Consider parallelogram below ABCD. Use the information given in the figure to find , angle B, and angle BAC

The approximate population 3 years after the population started being recorded is 2584 people option (C) is correct.

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×

where a is a constant and a>1

It is given that:

The population of a community is modeled by this exponential function, where x represents the number of years since the population started being recorded:

p(x) = 2,400(1.025)×

Plug x = 3 years in the above function.

P(3) = 2400(1.025)³

P(3) = 2400x1.0768

P(3) = 2584.53 ≈ 2584 people

Thus, the approximate population 3 years after the population started being recorded is 2584 people option (C) is correct.

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The solution to the system of equations is x = 8, y = 4.

First, let's define our variables as x and y.

"the sum of two numbers is twelve" is written as:

x + y = 12

"two times the first number minus three times the second number is four" is written as:

2x - 3y = 4

Then the system of equations is:

x + y  = 12

2x - 3y = 4

First, we isolate one of the variables in one equation, I will isolate x on the first one to get:

x = 12 - y

Now we replace this on the other equation, so we get:

2*(12 - y) - 3y = 4

Now we can solve this for y.

24 - 2y - 3y = 4

24 - 5y = 4

24 - 4 = 5y

20/5 = y = 4

Now we know the value of y, and:

x = 12 - y = 12 - 4 = 8

Then the solution of the system is:

x = 8, y = 4.

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[i] … … … x + 3y - z = 9

[ii] … … … 2x + 9y + 4z = 12

[iii] … … … x + 4y + z = 7

Eliminate z by combining …

• … 4 times equation [i] and equation [ii] :

4 (x + 3y - z) + (2x + 9y + 4z) = 4•9 + 12

(4x + 12y - 4z) + (2x + 9y + 4z) = 36 + 12

6x + 21y = 48

2x + 7y = 16

• … equation [i] and equation [iii] :

(x + 3y - z) + (x + 4y + z) = 9 + 7

2x + 7y = 16

Since we ended up with 2 copies of the same equation, we have infinitely many solutions for x, y, and z. That is, we have infinitely many choices for x and y that satisfy 2x + 7y = 16, and consequently infinitely many choices for z to satisfy any of the 3 original equations.

We can parameterize the solution by letting, for instance, x = t; then the solution set is

x = t

2x + 7y = 16   ⇒   y = (16 - 2t)/7

x + 3y - z = 9   ⇒   z = t + 3 (16 - 2t)/7 - 9   ⇒   z = (t - 15)/7

where t is any real number.

Answer:

105

Step-by-step explanation:

X=8

Y=20

So,

x/y = 8/20

     = 2/5

x=(2/5)y

y= (5/2)x

When x=42

y=(5/2)×42

  =105

Answer:

54

Step-by-step explanation:

6(+647)

34-56+78%25

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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Answer:

f

Step-by-step explanation:

Answer:

[-4, -2]

Step-by-step explanation:

We are looking for the interval where function f increases the fastest. Since the increase is fastest where the slope is highest, and the slope is highest from -4 to -2, we select this interval.

Answer:

Mathematics shaping the modern world.

The perfect square in this problem is given and factored as follows:

x² + x + 0.25 = (x + 5)².

The perfect square of the sum of two terms is given by the notable product presented as follows:

(x + a)² = x² + 2ax + a².

In the context of this problem, the expression is given as follows:

x² + x +

Then the coefficient a is obtained comparing the above function to the standard function as follows:

x² + x = x² + 2ax.

Then:

2a = 1

a = 0.5.

Hence the final term of the expression is given as follows:

a² = 0.5² = 0.25.

Thus the complete expression is:

x² + x + 0.25.

And the factored expression is of:

(x + 0.5)².

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Answer:

look around for it maybe it fell under your bed, couch etc just look

Step-by-step explanation:

Answer:

im pretty sure the top one

Step-by-step explanation:

The amount of Dividends of $3,000, $5,000, $34,500, and $71,000 were distributed to the 20,000 preferred and 25,000 common shareholders of Lightfoot Inc. over the first four years of operations.

To calculate the dividend per share of the preferred and common stock of Lightfoot Inc., the total amount of dividends paid out over the first four years must first be determined. This can be done by adding the given amounts of $3,000, $5,000, $34,500, and $71,000 to get a total of $113,500. To find the dividend per share for the preferred stock, the total dividend is divided by the number of shares (20,000) which gives a dividend per share of $5.68. To find the dividend per share for the common stock, the total dividend is divided by the number of shares (25,000) which gives a dividend per share of $4.54.

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Answer:

69310

Step-by-step explanation:

255*270+460

=68850+460

=69310

Answer:

x=4

Step-by-step explanation:

9x=36, divide both sides by 9

Answer:

Step-by-step explanation:

9x=22+14

9x=36

x=36/9

x=4

It will be nice if you give me brainliest. Good luck!

Answer:

0.0125

Step-by-step explanation:

The P-value can be calculated by using excel function T.DIST.RT(2.968,6).

Right tail is used in the function because our alternative hypothesis has greater than sign (>) whereas 2.968 represent test statistic value and 6 represents degree of freedom. The resultant p-value from excel function is 0.0125.

Or if we use t- distribution right tail area table, we see that 6 for degree of freedom the value in table is there are two value 2.44691 and 3.14627 which corresponds to p=0.025 and p=0.01. As 2.44691 is smaller than 2.968 so we take p=0.01 against 3.14627. Thus, in this scenario p-value would be 0.01.

Answer:

c

Step-by-step explanation:

To find the x-intercept, we set y to 0 and solve for x:

0 = x + 8

x = -8

Therefore, the x-intercept is -8.

To find the y-intercept, we set x to 0 and solve for y:

y = 0 + 8

y = 8

Therefore, the y-intercept is 8.

Hopes this helps

Answer:

There are 0

Step-by-step explanation:

Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true

Answer:

A 0

Step-by-step explanation:

There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.

If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.

Answer:

D

Step-by-step explanation:

When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"

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The point lies in the line 2y = 3x + 10 will be (3, 9.5). Then the correct option is B.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

The linear function is given below.

10 = -3x + 2y

2y = 3x + 10

y = (3/2)x + 5

At x = 3, the value of the variable 'y' is given as

y = (3/2)x + 5

y = (3/2)(3) + 5

y = (9/2) + 5

y = 4.5 + 5

y = 9.5

The point lies in the line 2y = 3x + 10 will be (3, 9.5). Then the correct option is B.

The graph is given below.

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The missing options are given below.

(3, 9), (3, 9.5), (3, 10), (3, 8)

The geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

It should be noted that to find the geometric mean of two numbers, we multiply them together and then take the square root of the result. So, for each pair of numbers, we can follow these steps:

Multiply the two numbers together.

Take the square root of the product.

Using this formula, we get:

7.16 and 27:

Geometric mean = √(7.16 × 27) ≈ 14.85

5 and 36:

Geometric mean = √(5 × 36) = √180 ≈ 13.42

10.8 and 48:

Geometric mean = √(10.8 × 48) ≈ 22.94

Therefore, the geometric means of the pairs of numbers are approximately:

14.85 for 7.16 and 27

13.42 for 5 and 36

22.94 for 10.8 and 48.

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Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20..

To estimate the value of the vehicle after 4 years, we can use the given equation A = 39500(0.86)^t, where A represents the value of the vehicle and t represents the number of years.

Substituting t = 4 into the equation:

A = 39500(0.86)^4

A ≈ 39500(0.5996)

A ≈ 23726.20

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20.

This estimation is based on the assumption that the vehicle's value decreases by 14% each year. The equation A = 39500(0.86)^t models the exponential decay of the vehicle's value over time. By raising the decay factor of 0.86 to the power of 4, we account for the 4-year period. The final result suggests that the value of the vehicle would be around $23,726.20 after 4 years of ownership.

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The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

We have,

Recall the trigonometric identities:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))

Using these identities, we can find the exact values of the expressions given.

(a) Sin (α + β)

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 - 8/25

= (-6√5 - 8)/25

(b) Cos (α + β)

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)

= -6/25 + 4√5/25

= (4√5 - 6)/25

(c) Sin (α - β)

sin(α - β) = sin(α)cos(β) - cos(α)sin(β)

= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 + 8/25

= (-6√5 + 8)/25

(d) tan (α - β)

tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))

= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)

= (9√5/5)/(1 - 4/5√5)

= (-9√5 + 45)/4

Therefore,

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Draw the triangles

step 2: Write the congruent sides

STEP 3: Find the measure of angle D

It can be seen from step 2 that angle D is congruent to angle A.

We find angle A as seen below:

Since angle D is congruent to angle A,

hence, m

Answer: $1856

Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856

Answer:

38.042 square units

Step-by-step explanation:

Steps to find the area of a regular polygon with 20 sides and a side length of 2

Find the apothem

apothem = s / (2 * tan(pi/n))

apothem = 2 / (2 * tan(pi/20))

apothem ≈ 1.9021

Calculate the perimeter

perimeter = n * s

perimeter = 20 * 2

perimeter = 40

Calculate the area

area = (1/2) * apothem * perimeter

area = (1/2) * 1.9021 * 40

area ≈ 38.042 square units

Therefore, the area of the regular polygon with 20 sides and a side length of 2 is approximately 38.042 square units.

Answer:

Answer 1008

Step-by-step explanation:

Using law of cosine and Pythagorean theorem, the length of BC is 18 foot and CD is 12.3 foot

a) To find the length of support member BC, we can use the Law of Cosines:

BC^2 = AC^2 + AB^2 - 2 * AC * AB * cos(m/C)

where m/C is the measure of angle C. We know that m/A = 40° and m/D = 45°, so m/C must be the supplementary angle to the sum of these angles:

m/C = 180° - (m/A + m/D) = 180° - (40° + 45°) = 95°

Substituting known values into the Law of Cosines equation, we have:

BC^2 = 10^2 + 8^2 - 2 * 10 * 8 * cos(95°)

BC^2 = 100 + 64 + 160

BC^2 = 324

BC = sqrt(324) = 18

So, the length of support member BC is 18 feet to the nearest hundredth of a foot.

b) To find the length of cable CD, we can use the Pythagorean Theorem:

CD^2 = BC^2 + AC^2 - 2 * BC * AC * cos(m/A)

Substituting known values into the equation, we have:

CD^2 = 18^2 + 10^2 - 2 * 18 * 10 * cos(40°)

CD^2 = 324 + 100 - 360 * cos(40°)

CD^2 = 424 - 360 * cos(40°)

Using the cosine formula, we can find the value of cos(40°):

cos(40°) = cos(90° - 40°) = sin(40°)

And using a reference table or calculator, we find that sin(40°) = 0.766

So, substituting the value of cos(40°) back into the equation for CD^2, we have:

CD^2 = 424 - 360 * 0.766

CD^2 = 424 - 276.56

CD^2 = 147.44

CD = sqrt(147.44) = 12.3

So, the length of cable CD is 12.3 feet to the nearest hundredth of a foot.

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