What is an SSS and SAS triangle?

Answer:

Planes A and B intersect

Answer:

\(\tan \left(\frac{\pi }{2}\right)\)

Step-by-step explanation:

We know that  tan(x) is defined as  sin(x)/cos(x):

\(\tan \left(\frac{\pi }{2}\right),\\\sin \left(\frac{\pi }{2}\right)=1,\\\cos \left(\frac{\pi }{2}\right)=0,\\\\\)

\(\tan \left(\frac{\pi }{2}\right) = 1/0 \\\)

1/0 is undefined as 0 is in the denominator

The volume of the solid below the surface of revolution and above the xy-plane, formed by revolving the curve z=4x−x^2 in the xz-plane around the z-axis, can be found using the shell method.

To find the volume using the shell method, we divide the solid into infinitesimally thin cylindrical shells along the x-axis. Each shell has a radius equal to the x-coordinate of the curve and a height equal to the difference between the curve and the xy-plane.

The formula for the volume of a shell is given by V = 2πrhΔx, where r represents the x-coordinate of the curve, h represents the height of the shell (4x-x^2), and Δx represents the thickness of each shell.

Integrating this formula over the interval where the curve intersects the x-axis (0 to 4) gives us the total volume of the solid:

V = ∫[0,4] 2πx(4x-x^2)dx

Simplifying and evaluating the integral yields the final volume of the solid.

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Answer:

it will be -10/-2 which will get you a slope of positive 5 since the negatives cancel out with each other

Step-by-step explanation:

Answer:

Its an up slope function that measures up to 10 apart diagonal. Also, I included a picture.

hope this helps!

Answer:

30 Miles per hour.

Step-by-step explanation:

60 mph = 1 mile per minute.

Returning took 3 times as long so 1 mile per 3 minutes.

Average speed is total distance divided by time.

120 miles divided by 4 minutes.

120 / 4 = 30

Answer:

Step-by-step explanation:

Well, slope intercept form is y = mx + b

A good way to find the slope is (y2 - y1)/(x2 - x1)

So, (-1 - 4)/(0 - -2) = (-5)/(2) = -5/2 or -2.5

y = -2.5x + b

b is for the y unit when the line crosses the x axis. Therefore, b = -1.

y = -2.5x -1

Number of students in the group initially is 7.

From the combination formula, C(n, r) = n!/(r!(n - r)!)

Let the number of students are in the group initially be 'n'.

The number of different committees of 4 students from n students is = C(n, 4).

When the number of students in the group increases by 1 then the total number of students becomes = n + 1

The number of different committees of 4 students from (n + 1) students is = C(n + 1, 4).

According to the question, the number of committees in both the cases are equal.

So the equation best suited for the situation is,

2C(n, 4) = C(n + 1, 4)

2n!/(4!(n - 4)!) = (n + 1)!/[4!(n + 1 - 4)!]

2n!/(n - 4)! = (n + 1)!/(n - 3)!

2n(n - 1)(n - 2)(n - 3) = (n + 1)n(n - 1)(n -2)

2(n - 3) = n + 1

2n - 6 = n + 1

2n - n = 6 + 1

n = 7

Hence the number of students are in the group is 7.

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For an infinite power series, \(f(x)=∑_{n = 1}^{∞} \frac{n² x^{n}}{5^n n!} \\ \), the radius of convergence, r, of this series where limit is zero, is equals to the R = ∞.

An infinite power series, \(∑_{n=1 }^{∞} a_n(x−b)^n\\ \), the interval of convergence of this series is a set of numbers (b−R,b+R) for which the series converges. The value R is called the radius of convergence. The formula of radius of Convergence by ratio test is

\(\frac{1}{R} = \lim_{n→ \infty} |\frac{ a_{n + 1}}{a_n} | = l\\ \)

We have a infinite series defined as

\(f(x)=∑_{n = 1}^{∞} \frac{n² x^{n}}{5^n n!} \\ \)

here, \(a_n = \frac{n²}{5^n n!}\)

\(a_{n+1} = \frac{(n + 1)²}{5^{n +1} (n+1)!}\). Using the above formula, \(l = \lim_{n→ \infty} |\frac{\frac{(n + 1)²}{5^{n +1} (n+1)!}}{ \frac{n²}{5^n n!}} | \\ \)

\( = \lim_{n→ \infty} {\frac{(n + 1)²}{5^{n +1} (n+1)!}}×\frac{5^n n!} { {n}^{2}} \\ \)

\(= \lim_{n→ \infty} \frac{(n + 1)²}{5(n+1) n²} \\ \)

\(= \lim_{n→ \infty} \frac{(n + 1)}{5 n²}\\ \)

\(= \lim_{n→ \infty} \frac{(1 + \frac{1}{n})}{5 n} \\ \) = 0

Since, this limit is zero,i.e., l = 0 < 1. Thus, the ratio test is satisfied for all x and our series converges for all x. Hence , R= ∞ and the interval of convergence is (−∞,∞).

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Answer:

It equals 3

Step-by-step explanation:

To solve this it is basically like a normal problem you would just take out the X in it and divide 7 by 21 which leaves you with 3.

2+1/6y=3x+4

3/6y=3x+4

3=3x+4×6y

3-4=3x×6y

-1=18xy

-1/18=xy

HOPE ITS RIGHT!! GIVE BRAINLIEST PLS

Answer:

Y would have to equal 1 over 2(3x+4) in order for this equation to even work properly. 2+1 over 6 would actually equal 1/2y which is basically 3/6y. And since 3 and 6 are like terms 3 divided by 3 is 1 and 6y divided by 3 is 2y

Hope this helps

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The given road rises 3 yards for every 16 yards measured on the surface of the road. We have to determine how far does a car travel horizontally when it travels 3.5 miles along the road. 1 mile = 1760 yards Therefore, 3.5 miles

= 3.5 × 1760 yards

= 6160 yards

A road rises 3 yards for every 16 yards measured on the surface of the road.We need to find the distance a car travels horizontally

=\((distance\,travelled\,horizontally)^2 + (distance\,travelled\,vertically)^2

= (distance\,travelled)^2\)Let the distance a car travels horizontally

= x

We know, the road rises 3 yards for every 16 yards measured  on the surface of the road. Therefore, the distance a car travels vertically

= \(\frac{3}{16}\) × distance a car travels horizontally

= \(\frac{3x}{16}\)

Using the Pythagorean Theorem,

=\(x^2 + \left(\frac{3x}{16}\right)^2

= (6160)^2\)\(x^2 + \frac{9x^2}{256}

= (6160)^2\)\(\frac{265x^2}{256}

= (6160)^2\)x²

= \(\frac{256 × 6160^2}{265}\)x

= \(\sqrt{\frac{256 × 6160^2}{265}}\)x

= 8926.03 yards

Therefore, the car travels 8926.03 yards horizontally when it travels 3.5 miles along the road. 1 yard = 0.000568182 miles

Therefore, the distance a car travels horizontally = 8926.03 × 0.000568182= 5.0761 miles (rounded to four decimal places) Hence, the car travels 5.0761 miles horizontally when it travels 3.5 miles along the road.

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When an organization with a functional structure diversifies into related product-markets, it generally maintains its functional structure.

In a functional structure, the organization is organized based on specialized functions such as marketing, finance, operations, and human resources. Each function operates independently, and decisions are made within each functional unit. When diversifying into related product-markets, the organization can leverage its existing functional expertise to support the new product lines or markets.

Maintaining the functional structure allows the organization to retain the benefits of specialization and efficiency within each function. It also enables the organization to capitalize on the existing knowledge, skills, and resources of each functional area, ensuring a smoother transition into new product-markets.

This approach minimizes disruption and allows the organization to effectively manage the integration of new product lines while maintaining focus on core competencies. By leveraging the existing functional structure, the organization can adapt and respond to the specific requirements of each product-market while maximizing operational efficiency.

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Answer:

1755.98

Step-by-step explanation:

1755.97809915

1 cent is 1 hundredth of a dollar, so to round to the nearest cent means to round to the nearest hundredth.

The 7 in boldface is the hundredths place.

Drop all digits to the right of the 7.

1755.97

dropped digits: 809915

Look at the leftmost digit that was dropped (in boldface). If it is from 0 to 4, you are done, and the answer is 1755.97. If the leftmost digit that was dropped is from 5 to 9, the hundredths digit goes up by 1. Here, the first digit that was dropped is an 8, so the 7 in the hundredth place goes up 1 to 8.

Answer: 1755.98

Based on the given data set, we can only determine a single mode, which is 4.

To determine the mode(s) of the given data set representing the number of new seeds planted in the garden for 15 varieties of sunflower, we need to find the value(s) that appear most frequently.

Here are the steps to find the mode(s):

1. Organize the data set in ascending or descending order to make it easier to identify repeated values. For example, let's say the data set is: 4, 5, 6, 2, 7, 4, 3, 5, 2, 4, 6, 4, 7, 3, 4.

2. Count the frequency of each value in the data set. In our example, we have:

  - Value 2 appears 2 times.
  - Value 3 appears 2 times.
  - Value 4 appears 5 times.
  - Value 5 appears 2 times.
  - Value 6 appears 2 times.
  - Value 7 appears 2 times.

3. Identify the value(s) with the highest frequency. In our example, the value 4 appears most frequently with a count of 5 times.

Therefore, the mode of the data set is 4, indicating that the number 4 is the most common value among the number of new seeds planted in the garden for the 15 varieties of sunflower.

It's important to note that in some cases, there may be multiple modes if two or more values have the same highest frequency.

However, based on the given data set, we can only determine a single mode, which is 4.

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Answer:

RN=5

Step-by-step explanation:

QR is congruent to RN therefore they are the same length

For c < 0, the level set g(v, w) = c can be related to the drawing in part (c) by applying a scaling factor of √|c|. This means that the level set curves for negative values of c will be scaled by a factor of the square root of the absolute value of c. As c becomes more negative, the level set curves will contract towards the origin of the vw-plane, with a smaller scale factor indicating a closer proximity to the origin. To sketch a contour map for g in the vw-plane, start by plotting level sets for various values of c, both positive and negative. Remember to apply the appropriate scaling factors as mentioned in part (e) for negative values of c. For positive values, the level sets will expand outwards from the origin, while for negative values, they will contract towards the origin. Make sure to label each level set with its corresponding value of c. This will result in a contour map that visually represents the function g(v, w) across the vw-plane.

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Positive values will cause the level sets to expand away from the origin.

What is the scaling factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger. K is the scaling factor for x in the equation y = Kx.

Here, we have

Given:  For c < 0, similarly relate the level set g(v, w) = c.

By using a scaling factor of |c|, the level set g(v, w) = c can be connected to the drawing in part (c) for c 0. The level set curves for negative values of c will therefore be scaled by a factor equal to the square root of the absolute value of c.

The level set curves will constrict toward the vw-plane's origin as c grows more negative, with a smaller scale factor indicating closer proximity to the origin. Plotting level sets for different values of c, both positive and negative, is the first step in creating a contour map for g in the vw-plane. For negative values of c, don't forget to use the necessary scaling factors as described in paragraph (e).

Make sure to label each level set with its corresponding value of c. This will result in a contour map that visually represents the function g(v, w) across the vw-plane. Positive values will cause the level sets to expand away from the origin, whereas negative values will cause them to contract toward the origin.

Hence, positive values will cause the level sets to expand away from the origin.

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The measurement that gives you the difference between the points on the scatterplot and the prediction line for the same value of x is the residual. Therefore, the correct answer is C. Residual.

In regression analysis, the residual represents the vertical distance between the observed data points and the corresponding predicted values on the regression line. It is calculated by taking the difference between the actual observed value and the predicted value for a specific value of the independent variable (x). The residuals provide a measure of how well the regression line fits the data, with smaller residuals indicating a better fit.

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The new store will have a profit of $3400 after its third month in business.

The correct option is D.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

George has opened a new store, and he is monitoring its success closely.

He has found that this store’s revenue each month can be modeled by r(x)=x²+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars.

He has also found that his expenses each month can be modeled by c(x)=x²−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.

(r−c)(x) = x²+5x+14 -x²+3x-4

(r−c)(x) = 8x+10

(r−c)(3) = 24+10 = 34 in hundreds of dollars.

Therefore, the new store has profit of $3400.

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Answer:

twetwe. eet   wvjhcjh

Step-by-step explanation:

wetwetwet wte ucytc

Answer:   1/2 |x| = -3?

Step-by-step explanation:

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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Answer:

y=0.5x+8

Step-by-step explanation:

The slope is 0.5 so y=0.5x. We can plug in the point to the equation and we get 8=0(0.5)+b or 8=0+b. b=8 so the equation is y=0.5x+8

In the given IS-LM model, the equilibrium real output, Y, and the equilibrium value of consumption, C, can be determined using the IS and LM equations. The IS equation relates output to the interest rate, while the LM equation represents the equilibrium condition in the money market. By substituting the given values into the equations, we can find the equilibrium values.

The IS equation is given by: Y = 1,586.27 - 3,145.45i.

The LM equation is given as: i = 0.04.

To find the equilibrium real output, we substitute the value of i from the LM equation into the IS equation:

Y = 1,586.27 - 3,145.45 * 0.04.

Calculating the right side of the equation, we have:

Y = 1,586.27 - 125.82,

Y ≈ 1,460.

Therefore, the equilibrium real output, Y, is approximately 1,460.

To find the equilibrium value of consumption, we substitute the equilibrium real output, Y, into the consumption function:

C = 217 + 0.51Y.

Substituting Y = 1,460, we have:

C = 217 + 0.51 * 1,460.

Calculating the right side of the equation, we find:

C ≈ 984.

Therefore, the equilibrium value of consumption, C, is approximately 984.

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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The contractor would have to work for 20 hours on the site to earn $555 total pay

What is total cost function?

Total cost function is the sum of the fixed charge, which is fixed cost to the person paying the contractor when the contractor visits the site and charge per hour multiplied by the number of hours spent working

TC=a+bX

TC=total cost=$555

a=fixed charged=$55

b=charge per hour=variable element of contractor's pay=$25

X=number of hours spent working=unknown

$555=$55+$25X

$555-$55=$25X

$500=$25*X

X=$500/$25

X=20

The contractor needs to work for 20 hours in order to earn a total pay of $555

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The measures of the interior and exterior angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠7, ∠8, and ∠9 are 90°, 90°, 90°, 122°, 58°, 58°, 148°, 32°, and 148°, respectively.

We are given a triangle. One of the angles is 122 degrees, as shown in the diagram. We need to find all the interior and exterior angles. The vertically opposite angles are equal. The angle ∠4 is vertically opposite to the given angle. So, ∠4 = 122°. The angle ∠5 and the given angle form a linear pair. So, the angle ∠5 = 180° - 122° = 58°. The angle ∠6 is vertically opposite to the angle ∠5. So, the angle ∠6 = 58°. The angles ∠1, ∠2, and ∠3 are angles made by coordinate axes that are perpendicular to each other. So, the angles ∠1 = ∠2 = ∠3 = 90°. Now we use the angle sum property of a triangle. The sum of all the interior angles of a triangle is 180°. So, we can write the equation : ∠6 + ∠1 + ∠8 = 180°. So, ∠8 = 180° - (∠6 + ∠1) = 180° - (58° + 90°) = 180° - 148° = 32°. The angles ∠8 and ∠9 form a linear pair. So, ∠9 = 180 - 32° = 148°. The angle ∠7 is vertically opposite to the angle ∠9. So, the angle ∠7 = 148°.

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