if the area of the triangle is 8 15/16ths and the base is 5 1/2, what is the height

(1) The result of the row operation R₂ ↔ R₃ is [ -5   1    0    8]

                                                                            [  8  8    -7   5 ]

                                                                            [ 2   2     6   -5]

(2) The result of the row operation  3R₁ ↔ R₁ is  [24  - 27   -21   - 18]

                                                                                [8       9      -4      -5]

                                                                                 [2       2       -7     -8]

The result of the row operation in the matrix is calculated as follows;

R₂ ↔ R₃, implies changing row 2 and row, and the result would be;

[ -5   1    0    8]

[  8  8    -7   5 ]

[ 2   2     6   -5]

The result of obtained from 3R₁;

3R₁ = [24  - 27   -21   - 18]

3R₁ ↔ R₁ is determined as; (the row interchange)

[24  - 27   -21   - 18]

[8       9      -4      -5]

[2       2       -7     -8]

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The correct answer is: D) distance traveled since leaving Bay Town; x ≥ 0

The equation y = -x + 175 represents the distance left to travel to Oak Glen.

In this equation, x is the distance traveled since leaving Bay Town, and y is the distance left to reach Oak Glen.

The domain represents the possible values of x, which is the distance traveled since leaving Bay Town.

Since distance traveled cannot be negative, the domain is x ≥ 0. Therefore, the correct answer is:

D) distance traveled since leaving Bay Town; x ≥ 0

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The question in English is:

The distance between Bay Town and Oak Glen is 175 miles. If the equation y = -x +175 represents the distance to go to Oak Glen, what does the domain represent? What is the domain?

Answer:

  x = ±1, ±√65

Step-by-step explanation:

You want the solution to (x² -1)³ = 64(x² -1)².

Subtracting the right side, we have ...

  (x² -1)³ -64(x² -1) = 0

  (x² -1)²(x² -1 -64) = 0

The solutions make the factors zero:

  x² -1 = 0   ⇒   x = ±1

  x² -65 = 0   ⇒   x = ±√65

Solutions are x = ±1 and x = ±√65.

__

Additional comment

The solutions ±1 are each multiplicity 2.

For every 3 days Rochelle helped, she did not help for 1 day.

For every 4 days Rochelle helped, she did not help for 1 day.

For every 7 days Rochelle helped, she did not help for 6 days.

For every 28 days Rochelle helped, she did not help for 21 days.

Let's use the terms provided to complete the sentences comparing Rochelle's time in the garden.
Since Rochelle helped in the garden for 7 days during the last 4 weeks, we can calculate the total number of days in 4 weeks and then find the number of days she did not help.
There are 7 days in a week, so in 4 weeks, there are 4 x 7 = 28 days.
Rochelle helped for 7 days, so she did not help for 28 - 7 = 21 days.
Now, let's complete the sentences:
For every 1 day(s) Rochelle helped, she did not help for 3 day(s).
For every 3 day(s) Rochelle did not help, she helped 1 day(s).

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The given trigonometric expression sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.

As we know that sin⁻¹(x) = -cos⁻¹(x) + π/2, which is the angle in the fourth quadrant whose cosine is 3sqrt(2)/2.

We have:

cos²θ + sin²θ = 1

Since sine is negative and cosine is positive, we know that:

sinθ = -sqrt(1 - cos²θ)

Substituting cosθ = 3√(2)/2, we get:

sinθ = -√(1 - (3√(2)/2)²) = -√(1 - 9/8) = -√(1/8) = -√(2)/2

Therefore, sin^(-1)(-3sqrt(2)/2) = -cos^(-1)(3sqrt(2)/2) + π/2.

Since cosine is positive in the fourth quadrant, we have:

cos⁻¹(3√(2)/2) = π/4

Substituting this value, we get:

sin⁻¹(-3√(2)/2) = -π/4 + π/2 = π/4

Therefore, sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.

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Answer:

  a)  |x -8| = 6

  b)  |x -15| = 0

Step-by-step explanation:

You want the values of 'b' and 'c' for the cases where the solutions to the equation |x -b| = c are ...

The solutions to |x -b| = c are the solutions to ...

  x -b = c   ⇒   x = b +c

  x -b = -c   ⇒   x = b -c

Given the two solutions P and Q, the values of 'b' and 'c' can be found from ...

  P = b +c

  Q = b -c

Adding these two equations gives ...

  P +Q = 2b   ⇒   b = (P +Q)/2

Subtracting the second equation from the first gives ...

  P -Q = 2c   ⇒   c = (P -Q)/2

  b = (2 +14)/2 = 8

  c = (14 -2)/2 = 6

The equation is ...

  |x -8| = 6

  b = (15 +15)/2 = 15

  c = (15 -15)/2 = 0

The equation is ...

  |x -15| = 0

If the third term is 31, then let's get the second term. We have to use the rule we were given and work backwards. So, we will add three and then divide by 2.

31 + 3 = 34

34 / 2 = 17

17 is the second term. Let's do the same thing we just did to find the first term: add three, divide by 2.

17 + 3 = 20

20 / 2 = 10

Answer: the first term is 10

Hope this helps!

Amy's total cost: $697.26

Mackenzie's total cost: $11904.62

Amount = P = 340

Amy's interest rate = ra = 6% = 0.06

Mackenzie's interest rate = rm = 30% = 0.3

Amount is compounded yearly.

Amount at the end of the year is calulated as

Pn= P(1+r)

We will use Excel to fill given table

Person APR 0 1 2 3 6

Amy 6% 340.00 360.40 382.02 404.95 482.30

Mackenzie 30% 340.00 442.00 574.60 746.98 1641.12

Amy has an annual rate of 6%. So Amy has a monthly rate of 6 /12 = 0.5% = 0.005

Mackenzie has an annual rate of 30%. So Mackenzie has a monthly rate of 30/12 = 2.5% = 0.025

Pn= P(1+r)

Here will be replaced by a number of months and r is relaced by monthly interest rate

We can modified this formula as

12n

Pn= P(1+)

Where n and r is same as in first part of question.

We will use excel to fill given table

Person APR 0 1 2 3 6

Amy 6% 340.00 360.97 383.23 406.87 486.90

Mackenzie 30% 340.00 457.26 614.97 827.06 2011.86

From the above two tables, it is clear that it does matter how the company charges interest. When compounded monthly, the amount will more as compared to when compounded yearly. So,

Yes it matters because the more often they calculate the interest the higher the amount goes.

If neither friend made any payments for 12 years, we can add one more column to calculate for n = 12.

Amy's total cost: $697.26

Mackenzie's total cost: $11904.62

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a) The future value of the account after 30 years can be calculated using the formula:

FV = P * ((1 + r/n)^(n*t))

where P is the monthly deposit, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $300, r = 0.02, n = 12 (monthly compounding), and t = 30. Plugging these values into the formula, we get:

FV = $300 * ((1 + 0.02/12)^(12*30)) = $150,505.60

So you will have $150,505.60 in the account after 30 years.

b) The total amount of money you will put into the account is simply the monthly deposit multiplied by the number of months in 30 years, which is 30*12 = 360 months. So the total amount of money you will put into the account is:

$300 * 360 = $108,000

c) The total interest earned can be calculated by subtracting the total amount deposited from the future value of the account. So the total interest earned is:

$150,505.60 - $108,000 = $42,505.60

Answer:

a) you will have approximately $133,381.85 in the account in 30 years.

b) a total of $108,000 into the account over 30 years.

c) a total of $25,381.85 in interest over 30 years.

Step-by-step explanation:

Answer:

So when the two vehicles meet, the van has travelled 87.5 km and the car has travelled 150 km.

Step-by-step explanation:

(a) Let's call the time it takes for the two vehicles to meet "t". We know that the distance between the two towns is 237.5 km, and the combined speed of the two vehicles is 35 km/h + 60 km/h = 95 km/h. Using the formula distance = speed × time:

237.5 = 95t

Solving for t:

t = 237.5/95

t ≈ 2.5 hours

So the two vehicles will meet on the way 2.5 hours after 11.30 a.m., which is at 2.00 p.m.

(b) To find how far each vehicle has traveled when they meet, we can use the formula distance = speed × time again. The van travels at 35 km/h for 2.5 hours, so it travels:

distance = speed × time = 35 km/h × 2.5 hours = 87.5 km

The car travels at 60 km/h for 2.5 hours, so it travels:

distance = speed × time = 60 km/h × 2.5 hours = 150 km

So when the two vehicles meet, the van has traveled 87.5 km and the car has traveled 150 km.

The time taken for the second car to travel the same distance as the first car is 6 hours.

The time taken for the second car to travel the same distance as the first car is calculated as follows;

let the time taken for the second car to travel the same distance = t

distance traveled by second car = 60t

the time taken for the first car = t + 2

distance traveled by the first car = 45(t + 2)

Since both distance are equal, we will have the following equations;

60t = 45 (t + 2)

60t = 45t + 90

15t = 90

t = 90/15

t = 6

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The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively. This can be solved by using trigonometric functions.

Trigonometric functions are used to describe relationships involving angles and sides of triangles. They are used to calculate the sizes of angles and distances between points. These include sine, cosine, tangent, secant, cosecant and cotangent.

This can be solved by using trigonometric functions.

First we need to find the length of FA to solve the question further.

FA = 1.5+ FD

AG = FA cos 30

AG = 1.5 √3

AG = 1.5 FD √3/2 = 1.5√3  (as cos 30 = √3/2)

DF = 1.5

Thus, FA = AB+BD+FD

FA = 1 + 0.5 + 1.5

So, the length of FA is 3.

Now, for the triangle, ΔABC

as ∠BAC= 30

BC = AB/2

= 0.5

This is because the angle of the right triangle is 30°and we know that when the angle of a right triangle is 30° the length of opposite side is exactly equal to half of the length of the hypotenuse.

For ΔADE,

as ∠DAE= 30, and AD= 1.5

DE= AD/2

= 0.75

For ΔGAF,

as ∠GAF= 30, and FA= 3

FG = FA/2

= 1.5

The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively.

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Carson can line up his textbooks on his bookshelf in 24 different ways

What is Permutation?

Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.

What is Combination?

The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.

According to the given information:

Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:

n! / (n - r)!

where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).

On substituting the values in the formula,

4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24

Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.

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The probability is given as follows:

P(34 < X < 46) = 0.5468 = 54.68%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 40, \sigma = 8[/tex]

The probability is the p-value of Z when X = 46 subtracted by the p-value of Z when X = 34, hence:

Z = (46 - 40)/8

Z = 0.75

Z = 0.75 has a p-value of 0.7734.

Z = (34 - 40)/8

Z = -0.75

Z = -0.75 has a p-value of 0.2266.

Hence:

0.7734 - 0.2266 = 0.5468 = 54.68%.

The probability is:

P(34 < X < 46).

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The volume of the prism is V = 4000 cm³

Given data ,

Let the volume of the prism be represented as V

Now , the value of V is

Let the height of the prism be h = 10 cm

Let the width of the prism be w = 20 cm

Let the length of the prism be l = 20 cm

So , the base area of prism = l x w

Base area = 400 cm²

Now , the volume of the prism is V = 400 x 10

V = 4000 cm³

Hence , the volume of prism is V = 4000 cm³

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The equation of a parabola with a vertical axis and vertex (h, k) is given by:

(x - h)² = 4p(y - k)

In the equation, where p is the distance from the vertex to the focus (and also the distance from the vertex to the directrix).

If the vertex is at the origin (h=0, k=0), then the equation simplifies to:

x² = 4py

where p is still the distance from the vertex to the focus (and also the distance from the vertex to the directrix).

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Answer:

To determine the longest rod that can be carried to the loading dock, we want to find the shortest distance from point T to line segment CD. We can use the Pythagorean theorem for this.

First, we need to find the equation of the line containing segment CD. We can find the slope of the line CD as:

m = (y2 - y1) / (x2 - x1) = (36 - 48) / (48 - 0) = -12/48 = -1/4

where (x1, y1) = (0, 48) and (x2, y2) = (48, 36).

Using point-slope form, we get the equation of the line CD as:

y - 48 = (-1/4)(x - 0)

y = (-1/4)x + 48

Now, we can find the perpendicular distance from point T to the line CD as follows:

d = |(-1/4)(30) + 72 - 48| / sqrt((-1/4)^2 + 1)

d = 42 / sqrt(17) ≈ 10.21

Therefore, the longest rod that can be carried to the loading dock is approximately 10.2 inches long (rounded to the nearest tenth of an inch).

The value of variable y from the system of vertical angles is equal to 125.

In this problem we need to determine by algebra properties the value of a variable y from a system of two pairs of vertical angles. The system is represented by the following expression:

x + 20 = 3 · x - 50

2 · x = 70

x = 35

Then, by definition of supplementary angles:

(x + 20) + y = 180

55 + y = 180

y = 125

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From the interior angle theorem:

The Interior Angle Theorem states that if two secants or chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.

Considering the given circles:

m∠AED = ¹/₂(45 + 109)

m∠AED = 77°

m∠AEB = 180 - 77

m∠AEB = 103°

m∠LK = (2 * 62) - 74)

m∠LK = 50°

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So the area of the larger square is 900% of the area of the smaller square.

Area is a measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters (m²) or square feet (ft²). To find the area of a shape, you need to measure the length and width of the surface or region and then multiply those measurements together.

Here,

If the sides of a square are increased by a scale factor of 3, then the new square will have sides that are 3 times as long as the original square. The area of a square is proportional to the square of its sides, so the area of the new square will be 3² = 9 times as large as the area of the original square. Therefore, the area of the larger square is 900% of the area of the smaller square.

Alternatively, we can use the formula for the area of a square, A = s², where A is the area and s is the side length. If the side length is increased by a scale factor of 3, then the new side length is 3s. Therefore, the area of the new square is:

A' = (3s)²

= 9s²

The ratio of the area of the new square to the area of the original square is:

A' / A = (9s²) / (s²)

= 9

Multiplying by 100% to convert to a percentage, we get:

A' / A = 900%

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The cubic polynomial is given as y = 0.25(x³ - 12x + 16). Then the value of y when x = 6 will be 40.

Therefore the option  C is correct.

A polynomial expression is described as an algebraic expression with variables and coefficients.

If the zeroes of the polynomial are negative 4, 2, and 2.

Then the factors will be (x + 4), (x - 2), and (x - 2).

Then the cubic polynomial will be

we can write the polynomial equation as:

y = C(x³ - 12x + 16)

Then the polynomial is maximum at (-2, 8) then the value of C will be 0.25.

y = 0.25 (x³ - 12x + 16)

y = 0.25 (6³ - 12 × 6 + 16)

y = 0.25 (216 - 72 + 16)

y = 0.25 (160)

y = 40

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The smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.

A figure known as an angle is created by two rays or line segments that meet at a place known as the vertex of the angle. The sides or legs of the angle are other names for the rays or line segments.

To determine the smaller angle made by the two hands of a clock when it is 3 o'clock, we can use the following formula:

angle = |(11/2) * m - 30h|

where:

m is the number of minutes past the hour (in this case, since it is 3 o'clock, m = 0)

h is the hour (in this case, h = 3)

By using this formula, we get:

angle = |(11/2) * 0 - 30(3)| = |0 - 90| = 90

Therefore, the smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.

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Answer:

Answer is D.

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The number of roof trusses that would be needed for the longest length is 2

The longest lengths from the question are given

Longest lengths = 28 and 22

Next, we expand the lengths of the roof trusses

This is to calculate the greatest common factor (GCF) of the lengths

So, we have

28 = 2 * 2 * 7

22 = 2 * 11

Multiplying the common factors gives the GCF

So, we have

GCF = 2

This means that the number of roof trusses that would be needed for the longest length is 2

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The horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.

Given that:-

The angle is = 45

The height of the skyscraper is 1140 feet.

The horizontal distance will be calculated by applying the angle property in the right angle triangle.

tan45  =  (  P  /  B  )

B  =  P  /  tan45

B  =  P                                 Since ( tan45 =1 )

B  =  1140 feet.

Therefore the horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.

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From the observation deck of a skyscraper, Brandon measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Answer:

The linear function is y = (1/3)x - 4.

Step-by-step explanation:

The y-intercept is -4. Starting at (0, -4), go up 1 unit and then right 3 units. You will end at (3, -1). So the slope of this line is 1/3, and it follows that the function is

y = (1/3)x - 4.

The initial temperature of the soda is 18 degrees Celsius.

Its temperature after 20 minutes is 2.73 degrees Celsius.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = a(b)^x

Where:

When time, t = 0, the initial value can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]

C(0) = 18(1)

C(0) = 18 degrees Celsius.

When time, t = 0 = 20, the temperature can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]

C(20) = 2.73 degrees Celsius.

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Complete Question:

A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.

[tex]C(t)=18(0.91)^{t}[/tex]

Find the initial temperature of the soda and its temperature after 20 minutes?

Answer:

it would be 9x

Step-by-step explanation:

because subtract 3 from 12 and leave the x