Evaluate the expression when g = 4 and h = 6.
h+7g

A. Applying the trigonometric ratio, the length of pole = 29.6 ft.

B. 23.1 ft.

C. Length of wire 1 = 45.1 feet.

The trigonometric ratios are:

Part A: Apply the trigonometric ratio, tan ∅ = opp/adj, to find the length of the pole

∅ = 41°

Opp. = length of pole

Adj. = 34 ft

Substitute

tan 41 = length of pole/34

Length of pole = (tan 41)(34) = 29.6 ft.

Part B:

Let the distance between the base of the pole and wire 2 be represented as x. Therefore, apply tan ∅ = opp/adj.

∅ = 38

Opp. = x

Adj. = 29.6 ft

Therefore:

tan 38 = x/29.6

x = (tan 38)(29.6)

x = 23.1 ft.

Part C: Use the Pythagorean theorem to find the length of wire 1.

Length of wire 1 = √34² + 29.6²)

= 45.1 feet.

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The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

As we know that the perimeter of rectangle

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

From the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.

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Answer:

Step-by-step explanation:

Move 6a to the other side

Subtract 7a and 6a

use inverse operations. So add 3 on both sides

Answer:

a = 6

Step-by-step explanation:

The given equation is,

→ 7a - 3 = 3 + 6a

Now the value of a will be,

→ 7a - 3 = 3 + 6a

→ 7a - 6a = 3 + 3

→ a = 3 + 3

→ [ a = 6 ]

Hence, the value of a is 6.

The value of the function g(x) when x = -2 is 6

The definition of the function is given as

g(x)=x to the power of 2 minus x

Rewrite the above function properly

So, we have the following representation

g(x) = x² - x

To find the function g(-2), we set the value of x in the equation g(x) = x² - x to -2

This is represented by

Calculate g(x), when x = -2

Substitute -2 for x in the equation g(x) = x² - x

So, we have the following equation

g(-2) = (-2)² - (-2)

Evaluate the exponents

This gives

g(-2) = 4 - (-2)

Evaluate the sum

g(-2) = 6

Hence, the value of the function is 6

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The probability that both Rachel and Robert are in the picture is 3/16.

The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.

Given that

Rachel and Robert both begin at the same point

Rachel completes a lap every 90 seconds.

Robert completes a lap every 80 seconds.

The photographer captures 1/4th of the track, centered on the starting line.

As a result, the photo captures 1/8th of the track on either side of the starting line.

The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.

Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.

Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.

Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).

Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.

i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.

Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}

= {90/8}/60

= 3/16

Therefore the probability that both Rachel and Robert are in the picture is 3/16

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The number of dime and the number of quarters that Aiden have are 10 and 8 respectively.

Aiden ha $3 worth of dime and quarter. Aiden has 2 more dime than quarter. The number of dime and the number of quarter that Aiden has can be calculated as follows:

let

x =  number of quarter

y = number of dime

Therefore,

y = 2 + x

y - x = 2

0.1y + 0.25x = 3

Multiply equation(ii) by 10

y - x = 2

y + 2.5x = 30

subtract equation(i) from equation(ii)

3.5x = 28

x = 28 / 3.5

x = 8

Hence,

y = 2 + 8

y = 10

Therefore,

number of dime  = 10

number of quarters = 8

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Answer:

Step-by-step explanation:

187

Arturo can select the days on which to have pizza in 70 ways using combination rule if he chooses any four of the next eight days.

What is combination?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

In combinations, one can select the items in any order.

Number of combination of a objects chosen from n objects

                                  ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]

According to the given question:

To select 4 days out of the next 8 days, use combination rule

ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]

⁸C₄ = [tex]\frac{8!}{4! (8-4)!}[/tex]

⁸C₄ = (8x7x6x5x4x3x2x1)/(4x3x2x1)(4x3x2x1)

⁸C₄ = (8x7x6x5)/(4x3x2x1)

⁸C₄ = 70

Therefore there are 70 ways Arturo can select the 4 days out of 8 to have pizza for dinner.

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The value of k is 4.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Volume= 16

Width = 4

So, we can write the relation as

Volume= k (width)

k = Volume/ width

k= 16/4

k = 4

Hence, the value of k is 4.

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The altitude of the original pyramid is about 75.11 units

Given that,

Let h stand in for the original pyramid's height. The cut-off top then stands at a height of (h -22). The square of the scale factor for height is the scale factor for area, therefore we get :

Altitude of Pyramid means The slant height of a regular pyramid is its lateral face's height. Slant height in a non-rectangular pyramid is not specified. When determining the height (or altitude) of a regular, right pyramid, the vertex (the top) is used as the point perpendicular to the base. The base will intersect at this position.

(Height ratio)^2 = 1/2

((h -22)/h) ^ 2 = 1/2

(h-22) / h = 1/[tex]\sqrt{2}[/tex]

h-22 = h /[tex]\sqrt{2}[/tex]

h = 75.11 units

Consequently, the original pyramid's altitude is around 75.11 units.

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The total number of times the dice will land on 1 or on 5 is 153.

What is probability?

All of the probabilities will add up to 1. This gives us the equation.

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

P(1) + 0.17 + 0.08 + 0.16 + 0.14 + 0.1 = 1

P(1) + 0.65 = 1

P(1) = 1 - 0.66

P(1) = 0.35

We now need to find the probability of 1 or 5.

P( 1 or 5) = P(1) + P(5)

= 0.35 + 0.16

= 0.51

We now use the predicting outcomes formula

Expected = P( 1 or 5) * No. of times

= 0.51 * 300

= 153

Hence, the total number of times the dice will land on 1 or on 5 is 153.

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Solve for 12 - h(7)

First find h(7)

h(7) = 7^2+3(7)-2

h(7) = 49 + 21 - 2

h(7) = 68

12 - 68 = - 56

12 - h(7) = -56.

I'm not sure if the question wants h(-56) as well, but just plug that in.

H(-56)=2966

hope this helps :)

Answer:

[tex] - 3 \leqslant w < 1[/tex]

Step-by-step explanation:

as shown in picture attached

The equation of the line parallel to the equation y = - 2 / 3 x + 5 is 2x - 3y = 21

The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.

Lines are parallel when they have the same slope.

Using slope intercept form,

y = mx + b

where

Therefore,

y = - 2 / 3 x + 5.

The slope of the equation is - 2 / 3.

Hence, let's find the equation that has the same slope as - 2 / 3. First, we will have to represent the equation in slope intercept form.

2x - 3y = 21

add 2x to both sides of the equation

2x + 2x - 3y = 21 + 2x

- 3y = 2x + 21

divide both ides by - 3

- 3y  / - 3 = 2x / -3 + 21 / - 3

y = - 2 / 3 x - 7

Therefore, the slope is - 2 / 3 , the equation is 2x - 3y = 21

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8.77 ft/sec  is the tip of her shadow moving with a speed of 6 ft/sec .

What is speed, for instance?

Let H = the height of the pole.

h = the height of the woman.

x = the length of the woman's shadow.

s = the distance from the pole to the woman.

By similar triangles,  H/h = (s + x)/x  or  Hx = h(s + x).

Differentiating, H dx/dt = h(ds/dt + dx/dt)

19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt

13 dx/dt = 36

dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.

The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.

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The equation to find the original cost of hat is

44.80 = (x + 35) - (x+35)× 10/3

In the given question we have,

Ms. emlyn buys a hat and gloves with coupon for 30% off her entire purchase.

discount on total purchase = 30%

cost of gloves before discount = $35

let the cost of hat be $x before discount . The bill paid by Ms emlyn after discount but without tax = $44.80

total cost ( hat+gloves) before discount= $(x+35)

Now, after sum up all information we get,

$(x+35) - 30%discount on $(x+35) = $44.80

=> x+35 - (x+35)100/30 = 44.80

=> x+35 - (x+35)10/3= 44.80

which is required equation for original cost of hat.

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Answer:

weight = 57 Kg

Step-by-step explanation:

We require to find the length of the diagonal (d) piece of metal

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

d² = 8² + 6² = 64 + 36 = 100 ( take square root of both sides )

d = [tex]\sqrt{100}[/tex] = 10

the length of the 5 pieces is then

8 + 8 + 6 + 6 + 10 = 38 m

the total weight of the 5 pieces is then

weight = 38 × 1.5 Kg = 57 Kg

The equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions.

A equation in mathematics is a mathematical statement depicting that the values of two mathematical expressions are equal. Some examples representing equations are -

y = 5x + 4

2x + 3y = 5x + 8π

cos(ny) = sin(πx)

Given is the following equation -

x - 4/5 - x + 1/6 = 1/3

We have -

x - 4/5 - x + 1/6 = 1/3

x - x - 4/5 + 1/6 = 1/3

- 4/5 + 1/6 = 1/3

Now, [x] will cancel out for ever possible value of [x], therefore, it will have infinitely many solutions

Therefore, the equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions

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Answer:

29

Step-by-step explanation:

1+3= 4

3+4=7

4+7=11

7+11=18

11+18=29

The probability that Joe and Mathew would have to purchase no books on this visit to the bookstore is given as 0.125.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

We are to find the probability where p(x) = 0 and p(y) = 0

This is where we would have

from the table,  p(x) = 0 is 0.5

p(y) = 0 is 0.25

0.25 x 0.5 = 0.125

Hence the probability that no books would be bought is 0.125.

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Answer:

B and D

Step-by-step explanation:

A is wrong because x has a negative exponent

C is wrong because x is a denominator

Answer:

A. $760

Step-by-step explanation:

Price: $8

Amount of goods; 95

revenue = price x total units

$8 x 95 = $760 revenue

The vertex of the curve will be at (-2, -4) and the axis of symmetry is at -2

From the graph, the roots of the equation are -4 and 0, therefore, (x + 4) is a factor and x is also a a factor.

The equation of the curve is the product of the factors of the curve which is y = x(x + 4)

y =  + 4x

The x coordinate of the vertex =

will be illustrated as:

-b/2a = axis of symmetry

a and b is the coefficient of x

so a = 1, b = 4

x coordinate of vertex = -4/2 = -2

Then, substitute x = -2 into y =   + 4x to find the y-coordinate of the vertex

y = (-2)² + 4(-2)

y = 4 -8

y = -4

vertex  = (-2, -4)

The axis of symmetry is -b/2a which is -2

Therefore, the vertex is at (-2, -4).

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The nature of the roots for y=2x²- 5 is there are 2 distinct real roots.

What is the nature of roots?

The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant

Δ > 0 means there are 2 distinct real roots.

Δ = 0 means there are 2 equal real roots or 1 distinct real root.

Δ < 0 means there are no real roots, but 2 complex roots.

Here,

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b² - 4ac

Substitute the values of a, b, and c.

Evaluate the given equation to find the discriminant, we get

= 0 - 4×2×(-5)

= 41

> 0

Since the discriminant is greater than 0

Hence, there are 2 distinct real roots.

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Answer:  love

Step-by-step explanation:  love

The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

the graph of the line is shown below .

In the question ,

point on the line and slope of the line is given

So , equation will be

Part(1)

(-6, -3), m = -1

(y -(-3)) = -1(x -(-6))

y + 3 = -1(x + 6)

y + 3 = -x - 6

y = -x -6 -3

y = -x -9

the equation is y = -x -9  .

Part(2)

(-7, 6), m = 0

(y - 6) = 0(x -(-7))

y - 6 = 0(x + 7)

y - 6 = 0

y = 6

the equation is y = 6

Part(3)

(-2, 11), m=4/3

(y - 11) = (4/3)(x -(-2))

y - 11 = (4/3)x + 8/3

y = (4/3)x + 8/3 + 11

y = (4/3)x + 41/3

the equation is y = (4/3)x + 41/3

the graph of all the three equations are shown below .

Therefore , The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

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The total amount paid in dollars per hour is $19.

Unitary Method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

It is given that the total amount given by the uncle is $133 for the work done by Barn for 7 hours.

We have to find the amount paid per hour.

Total amount given = $133

Number of hour Barn work = 7 hours

Amount paid per hour = 133/ 7

= $ 19

Therefore the amount paid per hour is $19.

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Answer:

Step-by-step explanation:

2x + 3 = 4x - 5

4x - 5 = 2x + 3

Step 1 : Add 5 on both sides.

4x = 2x + 3 + 5

4x = 2x + 8

Step 2 : Subtract 2x on both sides.

4x - 2x = 8

2x = 8

Step 3 : Divide 2 on both sides.

x = 8/2

x = 4

Hence proved.

Answer:

Collect like terms

3+5=4x-2x

(note that when - crosses a line it turns to +

8=2x

8/2=2x/2

x=4