Mitchell has decided to give his dog a longer leash to roam in the backyard. If the new 7 ft. leash is tied to the center pole in the yard, how much area in the yard does the dog have to move around?

Answer:

33.6

Step-by-step explanation:

As we can see in the graph, the points:

To find a distance between two points or the length of the segment, we use the following formula:

[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

Because the two points P and Q are located at the same libe y = 8

=> the lenght of PQ = [tex]\sqrt{(6- (-2))^{2} } = \sqrt{8^{2} } = 8\\[/tex]

Because the two points R and Q are located at the same libe x = 6

=>  the length of RQ = [tex]\sqrt{(8-2)^{2} } = \sqrt{6^{2} } = 6\\[/tex]

The lenght of RS is: [tex]\sqrt{(-5-6)^2+(0-2)^2} = \sqrt{-11^{2} +(-2)^{2} }[/tex] = [tex]\sqrt{125} = 11.1[/tex]

The lenght of SP is: [tex]\sqrt{(-5-(-2))^2+(0-8)^2} = \sqrt{-3^{2} +(-8)^{2} } = \sqrt{73}[/tex] = 8.5

=>  the perimeter of quadrilateral PQRS = PQ+RQ+RS+SP

= 8+6+11.1+8.5

= 33.6

Answer:33.7

Step-by-step explanation:

8+8.5+6+11.2=33.7

Answer:they change and are always equal to each other

part 2. they do not change

part 3. 1/2

i just did it on edge 2020

When AC changes, angles ABC and ADC are also changes and are equal to each other.

An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of a circle.

This is different than the central angle, whose vertex is at the center of a circle.

From given figure, It is observed When AC changes, angles ABC and ADC are also change but equal to each other.

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Answer: The distance of frog from the  base of the stump is 5.16 feet ( approx)

Step-by-step explanation:

Given, A frog sitting on a stump 3 feet high hops off and lands on the ground.

During its leap, its height h in feet is given by [tex]h= -0.5d^2 + 2d + 3[/tex], where [tex]d[/tex]  is the distance from the base of the stump.

When the stump landed on the ground, h= 0 .

So put h=0 in the given equation , we get

[tex]0=-0.5d^2 + 2d + 3\\\\\Rightarrow\ 0.5d^2-2d-3=0[/tex]

Multiply both sides by 2 , we get

[tex]d^2-4d-6=0\\\\\Rightarrow\ d=\dfrac{-(-4)\pm\sqrt{4^2-4(1)(-6)}}{2(1)}\\\\=\dfrac{4\pm\sqrt{16+24}}{2}\\\\=\dfrac{4\pm\sqrt{40}}{2}\\\\=\dfrac{4\pm2\sqrt{10}}{2}=2\pm\sqrt{10}[/tex]

[tex]i.e.\ d=2-\sqrt{10}\ \ or\ \ d=2+\sqrt{10}\\\\\ i.e. d=2-3.1622\ \ or\ \ d=2+3.1622\\\\ i.e. d= -1.1622\ \ or\ \ d=5.1622\approx5.16[/tex]

Since , distance cannot be negative.

Hence, the distance of frog from the  base of the stump is 5.16 feet ( approx).

Answer:

Angle 3 is also 100

Step-by-step explanation:

They are vertical angles and vertical angles are always congruent.

The angle 3 is in the given figure is ∠3 = 100°.

The parallel lines are a group of straight lines that never intersect with one another. The distance between two parallel is always the same.

The measure of angle 1 is given as ∠1 = 100°.

When two lines intersect each other, the pair of vertically opposite angles are equal.

Since, angle 1 and angle 3 are vertically opposite, they are equal.

Thus, ∠3 = 100°.

Hence, the measure of angle 3 is 100°.

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The weight of the guinea pig measured in kilograms is A = 1.130 kg

In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.

The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.

A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.

Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.

Given data ,

Let the measurement of unit be represented as A

Now , the weight of the guinea pig = 1,130 grams

where from the unit conversion

1000 grams = 1 kg

So , weight of the guinea pig measured in kilograms A = 1,130 grams / 1000

On simplifying , we get

The weight of the guinea pig measured in kilograms A = 1.130 kilograms

Therefore , the value of A is 1.13 kg

Hence , the measurement is A = 1.13 kg

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The guinea pig weight measured in kilograms is 1.13kgs.

To convert the weight of a guinea pig from grams to kilograms, you need to understand the relationship between these units:

In the metric system, 1 kilogram (kg) is equal to 1,000 grams (g).

Start with the weight of the guinea pig: 1,130 grams.

Use the conversion factor: 1,000 grams = 1 kilogram.

Divide the weight in grams by the conversion factor to find the weight in kilograms.

1,130 grams ÷ 1,000 = 1.13 kilograms.

Answer:

[tex] {( {x}^{2} + 3) }^{2} = {4x}^{2} + 12[/tex]

[tex] \bf \purple{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} } [/tex]

[tex] {( {x}^{2}) }^{2} + 2({x)}^{2} (3) + {(3)}^{2} = {4x}^{2} + 12[/tex]

[tex] {x}^{4} + {6x}^{2} + 9 = {4x}^{2} + 12[/tex]

[tex] {x}^{4} = {4x}^{2} - {6x}^{2} + 12 - 9 [/tex]

[tex] {x}^{4} = { - 2x}^{2} + 3[/tex]

[tex]( {x}^{2} \times {x}^{2}) = { - 2x}^{2} + 3[/tex]

[tex]2 \times {x}^{2} = { - 2x}^{2} + 3[/tex]

[tex] = \frac{ { - 2x}^{2} + 3 }{ {2x}^{2} } [/tex]

[tex] = 3[/tex]

Answer:72 IS THE ANSWER



Step-by-step explanation:

BRAINLIEST????? PLEASE

Number of one-fourth ounce doses are in 18 ounces is 72 doses

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.

Division is a simple operation in which a number is divided.

Given,

Bottle contains 18 ounces of medicine

Therefore

Number of one-fourth ounce doses are in 18 ounces = [tex]\frac{18}{0.25}=72[/tex] doses

Hence, Number of one-fourth ounce doses are in 18 ounces is 72 doses

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Answer:

4(9b+6) is equivalent to 4 x (9 x b + 6)

Answer:

-3, -6

Step-by-step explanation:

Any number of x that makes the bottom 0 makes the expression undefined.

Factor the polynomial in the denominator:

(x+3)(x+6)

Values of x that makes the expression undefined are -3 and -6

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Answer:

D. A histogram is shown with title Puppy Weight. On the horizontal axis, the title is Pounds. The title on the vertical axis is Puppies. The range on the horizontal axis is 10 to 11, 12 to 13, and 14 to 15. The values on the vertical axis are from 0 to 6 at intervals of 1. The bar for the first range goes to 4. The bar for the second range goes to 2, the bar for the third range goes to 3.

Answer:

A = 50.24

Step-by-step explanation:

Diameter = 8

8/2 = 4

4 is the radius

A = πr2

A = 3.14 x 42

4 x 4 = 16

A = 3.14 x 16

A = 50.24

Answer:

A = 50.24

Step-by-step explanation:

Diameter = 8

8/2 = 4

4 is the radius

A = πr2

A = 3.14 x 42

4 x 4 = 16

A = 3.14 x 16

A = 50.24

Answer:

0.25 (1/4) bowls a minute.

Step-by-step explanation:

If you divide 15 by 60, you get 0.25 (1/4) and then you just add your labels which is bowls a minute.

Answer:

Mean = 272.3

sd = 37.7

Step-by-step explanation:

Mean = sum/n

(221+248+251+255+259+263+264+272+291+297+374) ÷ 11

= 2995/11

= 272.2727273

Variance = (sum of x²)/n - mean²

[(221²+248²+251²+255²+259²+263²+264²+272²+291²+297²+374²)/11] - (2740/11)²

= (831067/11) - (2995/11)²

= 1419.107438

sd² = variance

sd = sqrt(1419.107438)

sd = 37.67104243

Answer:

20,4

Step-by-step explanation:

Suppose that x, y are the the length and width

Area=x*y=80

Parameter=2(x+y)=48....x+y=24

Xy=80...x(24-x)=80...x=20,y=4

Answer:

20,4

Step-by-step explanation:

20+20+4+4=48

20*4=80

Answer:

A=26

Step-by-step explanation:

well, A is less than 27 so A could be 26?

Answer:

y=0.5x+6

Step-by-step explanation:

6 is the y-intercept because you go up 1 over 2.

Answer: The equation of line is [tex]2y - x - 12 = 0[/tex]

Step-by-step explanation:

The formula for finding the equation of a line when slope and a point is gives is :

[tex]y-y_{1}=m(x-x_{1})[/tex]

[tex]x_{1}=-2[/tex]

[tex]y_{1}=5[/tex]

[tex]m = 1/2[/tex]

substituting into the formula , we have :

[tex]y - 5 = 1/2 ( x-(-2) )[/tex]

multiply through by 2 , we have

[tex]2(y-5) = 1(x+2)[/tex]

[tex]2y - 10 = x + 2[/tex]

[tex]2y - x - 10 - 2 = 0[/tex]

[tex]2y - x - 12 = 0[/tex]

Therefore : the equation of line is [tex]2y - x - 12 = 0[/tex]

Subtracting smaller 3-digit numbers from 920 results in 3-digit answers, subtracting larger 3-digit numbers gives 2-digit answers, and subtracting even larger 3-digit numbers results in 1-digit answers. Examples include: 920 - 120 = 800, 920 - 825 = 95, and 920 - 915 = 5.

This question involves simple subtraction operations. Here are three subtraction equations that meet the conditions:

As we increase the 3-digit number that we subtract from 920, the result decreases in the number of digits,

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To subtract 3 digit numbers from 920 and end up with a 1-digit, 2-digit or 3-digit number, the following equations are provided: 920 - 911 = 9, 920 - 815 = 105 and 920 - 100 = 820.

To find three subtraction equations that show the difference when subtracting a 3-digit number from 920, we need to consider all possible scenarios for the difference.

The smallest possible difference would be a 1-digit number.

To get a 1-digit number, 2-digit number, or a 3-digit number as the result while subtracting a 3-digit number from 920, here are three equations:

• The smallest possible difference would be a 1-digit number. 920 - 911 = 9

• The next possible difference would be a 2-digit number. 920 - 815 = 105

• The largest possible difference would be a 3-digit number. 920 - 100 = 820

In each equation, we started with 920 and subtracted a 3-digit number. Given that the numbers we subtract are less than 920, it becomes possible to get a 1-digit, 2-digit, or 3-digit result.

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Answer:

The slope -intercept form of the equation is;

y = [tex]\frac{3}{2}[/tex]  x  +   4

Step-by-step explanation:

The slope-intercept form of an equation is;

y = mx + c

where m is the slope and c represent the intercept

To represent the equation given; 3x - 2y = -8 in its slope intercept form, we will follow the steps below:

3x - 2y = -8

subtract 3x from both-side of the equation

3x - 3x -2y  = -3x - 8

-2y = -3x -8

Divide throught the equation by -2

-2y/-2 =-3x/-2  -8/-2

y = [tex]\frac{3}{2}[/tex]  x  +   4

The slope -intercept form of the equation is;

y = [tex]\frac{3}{2}[/tex]  x  +   4

Answer:

see below

Step-by-step explanation:

Prove : cos²(A-B)-sin²(A+B)=cos2Acos2B

LHS,

cos²(A-B) - sin²(A+B)     (expand using double angle identities)

= [tex]\frac{1 + cos [2(A-B)]}{2} - \frac{1 - cos [2(A+B)]}{2}[/tex]

= [tex]\frac{1}{2} + \frac{1}{2} cos[2(A-B)] - \frac{1}{2} + \frac{1}{2} cos[2(A+B)][/tex]

= [tex]\frac{1}{2} cos[2(A-B)] + \frac{1}{2} cos[2(A+B)][/tex]

= [tex]\frac{1}{2} cos(2A-2B) + \frac{1}{2} cos(2A+2B)[/tex]      (expand using sum/difference identities)

= [tex]\frac{1}{2} (cos2Acos2B + sin2Asin2B ) + \frac{1}{2} (cos2Acos2B - sin2Asin2B )[/tex]

= [tex]\frac{1}{2} cos2Acos2B + \frac{1}{2}sin2Asin2B + \frac{1}{2} cos2Acos2B - \frac{1}{2}sin2Asin2B[/tex]

= [tex]\frac{1}{2} cos2Acos2B + \frac{1}{2} cos2Acos2B[/tex]

= [tex]cos2Acos2B[/tex]  (= RHS , Proven)

Answer:

there will be 19 $100 bills

and 11 $10 bills

Step-by-step explanation:

[tex]100*19=1900\\10*11=110\\1900+110=2010[/tex]

Answer:

11

Step-by-step explanation:

Let x be how many $10 bills there are.

Let y be how many $100 bills there are

x + y = 30

x = 30 - y

10x + 100y = 2010

10(30 - y) + 100y = 2010

300 - 10y + 100y = 2010

-10y + 100y = 2010 - 300

90y = 1710

y = 1710 / 90

y = 19

x = 30 - 19

x = 11

Answer:

H=3

Step-by-step explanation:

1. 6(3)-15

2.18-15

3. 3

4. Brainliest please

Answer:

643.4

Step-by-step explanation:

Answer:

The answer is: 643.4

Step-by-step explanation:

Answer:

616

Step-by-step explanation:

Answer:

557.49

Step-by-step explanation:

Add the three bills together

450.00

 37.50

 69.99

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

557.49

Answer:

Volume of water left in the cylinder=[tex]76\frac{2}{3}\pi \:in^3[/tex]

Step-by-step explanation:

Height of the Cylinder=10 inches

Radius of the cylinder=4 Inches

Volume of the Cylinder

[tex]=\pi r^2h\\=4^2*10\pi\\=160\pi\:in^3[/tex]

Radius of the Hemisphere=5 Inches

[tex]\text{Volume of a Hemisphere}=\frac{2}{3}\pi r^3\\ =\frac{2}{3}\pi *5^3\\=\frac{250\pi}{3} in^3[/tex]

Since the Volume of the cylinder is greater than the Volume of the bowl, all the water will not fit.

[tex]\text{Therefore: volume of water left} =160\pi-\frac{250\pi}{3}\\=76\frac{2}{3}\pi \:in^3[/tex]

There are 71 dogs in the local animal shelter.

To determine the number of dogs and cats in the shelter, let's denote the number of dogs by D and the number of cats by C. According to the problem statement, there are twice as many cats as dogs, minus three. Mathematically, this is represented as C = 2D - 3. We also know that the combined total of cats and dogs is 210, which can be expressed as C + D = 210. To find the number of dogs, we can solve these two equations simultaneously.

From the first equation, we solve for C in terms of D: C = 2D - 3.

Substitute C into the second equation: (2D - 3) + D = 210.

Combine like terms: 3D - 3 = 210.

Add 3 to both sides of the equation: 3D = 213.

Divide both sides by 3 to solve for D: D = 71.

Therefore, there are 71 dogs in the local animal shelter.

Answer:

13.01d-2.65

Step-by-step explanation:

Since there r numbers with the variable d, combine them.

Answer:

1.75

Step-by-step explanation:

Use the distributive property first.

(3.5 x 2.25) (3.5 x X) = 14

7.875 + 3.5x = 14   Now subtract 7.875 from both sides

3.5x = 6.125  Now divide 3.5 by both sides

x = 1.75

The equation 3.5(2.25 + x) = 14 is solved by first distributing 3.5 through the parentheses, then isolating x on one side, yielding a result of x = 1.75.

In this mathematical equation, the first step is to distribute 3.5 to (2.25 + x). The result is 7.875 + 3.5x = 14. We then subtract 7.875 from both sides to isolate the term with x which gives 3.5x = 6.125. Finally, to solve for x, we divide both sides by 3.5. This gives us x = 1.75.

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Answer:

a) 984.6080 = 984.61 to 2 decimal places

b) 984.6080 = 984.6 to 4 significant figures

c) 984.6080 = 984.608 to 3 decimal places

d) 984.6080 = 984.61 to the nearest hundredth

Step-by-step explanation:

Answers to the approximation questions above are supplied below.

First, you needs to know approximation processes:

Step 1: Keep the required number of digits in question.

Step 2: Before rounding off the remaining digits, look at the next digit to the required number of accuracy, if it is 5 or more, increase the last digit of the number you're keeping by 1, otherwise leave it as it is and round down to zero all the unwanted digits.

Similarly, there is need know the meaning of each degree of accuracy.

1. Decimal places: These are the number of digits occurring after the decimal point. E.g. a set of figures in 1 decimal place has only one digit after decimal point, i.e. 65.4. In the case of the question above,

a) 984.6080 = 984.61 to 2 decimal places

c) 984.6080 = 984.608 to 3 decimal places

2. Significant figures: Basically, these are nonzero digits in a set of figures. However, when zero is in the middle of nonzero digits, i.e, 3045, such zero is a significant figure. In the question above,

b) 984.6080 = 984.6 to 4 significant figures

3. Hundredth: Under place value system, hundredth of a set of figures is located at two digits after the decimal point. In other words, hundredth is same as two decimal places so the same approach is required for the two. Thus;

d) 984.6080 = 984.61 to the nearest hundredth

You can see that the result for both 2 decimal places and nearest hundredth are the same, that is, 984.6080 = 984.61 to 2 decimal places and to the nearest hundredth respectively.

Therefore, the answers are summarized thus:

a) 984.6080 = 984.61 to 2 decimal places

b) 984.6080 = 984.6 to 4 significant figures

c) 984.6080 = 984.608 to 3 decimal places

d) 984.6080 = 984.61 to the nearest hundredth

Answer:

984.6080

a. 2 decimal places

984.61

b. 4 significant figures

984.6

c. 3 decimal places

984.608

d. the nearest hundredth

984.61