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The width of the picnic area in scale drawing is 91 inches.

The scale of the drawing was 13 inches : 6 yards.

The picnic area is 42 yards wide in real life.

The width of the picnic area in drawing is as follows:

Therefore,

6 yards = 13 inches

42 yards = ?

cross multiply

Hence,

width of the picnic in the scale drawing = 42 × 13 / 6

width of the picnic in the scale drawing = 546 / 6

width of the picnic in the scale drawing = 91

width of the picnic in the scale drawing = 91 inches

Therefore, the width of the picnic area in scale drawing is 91 inches.

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The line that is perpendicular to the line passing through the points (-4, 2) and (4, -1) is y = (8/3)x + 1/2

From the question, we are to determine the equation of the line that is perpendicular to the line passing through the given points

First, we will determine the equation of the line passing through the given points

The given points are (-4, 2) and (4, -1)

Using the formula,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

x₁ = -4

y₁ = 2

x₂ = 4

y₂ = -1

Thus,

(y - 2)/(x - -4) = (-1 - 2)/(4 - -4)

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

(y - 2)/(x + 4) = (-3)/(8)

8(y -2) = -3(x + 4)

8y - 16 = -3x -12

8y = -3x -12 + 16

8y = -3x + 4

y = -(3/8)x + 1/2

Now,

NOTE: A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line

In the above equation,

The slope of the line is -3/8

∴ The slope of the line that is perpendicular to the line will be 8/3

Thus,

The equation of the line will be y = (8/3)x + 1/2

Hence, the line that is perpendicular to the line passing through the points (-4, 2) and (4, -1) is y = (8/3)x + 1/2

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We have to add 90 pounds of chicken feed that is 40 % to make a chicken feed that is 70 % corn.

In this problem we have to prepare a chicken feed with a given concentration by blending two chicken feeds with different concentration. The addition of chicken feed needed can be determined by weighted averages:

(70 / 100) · (270 + x) = (80 / 100) · 270 + (40 / 100) · x

0.7 · (270 + x) = 0.8 · 270 + 0.4 · x

189 + 0.7 · x = 216 + 0.4 · x

0.3 · x = 27

x = 90

We have to add 90 pounds of chicken feed that is 40 % to make a chicken feed that is 70 % corn.

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The total equity of the company for  the year ended is $43,900

What is net income?

The net income is the excess of fees earned by Adventure Travel  in the year ended  over its total expenses, in essence, we need to determine its total expenses first and foremost, which comprises of salaries expense, rent expense, depreciation expense, advertising expense and office supplies expense

total expenses=32,800+16,800+3960+4000+2800

total expenses=60,360

fees earned=75,000

net income =fees earned-total expenses

net income=75,000-60,360

net income=$14,640

Now the closing retained earnings comprises of beginning retained earnings plus the net income minus the cash dividends paid

Retained earnings=$14,640+$ 10,260-$1,000

Retained earnings=$23,900

Having determined the retained earnings closing balance, the total equity , common stock plus the closing balance of retained earnings

Total equity=$20,000+$23,900

Total equity=$43,900

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Final answer : Shareholders' personal property cannot be taken to settle the company

Definition : A company is treated as a person with the legal capacity to enter into a contractual obligation, own properties, sue or be sued. A company uses a common seal as its signature and any documents bearing company seal are legally enforceable.

Given Data:

A private corporation owned by 35 shareholders is worth $1.7 million.

The corporation loses a lawsuit worth $3 million.

To find :

What is the value of any personal property of the shareholders that can be taken to pay the settlement?

Solution:

shareholders' liability is limited.

A shareholder cannot lose more than the value of stock owned in a company.

Shareholders' personal property cannot be taken to settle the company obligation because a company is a different entity from its shareholders.

Main Answer : Shareholders' personal property cannot be taken to settle the company

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The point (5, 3) is translated using the rule (x, y) ⇒ (x - 7.5, y + 6.8) to get the point (-2.5, 9.8)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane.

The point (5, 3) is translated using the rule (x, y) ⇒ (x - 7.5, y + 6.8) to get the point (-2.5, 9.8)

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Answer:

1. 27669.1 g

2. 110 kg

Answer:

y/3 + 5 = 7

Step-by-step explanation:

Five more would mean plus five, and in these types of equations you work almost backwards. So if you but +5 in your answer, you need to add the quotient, dividing(/) by 3, and the unknown number is y. so your finial equation would read, y divided by 3 plus 5 is equal to 7 (y/3 + 5 = 7) Hope this was helpful!

Answer:

3.17

Step-by-step explanation:

got dat big brain

Answer:

GCF = 6

The original sum rewrites to 6(2+3)

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

Explanation:

Notice we have these factorizations

12 = 6*2

18 = 6*3

Which shows that 6 is the greatest common factor (GCF)

So,

12+18 = 6*2+6*3 = 6*(2+3)

We use the distributive property which is a(b+c) = ab + ac

I'll leave the 2+3 part un-simplified so that you can see the two original pieces, and how the 6 can multiply with them both to get back to 12+18 again.

Answer:

x = 32

Step-by-step explanation:

Since m||n and the angles formed are on the same transversal, the angles are corresponding angles i.e. their sum adds up to 180°

Using given data
2x - 16 + 4x + 4 = 180

==> 6x - 12 = 180

==> 6x = 180 + 12   (by adding 12 on both sides)

==> 6x = 192

x = 192/6

x = 32

The object is dropped at a initial height of 99.4 feet. (Correct choice: B)

Herein we find the case of a specific object under free fall motion, that is, due to gravity and neglecting effects from air viscosity and Earth's rotation. The kinematic equation is presented below:

v = √(2 · a · h)          (1)

Where:

If we know that a = 32.2 ft / s² and v = 80 ft /s, then the initial height of the object is:

80 = √(2 · 32.2 · h)

80 = √(64.4 · h)

80² = 64.4 · h

h = 80² / 64.4

h =  99.379 ft

The object is dropped at a initial height of 99.4 feet. (Correct choice: B)

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The cake sharing process of the process using geometric progression gives the following values;

1. The amount of the cake left after the first division is one quarter of the cake

The amount of cake remaining after the fourth division is 1/256 of the original cake

2. The series is; (1/4 + 1/16 + 1/64+ 1/256 + 1/1024) of the original cake

3. 341/1024 of the original cake

4. If the process continues indefinitely each person gets (1/3) of the original cake

A geometric progression is a sequence of numbers such that a term is found from the previous term by multiplying the previous term by a constant number.

1. Taking the dimensions of the cake as a square, let x represent the side length of the cake, we have;

Amount of cake left after the first division = x/4

Amount left after the second sharing = x/(4×4) = x/16

Amount left after the third division = x/(4×4) = x/(16×4) = x/64

Amount left after the fourth division = x/(64×4) = x/256

2. After the fourth division, each person receives x/(256×4) = x/1024

The series that represents the amount each person receives after the fourth division is therefore;

3. The amount of the original cake each person gets after the fourth division is therefore;

4. The amount each person receives is given by the sum of a geometric series up to infinity, where;

The first term, a = 1/4

The common ratio, r = 1/4

S = (1/4)/(1 - (1/4)) = (1/4)/(3/4) = (1/4)×(4/3) = 1/3

The amount of the original cake each gets if the process continues indefinitely is (1/3) of the original cake.

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Answer:

RS= 45

Step-by-step explanation:

According to the rules of the triangle...

RS = RQ

The missing term of the second pair, such that both pairs are analogous is WKPA.

For the first two terms, S is 1 letter before Q,

For the first two terms, S is 1 letter before Q,F is 1 letter before D,

For the first two terms, S is 1 letter before Q,F is 1 letter before D,Y is next to X,

For the first two terms, S is 1 letter before Q,F is 1 letter before D,Y is next to X,N is next to FM.

For the first two terms S is 1 letter before Q,F is 1 letter before D,Y is next to X ,N is next M.Similarly, UIOZ : WKPA. Where W is 1 letter before U,K is 1 letter before I, O is next to P,Z is next A.

Therefore, the correct option is D.

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Refer to the terms given below. There is a pattern that defines the relationship between the first two terms. Determine this relationship and then identify the missing term of the second pair, such that both the pairs are analogous. QDXM : SFYN :: UIOZ : 1) PAQM 2) LPWA 3) QNLA 4) WKPA

Answer:

40

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

This is point-slope form, and these coordinates make both sides equal to 0.

Step By Step: Okay, so we have that. The Rectangular four of the classroom is 36 x 32 ft. And we have a skilled drawing where the length is nine, and I'm guessing who you want to know or with to find the area. So we'll equate this to 36 ft Over 32 ft. So first we'll cross multiply nine and 32 and divide by 36 to find X or with. So thus we have nine times eight inches Equalling 72" squared. And so that's the area of the floor and the scale drawing.

The equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

We know that the method to find the axis of the symmetry of the parabola is given by:

x = - b / 2 a

We have the general equation of the parabola as:

y = a x² + b x + c

We have the equation of the parabola as:

y = - 4 x² + 24 x - 35

Comparing from this equation, we get that:

a = - 4

b = 24

c = - 35

Now, substituting the values, we get that:

x = - 24 / 2 (- 4)

x = - 24 / - 8

x = 24 / 8

x = 3

Therefore, the equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

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The price of the DJI Mavic Air2 drones after the chain discount is applied will be $18,095.94.

An assortment of trade discount rates or their sum is referred to as a chain discount.

DJI produced the Mavic Air 2 quadcopter and gave its top clients a 10/8/7 chain discount. The company's main client, Drone Nerds, bought 15 Mavic Air2 drones for a total of $23,500 list price.

Then the price of the DJI Mavic Air2 drones after the chain discount is applied will be

⇒ $23,500 x 0.90 x 0.92 x 0.93

⇒ $18,095.94

The price of the DJI Mavic Air2 drones after the chain discount is applied will be $18,095.94.

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Answer:

g(x) = x² + 8x

x + 4

if x = -6 (replace x with -6 )

Using the formula above

g(-6) = -6² + 8(-6)

-6 + 4

= 36 - 48

-2

= -12

-2

(minus cancels each other)

Answer = 6

Remember you can always use a calculator to check (I'm using also)

Hope this helps xoxo :⁠-⁠)

Answer: 28

Step-by-step explanation:

5x + 8 = 7x

2x = 8

x = 4

BD = 7x

BD = 7(4)

      = 28

Answer:

it A because if u apply pressure the molecules will be cramped

Step-by-step explanation:

The value of x is -101001 using the base-2 system.

What is a binary number?

A binary number is a number that is expressed in the binary system or base 2 numeral system, according to digital technology and mathematics. It uses the symbols 1 and 0 to represent different numeric values (zero). The positional notation with 2 as a radix is known as the base-2 system.

Given:

1101₂+x₂+11001₂=111₂

To find the value of x.

First, we'll write the binary numbers and multiply each digit of the binary numbers by the corresponding power of two:

1101₂+x₂+11001₂=111₂

(1×2³+1×2²+0×2¹+1×2⁰) + x₂ + (1×2⁴+1×2³+0×2²+0×2¹+1×2⁰) = (1×2²+1×2¹+1×2⁰)

Now, solve the powers.

(8+4+0+1) + x₂ +(16+8+0+1) = (4+2+1)

Simplifying we get,

13+x₂+25=7

x₂=7-48

x₂=-41

Using binary converter, we get the value of x as -101001.

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