A hot-air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of 100 feet, passes over an intersection (see the figure). Find an expression for its distance d (measured in feet) from the intersection 1 seconds later.

Answer:

x = 0

Step-by-step explanation:

because the x coords are still 0 and y is changing.

Answer:

2/5x³ + 1/5x² + 1/5x

Step-by-step explanation:

You have to divide each term in the polynomial by the monomial.

(4x⁴ + 2x³ + 2x²)/10x

2/5x³ + 1/5x² + 1/5x

The solution is, 2/5x³ + 1/5x² + 1/5x is the answer of the division.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

(4x^4+2x^3+2x^2)÷10x

now,

we have to divide each term in the polynomial by the monomial.

so, we get,

(4x⁴ + 2x³ + 2x²)/10x

=(4x⁴/ 10x + 2x³/ 10x  + 2x²/ 10x )

=2/5x³ + 1/5x² + 1/5x

Hence, The solution is, 2/5x³ + 1/5x² + 1/5x is the answer of the division.

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Answer:

x = -3

Step-by-step explanation:

See steps of solution:

Answer is -3

Answer:

x = -3

Step-by-step explanation:

5(5x+3) - 4(2x-9) = 0     Multiply out.

5*5x + 5*3 - 4*2x + 36 = 0

25x + 15 - 8x + 36 = 0 Combine like terms.

25x - 8x + 15 + 36 = 0

17x + 51 = 0 Subtract 51 from both sides.

17x = - 51   Divide each side by 17.

17x/17 = -51/17

x = - 3

The coordinates of the point D of the rectangle after the translation is given by D' ( 1 , -12 )

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

Given data ,

Let the coordinates of the rectangle be ABCD

Now , the coordinate of the point D be D ( -5 , -2 )

And , the translation rule is ( x , y ) → ( x + 6 , y - 10 )

So , the point after translation be D'

where D' = D ( -5 + 6 , -2 - 10 )

The coordinates of D' = D' ( 1 , -12 )

Hence , the coordinates after translation is  D' ( 1 , -12 )

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Answer:

Step-by-step explanation:

1. m/-8 = -2.5

*-8 = *-8

m = -2.5*-8

m = 2.5*8

m = 20

2. 7/8a = 42

*8            *8

7a = 336

/7       /7

a = 336/7

a = 48

Hope this helped,

Kavitha

Step-by-step explanation:

Constructions are useful in life. From learning it, you are able to use the required tools, and get familiarized with different shapes and angles. This would help you prepare for the task of proving theorems that involved those shapes and angles. It is not the end, ultimately, it prepares you for real life. Constructions are applied in building houses, estates, etc, and constructions of roads, bridges, etc.

Answer:

Given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down, which is also T₍₋₃, ₋₅₎, by transformation notation

Step-by-step explanation:

The coordinates of the point C is (1, -1)

The coordinates of the point C' is (-2, -6)

Therefore, the translation required to shift the point C from to point C' is found as follows;

The difference between the x, and y-coordinates of the points C and C' are given as follows;

Δx, C to C' = (-2 - 1) = -3

Δy, C to C' = (-6 - (-1)) = (-6 + 1) = -5

Therefore, the the transformation from C to C' it T₍₋₃, ₋₅₎

Which can be presented as, given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down.

Answer:

[tex]Total\ Rent = 49 + 5m[/tex]

Step-by-step explanation:

Given

Rent per day = $49

Addition = 5 cents per mile

Required

Determine the rent for a day and m miles

First, we need to generate a formula from the given parameters;

Let d represent number of days and m represent additional miles;

[tex]Total\ Rent = 49 * d + 5 * m[/tex]

[tex]Total\ Rent = 49 d + 5 m[/tex]

Solving for the rent for a day and m miles

We have that: d = 1 and m = m

Substitute these in the formula above

[tex]Total\ Rent = 49 * 1 + 5 * m[/tex]

[tex]Total\ Rent = 49 + 5m[/tex]

Hence, the total rent is

[tex]Total\ Rent = 49 + 5m[/tex]

Answer:

5x-1

Step-by-step explanation:

8x-3(x+1)-4

{open the brackets}3x-3

8x-3x-3-4

5x+(-7), which is 5x-7

Answer:

The probability is 0.25

Step-by-step explanation:

Here is a probability question.

We want to know the probability of picking a card which is in the spades suit.

Now, what we know is that there are a total of 52 cards and we have 4 suites.

Each suite have equal number of cards. So definitely the number of cards in the spades suit will be 52/4 = 13 cards

Thus, the probability of picking any card in the spades suit = number of cards in the spades suit/ Total number of cards in the deck

Mathematically that would be 13/52 = 1/4 = 0.25

Answer:

Step-by-step explanation:

+ si

Answer: 0.137.

Step-by-step explanation:

Let p be the population proportion of musicians that are left-handed.

Given: Sample size : n= 2690   [subset of population]

Number of musicians that are left-handed: x= 368

Then the sample proportion: [tex]\hat{p}=\dfrac{368}{2690}\approx0.137[/tex]

Since sample proportion is the best point estimate of the population proportion.

Hence, a point estimate for p, the population proportion of musicians that are left-handed is 0.137.

==============================================

Explanation:

The left endpoint is -2. The right endpoint is 10. Both endpoints are open holes, meaning we do not include them as part of the green shaded solution region. If x is a solution, then the solution can be described as [tex]-2 < x < 10[/tex] which converts to the interval notation [tex](-2, 10)[/tex]. The curved parenthesis says "do not include the endpoint".

Note: this is not ordered pair notation (x,y). Unfortunately math tends to reuse symbols so it might be a bit confusing at first.

Answer:

CT= $950

Step-by-step explanation:

Dado la siguiente información:

Servicio= $300 primeros dos

Servicio adicional= $150

Descuento= $100

Para calculate el costo total, tenemos que usar la siguiente formula:

CT= 300x + 150y - 100

x= costo normal

y= costo promocional

CT= 300*2 + 150*3 - 100

CT= $950

Answer:

Domain: All Real numbers

CoDomain : All Real numbers

Range: [tex]\left\{y|y\geq 0 \right\}[/tex]; that is: Real numbers larger than or equal to zero

Step-by-step explanation:

Notice that the graphed function can use any Real number x (from - infinity to + infinity) and produce an output.  Therefore, the Domain of the function plotted in graph 3 is : All Real numbers.

The set of possible outputs (CoDomain) is also the set of all Real numbers (notice that the y-axis extends form - infinity to + infinity

But the Range (the actual set of the collection of outputs of the function) is just a subset of the CoDomain consisting of the Real numbers larger than or equal to zero (notice that the drawing of the function touches the x axis and lies completely on the upper half of the plane.

Answer:

sqrt 46

Step-by-step explanation:

irrational numbers are numbers cannot be define in a fraction. sqrt of 46 will give you infinite decimal which could not be express in a fraction form.

Answer:

[tex] \boxed{\sf D. \ x^2 + 2} [/tex]

Step-by-step explanation:

[tex] \sf Simplify \ the \ following: [/tex]

[tex] \sf \implies (2 {x}^{2} + 2x + 3) - ( {x}^{2} + 2x + 1)[/tex]

[tex] \sf - ( {x}^{2} + 2x + 1) = - {x}^{2} - 2x - 1 : [/tex]

[tex] \sf \implies (2 {x}^{2} + 2x + 3) - {x}^{2} - 2x - 1[/tex]

[tex] \sf Grouping \ like \ terms: [/tex]

[tex] \sf \implies (2 {x}^{2} - {x}^{2}) + (2x - 2x)+ (3 - 1)[/tex]

[tex] \sf 2 {x}^{2} - {x}^{2} = {x}^{2} : [/tex]

[tex] \sf \implies {x}^{2} + (2x - 2x)+ (3 - 1)[/tex]

[tex] \sf 2x - 2x = 0 : [/tex]

[tex] \sf \implies {x}^{2} + 0+ (3 - 1)[/tex]

[tex] \sf 3 - 1 = 2 : [/tex]

[tex] \sf \implies {x}^{2} +2[/tex]

Answer/Step-by-step explanation:

a. From the bar graph, 1 student scored 9, 4 students scored 10.

Therefore, the no. of students who scored above 8 is: [tex] 1 + 4 = 5 [/tex]

b. From the graph, we have the following:

3 students scored 1

5 students scored 2

2 students score 4

6 students scored 5

12 students scored 8

1 student scored 9

4 students scored 10

Total no. of pupils in year 7 class = 3 + 5 + 2 + 6 + 12 + 1 + 4 = 33 students

c. It is assumed that all the students in Mr Hassan's year 7 class took the test.

Your question has been heard loud and clear.

Lhs = 2cos[5A+3A/2]cos[5A-3A/2]+2cos[15A+7A/2]cos[15A-7A/2]

=2cos4AcosA+2cos11Acos4A

=2cos4A[cosA+cos11A]

=2cos4A[2cos[11A+A/2]Cos[11A-A/2]

=2cos4A2cos5Acos6A

=4cos4Acos5Acos6A=Rhs

Thank you

Answer:

yearly salary = $54,708

Step-by-step explanation:

Let monthly salary be x

Let yearly salary be y

Let number of months be n

To estimate your average monthly salary, divide your yearly salary by the number of months in a year. This can be written as

x = y divided by n

[tex]x = \frac{y}{n}[/tex]

Therefore, writing an equation to determine yearly salary is the same as making the yearly salary 'y' the subject of the formula above:

[tex]x = \frac{y}{n}\\cross-multiplying\\n\ \times\ x= y\\y\ =\ nx[/tex]

where y = ???

x = $4,559

n = 12 months

[tex]y = 4,559\ \times\ 12 \\= \$\ 54,708[/tex]

Therefore yearly salary = $54,708

Answer:

145 feet

Step-by-step explanation:

The computation of the elevation of the bottom of the canyon is shown below;

Given that

A = sea level

B = The point at which the canyon starts

C = Canyon bottom

AB = 40 feet

BC = 105 feet

Based on the above information

The AC or elevation of the canyon bottom is

AC = AB + BC

= 40 feet + 105 feet

= 145 feet

Answer:

2.2%

Step-by-step explanation:

Given the following :

Population in year 2000 (A) = 4.2 million

Expected population every 32 years = 2 *A

The growth rate per year =?

The population figure after 32 years = (2 * 4.2 million) = 8.4 million

Using the exponential growth formula :

P(t) = A × (1 + r)^t

(1 + r) = g = Total growth percent

A = Initial population

t = time

P(t) = 8.4 million

8,400,000 = 4,200,000 × g^32

g^32 = (8400000/4200000)

g^32 = 2

Taking the root of 32 on both sides

g = 1.02189714865

g = (1 + r)

1.02189714865 = 1 + r

r = 1.02189714865 - 1

r = 0.02189714865

.rate = 0.02189714865 * 100

= 2.18971486541%

= 2.2% ( nearest tenth)

Answer:

x = -16

Step-by-step explantion:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Hope this helps!

(・∀・(・∀・(・∀・*)

Answer:

.3

Step-by-step explanation:

P( defective) = number defective/ total

                     = 3/10

                      .3

Answer:

[tex]\huge\boxed{0.3}[/tex]

Step-by-step explanation:

Total CDs = 10

Defective CDs = 3

P(Defective) = 3/10

P(Defective) = 0.3

Answer:

7

Step-by-step explanation:

This is so because (+) × (-) is (-).

Just like (+) × (+) is (+) and (-) × (-) is (-).

So 10 + (-3) = 10 - 3 = 7.

Answer:

[tex]7[/tex]

Step-by-step explanation:

[tex]10 + ( - 3) \\ \\ (+) \: \times \: (- )= (- ) \\ so \: 10 - 3 \\ = 7[/tex]

Answer:

167°

Step-by-step explanation:

<LMN = <LMT + <TMN

23° + 144° = 167°

<LMN = 167°

Answer:

a. True.

Step-by-step explanation:

32k + 24 = 8(4k + 3)

32k + 24 = 32k + 24

32k - 32k = 24 - 24

0 = 0

Since 0 does equal 0, the statement is a. True.

Hope this helps!

Answer:

[tex]\Large \boxed{\mathrm{a. \ True}}[/tex]

Step-by-step explanation:

[tex]32k+24[/tex]

[tex]\sf Factor \ out \ 8 \ from \ the \ expression.[/tex]

[tex]8(4k)+8(3)[/tex]

[tex]8(4k+3)[/tex]

[tex]32k+24=8(4k+3)[/tex]

[tex]\sf The \ equation \ is \ true.[/tex]

Answer:

m= 4/5

Step-by-step explanation:

The equation of the line is in slope-intercept form.

y=mx+b

where m is the slope and b is the y-intercept.

Basically, the number that is being multiplied by x is the slope, and the number added or subtracted from that is the y-intercept.

We are given the equation:

y= 4/5x -3

4/5 is the coefficient of x. 3 is being subtracted from 4/5x.

Therefore, the slope of the line is 4/5 and the y-intercept is -3.

The question asks us to find the slope of the line, so the answer is 4/5.

The slope of the line represented by the equation y = 4x/5 - 3 is 4/5.

Given that an equation y = 4x/5 - 3 we need to find the slope of the equation.

In the slope-intercept form of a linear equation (y = mx + b), "m" represents the slope of the line.

The slope determines how steep or shallow the line is. It also tells us the rate at which the line is rising or falling as we move along the x-axis.

In the given equation, the coefficient of "x" is 4/5. This is the slope of the line.

To understand this better, compare the equation with the slope-intercept form: y = mx + b.

In the given equation, m (the slope) is 4/5. It means that for every 1 unit increase in the x-coordinate, the y-coordinate increases by 4/5 (or decreases by 4/5 if the slope were negative).

So, the line rises (or falls) at a rate of 4/5 for every unit increase along the x-axis.

In this case, since the slope is positive, the line will rise as we move from left to right on the coordinate plane.

Graphically, the line with a slope of 4/5 would look like a rising line, making an angle with the positive x-axis, and moving upwards from left to right.

So, the slope of the line represented by the equation y = (4/5)x - 3 is 4/5.

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Answer:

Step-by-step explanation:

We apply the properties of the power.

[tex]\left(r^3 \right)^{-2}=r^{3*(-2)}=r^{-6}=\dfrac{1}{r^6}[/tex]

Answer:

r^-6  OR  1 / (r^6)

Step-by-step explanation:

For this expression, we can use exponential power rules to simplify.

Power to a power, you multiply the exponents.

So, (r^3)^-2 == r^-6

We can use the fact that negative exponents will be the base to the power in the denominator.

r^-6 == 1/(r^6)

Cheers.