Find the length of the third side. If necessary, write in simplest radical form.

To find the dimensions of the rectangle, we need to use Cramer's rule, which is a method for solving systems of linear equations.

   Let's start by defining the variables:

Let x be the width of the rectangle in cm.

Let y be the length of the rectangle in cm.

According to the problem, we have two equations:

y = 3x - 6 (the length is 6cm less than three times the width)

2(x + y) = P (the perimeter of the rectangle is P)

We can rewrite the second equation as:

2x + 2y = P

To solve for x and y, we need to set up a matrix and apply Cramer's rule. The matrix is:

| 0 1 | | x | | -6 |

| 2 2 | x | y | = | P |

Using Cramer's rule, we can solve for x and y as follows:

x = (|-6 1| / |-2 1|) = 9

y = (|0 -6| / |-2 1|) = 12

Therefore, the width of the rectangle is 9 cm and the length of the rectangle is 12 cm.

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The sum of the x-values where f(x) = g(x) is 3

From the question, we have the following parameters that can be used in our computation:

f(x) = 3(2)ˣ

g(x) = 6x

When f(x) = g(x), we have

3(2)ˣ = 6x

Solving for x, we have

x = 1 and x = 2

When these values are added, we have

Sum = 1 + 2

Evaluate

Sum = 3

Hence, the sum of the x-values where f(x) = g(x) is 3

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The equation for finding amount of daily pay is bus-driver gets paid $100 each day plus $0.20 per kilometer, "k" is p = 100 + 0.20k.

The equation for finding the amount of daily pay, "p", in the given situation would be : p = 100 + 0.20k,

In this equation, "p" represents the total daily-pay, "100" is the fixed amount paid each day, and

"$0.20" is the rate per kilometer. "k" represents the number of kilometers driven on that day.

To calculate the daily pay, you add the fixed amount of $100 to the product of the rate per kilometer and the number of kilometers driven on that day.

Therefore, the required equation is p = 100 + 0.20k.

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The given question is incomplete, the complete question is

Write an equation for finding the amount of daily pay, p, in the following situation: A bus driver gets paid $100 each day plus $0.20 per kilometer, "k".

Answer:

(-0.8, 2.2)

Step-by-step explanation:

Where the two lines intersect is the solution to the System of Equations.

Answer:

the answer would be (-0.8, 2.2) since it hasn't hit -3 yet and if it were to be -1 it would be in the bottom left

Answer:

The price would be 7.20

Step-by-step explanation:

Answer:

A, C

Step-by-step explanation:

For A, it's correct because they both start with 865.4, but the number in the problem has numbers after the 4, so A is right. B, is not because they both have 865.47, but the one in the problem has a 3, and C has 5, so no. C, is right, because the the problem's thousandths place is greater than C's. D, is not, because it's ones place is greater than the original number.

The measure of arc ZWX is 180 degrees.

Given that WZ and XR are diameters, we know that they are both perpendicular to chord WX. This creates four right angles at point X, and as a result, we have a rectangle formed by the four line segments.

Since WZ and XR are diameters, they each extend from one end of the rectangle to the other. This means that arc ZWX is actually a semicircle, with a measure of 180 degrees.

To see why this is the case, consider that a full circle has a measure of 360 degrees. Since arc ZWX spans exactly half of the circle, it must have a measure of half the circle, or 180 degrees.

In summary, the measure of arc ZWX is 180 degrees. This can be derived from the fact that WZ and XR are diameters, which create a rectangle and a semicircle in the process. While the figure may not be drawn to scale, the relationships between the different line segments and angles remain constant, allowing us to determine the measure of arc ZWX with confidence.

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Answer:

1 cup

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve for the total number of cups used, we need to first convert each fraction to have a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

As of now, each fraction looks like this:

Looking at each of the denominators, we can see that 12 is a multiple of both 4 and 3!

So, let's convert [tex]\frac{1}{3}[/tex].

Now that we have the denominator, we need to multiply the numerator by the same amount, so it stays equivalent.

Now let's convert [tex]\frac{1}{4}[/tex].

4 can be multiplied by 3 to get 12.

1 can be multiplied by 3 to get 3.

Now, each fraction looks like this:

Adding up the numerators:

Adding that back on top of the denominator:

So, [tex]\frac{4}{12}+ \frac{3}{12}+ \frac{5}{12} = \frac{12}{12}[/tex] or 1.

Therefore 1 cup of flour was used that day.

The value of the measure of each sides indicated are:

The measurement of the indicated side can be obtain as illustrated below:

1. The value of x can be obtain as follow:

Tan θ = Opposite / Adjacent

Tan 20 = x / 11

Cross multiply

x = 11 × Tan 20

Value of x = 4

2. The value of x can be obtain as follow:

Sine θ = Opposite / Hypotenuse

Sine 27 = 5 / x

Cross multiply

x × Sine 27 = 5

Divide both sides by Sine 27

x = 5 / Sine 27

Value of x = 11

3. The value of x can be obtain as follow:

Sine θ = Opposite / Hypotenuse

Sine 27.2 = 10 / x

Cross multiply

x × Sine 27.2 = 10

Divide both sides by Sine 27.2

x = 10 / Sine 27.2

Value of x = 21.9

4. The value of x can be obtain as follow:

Tan θ = Opposite / Adjacent

Tan 25 = 15 / x

Cross multiply

x × Tan 25 = 15

Divide both sides by Tan 25

x = 15 / Tan 25

Value of x = 32.2

5. The value of x can be obtain as follow:

Cos θ = Adjacent / Hypotenuse

Cos 64 = 4 / x

Cross multiply

x × Cos 64 = 4

Divide both sides by Cos 64

x = 4 / Cos 64

Value of x = 9.1

6. The value of x can be obtain as follow:

Tan θ = Opposite / Adjacent

Tan 33 = x / 14

Cross multiply

x = 14 × Tan 33

Value of x = 9.1

7. The value of x can be obtain as follow:

Sine θ = Opposite / Hypotenuse

Sine 49.6 = 5.6 / x

Cross multiply

x × Sine 49.6 = 5.6

Divide both sides by Sine 49.6

x = 5.6 / Sine 49.6

Value of x = 7.4

8. The value of x can be obtain as follow:

Cos θ = Adjacent / Hypotenuse

Cos 40 = x / 10.2

Cross multiply

x = 10.2 × Cos 40

Value of x = 7.8

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The first term of an A.P is 14 and the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the A.P is 70/11.

The first term of an A.P is 14. Let the common difference be d. Then the second term of the A.P is given by 14 + d. Similarly, the third term of the A.P is given by 14 + 2d.

The third term of the A.P.Solution:

Sum of the first 5 terms of the A.P can be expressed as:

5/2 [2a + (5 - 1) d] = 5/2 [2(14) + 4d] = 35 + 10d

Sum of the first 10 terms of the A.P can be expressed as:

10/2 [2a + (10 - 1) d] = 10/2 [2(14) + 9d] = 70 + 45d

According to the question, the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. It can be written as follows: 35 + 10d = - (70 + 45d)

Simplifying the above equation, we get:

55d = -105⇒ d = -105/55 = -21/11

Substituting the value of d in 14 + 2d, we get:

14 + 2d = 14 + 2(-21/11) = 14 - 42/11= 112/11 - 42/11= 70/11

Hence, the third term of the A.P is 70/11.

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Answer:

r≈19.1cm

Step-by-step explanation:

Using the formula

C=2πr

Solving forr

r=C

2π=120

2·π≈19.09859cm

Hope this helps

To convert the vertex form of a quadratic equation to standard form, we need to expand the squared term and simplify the expression.

Starting with the vertex form of the equation of a parabola:

y = 2(x - 3)^2 + 5

We can expand the squared term using the square of a binomial formula:

y = 2(x^2 - 6x + 9) + 5

Next, we distribute the coefficient 2:

y = 2x^2 - 12x + 18 + 5

Simplifying the constant terms:

y = 2x^2 - 12x + 23

This is the standard form of the equation of the parabola.

Therefore, the polynomial that passes through the given points is: f(x) = 6 - 38x - 6x^2 + 4x^3 + 3x^4.

To find the polynomial that passes through the given points, we can use the method of interpolation. Since we have five points, we can use a fourth-degree polynomial to fit the data.

Let's assume that the polynomial is of the form:

f(x) = a0 + a1x + a2x^2 + a3x^3 + a4x^4

We can find the coefficients a0, a1, a2, a3, and a4 by substituting the given points into the equation and solving the resulting system of linear equations.

Substituting (-4, 89) into the equation, we get:

89 = a0 - 4a1 + 16a2 - 64a3 + 256a4

Substituting (-3, 7) into the equation, we get:

7 = a0 - 3a1 + 9a2 - 27a3 + 81a4

Substituting (-1, -1) into the equation, we get:

-1 = a0 - a1 + a2 - a3 + a4

Substituting (1, -1) into the equation, we get:

-1 = a0 + a1 + a2 + a3 + a4

Substituting (4, 329) into the equation, we get:

329 = a0 + 4a1 + 16a2 + 64a3 + 256a4

Now we have five linear equations with five unknowns, which we can solve using any method of linear algebra. One possible way is to use matrix inversion. After solving for the coefficients, we get:

a0 = 6

a1 = -38

a2 = -6

a3 = 4

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Answer:

6 units right

Step-by-step explanation:

To translate figure P onto figure Q, just translate the figure 6 units to the right.

We can match the terms in the left column to the correct bolded examples as follows:

Sum: 1 + 1 = 2

Difference: 7 - 2 = 5

Term: 2x

Product: 9 * 9 = 81

Factor: 81 ÷ 9 = 9

Quotient: 81 ÷ 9 = 9

Coefficient: 7x - 8y

Variable: 5x + 3

To match the correct expression, an understanding of the mathematical terms is essential. The sum is the addition of terms and in the list, 1 + 1 is an example of a sum. Also, the product is the multiplication of numbers and 9 * 9 = 81 is an example of a product.

Coefficients are numbers that are matched with letters in algebra. A variable is a letter beside a number in an expression. In the option, x is the variable besides 5.

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In the chi-square test expected frequencies represent The frequencies one would expect if the null hypothesis were true

The expected frequencies in the chi-square test represent the frequencies one would expect if the null hypothesis were true. This means that the expected frequencies are calculated based on the assumption that there is no significant difference between the observed and expected frequencies, as suggested by the null hypothesis. The chi-square test compares the observed frequencies with the expected frequencies to determine if there is a significant association or difference between the variables being studied.

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If log 7 equals a and log 8 equals b then log 224 equals: E: none of the above.

Simplify the expression for log (224) by using:

log (ab) = log (a) + log (b) and log (a/b) = log (a) - log (b):

So,

log (224) = log ( 7 × 8 × 4)

= log (7) + log (8) + log (4)

Since log(4) = 0 (since 4 = 2^2)

Simplify

log(224) = log (7) + log (8) + log (4)

= log 7 + log 8

= a + b

Therefore the correct option is E.

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Answer:

a) It would have taken 1 person 14 days to do this amount of work.

b) It would take 1 person 56 days to finish building this house extension.

We know that 1 person can build a house extension in 70 days. This means that in 1 day, 1 person can do 1/70 of the work. In 7 days, 2 people can do 2 * 7 * 1/70 = 2/10 of the work. This means that 1 person can do 1/10 of the work in 7 days. To finish the remaining 8/10 of the work, 1 person would need 7 * 8 = 56 days.

Step-by-step explanation:

The approximated value of the logarithm expression is 0.5646  + 4log(b)

From the question, we have the following parameters that can be used in our computation:

log, 2≈ 0.3562,

log, 3≈ 0.5646, and

log, 5 ≈ 0.8271

Also, we have

logb (3b⁴)

Using the logarithms property, we have

logb (3b⁴) = logb (3) + log(b⁴)

This gives

logb (3b⁴) = logb (3) + 4log(b)

Substitute the known values in the above equation, so, we have the following representation

logb (3b⁴) = 0.5646  + 4log(b)

Hence, the approximated value is 0.5646  + 4log(b)

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Nakeisha sold 8 lollipops and 5 fruit snacks to make a total of $18.25.

Let's fix this issue using a set of equations. Assume that x is the quantity of lollipops sold and y is the quantity of fruit snacks sold.

Then we have two equations based on the information given:

x + y = 13.(Total number of fruit snacks and lollipops sold)

1.5x + 1.25y= 18.25 (total amount of money earned)  

To solve for x and y, we can use the substitution method :

x + y = 13 (equation 1)

1.5x + 1.25y = 18.25 (equation 2)

From equation 1, we have x = 13 - y. Substituting this into equation 2, we get:

1.5(13 - y) + 1.25y = 18.25

Simplifying and solving for y, we get

19.5 - 0.25y = 18.25

-0.25y = -1.25

y = 5

Nakeisha therefore sold 5 fruit treats. We may change y = 5 into equation 1 and solve for x to get the quantity of lollipops sold:

x + 5 = 13

x = 8

Therefore, Nakeisha sold 8 lollipops and 5 fruit snacks to make a total of $18.25.

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Answer:

the answer is lateral area

There is convincing evidence to support the conclusion that the true proportion of blocks that contain gold is less than 0.20.

The null hypothesis is that the true proportion of blocks that contain gold is equal to 0.20. The alternative hypothesis is that the true proportion of blocks that contain gold is less than 0.20.

The test statistic is calculated as follows:

z = (p - p₀) / √(p₀(1-p₀) / n)

The test statistic is equal to -2.00.

The p-value is calculated as follows:

p-value = 2 * P(Z < -2.00)

The p-value is equal to 0.0477.

Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. Therefore, there is convincing evidence to support the conclusion that the true proportion of blocks that contain gold is less than 0.20.

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Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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Answer:

  322 in²

Step-by-step explanation:

You want the surface area of the rectangular prism with edge lengths 7 in, 14 in, and 3 in.

The surface area can be computed using the formula ...

  A = 2(LW +H(L +W))

  A = 2(7·14 + 3(7 +14)) = 2(98 +63) = 322

The area of the prism is 322 square inches.

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Given 20% of the pupils are girls and the rest are boys. So, there are a total of 1785 pupils in the school.

To solve this problem, we can start by using the information that 20% of the pupils are girls to find the total number of girls and boys in the school. If there are a total of x pupils, then 0.2x are girls and 0.8x are boys.

Next, we can use the fact that the ratio of the number of pupils who wear spectacles to those who do not wear spectacles is 1:5 to find the number of pupils who wear spectacles. Let the number of pupils who wear spectacles be y, then 1/6y are girls who wear spectacles and 5/6y are boys who wear spectacles.

We also know that there is an equal number of girls and boys who wear spectacles, so we can write:

1/6y = 5/6y / 4

where 4 is the ratio of boys to girls who wear spectacles.

Solving for y, we get y = 357 * 24 = 8568. Therefore, the total number of pupils in the school is:

x = 0.2x + 0.8x = 1785

Hence, there are 1785 pupils altogether in the school.

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Answer:

Step-by-step explanation:

The transformation for the function g(x) = 5ˣ - 2 involves a vertical shift downward by 2 units compared to the parent function f(x) = 5ˣ. This is because the constant term (-2) is subtracted from the function. So, the graph of g(x) will be identical to the graph of f(x), except that it will be shifted downward by 2 units. Specifically, the point (0, 1) on the graph of f(x) will be shifted down to (0, -1) on the graph of g(x), and similarly, all other points on the graph will be shifted downward by 2 units.

To find the probability of selecting either a Red or a Brown almond M&M, we need to add their respective probabilities. The probability of selecting either a red or brown almond M&M is 0.2 or 20%.

P(R or Br) = P(R) + P(Br)

From the table given, we know that the probability of selecting a Red almond M&M is 0.1 and the probability of selecting a Brown almond M&M is also 0.1. Therefore,

P(R or Br) = 0.1 + 0.1 = 0.2

So, the probability of selecting either a Red or a Brown almond M&M is 0.2 or 20%.

In summary, to find the probability of selecting either one event or another event, we add their probabilities together. In this case, the probability of selecting a Red or a Brown almond M&M is 0.2 or 20%.

To find the probability of selecting either a red (R) or brown (Br) almond M&M, you can simply add the individual probabilities for each color since they are mutually exclusive events (selecting one does not affect the other).

According to the given probability distribution, the probability of selecting a red M&M (R) is 0.1, and the probability of selecting a brown M&M (Br) is 0.1.

So, to find the probability of selecting either a red or brown M&M (P(R or Br)), you can use the formula:

P(R or Br) = P(R) + P(Br)

Plugging in the given probabilities:

P(R or Br) = 0.1 (for R) + 0.1 (for Br)

P(R or Br) = 0.2

So, the probability of selecting either a red or brown almond M&M is 0.2 or 20%.

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Answer:

3 ways

Step-by-step explanation:

Using the arrows that they gave us, (which are the directions). The only possible ways are 3. Which I have shown in the screenshot attached below.

If we were to try to do it another time using the directions, it wouldn't work and we would most likely skip a step

Hope I helped!

Answer: 6 cups

Step-by-step explanation:

To find the maximum volume of a cylinder inscribed in a sphere of radius r, we need to use optimization techniques. The cylinder should be such that its height is equal to its diameter and both should be equal to the diameter of the sphere. This means that the cylinder should be a cube with its diagonal equal to the diameter of the sphere.

Let the diameter of the sphere be 2r. The diagonal of the cube is equal to the diameter of the sphere, so its side is r√3. The volume of the cube is (r√3)^3 = 27r^3.

Since the cylinder is inscribed in the sphere, its radius is r and its height is 2r. The volume of the cylinder is πr^2(2r) = 2πr^3.

To maximize the volume of the cylinder, we need to differentiate the volume equation with respect to r and set it equal to zero:

d/dx (2πr^3) = 6πr^2 = 0

This gives us r = 0, which is not a valid solution. Therefore, the maximum volume of the cylinder inscribed in the sphere of radius r is 2πr^3, when the cylinder is a cube with its diagonal equal to the diameter of the sphere.

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