the base and height of a parallelogram is (x-7)meters and (x+9)meters respectively.if the area of a paralellogram 192 square meters.find the actual values of its dimensions.

Answer:

-2 - 24i

Step-by-step explanation:

a + bi + (7 - 3i) + (5 + 9i) + 13i = 10 - 5i

a + bi + 7 + 5  - 3i + 9i + 13i = 10 - 5i

                a + bi  + 12  + 19i = 10 - 5i

                         a + bi          = 10 - 5i - 12 - 9i

                                 a + bi = 10 - 12 - 5i - 9i

                                 a + bi = -2 - 24i

The angle is increased in approximately 0.095 radians (5.443°) for \(x = 0.45\,m\).

Based on the statement we construct the geometric diagram, by definition of tangent we have expressions for the initial and final angles (\(\theta_{1}\), \(\theta_{2}\)), in radians, of the figure:

Initial triangle

\(\tan \theta_{1} = \frac{y_{1}}{x_{1}}\) (1)

Final triangle

\(\tan \theta_{2} = \frac{y_{2}}{x_{2}}\) (2)

By using (2), the equivalence \(\theta_{2} = \theta_{1}+\Delta \theta\) and trigonometric identities we have the following expression:

\(\frac{y_{2}}{x_{2}} = \frac{\tan \theta_{1}+\tan \theta_{2}}{1-\tan \theta_{1}\cdot \tan \theta_{2}}\) (3)

By (1), we simplify the expression:

\(\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}} + \tan \Delta \theta}{1-\frac{y_{1}}{x_{1}}\cdot \tan \Delta \theta}\) (3b)

If \(0 \le \Delta \theta \le \frac{\pi}{6}\), then we can use the following approximation:

\(\tan \Delta\theta \approx \Delta \theta\) (4)

Then, we reduce (3b) into an entirely algebraic expression:

\(\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}}+\Delta \theta }{1-\frac{y_{1}}{x_{1}}\cdot \Delta \theta }\) (3c)

Where \(y_{2} = \sqrt{r^{2}-x_{2}^{2}}\).

Now we clear \(\Delta \theta\) within the formula:

\(\Delta \theta = \frac{\frac{y_{2}}{x_{2}}-\frac{y_{1}}{x_{1}}}{\frac{y_{1}}{x_{1}}\cdot \left(1+\frac{y_{2}}{x_{2}} \right) }\)  (5)

If we know that \(x_{1} = y_{1} = 0.5\), \(r = 0.707\) and \(x_{2} = 0.45\), then we estimate the angle change:

\(y_{2} = \sqrt{0.707^{2}-0.45^{2}}\)

\(y_{2} \approx 0.545\)

\(\Delta \theta = \frac{\frac{0.545}{0.45}-1 }{1\cdot \left(1+\frac{0.545}{0.45} \right)}\)

\(\Delta \theta = 0.095\)

As \(\Delta \theta < \frac{\pi}{6}\), then the result seems to be reasonable. The angle is increased in approximately 0.095 radians (5.443°) for \(x = 0.45\,m\).

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The total percentage of all the athletes who enjoy cycling are 45%.

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B.

The intersection of two sets A and B is the set of all elements which are common.

Given is that a coach asked her athletes if they enjoy running. Sixty-five percent of the team do not like to run. Of those, 60% enjoy cycling, while 80% of those who enjoy running also enjoy cycling.

Assume the total team is represented by 100%.

Then -

65 members do not like to run {R'}

60 members enjoy cycling {C}

80 members enjoy running and cycling both {R ∩ C}.

We can write -

{R} ∪ {C} = n{R} + n{C} + n{R ∩ C}                             ... Eq { 1 }
{R} ∪ {C} = (100 -  n{R}') + n{C} + n{R ∩ C}
{R} ∪ {C} = 35 + 60 - 80
{R} ∪ {C} = 15

Now -

n{C} = 60 - n({R} ∪ {C})                                 ... Eq { 2 }

n{C} = 45

Therefore, the total percentage of all the athletes who enjoy cycling are 45%.

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Answer:

9

Step-by-step explanation:

28 x 4=112

112 x 12= 1344

1344-875-330-130=9

Answer:

he will have $9 left over

Therefore, if 24 teaspoons of vegetable oil were used, we would need 16 teaspoons of vinegar to make the recipe correctly.

According to a salad recipe, each serving requires 6 teaspoons of vegetable oil and 9 teaspoons of vinegar. If 24 teaspoons of vegetable oil were used, we can determine the amount of vinegar needed for the recipe to be correct as follows:

First, we must determine the ratio of vinegar to oil in the recipe. To do this, we divide the amount of vinegar needed per serving (9 teaspoons) by the amount of oil needed per serving (6 teaspoons):

9 ÷ 6 = 1.5

This means that for every 1.5 teaspoons of oil used, we need 1 teaspoon of vinegar. Next, we use this ratio to determine the amount of vinegar needed when 24 teaspoons of oil are used:

1.5 ÷ 1 = 1.5

(teaspoons of oil per 1 teaspoon of vinegar)

24 ÷ 1.5 = 16

(teaspoons of vinegar needed)

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Answer:

The vertex form of a quadratic function is given by f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.

Step-by-step explanation:

Answer:

sorry for delay. 37.3 is the answer.

Step-by-step explanation:

The length of arc EC, in the given circle is: 37.3 cm

Length of arc = ∅/360 × 2πr

Given the following:

Radius (r) = FA = 23 cm

∅ = m∠EFC = 180 - 87 = 93°

Length of arc EC = 93/360 × 2π(23)

Length of arc EC = 0.258 × 144.5

Length of arc EC = 37.3 cm

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Step-by-step explanation:

hi hi hi nice to meet you meet you

Answer:

acute?

Step-by-step explanation: wheres the shape??

Answer: no picture?

Step-by-step explanation:

Answer:

The approximate percentage of lightbulb replacement requests numbering between 47 and 68 is 49.85%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 47

Standard deviation of 7

What is the approximate percentage of lightbulb replacement requests numbering between 47 and 68?

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% of the above.

Between 47 and 68:

68 = 47 + 7*3

So 68 is three standard deviations of the mean.

Of the 50% above the mean, approximately 99.7% are between the mean of 47 and 3 standard deviations above the mean, which is 68. So

0.5*0.997 = 0.4985

0.4985*100 = 49.85%

The approximate percentage of lightbulb replacement requests numbering between 47 and 68 is 49.85%.

The equation of the line passing through the points (-4, -3) and (2, -1) is y = (1/3)x - (5/3).

To find the equation of a line given two points, we can use the point-slope form of the equation.

y - y₁₁ = m(x - x₁)

where m is the slope of the line, and (x₁, y₁) is one of the given points.

First, we need to find the slope of the line. We can use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the two given points.

m = (-1 - (-3)) / (2 - (-4))

m = 2/6

m = 1/3

Now we can choose one of the given points and substitute its coordinates into the point-slope form, along with the slope we just found:

y - (-3) = (1/3)(x - (-4))

Simplifying this equation, we get:

y + 3 = (1/3)(x + 4)

y = (1/3)x - (5/3)

Therefore, the equation of the line passing through the points (-4, -3) and (2, -1) is y = (1/3)x - (5/3).

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The worker recieves 3 hours of break time per day.

Given is that a a fast-food worker works Monday through Friday, 8 hours per day. Daily, the worker receives a hour break in the morning, a hour break for lunch, and a hour break in the afternoon.

The worker recieves three breaks, meaning it recieves 3 hours of break time per day.

Therefore, the worker recieves 3 hours of break time per day.

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Answer:

-4x - 6 = -14

      + 6.  + 6

-4x = -8

——————

-4.      -4

—————

x = 2 :) copy it down like that :)

Step-by-step explanation:

You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.

Businesses, a noun in plural. a group of people who are connected or who have joined together. a guest or guests: We're having people over for dinner. a collection of individuals together for social purposes. association, camaraderie, and fellowship She is a lot of joy to be around.

The Old French word "compagnie," which was first used in the Salic code and meaning "one who eats bread with you," is where the English word "company" originates. To describe a "society, friendship, closeness, or body of troops," it was first used in 1150.

You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.

Total Amount to be when start the company is $12000 + $12000

= $24000

Out of which company owns land and a building worth $8,878 and equipment worth $4,230 and have retained $1,291 in earnings to be reinvested in the company, and you decided to put $1,000 of it aside for a long-term investment.

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The measure of the angle that turns through 3/10 of the circle is 108 degrees.

An angle is a geometric figure that is formed by two rays that share a common endpoint, which is called the vertex of the angle. The rays are referred to as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees.

Angles can be classified based on their degree of measurement: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.

Since a full circle has 360 degrees, 3/10 of the circle can be represented as:

(3/10) x 360 degrees = 108 degrees

Therefore, the measure of the angle that turns through 3/10 of the circle is 108 degrees.

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The complete question is :

The angle turns through 3/10 of the circle. What is the measure of the angle?

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

Step-by-step explanation:

NO x=3

Answer:

Step-by-step explanation:

18x² + 2 = 2 * 9x² + 2 *1

             = 2*(9x² + 1)

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

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Answer:

Step-by-step explanation:

10.9

Answer:

75%

Step-by-step explanation:

Let us being by constructing a rectangle. The length is x, and the width is y. The area is xy units squared.

Now, let's divide that by two. X is now x/2, and y is now y/2. The area is now xy/4.

We have xy as the original area, and xy/4 as the new area. The /4 indicates that the new rectangle is a fourth of what it was before, meaning it is only 25 percent as much.

Therefore, it had decreased 75perdent

The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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Answer:

The solution (x,y) is (3,19).

Step-by-step explanation:

We are given two equations for y.

y = 5x + 4

y = 3x + 10

They are equal, which means that we can find x. So

5x + 4 = 3x + 10

2x = 6

x = 3

With x, we can find y:

y = 5*3 + 4 = 19

So the solution (x,y) is (3,19).

Answer:

Check out the image below!

Step-by-step explanation:

Answer:

sine and tangent

will be positive.

Answer:

.5 of a minute

Step-by-step explanation: