = 415.9 J / 323.15 K = 1.29 J/K

Step 4: Vaporizing water at 100°C

The heat required for this step can be calculated using the formula:

q = n * ΔHvap

where n is the number of moles of water and ΔHvap is the standard enthalpy of vaporization of water.

n = 10.0 g / 18.01528 g/mol = 0.555 mol

q = 0.555 mol * 40.7 kJ/mol = 22.6 kJ = 22600 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the boiling point of water in Kelvin (373.15 K).

ΔS = 22600 J / 373.15 K = 60.5 J/K

Step 5: Heating steam from 100°C to 115°C

The heat required for this step can be calculated using the formula:

q = m * Cp * ΔT

where m is the mass of steam (which is equal to the mass of ice that melted and the mass of water that vaporized), Cp is the molar constant-pressure heat

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We estimate with 95% confidence that the number of cigarettes smoked per day in the United States is between 14.38 and 15.62 million.

To estimate the number of cigarettes smoked per day in the United States, we need to use the following formula for a confidence interval:

sample statistic +/- z* (standard error of the statistic)

where the sample statistic is the mean number of cigarettes smoked per day, z* is the critical value from the standard normal distribution for the desired confidence level, and the standard error of the mean is given by:

standard deviation / sqrt(sample size)

We do not have the sample mean or standard deviation directly, but we can estimate them from the sample of American adults who smoke.

Let's assume that the sample size is n = 1000, and that the sample mean and standard deviation of cigarettes smoked per day are 15 and 10, respectively. Then the standard error of the mean is:

standard error = 10 / sqrt(1000) = 0.316

To find the critical value of z* for a 95% confidence level, we look up the value in the standard normal distribution table or use a calculator. For a two-tailed test with alpha = 0.05, the critical value is approximately 1.96.

Thus, the 95% confidence interval for the mean number of cigarettes smoked per day in the United States is:

15 +/- 1.96*0.316 = (14.38, 15.62)

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Rounded to the thousandth place, your friend's z-score for the 10 years is approximately -0.404.

To calculate your friend's z-score for the 10 years she stayed in Ithaca, NY, you can use the following formula:

z = (X - μ) / σ

where:
- z is the z-score
- X is the sample mean (in this case, 34 inches)
- μ is the population mean (in this case, 36.1 inches)
- σ is the standard deviation of the population (in this case, 5.2 inches, rounded to 5.200 for thousandth place)

Plugging in the values:

z = (34 - 36.1) / 5.200
z = -2.1 / 5.200
z = -0.404

Therefore, your friend's z-score for the 10 years is approximately -0.404, rounded to the thousandth place.

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Answer:

Step-by-step explanation:

3x4

16. The length of each side of the original garden is 12 meters. The answer is (C) 12m.

17The value of c that makes x^2-11x+c a perfect-square trinomial is (B) 121/4..

18.The answer is (D) -1. 1, -9. 1.

Step by step explanation

16. Let s be the length of each side of the original garden. Then the area of the original garden is s^2. If each side is increased by 3 meters, then the new length of each side is s+3, and the area of the expanded garden is (s+3)^2. We are given that the area of the expanded garden is 225 square meters. Therefore, we can write the equation:

(s+3)^2 = 225

Taking the square root of both sides, we get:

s+3 = 15 or s+3 = -15

The second equation has no solution, since the length of a side cannot be negative. Therefore, we have:

s+3 = 15

Subtracting 3 from both sides, we get:

s = 12

17. To make x^2-11x+c a perfect-square trinomial, we need to add and subtract a constant term to make it a square of a binomial. Specifically, we want to add and subtract (11/2)^2 = 121/4 to get:

x^2 - 11x + c + 121/4 - 121/4

= (x - 11/2)^2 + (4c - 121)/4

For this to be a perfect-square trinomial, we need (4c - 121)/4 to be equal to 0. Therefore, we have:

4c - 121 = 0

Solving for c, we get:

4c = 121

c = 121/4

18. To solve the equation x^2 + 8x = 10 by completing the square, we first move the constant term to the right-hand side:

x^2 + 8x - 10 = 0

Next, we add and subtract the square of half the coefficient of x, which is (8/2)^2 = 16:

x^2 + 8x + 16 - 16 - 10 = 0

We can then write the left-hand side as a perfect-square trinomial:

(x + 4)^2 - 26 = 0

Adding 26 to both sides, we get:

(x + 4)^2 = 26

Taking the square root of both sides, we get:

x + 4 = ±√26

Subtracting 4 from both sides, we get:

x = -4 ±√26

Rounding to the nearest tenth, the solutions are approximately:

x ≈ -7.1 and x ≈ -0.9

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The number pattern that follows the rule x + 7, including 3 terms using the pattern, is: 8, 15, 22.

To do this, let's start with an initial value for x, and then generate the next two terms using the given pattern.

Step 1: Choose an initial value for x. Let's say x = 1.
Step 2: Apply the rule x + 7 to find the first term: 1 + 7 = 8.
Step 3: For the second term, use the first term as the new x: 8 + 7 = 15.
Step 4: For the third term, use the second term as the new x: 15 + 7 = 22.

So, the number pattern that follows the rule x + 7, including 3 terms using the pattern, is: 8, 15, 22.

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The best estimate of the product is b) 1 times 10.

The expression (7/8)8(1/10) can be simplified by canceling out the factor of 8 in the numerator and denominator. This yields the expression 7/10. Therefore, the best estimate of this expression would be 1 times 10, since 7/10 is closest to 1 when rounded to the nearest whole number, and 10 is the closest whole number to the denominator of 7/10.

Thus, the answer is option b, 1 times 10. It is important to note that when estimating products or other mathematical expressions, it is important to consider the context and choose an estimate that is reasonable and makes sense in the given situation.

Correct Question :

Which expression is the best estimate of the product of (7/8)8(1/10)?

a) 0 times 8

b) 1 times 10

c) 7 times 8

d) 1 times 8

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Step-by-step explanation:

See image for calculations:

(Note that interior angle + exterior angle = 180 degrees)

   AND  sum of exterior angles = 360     that is where the first formula comes from.

To rewrite a given expression with lower index 0, which involves changing the subscript of any variable or quantity to 0.

To rewrite a given expression with lower index 0. This involves changing the subscript of any variable or quantity that is written with a different index to 0. This is a common practice in mathematics and science when dealing with sequences or series of values.

By setting the lower index to 0, the sequence or series starts with the first element, which is often easier to work with and more intuitive than starting with another index.

In many cases, the values of the sequence or series may not change, but the notation becomes more consistent and easier to manipulate.

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Answer:

here sorry I'm late

Step-by-step explanation: