A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of enclosed area. What is the maximum area that can be enclosed by fencing?

The large dog and small boy working together will take 2/3 hour to destroy Mr McGregor's garden.

To solve this problem, we can add the rates at which the large dog and the small boy work together:

Large dog's rate = 1 garden / 2 hours = 1/2 garden per hour

Small boy's rate = 1 garden / 1 hour = 1 garden per hour

Combined rate = 1/2 garden per hour + 1 garden per hour = 3/2 gardens per hour

Now, we can use the combined rate to find the time it would take for the large dog and the small boy to destroy Mr. McGregor's garden:

Time = 1 garden / Combined rate = 1 garden / (3/2 gardens per hour) = 2/3 hour

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Answer:

option C

Step-by-step explanation:

Area of the triangle=4x²+4x+1

Answer:

33.75

Step-by-step explanation:

Step 1- Find the decimal form of 35%

Step 2- When you find that multiply that by 25

Step 3- When you find the answer to step 2 add that to 25

That is your answer

Final answer:

The price that Fred will pay the groomer the next time when his dog has a haircut is  $33.75.

Explanation:

The question asks us to calculate the new price Fred will pay for his dog's haircut after the groomer increases the price by 35%. To find the new price, we'll use the formula for calculating percentage increase, which is: New Price = Original Price + (Original Price * Percentage Increase).

First, convert the percentage increase to a decimal by dividing it by 100, so 35% becomes 0.35. Then, multiply the original price of $25 by 0.35 to find the amount of the increase, which is $8.75.Finally, add the increase to the original price to find the new price, which is $25 + $8.75 = $33.75. So, Fred will pay $33.75 the next time his dog has a haircut.

Let [tex]a_1,\ldots,a_4[/tex] denote the ages of the 4 candidates. Then

[tex]\dfrac{a_1+a_2+a_3+a_4}4=40[/tex]

[tex]a_1+a_2+a_3+a_4=160[/tex]

[tex]\dfrac{a_1+a_2+a_3}3+\dfrac{a_4}3=\dfrac{160}3[/tex]

The average age of the first 3 candidates is 42, so

[tex]\dfrac{a_4}3=\dfrac{160}3-42[/tex]

[tex]\implies\boxed{a_4=160-3\cdot42=34}[/tex]

Answer:

b = 17

Step-by-step explanation:

Since PQ = RQ then ΔPQR is isosceles and QS is a perpendicular bisector

Hence PS = RS = 17 ⇒ b = 17

Answer:

6√2.

Step-by-step explanation:

The two radii are equal length and form a right angle, so the resulting triangle is 45-45-90.  Therefore, the length of the chord (the hypotenuse of the triangle) is 6√2.

Answer:

a) Function

b) Not a function

c) Function

d) Not a function

Step-by-step explanation:

a) Domain = { 7,-6,2}

   Range = {5,0,3}

It is a function as every value in domain has some and unique value mapped to it in Range

b)

Domain = { 7,-6,2}

   Range = {5,0,-2,3}

It is not a function as -6 value in domain has two values mapped to it in Range

c)

Domain = { 7,2}

   Range = {-6,-7}

It is a function as every value in domain has some and unique value mapped to it in Range

d)

Domain = { 7,-6}

   Range = {5,0,3}

It is not a function as 7 value in domain has two values 3 and 5 mapped to it in Range

Answer:

20√2 meters (approximately 28.28 m)

Step-by-step explanation:

It may help to make a diagram. Because this is a 45 45 90 triangle, you can use those rules to help solve.

Final answer:

The distance from the top of a totem pole to the end of its shadow, when the angle of elevation of the sun is 45 degrees, is approximately 28.28 meters.

Explanation:

The student has presented a problem that involves using trigonometry to calculate the distance from the top of a totem pole to the end of its shadow when the angle of elevation of the sun is 45 degrees. To solve this, we can use the concept of right-angled triangles and the properties of special triangles, specifically a 45-45-90 triangle where the two legs are congruent. Since the angle of elevation is 45 degrees and the length of the shadow is given as 20 meters, we know that in this special right triangle, the lengths of the two legs are equal. Therefore, the distance from the top of the totem pole to the end of the shadow (the hypotenuse of the triangle) is the length of the shadow times the square root of 2, based on the Pythagorean theorem.

Using the formula hypotenuse = leg × √2, we substitute the leg length of 20 meters to get hypotenuse = 20 m × √2, which equals approximately 28.28 meters.

Answer:

x = -9

Step-by-step explanation:

Multiply both sides by √(x - 6) to eliminate the fraction:

√(3x) = 3√(x - 6)

Now square both sides:  

3x = 9(x - 6), or 3x = 9x - 54.  

Combining the x terms results in -6x = -54, and thus x = 9.

Answer:

The correct answer is option D.  x = 9

Step-by-step explanation:

From the attached question we get an expression,

√3x/√(x - 6) = 3

To find the solution of given expression

√3x/√(x - 6) = 3

Squaring both side we get,

3x/(x - 6) = 9

3x = 9 * (x - 6)

3x = 9x - 54

9x - 3x = 54

6x = 54

x = 54/6 = 9

Therefore the correct option is D.  x = 9

Answer:

[tex]t=7.4years[/tex]

Step-by-step explanation:

Let's clear t from the equation [tex]N=16.10^{0.15t}[/tex]. In order to clear t, we have to apply [tex]log_{10} (x)[/tex] in both side of the equations.

[tex]log_{10}N=log_{10}(16.10)^{0.15t}[/tex]

By using properties of the logarithm

[tex]log_{10} (a.b)}= log_{10}a+log_{10}b[/tex]

We obtain:

[tex]log_{10}N=log_{10}(16)+log_{10} (10^{0.15t})[/tex]

Ordering using the logarithm property  [tex]log_{10}a^{n} =nlog_{10}a[/tex] and [tex]log_{10} 10=1[/tex]

[tex]log_{10}N=log_{10}(16)+0.15tlog_{10}10[/tex]  

[tex]log_{10}N=log_{10}(16)+0.15t[/tex]

Clearing t

[tex]t=\frac{log_{10}N-log_{10}(16)}{0.15}[/tex] using the logarith property [tex]log_{10}a-log_{10}b=log_{10}\frac{a}{b}[/tex]

we obtain:

[tex]t=\frac{log_{10}\frac{N}{16} }{0.15}[/tex]

The number of Elm trees is N = 204

Solving

[tex]t=\frac{log_{10}\frac{204}{16} }{0.15}\\t=\frac{log_{10}12.75}{0.15}=7.370[/tex]

Round to the nearest tenths place [tex]t=7.4years[/tex]

Answer:

F. Hyperbola

Step-by-step explanation:

In each napped, you'll have a parabola, combined they form an hyperbola.

It's one of the various shapes that can be produced by a plane intercepting a right circular cone, as you can see in the attached picture.

Each plane intersection is different, based on the angle and the position it passes through.

I hope that helps.

Answer:

hyperbola

Step-by-step explanation:

apeex

Let's call dimes x and the quarters x+3 since we have 3 more of them.

x+x+3=45

2x=42

x=21

we have 21 dimes and 23 quarters

21*0.10=2.1

23*0,25=5.98

if we add those together it equals 8.08

Answer:

$8.10

Step-by-step explanation:

Let d and q represent the # of dimes and quarters, respectively.  Then write equations reflecting this story:

q = d + 3, and d + q = 45.  Substitute d + 3 for q in the second equation, obtaining:

d + d + 3 = 45, or 2d = 42, or d = 21.  Then there are 21 dimes and 24 quarters.  That comes to $2.10 + $6.00, or $8.10.

Answer:

The Answer is likely 60.

Step-by-step explanation:

Two standard deviations from 70 is 60, because the actual deviation is 5, so 2 of those equals 10. 10 - 70 = 60.

Answer:

60

Step-by-step explanation:

Two standard deviations below the mean is:

70 - 2(5) = 60

Answer:

the third one.

Answer: C) V = 562.5π [tex]in^{3}[/tex] ; S = 225π [tex]in^{2}[/tex]

Step-by-step explanation: Please see the image below!

Answer:

yellow b/c there are the most

Step-by-step explanation:

Answer:

7ab+5

Step-by-step explanation:

add like terms (3ab+4ab=7ab)

5 doesn't have a like term so it stays by itself

Hey there! :)

3ab + 4ab + 5

In order to simplify this, we must add like terms. In addition, when simplifying, you can ONLY add like terms.

Since both "3ab" & "4ab" contain "ab," you are able to combine them together!

When combining like terms, you only add the numerical value, not the letters.

This leaves us with : 7ab + 5

Therefore, your answer is 7ab + 5

~Hope I helped!~

Answer:

D. 2(√{x} + √{x - 2})

Step-by-step explanation:

As hinted in the question, we have to simplify the denominator.

To understand it easier, let's imagine we have x - y in the denominator.  If we multiply it with x + y we'll get x² - y², right?  Check the next line:

(x - y) (x + y) = x² + xy -xy - y² = x² - y²

If we have the square of those nasty square roots, it will be much simpler to deal with.  So, let's multiply the initial fraction using x+y, but with the real values:

[tex]\frac{4}{\sqrt{x} - \sqrt{x - 2} } * \frac{\sqrt{x} + \sqrt{x - 2}}{\sqrt{x} - \sqrt{x - 2}} = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} }[/tex]

Then we simplify:

[tex]\frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(x) - (x - 2) } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{ 2 } = 2(\sqrt{x} + \sqrt{x - 2})[/tex]

Answer is D. 2(√{x} + √{x - 2})

m<6 = 180° - m<3

m<6 = 180° - 130°

m<6 = 50°

Answer: m6 equals 50 degrees

Step-by-step explanation: Since AB and CD are parallel u just solve for m2 which is the same as m6 which would be 180-130=50

 The answer is C. I have the work for it in the image bellow

Hope this helped!

~Just a girl in love with Shawn Mendes

see picture attached.

i hope this helped !!

ANSWER

Point-slope form:

[tex]y + 5 = -3(x - 1)[/tex]

Slope-intercept form;

[tex]y = - 3x - 2[/tex]

EXPLANATION

The point-slope form of a line is given by:

[tex]y-y_1=m(x-x_1)[/tex]

We need to find the slope using the formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

Let us substitute the point (1, –5) and (–3, 7).

This implies that,

[tex]m = \frac{7 - - 5}{ - 3 - 1} [/tex]

[tex]m = \frac{12}{ - 4} = - 3[/tex]

The point slope form now becomes,

[tex]y - - 5 = - 3(x - 1)[/tex]

[tex]y + 5 = -3(x - 1)[/tex]

To find the slope intercept form, we expand to obtain;

[tex]y = - 3x + 3 - 5[/tex]

[tex]y = - 3x - 2[/tex]

Answer:

4.6

Step-by-step explanation:

We are given the results of a survey of patients at a hospital of their blood type, categorized by their gender.

We are to find the percentage of patients with blood type AB among all patients.

Number of patients with blood type AB = 33

Total number of patients = 714

Percent of patients with blood type AB = [tex] \frac { 3 3 } { 7 1 4 } \times 100 [/tex] = 4.6

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-9)^2+y^2=4\implies (x-\stackrel{h}{9})^2+(y-\stackrel{k}{0})^2=2^2~\hfill \stackrel{center}{(9,0)} \\\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{2})^2=4\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{2})^2=2^2~\hfill \stackrel{center}{(3,2)}[/tex]

Check the picture below.

well, its radius didn't change, anyhow, you know what to check out.

Answer:

The circle moves left and up

Step-by-step explanation:

The circle's center changes from (9, 0) to (3,2) and the radius stayed the same.

Step-by-step answer:

Given:

Geometric sequence with

second term, T2 = 6

third term, T3 = 12

Wants to have the explicit and recursive rules.

Solution:

common ratio, r = 12/6 = 2

Therefore the first term, T1

= second term /r

= 6/2

=3

Thus the absolute rule is

Tn = T1 *r^(n-1)      where T1 = 3, r=2.  Check: T3 = T1*2^(3-1) = 3*2^2=12 ...good

The recursive rule (depending on the previous term)

Tn = Tn-1*r = 2*Tn-1

The explicit rule for the sequence is a_n = 3 * 2^(n-1), and the recursive rule is a_n = a_(n-1) * 2. These were determined by identifying the common ratio of the sequence as 2.

In a geometric sequence, each term is generated by multiplying the previous term by a common ratio. Given the second term (6) and third term (12) in the sequence, we can identify the common ratio by dividing the third term by the second term. So, 12 divided by 6 equals 2. Therefore, the common ratio is 2.

So, the explicit rule (the nth term) of this sequence would be: a_n = a_1 * r^(n-1) = 6 / 2 * 2^(n-1) = 3 * 2^(n-1).

The recursive rule for the sequence would be: a_n = a_(n-1) * r = a_(n-1) * 2.

To summarize, we determined the common ratio to be 2 by dividing the third term by the second term. We then used this ratio to create the explicit and recursive rules for the geometric sequence.

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Answer:

If you could insert a picture of the graphs that would help! thank you!

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

80 divided by three = 26.666666

26 times 3 = 78

2 leftover

The number sticker each student get is 26 and the number stickers teacher got is 2.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, three friends buy one pack of 80 stickers.

Now, number of stickers each friend = 80/3

3|80|26

  78
_____
   2

Therefore, the number sticker each student get is 26 and the number stickers teacher got is 2.

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Answer:

  (x, y) = (7/12, 11 1/6)

Step-by-step explanation:

A graph will show you the solution is near (x, y) ≈ (0.6, 11.2). For an exact answer, an algebraic solution is indicated.

Subtracting the second equation from the first gives ...

  0 = 12x -7

  7/12 = x

Substituting for x in the second equation gives ...

  y = 2(7/12) +10 = 7/6 +10

  y = 11 1/6

Answer: 45°

Step-by-step explanation:

There are 180 degrees in a triangle so

180-80=100-55=45°

Answer:

54 ft^2

Step-by-step explanation:

Bathroom area is 15 ft^2

The kitchen is twice the bathroom

2*15 = 30 ft^2

Kitchen: 30 ft^2

Front door: 9ft^2

The total is all the areas added together

Total = bathroom + kitchen + front door

         = 15 ft^2     + 30 ft^2  + 9 ft^2

         = 54  ft^2

Answer:

d. 3x³ and 2x³

Step-by-step explanation:

In standard form, the terms of a polynomial expression are written in order of descending powers of the variable. There will be only one term for any given power of the variable.

Here, there are two terms that have x to the third power. These terms must be combined to write the expression in standard form. They are the only terms that can be combined: 3x³ + 2x³ = 5x³.