A farmer wants to build a rectangular pen with 80 feet of fencing. The pen will be built against the wall of the barn so one side of the rectangle won’t need a fence. What dimensions will maximize the area of the pen?

a=80 because it is equal to the 80 by the corner R

The expression [tex]\frac{7\sqrt{x^2}}{5\sqrt{y^3}}[/tex] can be simplified to  [tex]\frac{7\sqrt{x^2}}{5y\sqrt{y}}[/tex].

Let's simplify the expression [tex]\frac{7\sqrt{x^2}}{5\sqrt{y^3}}[/tex]:

First, simplify the square root terms:

[tex]\frac{7|x|}{5\sqrt{y^3}}[/tex]

Now, combine the constants:

[tex]\frac{7}{5} \cdot \frac{|x|}{\sqrt{y^3}}[/tex]

To simplify further, you can rewrite [tex]\sqrt{y^3}[/tex] as [tex]\sqrt{y^2 \cdot y}[/tex] and then cancel out one of the y terms:

[tex]\frac{7}{5} \cdot \frac{|x|}{y\sqrt{y}}[/tex]

So, the simplified expression is [tex]\frac{7|x|}{5y\sqrt{y}}[/tex], or equivalently, [tex]\frac{7\sqrt{x^2}}{5y\sqrt{y}}[/tex].

Hello there! The value of y is -5/4.

So, basically look at it like an ordered pair, (x, y). When we have (5, y), we have a value of x and are looking for a value of y. To do this, plug the value for x (5) into the equation and solve for y.

5x+4y-20=0

5(5)+4y-20=0

Now that you have the value for x, solve for y.

5(5)+4y-20=0 - Start by multiplying out the parenthesis.

25 + 4y - 20 = 0 - Next, combine like terms.

25 - 20 + 4y = 0

5 + 4y = 0 - Now, subtract 5 from both sides.

4y = -5 - Lastly, divide both sides by 4.

y = -5/4.

This is your final answer. I hope this helps and have a great day! :)

To find the value of y, substitute the given coordinates (5, y) into the equation 5x + 4y - 20 = 0. Simplify the equation and solve for y to get y = -1.25.

To find the value of y, we can substitute the given coordinates (5, y) into the equation.

According to the equation 5x + 4y - 20 = 0, when x is 5, we have:

5(5) + 4y - 20 = 0.

Simplifying this equation gives us:

25 + 4y - 20 = 0.

Combining like terms, we get:

4y + 5 = 0.

Next, we can isolate the y-term by subtracting 5 from both sides of the equation:

4y = -5.

Finally, we can solve for y by dividing both sides of the equation by 4:

y = -5/4, or y = -1.25.

Answer:

y=2x

Step-by-step explanation:

2 up, 1 over. put rise over run so that concludes the 2x.

The line starts at 0 so there is no y-intercept

y=2x The "formula" would be y=mx+b where m is the slope and b is the y-intercept. in this case, the slope is 2 and the y-intercept is 0 therefore the equation is y=2x (no zero because we can atoumtucally assume that its a zero)

the only like-terms are on the right-hand-side, since the left-hand-side has only 1 term anyway.

[tex]\bf \cfrac{5}{2}s=\cfrac{3}{2}s+s\implies \cfrac{5}{2}s=\cfrac{3}{2}s+\cfrac{s}{1}\implies \cfrac{5}{2}s=\stackrel{\textit{using the LCD of 2}}{\cfrac{(1)3s+(2)s}{2}} \\\\\\ \cfrac{5}{2}s=\cfrac{3s+2s}{2}\implies \cfrac{5}{2}s = \cfrac{5}{2}s[/tex]

Answer:

x = [tex]\frac{5}{26}[/tex]

Step-by-step explanation:

Given equation:

[tex]\frac{3}{4}x + \frac{5}{8} = 4x[/tex]

[tex]\frac{3(2)x + 5}{8} = 4x[/tex]            ∵taking GCF 8

[tex]\frac{8 (6x + 5) }{8}[/tex]  = 4x × 8

6x + 5 = 32x    ⇒   5 = 32x - 6x   ⇒  5 = 26x   ⇒  x = [tex]\frac{5}{26}[/tex]

The equivalent of the given expression 3 × 7.2 will be 21.6.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The result of 3 times 7.2 can be found by simply multiplying 3 and 7.2 together:

3 × 7.2 = 21.6

Therefore, the equivalent of 3 times 7.2 is 21.6.

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To determine what is equivalent to 3×7.2, simply multiply 3 by 7.2 to get 21.6.

Raul used the model to calculate 3×7.2. To find what is equivalent to 3×7.2, we can multiply the two numbers directly. Multiplying 3 by 7.2 gives us 21.6, so 3×7.2 is equivalent to 21.6.

The question seems to be asking for a calculation based on a model, but without the specifics of the model, the best we can do is a straightforward multiplication. Remember, when multiplying by a whole number and a decimal, you multiply as if they were both whole numbers and then place the decimal in the product based on the number of decimal places in the original numbers.

Answer:

Length = 17 inches, Width = 14 inches

Step-by-step explanation:

Let the width(W) of the rectangle be x inches

The length(L) of the rectangle will be x + 3 inches

Perimeter(P) of the rectangle is 62 inches

i.e

P = 2L + 2W

2(x + 3) + 2x = 62

2x + 6 + 2x = 62

4x = 62 - 6 = 56

x = [tex]\frac{56}{4}[/tex] = 14 inches

So the width is 14 inches and;

The length is 14 + 3 = 17 inches

The width of the rectangle is 14 inches, and the length is 17 inches.

To find the length and width of a rectangle, we can use the information given in the problem and set up an equation. Let's say the width of the rectangle is x inches. The length would then be x + 3 inches. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Plugging in the given values for the perimeter, we get:

62 = 2(x + 3) + 2x

Simplifying the equation:

62 = 2x + 6 + 2x

Combine like terms:

62 = 4x + 6

Subtract 6 from both sides:

56 = 4x

Divide both sides by 4:

x = 14

So the width of the rectangle is 14 inches. Substituting this value back into the equation for the length, we get:

Length = 14 + 3 = 17 inches

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Simplify the expression.

Exact Form:

−37/4

Decimal Form:

−9.25

Mixed Number Form:

−9 1/4

[tex]\text{Hey there!}[/tex]

[tex]-5\frac{3}{4}-3\frac{1}{2}=?[/tex]

[tex]\text{-5}\frac{3}{4}=\text{-5}\times\text{4+3}\rightarrow\text{-5}\times4=-20\rightarrow\text{-20 + 3 = -23}[/tex]

[tex]\text{The denominator stays the same:}-5\frac{3}{4}=-\frac{23}{4}[/tex]

[tex]\text{3}\frac{1}{2}=3\times2+1\rightarrow3\times2=6+1\rightarrow6+1=7[/tex]

[tex]\text{3}\frac{1}{2}=\frac{7}{2}[/tex]

[tex]\frac{-23}{7}-\frac{7}{2}=?[/tex]

[tex]\text{Solve the NEWER question above}\uparrow\text{and you will see your answer}[/tex]

[tex]\boxed{\boxed{\bf{Answer:Improper\ fraction:\frac{-37}{4}\ or\ Mixed\ number:-9\frac{1}{4}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

[tex]\frak{LoveYourselfFirst:)}[/tex]

Final answer:

The volume of a cone with a diameter of 6 inches and a height of 6 inches is approximately 56.5 cubic inches when rounded to the nearest tenth, using the volume formula for a cone.

Explanation:

To calculate the volume of a cone, we can use the formula

V = [tex]\(\frac{1}{3}\)\pi r^2 h[/tex]

First, find the radius (r) by dividing the diameter by 2.

The cone's diameter is 6 inches, thus the radius[tex]\(r = \frac{6}{2} = 3\) inches.[/tex]

Next, apply the values to the cone volume formula:

V =[tex]\(\frac{1}{3}\)\pi (3)^2 \times 6\)[/tex]

Now perform the calculations

V = [tex]\(\frac{1}{3}\)\times 3.14 \times 9 \times 6[/tex]

V = 56.52 cubic inches

Therefore, the volume of the cone is approximately 56.5 cubic inches to the nearest tenth.

Answer:

x = -2 or x=6

Step-by-step explanation:

Given

f(x) = 3Ix-2I + 6

As we know that

f(x) = 18

Putting both equal

3Ix-2I+6 = 18

Two cases are possible

Case 1: Negative Modulus

3* -(x-2) + 6 = 18

3(-x+2)+6 = 18

-3x+6+6 = 18

-3x +12 = 18

-3x = 18 - 12

-3x = 6

x = 6/-3

x = -2

Case 2: Positive Modulus

3(x-2)+6 = 18

3x-6+6 = 18

3x = 18

x = 18/3

x = 6

So for x= -2 or x=6 the value of function will be 18..

Answer:

g(x)=(x+7)^2-3

Step-by-step explanation:

Given:

f(x)= x^2

Now we have to translate f(x) 7 units to the left and 3 units down to form the function g(x).

As per the rules of translation

when any parent function, in given case f(x)=x^2, is translated to 'a' units to the left then 'a' is added to the value of x. thus making f(x+a)

Also when the parent function is translated any 'a' units down then 'a' is subtracted from the value of function. thus making f(x)-a

Translating f(x), 7 units to the left

f(x+7)= (x+7)^2

Translating f(x+7), 3 units down

f(x+7)-3 = (x+7)^2-3

Hence new function g(x)=(x+7)^2-3!

If [tex]m\widehat{BY}=40^\circ[/tex], then the central angle [tex]\angle BOY[/tex] has the same measure, and by the inscribed angle theorem we have

[tex]m\angle BAY=\dfrac12m\angle BOY=20^\circ[/tex]

It's impossible to know what the measure of angle YAC is from this information alone, but assuming AC is tangent to the circle, then angles BAY and YAC are complementary, so that [tex]m\angle YAC=70^\circ[/tex].

The line AC is the tangent of the line, and the measure of the angle YAC is 70 degrees

The measure of the arc is given as:

Arc BY = 40 degrees

The measure of angle BAY is calculated using:

BAY = 0.5 * BY

This gives

BAY = 0.5 * 40

BAY = 20

The angle at a tangent is 90 degrees.

This means that:

BAY + YAC = 90

Substitute 20 for BAY

20 + YAC = 90

Subtract 20 from both sides

YAC = 70

Hence, the measure of the angle YAC is 70 degrees

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Answer:

From the information provided we have:

PD ≅ RD (= 11)

∠CPD ≅ ∠CRD (= 90°)

They both have CD as the hypotenuse.

=> ΔCPD ≅ ΔCRD

=> ∠PCD ≅ ∠RCD

Now we know that:

∠RCP = ∠PCD + ∠RCD

∠RCP = 2 · ∠RCD

∠RCP = 2 · 33° = 66°

So the answer is B

Answer: B. 66°

Step-by-step explanation:

In then figure figure , we consider two triangle ΔPCD and Δ RCD in which

∠P ≅ ∠R = 90°

PD≅RD =11

CD≅CD   [Reflexive Property]

Hence, By HL theorem we have

ΔPCD ≅ Δ RCD

[ HL theorem says that if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of other right triangle, then the triangles are said to be congruent.]

Now , By CPCTC we have

∠PCD≅∠RCD

Then , ∠RCP = 33°+33°=66°

8 & 4 when you add them together it’s 12 and when you multiply then it’s 32. When you see sum in a problem it means add. When you see product in a problem it means multiply.

Step-by-step explanation:

We can do this either by looking at:

the bonds of 12, (of which there are 7 pairs)

(which pairs of numbers add up to 12?)

or the factors of 32 (of which there are 3 pairs)

Using the factors seems quicker.

Write the factors and in each find their sum.

As 12 is quite small in comparison to 32, I would expect that the middle factors will be the ones we want - they have the smallest sum and the smallest difference of all the pairs:

1×32

=32

1+32

=33

2×16

=32

2+16

=18

4×8

=32

4+8

=12

these are the ones we want.

Answer:

The centre is at (-12, 9) and the radius = 5 units.

Step-by-step explanation:

x^2 + y^2 + 24x - 18y + 200 = 0

x^2 + 24x + y^2 - 18y = -200

Completing the square on the x and y terms:

(x + 12)^2 - 144 + (y - 9)^2 - 81 = -200

(x + 12)^2 + (y - 9)^2 = -200 + 144 + 81

(x + 12)^2 + (y - 9)^2 = 25

So the centre is at (-12, 9) and the radius = the square root of 25 = 5.

Answer:

centre = (- 12, 9), radius = 5

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² + 24x - 18y + 200 = 0

Collect the terms in x/ y together and subtract 200 from both sides

x² + 24x + y² - 18y = - 200

Using the method of completing the square

add ( half the coefficient of the x/ y term )² to both sides

x² + 2(12)x + 144 + y² + 2(- 9)y + 81 = - 200 + 144 + 81

(x + 12)² + (y - 9)² = 25 ← in standard form

with centre (- 12, 9) and r = [tex]\sqrt{25}[/tex] = 5

3.542 is the answer; you just need to move the decimal 2 places to the left.

Answer:

40 meters

Step-by-step explanation:

add 28 and 12

Answer: its 300

aka D

Step-by-step explanation:

I did the quiz

Answer:

The vertex is the point (-1,2)

Step-by-step explanation:

we have

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

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

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

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]f(x)-3+1=x^{2}+2x+1[/tex]

[tex]f(x)-2=x^{2}+2x+1[/tex]

Rewrite as perfect squares

[tex]f(x)-2=(x+1)^{2}[/tex]

[tex]f(x)=(x+1)^{2}+2[/tex] ----> equation in vertex form

The vertex is the point (-1,2)

Answer: p+(q÷r) this is because you divide a and r and add p to it

Should be “p+q/r”.

Using English grammar, one can group the terms using “sum of...”, “product of...”, and “quotient of x and y.” (Where ... can be “x and y”)

Subtracting in English is slightly different using “x subtracted from y” meaning “y-x”.

All of these terms can be used in tandem to create expressions like the given answer.

Answer:

1,206

Step-by-step explanation:

Since we'll have to deal with cubic inches (with the ball volume), we should also calculate the volume of the car in cubic inches.

We are told the car is a rectangular prism measuring 10ft x 5 ft x 3 ft.

So, in inches (12 inches/foot), we have: 120 in x 60 in x 36 in = 259,200 cu inches.

The ball is a sphere with a radius of 3 inches.

Real volume of the ball: V = (4/3) π r³

V = (4/3) π 3³ = 36 π = 113.1 cu inches

But of course, balls don't fit perfectly one next to another, like cubes, so we have to take into account the loss... the question tells us to use a factor of 190%.

So, the packing volume of a ball is 190% its real volume:

PV = 190% * 113.1 = 214.9 cu inches

Now, how many times does that fit inside the car?

259,200 / 214.9 = 1,206.14

Let's round it to 1,206, which is a possible answer.

Answer:

Answer is line and ray.

Step-by-step explanation:

Ray -  A ray starts from a point and ends to the infinity.

Therefore, ray is one dimensional and has infinite length.

Point - It is one dimensional but has no length.

Plane - It may be three/two dimensional.

Segment - It is one dimensional but has a limited length.

Line - It's one  dimensional with infinite length.

Angle - It's two dimensional structure.

Answer is line and ray.

One-dimensional objects with infinite length are infinite straight wires. An example is a transmission line used for electricity distribution.

The one-dimensional objects that have infinite length are infinite straight wires. An infinite straight wire is a wire that has a length much greater than its other dimensions. In the limit  L→ ∞, the field of an infinite straight wire is obtained.

An example of a one-dimensional object with infinite length is the transmission line used for electricity distribution. These lines can stretch for many kilometers and are considered one-dimensional because their length is much greater than their width and height.

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Answer:1/2(2)(4.4)(5) + 1/3(1/2)(2)(4.4)(3.9)

The product of [tex](8.8 \times 10^{6} )(5 \times 10^{2})[/tex] is [tex]4.4 \times 10^{9}[/tex]. The correct option is B,  4.4 × 109

From the question,

We are to determine the product of (8.8 × 106)(5 × 102)

First, we will write the expressions properly

The given expression written properly is

[tex](8.8 \times 10^{6} )(5 \times 10^{2})[/tex]

Now, the product of the expression can be determined as shown below

[tex](8.8 \times 10^{6} )(5 \times 10^{2})[/tex]

This becomes

[tex]8.8 \times 10^{6} \times 5 \times 10^{2}[/tex]

= [tex]8.8 \times 5 \times 10^{2}\times 10^{6}[/tex]

= [tex]44 \times 10^{2}\times 10^{6}[/tex]

= [tex]44 \times 10^{2+6}[/tex]

= [tex]44 \times 10^{8}[/tex]

= [tex]4.4 \times 10^{9}[/tex]

Hence, the product of [tex](8.8 \times 10^{6} )(5 \times 10^{2})[/tex] is [tex]4.4 \times 10^{9}[/tex]. The correct option is B,  4.4 × 109

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Answer:

She'll have to pay $46.75

Step-by-step explanation:

42.50 divided by 10% is 425 which equals $4.25. 42.50 + 4.25 = 46.75

42.50 + 10% = 46.75. So therefore you can check your answer twice and it will be the same answer.

Answer:

3.4 x 10 ^-3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

The scientific or the exponential form of the number is A = 3.4 × 10⁻³

Given data ,

To express 0.0034 in scientific notation, we need to represent it as a number between 1 and 10 multiplied by a power of 10.

First, we move the decimal point to the right until we have a number between 1 and 10. In this case, we move the decimal point three places to the right, resulting in 3.4.

Next, we determine the power of 10 by counting the number of places we moved the decimal point.

Since we moved it three places to the right, the power of 10 is -3

So , the exponential form is

Putting it all together, 0.0034 in scientific notation is 3.4 × 10⁻³

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Answer:

A∩B={[tex]25, 45, 65[/tex]}

B is a proper subset of A:

B⊂A

Step-by-step explanation:

A∩B means the intersection of the set A and the set B. In other words, is the set of elements contained in these both sets.

Given the set A and the set B:

[tex]A =[/tex]{[tex]15, 25, 35, 45, 55, 65[/tex]}

[tex]B =[/tex]{[tex]25, 45, 65[/tex]}

You can indentify that the numbers common in both sets are: 25,45 and 65.

Therefore you get:

A∩B={[tex]25, 45, 65[/tex]}

Since all elements of B are in A, and A contains elements that are not in B, then B is a proper subset of A:

B⊂A

Answer:

Step-by-step explanation:

B:  to get 4/8 = 1/2 That is not the whole answer, but it gets one started.

D: Very large because -4 -(-9) = 5 That's the power. This is going to make the result large.

That's all I would pick, but the second from the bottom might be an answer.

Answer:

452.39

Step-by-step explanation:

A=(pi)r^2

A=3.14(12)^2

A=452.39

Answer: The area of the circle is 452.16 square units.

Step-by-step explanation:

To find the area of a circle you need to use the area of a circle formula. The formula is A= π x r^2.

π= 3.14

r= 12

The r is radius which is half of the diameter. When you apply the formula you get :

A = 3.14 x 12^2

A= 3.14 x 144

A= 452.16

Answer: 12 pies.

Step-by-step explanation: Divide 72(pieces) by 6 = 12

72÷6=12.

Hope it's the answer you are looking for.✌