1. A plane flies due east for 500 km and then on a heading of 120" for 150 km. What are its distance and bearing from its starting point?
2. A ship leaves port and sails due west for 120 km, then due south for 40 km. What are the distance and bearing of the port from the ship?

Answer:

The two points given are (-2, -8) and (8, -8), which lie on a horizontal line. Since the line is horizontal, the slope is zero.

To see this, we can use the formula for the slope of a line between two points:

slope = (y2 - y1)/(x2 - x1)

Substituting the coordinates of the two given points, we get:

slope = (-8 - (-8))/(8 - (-2)) = 0

Therefore, the slope of the line through the points (-2, -8) and (8, -8) is 0.

Step-by-step explanation:

Answer:  d = √(Δy2 + Δx2) = √(02 + 102) = √100 = 10

Step-by-step explanation:

Answer:

-1 ⇒ -6

0 ⇒ -2

1 ⇒ 2

2⇒6

Step-by-step explanation:

The company will need 58,800 cubic inches of wax to make 420 candles.

To calculate the amount of wax required to make 420 candles,

The volume of a rectangular prism is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height.

So, we have

V = 5 in x 4 in x 7 in = 140 cubic inches

To find the total amount of wax required to make 420 candles,

We have

Total amount of wax = 140 cubic inches/candle x 420 candles

= 58,800 cubic inches

Hence, the company needs 58,800 cubic inches

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If Jason claims no allowances this year, $17 more will be deducted from his weekly check for taxes compared to last year when he claimed one allowance.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

The amount of money deducted from Jason's paycheck for taxes depends on the number of allowances he claims.

Claiming more allowances reduces the amount of taxes withheld from his paycheck while claiming fewer allowances increases it.

If Jason claimed 1 allowance last year, his employer would have withheld taxes from his paycheck based on that information.

If he claims no allowances this year, more taxes will be withheld.

To calculate how much more will be deducted from his weekly check if he claims no allowances, we need to know his tax bracket and the amount of taxes that will be withheld for each allowance.

Assuming Jason is paid on a weekly basis, we can use the IRS tax withholding tables for 2021 to estimate the additional amount of taxes that will be withheld if he claims no allowances.

Using these tables, we find that for a single person earning $232.50 per week, claiming no allowances would result in an additional withholding of $17 per week.

Therefore, claiming no allowances would result in an additional withholding of $17 per week.

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To solve this problem, we can use a system of equations.

Let's call the number of Php 5 coins x and the number of Php 10 coins y. The first equation will represent the total number of coins: x + y = 120. The second equation will represent the total amount of money: 5x + 10y = 950. Now we can use the elimination method to solve for one of the variables. Let's multiply the first equation by -10 and then add the two equations together:

-10x - 10y = -1200

5x + 10y = 950

-----------------

-5x = -250

Divide both sides by -5 to get x:

x = 50. Now we can plug this value back into the first equation to solve for y:

50 + y = 120

y = 70

So there are 50 Php 5 coins and 70 Php 10 coins.

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1). W is closed under addition.  

  W is not closed under scalar multiplication

2. W is not closed under addition

   W is closed under scalar multiplication

1. Let V be the vector space of all 2x2 matrices with real entries. Consider the subset W of V consisting of matrices of the form:

| a b |

| 0 c |

where a, b, and c are real numbers. Note that W is non-empty, since the matrix |0 0| is in W.

|0 0|

Now, let A and B be any two matrices in W, so that A has the form:

| a1 b1 |

| 0 c1 |

and B has the form:

| a2 b2 |

| 0 c2 |

Then the sum of A and B has the form:

| a1+a2 b1+b2 |

| 0 c1+c2 |

which is clearly also in W. Therefore, W is closed under addition.

However, W is not closed under scalar multiplication. Let A be any matrix in W, so that A has the form:

| a b |

| 0 c |

where a, b, and c are real numbers. Then, if we multiply A by a non-real scalar k = xi (where x is a real number and i is the imaginary unit), we get:

kA = xi * | a b | = | xia xib |

| 0 c | | 0 xc |

which is not in W, since the entry in the (1,2) position is non-zero. Therefore, W is not closed under scalar multiplication.

2. Let V be the vector space of all polynomials with real coefficients. Consider the subset W of V consisting of all polynomials of degree at most 2.

Note that W is non-empty, since the polynomial p(x) = 0 is in W.

Now, let c be any real scalar, and let p(x) be any polynomial in W.

Then cp(x) is a polynomial of degree at most 2, since multiplying a polynomial of degree at most 2 by a scalar does not change its degree. Therefore, W is closed under scalar multiplication.

However, W is not closed under addition. Let p(x) and q(x) be any two polynomials in W of degree at most 2. Then the sum p(x) + q(x) may have degree greater than 2, and hence may not be in W. For example, if p(x) = x^2 + 2x + 1 and q(x) = -x^2 + x - 1, then p(x) + q(x) = 3x, which is not in W. Therefore, W is not closed under addition.

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The answer of the given question based on the Irons is trying to lay out the bases for a game of kickball such that the infield is a square the answer is  first base and third base should be about 35.4 feet apart.

The Pythagorean theorem is  fundamental concept in geometry that relates to three sides of right triangle. It states that in right triangle, the square of  length of  hypotenuse (the side opposite the right angle) is equal to  sum of the squares of  lengths of other two sides.

We can use the Pythagorean theorem to find this distance.

Let's call the distance between home base and first base "a". We know that the distance between home base and third base is also "a", because the infield is a square. We also know that the distance between home base and second base (which is the hypotenuse of the right triangle formed by home base, first base, and second base) is 25 feet.

Using the Pythagorean theorem, we can solve for "a":

a² + 25² = a² + a²

2a² = 25²

a² = (25²)/2

a = sqrt((25²)/2) ≈ 17.7 feet

So the distance between first base and third base should be approximately 35.4 feet (2a). Rounding to the nearest tenth of a foot, this is 35.4 feet. Therefore, first base and third base should be about 35.4 feet apart.

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a)z-score

b)z-score > 1.64

c)comparing the z-score to a z-table

d)a majority of the population of soft drink consumers prefer Pepsi over Coke.

To test the hypothesis that a majority of the population of soft drink consumers prefer Pepsi over Coke, we will use a significance level of α = .10.

H0: The proportion of soft drink consumers who prefer Pepsi is ≤ 0.5.
Ha: The proportion of soft drink consumers who prefer Pepsi is > 0.5.

Test statistic: z-score

Rejection Region: z-score > 1.64

We will obtain the P value by comparing the z-score to a z-table.

Conclusion: Based on the P value, if it is less than or equal to the significance level of 0.10, then we reject the null hypothesis. We can conclude that there is sufficient evidence to suggest that a majority of the population of soft drink consumers prefer Pepsi over Coke.

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The answer of values of m for which the equation has two complex (non-real) solutions are all values greater than 1/8. In other words, m > 1/8

To find all values of m for which the equation has two complex (non-real) solutions, we need to use the discriminant of the quadratic formula.

The discriminant is the part of the quadratic formula under the square root: b²-4ac. If the discriminant is less than 0, then the equation will have two complex (non-real) solutions.

So, let's start by setting the discriminant to be less than 0:

b²-4ac < 0

Now, let's plug in the values from the equation into the discriminant. The equation is in the form ax²+bx+c=0, so we can plug in the values for a, b, and c:

(1)²-4(m)(2) < 0

Simplify:

1-8m < 0

Subtract 1 from both sides:

-8m < -1

Divide both sides by -8:

m > 1/8

So, the values of m for which the equation has two complex (non-real) solutions are all values greater than 1/8. In other words, m > 1/8.

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Answer:

Step-by-step explanation:

216

The final values of n for which the denominator equals zero are n = -3 and n = -6.

The rational expression [tex](20n^2-180)/(4n^2+36n+72)[/tex]is not defined for any values of n for which the denominator equals zero. To find the values of n for which the denominator equals zero, we need to solve the equation [tex]4n^2+36n+72 = 0.[/tex]

First, we can simplify the equation by dividing all terms by 4:

[tex]n^2+9n+18 = 0[/tex]

Next, we can use the quadratic formula to find the values of n:

n = [tex](-9 ± √(9^2-4(1)(18)))/(2(1))[/tex]

n = (-9 ± √(81-72))/2

n = (-9 ± √9)/2

n = (-9 ± 3)/2

The two values of n are:

n = (-9 + 3)/2 = -6/2 = -3

n = (-9 - 3)/2 = -12/2 = -6

So the values of n for which the denominator equals zero are n = -3 and n = -6.

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Answer: 10

Step-by-step explanation:

Since both points have the same y value, we just need to find the change of x, which would be the distance of the points.

Reading the points from left to right on an imaginary graph, point B would come first as it has the lesser x value.

To find the change of x subtract the x value of the second point from the first, so...

6 - (-4) = 10

The change of x = 10

The distance between the points is 10

Hope this helps!

The distance between the points C=(-7,6) and E=(-2,2) is 6.4 units.

To calculate the distance between two points, we use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the points are C=(-7,6) and E=(-2,2), so we can plug in the values into the formula:

d = √((-2 - (-7))^2 + (2 - 6)^2)

d = √((5)^2 + (-4)^2)

d = √(25 + 16)

d = √(41)

d = 6.4

Therefore, the distance between the points C=(-7,6) and E=(-2,2) is 6.4 units.

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The measure of the angle that is created when we move the hour hand to 5 and the minute hand to 1 is 144°.

To find the measure of the angle that is created when we move the hour hand to 5 and the minute hand to 1, we need to calculate the difference between the two positions on the clock.

Each hour on the clock represents (360°/12) = 30°, and each minute represents (360°/60) = 6°.

Therefore, the hour hand at 5 represents 150° (5 x 30°) and the minute hand at 1 represents 6° (1 x 6°). The difference between the two positions is 144° (150° - 6°).

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The time can be obtained from 1/0.042 * ln (p(t)/1000)

An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant and x is a variable. The base a is usually a number greater than 1, although it can be any positive number.

Exponential functions have a distinctive characteristic that sets them apart from other types of functions: the value of the function increases or decreases exponentially as the value of x increases or decreases. In other words, the rate of change of the function is proportional to its current value, which results in a rapid growth or decay.

We have that;

p(t) = 1000e^0.042t

p(t)/1000 = e^0.042t

ln (p(t)/1000) = 0.042t

t = 1/0.042 * ln (p(t)/1000)

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A figure which is a dilation of figure E include the following: A. figure F.

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.

In Geometry, a scale factor is the ratio of two corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, quadrilaterals, and other types of polygons.

Based on the image (see attachment), we can logically deduce that only figure E and figure F share the same (common) line of symmetry.

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x = 18 ...... y = 20/3

x = 30 ..... y = ?

____________

[tex]y = \dfrac{30 \cdot 20}{3 \cdot 18} = \dfrac{100}{9}[/tex]

The sum of the polynomials is 6x^(2)-3x-6.

To add the polynomials using a vertical format, we will first write each polynomial in a column, lining up like terms vertically. Then, we will add the coefficients of each like term together to find the sum.

Here is the solution in a vertical format:

So, the sum of the polynomials is 6x^(2)-3x-6.

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In a case whereby Malcolm is finding the solutions of this quadratic equation by factoring 3x²-24x=-45, the correctly factored equation that can be used to find the solutions is 3(x-3)(x-5)=0

The given equation is  3x²-24x=-45

The equation can be re written as;

3x²-24x=-45

3x²-24x+45 = 0

Then we can divide by 3 and have

x²-8x + 12= 0

thene if we factorize we have

x= 5, x= 3

Therefore, option B is correct.  which is 3(x-3)(x-5)=0

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a) Tοtal cοst C(x) = 200x + 1500

   Revenue cοst R(x) = 300x

The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.

Let x be the number οf scοοters.

It cοsts yοu $1500 fοr tοοls and equipment tο get started, and the materials cοst $200 fοr each scοοter.

Here fixed cοst = $1500 and variable cοst = $200

We knοw that cοst functiοn = variable cοst per unit + fixed cοst

Cοst functiοn :

C(x) = 200x+1500

Yοur scοοter sell fοr $300

Revenue functiοn :

R(x) = 300x

(b) The sοlutiοn means

When yοu start a business assembling initial cοst is $1500 fοr tοοls and equipment.

The material cοst will increase $200 fοr each number οf scοοter increases.

The revenue will increase $300 fοr each number οf scοοter increases.

c) Let us take number οf scοοters x=50

Then cοst C(50)=200*50+1500 = 10000+1500=$11500

Revenue Cοst R(50)=300*50=$15000

Then prοfit = Revenue- cοst = 15000-11500 = $3500.

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The value of Function f(x) =  5x²+ 3x + 1 at x=2 is 27.

A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

Given:

We have the Function as

f(x) = 5x²+ 3x + 1

Now, we have to find value of function at x= 2 so

f(x) = 5x²+ 3x + 1

f(2) = 5(2)²+ 3(2) + 1

f(2) = 5(4)+ 6 + 1

f(2) = 20 + 7

f(2)= 27

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Answer:

Zoe will save 30% of the original cost of the sweater, which is $40. To calculate the amount saved, we must multiply 30% by the original cost of the sweater, which gives us 0.30 x $40 = $12. Therefore, Zoe will save $12 on the sweater with the 30% discount

Step-by-step explanation:

Answer:

She will save $12.00

Step-by-step explanation:

.3 x 40 = 12

30% as a decimal is .3.

The cost of the sweater on sale would be

.7 x 40 = 28

If we take 30% off, we are leaving 70% on.

28 + 12 = 40 the original cost.

Helping in the name of Jesus.

To solve this problem, use logarithmic properties to combine the two equations into one.

First, use the product rule to combine the two equations:
$\log_2(32) + \log_2(x-4) + \log_2(x) = 5$
Then use the power rule to combine the last two terms:
$\log_2(32) + \log_2(x^2 - 4x) = 5$
Finally, use the quotient rule to separate the terms:
$\log_2\frac{32}{x^2 - 4x} = 5$

To solve for $x$, take the inverse logarithm of both sides:
$\frac{32}{x^2 - 4x} = 2^5$
Expand and simplify the left side to get a quadratic equation:
$x^2 - 4x - 32 = 0$
Solve the quadratic equation using the quadratic formula:
$x = \frac{4 \pm \sqrt{4^2 + 4(32)}}{2}$
$x = \frac{4 \pm \sqrt{136}}{2}$
$x = 4 \pm \sqrt{17}$

Therefore, the solutions are:
$x = 4 + \sqrt{17}$
$x = 4 - \sqrt{17}$

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Answer:

To find the area of the trapezoid-shaped playground, we need to use the formula:

Area = (1/2) × (base1 + base2) × height

In the given diagram, the length of the top base is 24 feet, the length of the bottom base is 48 feet, and the height is 52 feet.

So, the area of the playground is:

Area = (1/2) × (24 + 48) × 52

= (1/2) × 72 × 52

= 1,872 square feet

Therefore, the area of the playground is 1,872 square feet.

The closest option to this answer is option B, which is 1,768 square feet. However, the correct answer is actually 1,872 square feet.

Phil spent 18.26% of his pocket money on eating out for one meal.

The following is the formula for calculating the percentage difference between two values:

100% of ((new value - old value) old value)

In order to describe the change as a percentage, this formula calculates the difference between the new and old values, divides that difference by the old value, and multiplies the result by 100.

Given that, Phil spent $21 of his $115 pocket money.

Thus,

$21 ÷ $115 × 100% = 18.26%

Hence, Phil spent 18.26% of his pocket money on eating out for one meal.

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Answer:

t = 56 degree

Step-by-step explanation:

A triangle is 180 degrees.

The angle on the right is a vertical angle to the 34-degree angle, meaning their angles are equal.

We know two angles; one is 90 degrees, and the other is 34 degrees. To find the angle t, we take

180 - 90 - 34 = 56 degree

So, t = 56 degree

"f " is continuous at x = 0.

a) To determine if f is continuous from the left at x = 0, we need to evaluate the limit of f(x) as x approaches 0 from the left. This means we need to use the first piece of the function, x + sin x, since this is the piece that applies when x < 0:

lim(x->0-) f(x) = lim(x->0-) (x + sin x) = 0 + sin 0 = 0

Since the limit exists and is equal to the value of the function at x = 0 (which is 2), f is continuous from the left at x = 0.

b) To determine if f is continuous from the right at x = 0, we need to evaluate the limit of f(x) as x approaches 0 from the right. This means we need to use the third piece of the function, 2/(1+x^2), since this is the piece that applies when x > 0:

lim(x->0+) f(x) = lim(x->0+) (2/(1+x^2)) = 2/(1+0^2) = 2

Since the limit exists and is equal to the value of the function at x = 0 (which is 2), f is continuous from the right at x = 0.

c) To determine if f is continuous at x = 0, we need to make sure that the limits from the left and right both exist and are equal to each other and to the value of the function at x = 0. We already found that the limits from the left and right are both equal to 2, which is also the value of the function at x = 0. Therefore, f is continuous at x = 0.

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