A farmer creates a rectangular pen using part of the wall of a barn for one side of the pen and a total of 130 feet of fencing for the remaining 3 sides, as shown in the diagram. Write and equation which gives the area of the pen, A, as a function of x, the length of fence parallel to the barn

Answer:

[tex](x+5)^2+y^2=117[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Given:

[tex]\implies (x-(-5))^2+(y-0)^2=r^2[/tex]

[tex]\implies (x+5)^2+y^2=r^2[/tex]

To find r², input the coordinates of the given point (4, -6) into the equation:

[tex]\implies (4+5)^2+(-6)^2=r^2[/tex]

[tex]\implies 81+36=r^2[/tex]

[tex]\implies r^2=117[/tex]

Therefore, the equation of the circle is:

[tex]\implies (x+5)^2+y^2=117[/tex]

Answer:

Standard form = (x + 5)² + y² = 117

General Form = x² + 10x + y² - 92 = 0

Explanation:

(x - h)² + (y - k)² = r²

Find radius using:

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]\rightarrow \sf radius : \sqrt{(-5-4)^+(0-(-6))^2} \ = \ 3\sqrt{13} \ \ units[/tex]

Find equation inserting values:   Given center: (-5, 0)

⇒ (x - (-5))² + (y - 0)² = (3√13)²

⇒ (x + 5)² + y² = 117

⇒ x² + 10x + 25 + y² - 117 = 0

⇒ x² + 10x + y² - 92 = 0

Answer: 2,444

Step-by-step explanation: We can find the answer to this problem by simplifying the scientific notation, and then adding. You would end up with 2,000 + 400 + 40 + 4 if done correctly. Hope this helps!

Answer:

  a. $0.47 per ounce

  b. $0.36 per ounce

  c. the gallon size costs less per ounce

Step-by-step explanation:

A unit rate is a rate that is expressed with one unit in the denominator. That is, it is <some amount> per unit. The <some amount> value will generally depend on what unit is chosen. This problem suggests the desired unit is 1 oz of paint.

__

Unit cost for a quart:

  ratio = cost/ounces = $14.99/(32 oz) ≈ $0.468/oz ≈ $0.47/oz

__

Unit cost for a gallon:

  ratio = cost/ounces = $45.99/(120 oz) ≈ $0.359/oz ≈ $0.36/oz

__

The cost per ounce is less for the gallon size. If at least 3 quarts of paint is needed, then buying it in the gallon size will cost less.

If less than 3 quarts are needed, then a gallon container will cost more than is necessary for the paint required. The "better deal" depends on the amount of paint required.

Answer:

x=1 y=1

Step-by-step explanation:

Let's use the elimination method.
3x+4y=7
2x-y = 1 (multiply both sides by 4)
8x-4y=4
3x+4y=7

(add both equations together)
11x=11
x=1
Plug x=1 into either of the equations
2(1) - y=1
2-y=1
2=1+y
y=1

Exact Form:

5

27

Decimal Form:

0.

¯¯¯¯¯¯

185

i hope this helps please have a nice day/night

Answer:

Exact Form:

5

27

Decimal Form:

0.

¯¯¯¯¯¯

185

i hope this helps please have a nice day/night

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Vertical lines are parallel so the given interior angles are supplementary and their sum is equal to 180:

4x + 9 + 16x - 9 = 180 add like terms

20x = 180 divide both sides by 20

x = 9

How you do it is add the 44% of 132 to 132 (132 + (132×44%))

First you have to find out how much 44% is. Change it into decimal form (0.44) and then multiply the two together. 132 × 0.44 is 58.08 miles. Then you add that to the rest of the trip, 132 miles. (132 + 58/08 is 190.08)

The value of x is 8 from the diagram given.

The corresponding sides of a similar triangle are said to be in proportion if and only if the corresponding angle are also equal.

To calculate the side of line x (|x|), we have to determine the ratios of the corresponding sides as:

[tex]\mathbf{\dfrac{BC}{DC} = \dfrac{AC}{EC}}[/tex]

[tex]\mathbf{\dfrac{x}{10} = \dfrac{12}{15}}[/tex]

x = 120/15

x = 8

Therefore, we can conclude that the value of x is 8.

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The probability that the book is nonfiction given that it is hard-covered is 4/11

From the complete question, we have:

Total = 20

n(H ∩ N) = 4

n(H) = 11

This means that:

P(H ∩ N) = n(H ∩ N)/Total

So, we have:

P(H ∩ N) = 4/20

The conditional probability is then calculated using:

P(N | H) =4/20 ÷ 11/20

Evaluate

P(N | H) = 4/11

Hence, the probability that the book is nonfiction given that it is hard-covered is 4/11

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Answer:

Step-by-step explanation:

4/20

11/20

4/11

yw :)

The volume of the sphere is 3,052.08 cubic millimeters. The correct answer is A.

If the given sphere is of radius r units, then its volume is given as:

[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]

A glass marble has a diameter of 18 millimeters.

The radius is 9

[tex]V= \dfrac{4}{3} (3.14) (9)^3 \: \rm unit^3\\\\V = 3,052.08 cubic millimeters[/tex]

The volume of the sphere is 3,052.08 cubic millimeters. The correct answer is A.

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Answer:

y = 3x - 12

Step-by-step explanation:

Forming the slope-intercept equation :

y = mx + b

Substitute m = 3 and b = -12 in the equation :

Answer:

y = 3x - 12

Step-by-step explanation:

The slope intercept form of a line is y = mx + b, where m is the slope and b is the y intercept. Here, m = 3 and b = -12. Therefore, the slope intercept form for this line is y = 3x - 12.

The equation is y = 27x. The amount she pays for an 8-day rental will be $ 216. Then the domain and range will be (0, ∞) and (0, ∞).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Connie Nardelli rents a car for $27 per day.

The total cost is a function of the number of days she rents the car.

Let x be the number of days ad y be the total rent cost.

Then the equation will be

y = 27x

The amount she pays for an 8-day rental will be

y = 27 × 8

y = 216

The domain and range will be (0, ∞) and (0, ∞).

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Hey there!

4 3/5 - 2 5/6

= 23/5 - 17/6

= 53/30

≈ 1 23/30

Therefore, the answer should be:

53/30

OR

1 23/30

(Either should work because they are equivalent to each other)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Value of the given mixed fraction [tex]4\frac{3}{5} -2\frac{5}{6}[/tex] is equals to [tex]1\frac{23}{30}[/tex] .

" Mixed fraction is defined as the fraction representing whole fraction along   with the quotient and remainder."

Convert mixed fraction into improper fraction

[tex]m\frac{p}{q} = \frac{q*m+p}{q}[/tex]

According to the question,

Given mixed fraction,

   [tex]4\frac{3}{5} -2\frac{5}{6}[/tex]

Convert mixed fraction into improper fraction we get,

[tex]=\frac{23}{5} -\frac{17}{6} \\\\=\frac{138-85}{30} \\\\=\frac{53}{30}\\ \\= 1\frac{23}{30}[/tex]

Hence, value of the given mixed fraction [tex]4\frac{3}{5} -2\frac{5}{6}[/tex] is equals to [tex]1\frac{23}{30}[/tex] .

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Answer:

Here is the ans ...hope it helps:)

Answer:

[tex]\large\boxed{\sf x^3 - 7x^2 + 7x - 10}[/tex]

Explanation:

Given:

(a) f(x) = x³ - 3x² + 2x - 3

(b) g(x) = 4x²- 5x + 7

Solve for (f - g)(x) = f(x) - g(x) :

⇒ x³ - 3x² + 2x - 3 - (4x²- 5x + 7)

distribute inside parenthesis

⇒ x³ - 3x² + 2x - 3 - 4x² + 5x - 7

group the variables

⇒ x³ - 3x² - 4x² + 2x + 5x - 3 - 7

add or subtract variables

⇒ x³ - 7x² + 7x - 10

Answer:

x³ - 7x² + 7x - 10

Step-by-step explanation:

Subtracting functions: (f - g)(x) is equivalent to f(x) - g(x)

Given:

Simplify:

(x³ - 3x² + 2x - 3) - (4x² - 5x + 7)

(x³ - 3x² + 2x - 3) - (4x²) + - (- 5x) - (7)

x³ - 3x² + 2x - 3 - 4x² + 5x - 7

x³ - 3x² - 4x² +2x + 5x - 3 - 7

x³ - 7x² + 7x - 10

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Answer:

B

Step-by-step explanation:

When you have a double negative (ie. 5 -(-10)) they cancel eachother out and become a plus. If you have + and - together, its always a minus, if you have + and + or - and -, its always plus.

Since in 4-(-3), the two minuses cancel each other out and become a plus, you move 3 to the right, since right is the positive direction.

subtracting a negative number changes the equation to an addition.

4 -(-3) becomes 4 + 3 = 7

you would start at 4 and move 3 places to the right.

the answer is B.

Step-by-step explanation:

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The value of x is 6.

Complementary angles are angles that sum up to 90°.

Analysis:

For angles A and B, to be complementary, the sine of angle A  must be equal to the cosine of angle B.

sin A = cos B

5X+9 = 3x+21

5x - 3x = 21 - 9

2x = 12

x = 6

In conclusion, the value of x to make angles A and B complementary is 6.

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The measure of the missing angle x is 23.22 degrees

The expression for representing cosine rule is expressed as:

c² = a² + b² - 2ab cos C

Given the following parameters

a = 26

b = 50

c = 29

Substitute

c² = a² + b² - 2ab cos C

29² = 26² + 50² - 2(26)(50) cos C

841 = 676 + 2500 - 2600cosC

2335 =2600cos C
cos C = 2335/2660

C = 23.22 degrees

Hence the measure of the missing angle x is 23.22 degrees

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Answer:

23.2 is the correct answer given you need to round to the nearest tenth.

Answer:

150

Step-by-step explanation:

Let :

⇒ The numbers can be denoted as x, 3x, and 5x

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

Solving :

⇒ It mentions their sum is 270

⇒ x + 3x + 5x = 270

⇒ 9x = 270

⇒ x = 30

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

Largest number :

⇒ 5x

⇒ 5(30)

⇒ 150

Answer :

Step by step explaination :

Here we have been given with the ratio of three numbers that is 1 : 3 : 5. So let us assume a common factor for them , we are assuming it as y.

Therefore,

Sum of them is 270 :

>> 1y + 3y + 5y = 270

>> 4y + 5y = 270

>> 9y = 270

>> y = 270 / 9

>> y = 90 / 3

>> y = 30

Henceforth, value of y is 30.

★ Finding out first number :-

>> First number = 1y

>> First number = 1 × 30

>> First number = 30

★ Finding out second number :-

>> Second number = 3y

>> Second number = 3 × 30

>> Second number = 90

★ Finding out third number :-

>> Third number = 5y

>> Third number = 5 × 30

>> Third number = 150

Answer:

y = 4 - 2x

Step-by-step explanation:

That is the formula, in y = a + mx but it you want it in y = mx+c, it is y = -2x + 4

Step-by-step explanation:

here, given points are

(-2,-1),(-5,-3),(-5,-4)

now

(X,y)________ (-y,X)

(-2,-1)________ (1,-2)

(-5,-3)________ (3,-5)

(-5,-4)________ (4,-5)

now plot the points in the graphs

Answer:

300:288

Step-by-step explanation:

5+2=7

280 /7 = 4

20:8

300:288

Answer:

here we have to divide the number of words per hour to the number of minutes per hour.

Step-by-step explanation:

5400÷60

=90.

therefore in a minute she types 90 words.

area of square = s×s

9×9

81cm²

hope it helps...!!!

Answer:

81 cm^2

Step-by-step explanation:

A square is a 2d shape with side lengths all the same.

To find the area, all you need is one side length, which is 9cm in this case.

Then you just square the number (9 x 9) to get 81 cm^2 (centimetre squared).