A soccer goal, as shows below, is composed of a pair of 8foot upright posts, positioned 48ft apart with a horizontal crossbar and netting boxing in the goal. A soccer ball is positioned directly in front of the right goal post. If the ground distance from the ball to the right goal is 14ft, what is the ground distance from the ball to the left goal post?

Answer:

4.5

Step-by-step explanation:

7 1/2 X 6 = 45.

Then you just add the decimal point to get 4.5.

The inequality can be written as 65L + 35S ≤ 500. The number of large boxes will be 5.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that Renaldo has $500 to spend on gift boxes for a party. The cost of a large box is $65 and a small box is $35.

The inequality can be written as:-

65L + 35S ≤ 500

The number of the large boxes will be calculated as:-

65L + 35S ≤ 500

65L + ( 35 x 6 ) ≤ 500

65L = 500 - 210

65L = 290

L = 4.523

L = 5 boxes

Therefore, the number of large boxes is 5 and the inequality is 65L + 35S ≤ 500.

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The required answer is a non-decreasing function f, even if it is not necessarily continuous.

To prove that a non-decreasing function f is Riemann integrable on any finite interval, the fact that any bounded non-decreasing function is Riemann integrable.

step-by-step explanation:

1. Start by considering a non-decreasing function f defined on a closed and bounded interval [a, b].
2. Since f is non-decreasing, its values can only increase or remain constant as the input increases.
3. Now, let's define a partition P of the interval [a, b]. A partition is a collection of subintervals that cover the interval [a, b].
4. For each subinterval [x_i, x_(i+1)] in the partition P,  the difference f(x_(i+1)) - f(x_i).
5. Since f is non-decreasing, the difference f(x_(i+1)) - f(x_i) will be non-negative or zero for every subinterval in the partition.
6. Next, we calculate the upper sum U(P,f) and lower sum L(P,f) for the partition P. The upper sum is the sum of the products of the lengths of the subintervals and the supremum of f on each subinterval. The lower sum is the sum of the products of the lengths of the subintervals and the infimum of f on each subinterval.
7. By considering different partitions, we can observe that the upper sums U(P,f) are non-decreasing, and the lower sums L(P,f) are non-increasing.
8. Since f is bounded on the closed and bounded interval [a, b], the upper sums U(P,f) are bounded above, and the lower sums L(P,f) are bounded below.
9. By the completeness property of the real numbers, the sequence of upper sums U(P,f) converges to a limit, denoted by U, and the sequence of lower sums L(P,f) converges to a limit, denoted by L.
10. If U = L, then the function f is Riemann integrable on the interval [a, b], and the common value U = L is called the Riemann integral of f on [a, b].

Therefore, that a non-decreasing function f, even if it is not necessarily continuous, is Riemann integrable on any finite interval.

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The method applied for determining the density of a solid (regular and irregular) and a liquid is based on the concept of mass and volume.

For solids (regular and irregular):

Determining the mass: The mass of the solid can be measured using a balance or scale. The unit of mass is typically grams (g) or kilograms (kg).

Determining the volume:

Regular solids: The volume of regular solids, such as cubes or rectangular prisms, can be calculated using their geometric formulas. For example, the volume of a cube is calculated by cubing the length of one of its sides: Volume = side length^3.

Irregular solids: The volume of irregular solids can be determined using various methods such as water displacement. The solid is immersed in a known volume of liquid (e.g., water), and the increase in the volume of the liquid is measured. This increase represents the volume of the solid.

Calculating the density: The density of a solid is calculated by dividing its mass by its volume. The unit of density is typically grams per cubic centimeter (g/cm^3) or kilograms per cubic meter (kg/m^3).

For liquids:

Determining the mass: Similar to solids, the mass of the liquid can be measured using a balance or scale.

Determining the volume: The volume of a liquid can be measured directly using a graduated cylinder or other volumetric measuring devices. The unit of volume is typically milliliters (mL) or liters (L).

Calculating the density: The density of a liquid is calculated by dividing its mass by its volume. The unit of density is typically grams per milliliter (g/mL) or kilograms per liter (kg/L).

The method for determining the density of a solid (regular and irregular) involves measuring the mass and volume of the solid and calculating the density by dividing the mass by the volume. For liquids, the density is determined similarly by measuring the mass and volume.

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Answer:

25.6 grams of the second ingredient (25% protein) to make 28 grams of the mixture that is 30% protein.

Step-by-step explanation:

To make 28 grams of a substance that is 30% protein, Becky will need to mix together different ingredients to get the desired amount of protein.

Let's call the amount of the first ingredient (50% protein) "x" and the amount of the second ingredient (25% protein) "y".

We know that:

The total amount of the mixture is 28 grams

The mixture is 30% protein

The first ingredient is 50% protein

The second ingredient is 25% protein

We can set up the following equations to represent the problem:

x + y = 28 (the total amount of the mixture is 28 grams)

(0.50)x + (0.25)y = 0.30(28) (the mixture is 30% protein)

Now we can use the first equation to solve for one variable in terms of the other. If we solve for y, we get:

y = 28 - x

We can substitute this into the second equation:

(0.50)x + (0.25)(28-x) = 0.30(28)

Which gives us:

0.50x + 7 - 0.25x = 8.4

And further simplifying

0.25x = 0.6

x = 2.4

Now we know that the first ingredient, which is 50% protein, makes up 2.4 grams of the mixture. We can use this information to find the amount of the second ingredient:

y = 28 - x = 28 - 2.4 = 25.6 grams

So, Becky needs to use 2.4 grams of the first ingredient (50% protein) and 25.6 grams of the second ingredient (25% protein) to make 28 grams of the mixture that is 30% protein.

Answer:

Step-by-step explanation:

The equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to the yz-plane can be found by using the distance formula in three dimensions.

Let (x, y, z) be a point P on the surface. The distance from P to the x-axis is |x|, and the distance from P to the yz-plane is sqrt(y^2 + z^2). Setting these two distances equal and solving for x, we get:

|x| = 2 * sqrt(y^2 + z^2)

x = 2 * sqrt(y^2 + z^2) if x >= 0

x = -2 * sqrt(y^2 + z^2) if x < 0

This is the equation for a hyperboloid of one sheet. The hyperboloid of one sheet is a three-dimensional surface with two connected components that are mirror images of each other across the x-axis.

A parametric equation for the line that passes through the point P(2, 1, 2) in the direction of the vector v = [-1, 1, 3] can be written as: r(t) = P + tv.  the velocity of the moving point is [-1, 1, 3], and its speed is √(11) units per time unit.

To find the parametric equation for the line passing through (2, 1, 2) in the direction of the vector [-1, 1, 3], we can use the following formula:

r(t) = r0 + tv

where r(t) is the position vector of a point on the line at time t, r0 is the initial position vector (in this case, (2, 1, 2)), t is a scalar parameter, and v is the direction vector (in this case, [-1, 1, 3]).

Plugging in the given values, we get:

r(t) = [2, 1, 2] + t[-1, 1, 3]

Expanding the vector multiplication, we get:

r(t) = [2 - t, 1 + t, 2 + 3t]

This is the parametric equation of the line.

To sketch the line, we can plot the initial point (2, 1, 2) and then draw the line in the direction of the vector [-1, 1, 3]. Since the direction vector has components [-1, 1, 3], we can think of it as starting at the initial point and moving -1 units in the x-direction, 1 unit in the y-direction, and 3 units in the z-direction. Therefore, we can sketch the line by connecting the initial point to a point that is -1 units to the left, 1 unit up, and 3 units forward from the initial point.

To parameterize the line, we use the equation r(t) = [2 - t, 1 + t, 2 + 3t] as mentioned above. The parameter t can be thought of as time, where t = 0 corresponds to the initial position vector (2, 1, 2), and as t increases or decreases, we move along the line in the direction of the vector [-1, 1, 3].

To calculate the velocity and speed of the moving point, we can take the derivative of r(t) with respect to t:

r'(t) = [-1, 1, 3]

This gives us the velocity vector, which is constant along the line. The magnitude of the velocity vector is the speed of the moving point, which is:

|[-1, 1, 3]|

= √((-1)² + 1² + 3²)

= √(11)
Therefore, the speed of the moving point is √(11).

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To simplify the given expression and determine the number of terms in the numerator and denominator, let's break it down step by step:

Expression: (x^2 - 6x^2 - 6x^5) / (x^2 + 2x - 3x^2 - 7x + 10)

Simplifying the numerator:

x^2 - 6x^2 - 6x^5 = -5x^2 - 6x^5

Simplifying the denominator:

x^2 + 2x - 3x^2 - 7x + 10 = -2x^2 - 5x + 10

The simplified expression becomes:

(-5x^2 - 6x^5) / (-2x^2 - 5x + 10)

Now, let's count the number of terms in the numerator and denominator separately:

Numerator: -5x^2 - 6x^5

The numerator has two terms: -5x^2 and -6x^5.

Denominator: -2x^2 - 5x + 10

The denominator has three terms: -2x^2, -5x, and 10.

Therefore, the expression has two terms in the numerator and three terms in the denominator.

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Answer:

Step-by-step explanation:

Looks like the clockwise rotation of 180 degrees about the point (6,−2), followed by a translation of 9 units in a negative x-direction. That is because once it's rotated it will be at x=15 and then if you subtract -9x you will land exactly where you started

The life expectancy will reach 75 years old in the year 1970.

We have,

Let's start by defining the variables:

L = life expectancy in years

t = time in years since 1900

We know that from 1900 to 1960, life expectancy increased at a constant rate of 0.401 years per year.

So, we can write the following equation to represent the relationship between L and t:

L = 0.401t + b

where b is the life expectancy in 1900.

To find b, we can use the fact that the life expectancy in 1900 was around 47 years old.

b = 47

So, the equation becomes:

L = 0.401t + 47

We also know that in 1942, the life expectancy was 62.9 years old.

So, we can use this information to find the value of t in 1942:

62.9 = 0.401t + 47

Solving for t, we get:

t = (62.9 - 47) / 0.401 = 39.15

In 1942,

t = 39.15.

To find the year when the life expectancy reaches 75 years old, we can plug in L = 75 into the equation and solve for t:

75 = 0.401t + 47

Solving for t.

t = (75 - 47) / 0.401 = 69.82

So, the life expectancy will reach 75 years old in the year:

1900 + 69.82 = 1969.82

Therefore,

The life expectancy will reach 75 years old in the year 1970.

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Answer:

1 granola bar =

Step-by-step explanation:

10 granola bars= $4.00 x 2 = $8.00

15 granola bars=$4.00 x 3 = $12.00

20 granola bars=$4.00 x 4 = $16.00

1 granola bar = $0.80p

1. If g(20) = 35 and g'(20)= -2, in this case we can use the first-order Taylor approximation method to estimate the value of g(22) which is 31.

We can use the information provided in the problem to estimate the value of g(22), which contains the values of g(20) and g'(20). We know that g'(20) equals -2 as the derivative of g(x) for x = 20.

A differentiable function g(x)'s first-order Taylor approximation about x = a is:

g(x) = g(a) + g'(a) (x-a)

When we use this formula with a=20

g(a) = g(20) = 35

g'(a) = g'(20) = -2

x=22

we get:

g(22) ≈ g(20) + g'(20) (22-20)

≈ 35 + (-2) (2) ≈ 31

g(22) ≈ 31

As a result, the value of g(22) is estimated to be 31.

2.  If g(1)= -17 and g'(1)= 5, in this case we can use the first-order Taylor approximation method to estimate the value of g(1.2) which is -16.

We can use the information provided in the problem to estimate the value of g(1.2), which contains the values of g(1) and g'(1). We know that g'(1) equals 5 and is the derivative of g(x) at x = 1.

We may use the following formula to get g(1.2):

g(x) = g(a) + g'(a) (x-a)

g(1.2) ≈ g(1) + g'(1) * (1.2 - 1)

We may use the numbers supplied in the problem to replace g(1) = -17 and g'(1) = 5 in the formula above:

g(1.2) ≈ -17 + 5 * (1.2 - 1)

When we simplify the equation, we get;

g(1.2) ≈ -17 + 5 * 0.2

g(1.2) ≈ -17 + 1

g(1.2) ≈ -16

As a result, based on the information provided in the issue, we may estimate that g(1.2) is about equivalent to -16.

3. The Tangent Line Approximation method is used to estimate the cube root of numbers. By using this method it gives us the value of cube root of 9 which is 2.08.

To estimate the cube root of 9 using the tangent line approximation, we must first identify a point around 9 as our starting point. Let's go with 8 because it's a perfect cube and near 9.

We want to approximate the function f(x) = ∛x, which gives us the cube root of x. Taking the derivative, we can derive the equation of the tangent line to this function at x = 8.

f(x)= f'(a) (x-a) + f(a)

f(x) = ∛x

f'(x) = (1/3)x^(-2/3)

At x = 8, the derivative is:

f'(a) = f'(8) = (1/3)(8)^(-2/3) = 1/12

f'(a) = 1/12

So the equation of the tangent line at x = 8 is:

f(x) ≈ 1/12 (x - 8) + 2

Now we can use this tangent line to approximate the value of f(x) at x = 9:

f(9) ≈ 1/12 (9 - 8) + 2

≈ 1/12(1) + 2

≈ 1/12 + 2

f(9) ≈ 25/12 = 2.083333

f(9) ≈ 2.083333

∛9 ≈ 2.08

Therefore, using the tangent line approximation, we estimate the cube root of 9 to be approximately 2.08.

4. The Tangent Line Approximation to estimate the fifth root of of numbers. By using this method it gives us the value of fifth root of 30 which is 1.975.

To estimate the fifth root of 30, we must first identify a function that approximates the fifth root of x near x=30, and then use the tangent line to that function at x=30 to estimate the value. We take 2, because the nearest fifth root is 32.

f(x)= f'(a) (x-a) + f(a)

f(a) = \(\sqrt[5]{a}\)

f'(a) = 1/(5\(\sqrt[5]{a^{4} }\))

a = 32

f(a) = \(\sqrt[5]{32}\) = 2

f'(a) = 1/ (5\(\sqrt[5]{32^{4} }\)) = 1/80

Therefore, substituting the values  in the equation.

f(30) = f(32) + f'(32)(30-32)

\(\sqrt[5]{30}\) = 2 + (1/80) (-2)

= 2 - (1/40) = 79/40

f(30) ≈ 1.975

\(\sqrt[5]{30}\) ≈ 1.975

Therefore, using the tangent line approximation, we estimate the fifth root of 30 to be approximately 1.975.

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If the mass m of the wrecking ball is 3620 kg, 902 N is the tension TB in the cable that makes an angle of 40∘ with the vertical

70.51kg is the tension TA in the horizontal cable, derived by static equilibrium

According to the static equilibrium condition, the net force on the object in the horizontal and vertical direction must be zero along the moment about any point. If an object follows the above three condition then it can be said into an equilibrium position.

If the mass m of the wrecking ball is 3620 kg, what is the tension TB in the cable that makes an angle of 40∘ with the vertical 902 N.

70.51 kg  is the tension TA in the horizontal cable

Let’s write the conditions of the equilibrium for the wrecking ball:

∑\(F_{x} = 0 ,\) ∑\(F_y = 0\)

Let’s consider the forces that act on the wrecking ball in the horizontal x- and vertical y-direction:

\(T_a - T_b sin\)∅ = 0, (1)

\(T_b cos\)∅ \(- mg = 0. (2)\)

a) We can find the tension \(T_b\) in the cable that makes an angle of 40° with the vertical from the first equation:

\(T_b = \frac{T_a}{sin}\) = \(\frac{580 N}{sin 40} = 902 N\)

b) We can find the mass of the wrecking ball from the second equation:

\(T_b cos\)∅ \(= mg\)

\(m = \frac{T_b cos}{g} = \frac{902 N * cos 40 }{9.8 m/s^2} = 70.51 kg\)

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Answer:

y=-5x+2

Step-by-step explanation:

Before we get started, we should identify slope-intercept form.

y=mx+b.

Step 1 : Isolate the y by dividing everything by 3.

(15x+3y=6)/3 = 5x+y=2

Step 2 : Move the x value to the right side.

y=-5x+2

Answer:

y=5x-2

Step-by-step explanation:

15x+3y=6

3y=15x-6....both side divide by 3

y=5x-2

Answer: x=25

Step-by-step explanation:

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

3x-15=2x+10

x-15=10

x=25

Answer:

x = 25

Step-by-step explanation:

Given expression:

\(\sf 3(x - 5) = 2(x + 5)\)

distribute inside parenthesis

\(\sf 3x - 15 = 2x + 10\)

collect like terms

\(\sf 3x -2x = 10+15\)

simplify following

\(\sf x =25\)

To check answer:

substitute x = 25 in equation

\(\sf 3(25 - 5) = 2(25+5)\)

simplify

\(\sf 3(20) = 2(30)\)

evaluate

\(\sf 60=60\)

As the statement is true, the answer is correct.

Answer:

A

Step-by-step explanation:

The height of the triangle must be perpendicular to the base of the triangle and the segment A is perpendicular to the given height.

Let's assume that f(x) has two. If these roots occur at x = α and x = β.

The Intermediate Value Theorem (IVT) states that there must be a value c, with α < c < β, such that f(c) = 0.Since f(x) is a polynomial function, it is continuous on the interval [1, 6] according to the intermediate value theorem (IVT).If f has only two roots at x = α and x = β, then f is negative for some values of x between 1 and α, and positive for other values of x between α and β, and negative again for other values of x between β and 6.We can easily conclude that 1.21 < α < 1.22 and 5.87 < β < 5.88 by checking the sign of f(1.21) and f(5.87), and also by checking the sign of f(1.22) and f(5.88).We can write this as follows(1.21) < 0, and f(1.22) > 0 because f has a root at α, which is between 1.21 and 1.22.f(5.87) > 0, and f(5.88) < 0 because f has a root at β, which is between 5.87 and 5.88.

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Answer:

1st option

Step-by-step explanation:

let y = h(x) and rearrange making x the subject , that is

y = 6x - 6 ( add 6 to both sides )

y + 6 = 6x ( divide both sides by 6 )

\(\frac{y+6}{6}\) = x

change y back into terms of x with x = \(h^{-1}\) (x)

\(h^{-1}\) (x) = \(\frac{x+6}{6}\)

17) its equivalence is 3(x + 2y + 1) (option A)

To determine its equivalence, we will factorize the expression:

Hence, its equivalence is 3(x + 2y + 1) (option A)

Answer:

2 fish

Step-by-step explanation:

FISH DON"T DROWN

1. The break-even point in unit sales and in dollar sales is 4,500 units and $324,000 respectively.

2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher break-even point.

3. Income statements before and after changes are implement net income of $36,000 and $(28,000) respectively.

4. The company has to sell 5,401 units to achieve the target profit of $35,000 per month.

1. The break-even point in unit sales and dollar sales is computed as follows:

Break-Even Point in Unit Sales = Fixed Costs / Contribution Margin per Unit = $108,000 / ($50 - $32) = 4,500 units

Break-Even Point in Dollar Sales = Fixed Costs / Contribution Margin Ratio = $108,000 / ($50 / $18) = $324,000

2. If variable expenses per stove increase as a percentage of selling price, it will result in a higher break-even point. Since variable expenses would have a higher percentage of revenue, contribution margin would be lower, making it more challenging to cover fixed costs.

3. Present Income Statement

Sales (8,000*$50) $400,000

Less variable expenses (8,000*$32) (256,000)

Contribution Margin $144,000

Less fixed expenses 108,000

Net Income $36,000

Income Statement if Changes are Implemented

Sales (8,000*$45) $360,000

Less variable expenses (8,000*$35) (280,000)

Contribution Margin $80,000

Less fixed expenses 108,000

Net Loss $(28,000)

4. The contribution margin ratio is 36% ($18/$50). So, the sales revenue required to achieve the target profit is:

$35,000 / 0.36 = $97,222

The number of units required to be sold is:

$97,222 / $18 = 5,401 units

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Given statement solution is :- The correct answer is: a reflection over the y-axis and then a 90-degree counterclockwise rotation about the origin.

To map triangle J''K''L'' back to JKL, we need to reverse the transformations that were applied to create J''K''L'' in the first place.

The given transformations are a 90-degree clockwise rotation about the origin and then a reflection over the y-axis. To reverse these transformations, we need to perform the opposite operations in reverse order.

The opposite of a reflection over the y-axis is another reflection over the y-axis.

The opposite of a 90-degree clockwise rotation about the origin is a 90-degree counterclockwise rotation about the origin.

Therefore, the transformation that will map J''K''L'' back to JKL is a reflection over the y-axis (first) followed by a 90-degree counterclockwise rotation about the origin (second).

So the correct answer is: a reflection over the y-axis and then a 90-degree counterclockwise rotation about the origin.

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Answer:

B: a reflection over the x-axis and then a 90degree counterclockwise rotation about the origin.

the 10th term of the AP(Arithmetic Progression) is -233/46.

Given,

The sum of first 5 terms of an AP is 25 and the sum of the next 5 terms is -75, to find the 10th term.

Let us assume the first term of the AP is 'a' and the common difference be 'd'.

So, 2a + 4d + 6d + 8d + 10d

= 25 ⇒ 2a + 28d

= 25

Similarly, 12d + 14d + 16d + 18d + 20d

= -75 ⇒ 80d

= -75 - 12d ⇒ 92d

= -75 ⇒ d = -75/92

Now,

2a + 28d = 25 ⇒ 2a

= 25 - 28d ⇒ 2a

= 25 - 28(-75/92) ⇒ 2a

= 316/23 ⇒ a

= 158/23

Hence, the 10th term of the AP is a + 9d which is (158/23) + 9(-75/92) = -233/46

Therefore, the 10th term of the AP is -233/46.

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The bottom of the ladder is 9 feet from the wall.

Using the Pythagorean Theorem, we can calculate the distance from the wall. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. In this case, the hypotenuse is 15 feet and the side adjacent to the wall is 12 feet.

The formula for the Pythagorean Theorem is a^2 + b^2 = c^2.

We can solve for the distance from the wall (a). a^2 = c^2 - b^2, so a^2 = 15^2 - 12^2, which equals a^2 = 225 - 144, so a^2 = 81. Taking the square root of both sides, a = 9 feet.

Therefore, the bottom of the ladder is 9 feet from the wall.

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Thus, It takes Jacob a total of hours from San Antonio to Houston and then from Houston to Dallas 7 5/12 hours.

A mixed number combines a proper fraction and a whole number. To express a quantity higher than a but that less than the next whole number, mixed numbers as well as mixed fractions are utilised. Improper fractions can be used to create mixed numbers.

Given that:

Convert the given mixed fraction into proper fractions:

San Antonio to Houston = 3 1/3 hours

                                        = (3*3 + 1)/3 hours

                                        = (9 + 1)/3 hours

                                        = 10/3 hours

Now,

Houston to Dallas = 4 1/12 hours

                              = (4*12 + 1)/12 hours

                              = (48 + 1)/12 hours

                              = 49/12 hours

Total time from San Antonio to Dallas = San Antonio to Houston + Houston to Dallas

Total time from San Antonio to Dallas = 10/3 + 49 / 12

Taking LCM:

Total time from San Antonio to Dallas = (10*4 + 49)/12

Total time from San Antonio to Dallas = (40 + 49)/12

Total time from San Antonio to Dallas = 89/12

Total time from San Antonio to Dallas = 7 5/12 hours

Thus, It takes Jacob a total of hours from San Antonio to Houston and then from Houston to Dallas 7 5/12 hours.

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Answer: 205.14

Step-by-step explanation:

Multiply

Add

Insert Decimal Point

205.14

Answer:

205.14

Step-by-step explanation:

Step 1: Multiply without the decimal points, then put the decimal point in the answer:

263x78

Step 2: Line up the numbers:

2 6 3

x 7  8

Step 3: Multipy the top number by the bottom number one digit at a time starting from left to right:

\(\frac{\begin{matrix}\:\:&\:\:&2&6&3\\ \:\:&\times \:&\:\:&7&8\end{matrix}}{\begin{matrix}0&2&1&0&4\\ 1&8&4&1&0\end{matrix}}\)

Step 4: Add:

\(\frac{\begin{matrix}\:\:&\textbf{1}&\:\:&\:\:&\:\:&\:\:\\ \:\:&\textbf{0}&2&1&0&4\\ +&\textbf{1}&8&4&1&0\end{matrix}}{\begin{matrix}\:\:&\textbf{2}&0&5&1&4\end{matrix}}\)

Step 5: Insert Decimal Point:

205.14

Answer:

2

Step-by-step explanation:

Answer:

i^32=1

i^25=i

i^86=-1

i^51=-i

Step-by-step explanation:

Follow the Rule of Four of I for this,

i^1=\(\sqrt{-1}\)

I^2=-1

I^3=-i

I^4=1

Answer: first one is 1

Second one is i

Third one is -1

Fourth one is -1

Step-by-step explanation: