Mr. McGregor has discovered that a large dog can destroy his entire garden in 2 hours and that a small boy can do the same job in 1 hour. How long would it take the large dog and the small boy working together to destroy Mr McGregor's garden?

Answer:

Choice A is the correct answer

Step-by-step explanation:

[tex]2x\sqrt{2x}[/tex]

Find the attachment below for the explanation

For this case we must indicate an expression equivalent to:

[tex]\sqrt {18x ^ 3} - \sqrt {9x ^ 3} +3 \sqrt {x ^ 3} - \sqrt {2x ^ 3}[/tex]

So, rewriting the terms within the roots we have:

[tex]18x ^ 3 = (3x) ^ 2 * (2x)\\9x ^ 3 = (3x) ^ 2 * (x)\\x ^ 3 = x ^ 2 * x\\2x ^ 3 = (2x) * x ^ 2[/tex]

So:

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

Removing the terms of the radical:

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

We simplify adding terms:

[tex]3x \sqrt {2x} -x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} =\\2x \sqrt {2x} + 0 =\\2x \sqrt {2x}[/tex]

Answer:

Option A

Answer:

100.

Step-by-step explanation:

The percentage of children's watches = 100 - 20 - 40 = 100-60

= 40%.

40% = 0.40 as a decimal fraction.

So the number of children's watches

= 0.40 * 250

= 100.

Answer:

D

Step-by-step explanation:

There are 4 colors to choose from, so use numbers 1-4 to represent each color.

Answer:

I think it's the last one, BD/AE

Step-by-step explanation:

Answer:

(x - 5)² + (y + 3)² = 16

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

here (h, k) = (5, - 3) and r = 4, thus

(x - 5)² + (y - (- 3))² = 4², that is

(x - 5)² + (y + 3)² = 16 ← equation of circle

Answer:

True

Step-by-step explanation:

we know that

sin(-360°)=sin(360°)=0

therefore

y=sin(-360°)=0

CCCCCCCCCCCCCCCCCCCCCC

Answer:

The correct answer is option "C"

"The interquartile range increases"

The value of the (RIC) will increase from 4 to 5.75, that is, 44%

Step-by-step explanation:

The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin

The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.

Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%

Answer:

F. (0, 5) and (-4, 2)

Step-by-step explanation:

We need to calculate the slope of each of the given sets of points until we find the set associated with a slope of 3/4:

F. (0,5) and (-4,2)  As we go from (-4, 2) to (0,5), x increases by 4 and y increases by 3, so the slope is m = rise / run = 3/4.  This is the line with slope 3/4.

Answer:

Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend. The result is the difference.

Step-by-step explanation:

The result of subtracting two or more numbers in mathematics is called the difference. In vector subtraction, this applies as we add the first vector to negative of the vector that needs to be subtracted, resulting in a difference vector. This is equivalent to subtracting scalar values.

In mathematics, the result of subtracting two or more numbers is known as the difference. This concept also applies to vectors in a process called Vector Subtraction.

For instance, if we have two vectors A and B, and we wish to subtract B from A (usually written as A - B), we do so by adding the first vector, A, to the negative (-) of the second vector, B (written as A + (-B)). Here, -B (negative B) represents the same vector as B but in the opposite direction. The subtraction of A and B results in a difference vector, D, i.e., D = A - B.

The same principle is true for ordinary numbers. Take the numbers 5 and 2 for example. If we subtract 2 from 5 (5 - 2), it's equivalent to adding 5 and -2 (5 + (-2)). Here, the difference is 3.

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Answer:

  151.4496 cm²

Step-by-step explanation:

The area of a trapezoid is found using the formula ...

  A = (1/2)(b1 +b2)h

where b1 and b2 are the lengths of the parallel bases and h is the distance between them. Fill in the numbers and do the arithmetic.

  A = (1/2)(22.2 cm + 8.52 cm)(9.86 cm) = 151.4496 cm²

The greatest common factor of 8m^3 and 6m^4 is 2m^3. This is found by determining the highest number or term that can divide both terms exactly, considering both the coefficients and the power of the variable.

The question asks for the greatest common factor of the terms 8m3 and 6m4. The greatest common factor (GCF) is the highest number or term that divides both numbers exactly. Ignoring the coefficients (8 and 6), we can easily see that these terms both contain the variable 'm', raised to the powers 3 and 4, respectively.

The rule for dealing with variables when finding the GCF is to take the variable to the power which is the lesser of the two. In this case, that would be m3. Now, looking at the coefficients (8 and 6), the highest number that can divide them both exactly is 2. Therefore, the greatest common factor of 8m3 and 6m4 is 2m3.

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The greatest common factor of 8m³ and 6m⁴ is 2m³, which is found by identifying the shared prime factors and the lowest power of 'm' present in both terms.

To find the greatest common factor (GCF) of 8m³ and 6m³, we need to find the highest power of each prime number and the variable that is contained in both terms. The prime factorization of 8 is 23, and for 6, it is 2 × 3. Since both have at least one factor of 2, we'll use that in our GCF. Additionally, since the lowest power of 'm' that appears in both terms is m3, we will also use that.

The GCF is the product of these shared factors. So, we have:

2 (the common prime factor)

m3 (the lowest power of 'm' in both terms)

Therefore, the GCF of 8m³ and 6m⁴ is 2m³.

Answer:

51

Step-by-step explanation:

Given

P(x) = 2x³ + 4x² - 10x - 9, then

P(a) = 2a³ + 4a² - 10a - 9 ← substitute x = a into P(x)

To evaluate P(3) substitute a = 3 into P(a)

P(3) = 2(3)³ + 4(3)² - 10(3) - 9 = 54 + 36 - 30 - 9 = 51

Since P(3) ≠ 0 then (x + 3) is not a factor of P(x)

Answer:

51

Step-by-step explanation:

2(3)³ + 4(3)² - 10(3) - 9

= 51

Answer:

14 feet below. the deck.

Step-by-step explanation:

That would be (20 + 78 - 85 +103 - 110 )  feet above the ground

= 6 feet above the ground.

That is 20 - 6 = 14 feet below the deck.

Answer:

B

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

To obtain this form use the method of completing the square

Given

x² - 8x + y² - 2y - 8 = 0 ( add 8 to both sides )

x² - 8x + y² - 2y = 8

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

x² + 2(- 4)x + 16 + y² + 2(- 1)y + 1 = 8 + 16 + 1

(x - 4)² + (y - 1)² = 25 → B

Final answer:

The standard form of the given circle equation is (x - 4)^2 + (y - 1)^2 = 25, which is option (B).

Explanation:

To rewrite the given equation of a circle in standard form, we need to complete the square for both x and y terms. The equation is given as:

x² − 8x + y² - 2y - 8 = 0

We organize the equation by grouping x and y terms:

(x² − 8x) + (y ² - 2y ) = 8

To complete the square, we add to each side (½ the coefficient of x) ² for the x-terms and (½ the coefficient of y) ² for the y-terms:

For the x terms: (½ × -8)² = (-4)² = 16. Add 16 to both sides.

For the y terms: (½ × -2)² = (-1)² = 1. Add 1 to both sides.

Our equation becomes:

(x² − 8x + 16) + (y² - 2y + 1) = 8 + 16 + 1

Which simplifies to:

(x - 4)² + (y - 1)² = 25

Therefore, the standard form of the given equation is (x - 4)² + (y - 1)² = 25, and the correct answer from the options is (B).

Answer:

65/4 cm³, or 16.25 cm³

Step-by-step explanation:

Here, Volume V = (length)(width)(height).  Those measurements are included here:

V = (1  1/4 cm)(4 cm)(3  1/4 cm), or

V  = (5/4 cm)(4 cm)(13/4 cm)

V  =    (5 cm²(13/4 cm) = 65/4 cm³, or 16.25 cm³

Answer:

270

Step-by-step explanation:

The mean is 228 and the standard deviation is 18.

2.3 standard deviations above the mean is:

228 + 2.3×18

228 + 41.4

269.4

Since scores are usually integers, we round up to 270.

The answer is C: Three real zeros and 2 imaginary zeros

Answer:  C) 3 real zeros & 2 imaginary zeros

Step-by-step explanation:

Since the function has a degree of 5, then there must be 5 zeros.  

If each of the 3 given zeros crosses the x- axis (which is what happens when it has an odd-numbered multiplicity), then there are 2 zeros missing.

The missing zeros are imaginary.

(3 zeroes × multiplicity of 1) + (2 imaginary)

                  3                         +          2           = 5  [tex]\large\checkmark[/tex]

Answer:

See below.

Step-by-step explanation:

The 2 functions have the same output value when x = 7  ( that is what m(x) = p(x) at x = 7 means).

Answer:

The inequality is [tex]0.6x < 12.5[/tex]

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Step-by-step explanation:

14 gallons-1.5 gallons=12.5 gallons  

we know that

If the remaining fuel is greater than  1.5 gallons Diego's father can drive the car without the warning light coming on  

so

Let

x ----> the number of days

[tex]0.6x < 12.5[/tex] ----> inequality that represent the situation

Solve for x

[tex]x < 12.5/0.6[/tex]

[tex]x < 20.8\ days[/tex]

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

An inequality is similar to an equation in that they both describe the relationship between two expressions.

The inequality represents the number of days Diego's father can drive the car without the warning light coming on is [tex]\rm x<20.8[/tex].

Diego's family car holds 14 gallons of fuel.

Each day the car uses 0.6 gallons of fuel.

A warning light comes on when the remaining fuel is 1.5 gallons or less.

An inequality is similar to an equation in that they both describe the relationship between two expressions.

The inequality represents the number of days Diego's father can drive the car without the warning light coming on is,

The remaining fuel is greater than 1.5 gallons Diego's father can drive the car without the warning light coming on.

Here, x represents the number of days.

Therefore,

The inequality represents the number of days Diego's father can drive the car without the warning light coming on is,

[tex]\rm 0.6x<12.5\\\\x < \dfrac{12.5}{0.6}\\\\x<20.8[/tex]

Hence, The inequality represents the number of days Diego's father can drive the car without the warning light coming on is [tex]\rm x<20.8[/tex].

To know more about Inequality click the link given below.

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Answer:

Option 'B'

Step-by-step explanation:

The law of cosines states that given a triangle with sides a, b, c, then:

[tex]c^{2} =a^{2}+b^{2} -2abcos(y)[/tex] where 'y' is the opposite angle to the side 'c'.

In this case, given that the equation is: [tex]15^{2} =8^{2} + 17^{2} -2(8)(17)cos(y)[/tex] we can clearly see that c=15, and the opposite angle to 'c' is 62 degrees.

The correct option is Option 'B'

ANSWER

B. 62°

EXPLANATION

The cosine rule is given by:

[tex] {b}^{2} + {c}^{2} - 2(bc) \cos(A) = {a}^{2} [/tex]

where A is the angle that is direct opposite to the side length which is 'a' units.

The given relation is:

[tex]8^{2} + {17}^{2} - 2(8)(17) \cos( - ) = {15}^{2}[/tex]

The missing angle should be the angle directly opposite to the side length measuring 15 units.

From the diagram the missing angle is 62°

Answer:

50.8%

Step-by-step explanation:

That is the one my friend and I chose. It is 31/61 when all the stuff is added together and that is put to 50.8 as a percentage..

I used 3,14 for pi since it was only way it made sense based on the answers.

The question probably provided you with this.

If you have any more questions do not hesitate :)

The probability that a point picked at random in the square is in the shaded region will be 86/314. Thus option C is correct.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Given:

A circle with a diameter of 20 m is inscribed in a square .

Thus side of square = 20 m

Now, area of square = 20 x 20

                                   = 400 sq m

The radius of circle = 10 m

Area of circle

[tex]A = \pi r^2\\\\A = 3.14 \times 10^2\\\\A = 314 m^2[/tex]

Now, Area of shaded region = Area of the square - an area of circle

Area of shaded region = 400 - 314

                                      = 86

The probability that a point picked at random in the square is in the shaded region will be 86/314. Thus option C is correct.

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Answer:

4:The denominator can't be equal to 0, therefore -  5

5: 4)The denominator can't equal to 0 -4

Answer:

Question 4:

(x² - 25) / (x - 5)

= (x² - 5²) / (x - 5)

= [(x - 5) · (x + 5)] / (x - 5)

= x + 5

The denominator can't be equal to 0, therefore:

x - 5 ≠ 0 ⇔ x ≠ 5

Question 5:

(3x² - 6x) / (x² - 2x - 8)

= [3x (x - 2)] / (x² + 4x - 2x - 8)

= [3x (x - 2)] / [x (x + 4) - 2 (x + 4)]

= [3x (x - 2)] / [(x - 2) (x + 4)]

= 3x / (x + 4)

The denominator can't equal to 0, therefore:

x + 4 ≠ 0 ⇔ x ≠ -4

Answer:

  x² +y² = 14x

Step-by-step explanation:

Making the usual substitution x = r·cos(θ) and r² = x² +y², we can get there this way:

Substitute cos(θ) = x/r:

  r = 14·x/r

Multiply by r:

  r² = 14x

Substitute for r²:

  x² + y² = 14x

_____

The original equation is shown dotted; the rectangular version is shown as a solid line. The graphs are identical.

x2 + y3 = 14x is the soulution of your answer (sorry for bad grammar)

Answer:

x = 2

Step-by-step explanation:

2 + 4x = 10

4x = 10 - 2

x = 8

x = 8 ÷ 4

x = 2

Answer:

A. -25° 29' 24"

Step-by-step explanation:

It is easier to talk about this by considering the magnitude of the angle, then applying the sign to the result.

The fractional part, 0.49°, can be multiplied by 60' per degree to get the number of minutes:

0.49° × 60'/1° = 29.4'

The fractional part of this, 0.4', can be multiplied by 60" per minute to get the number of seconds:

0.4' × 60"/1' = 24"

Then the angle is ...

-25.49° = -25° 29' 24"

_____

Alternate solution

You can recognize this is 0.01° less than 25° 30', so is ...

0.01° × 60' = 0.6' = 0.6 × 60" = 36"

When 36" is subtracted from 25.5° = 25° 30', the result is 25° 29' 24". Of course, your angle is negative: -25° 29' 24".

_____

Comment on base-60 arithmetic

In base-10 arithmetic, when you borrow 1 from the next higher place in the number, you are borrowing ten of the current place. For example, when you are doing arithmetic with hundreds, and you borrow 1 from the thousands place, you have effectively borrowed 10 hundreds.

In base-60 arithmetic, when you borrow one from the next higher place, you borrow 60 of the current unit. That is, borrowing one minute gives you 60 seconds. Thus, 30 minutes is the same as 29 minutes and 60 seconds. Subtracting 36 seconds from this value gives 29 minutes and 24 seconds.

The term "borrowing" was used when I learned arithmetic. More recently, I've seen it called "rewriting" the number. I also think of it as "making change": changing a higher unit to an equivalent number of smaller units.

Answer:

5 seconds

Step-by-step explanation:

In order to find the time when it landed, we will have to find the x-intercepts.

Equation given to us : -16t² + 48t + 160

Let's take the GCD, which is -16.

-16( t² - 3t - 10 )

Factoring what's inside the brackets, we get the x-intercepts.

What multiples to -10 but adds up to -3? The numbers are -5 and 2

-16 ( t - 5 ) ( t - 2 )

X-intercepts are t - 5 and t - 2

Which is 5 and 2 seconds. But one of this is an extraneous solution and that is 2.

If we substitute the value of 2 in the equation, we will not get 0.

During the x-intercept, the x has a value and y is 0. If we substitute 5 ans x. we will get y as 0.

Hence, the answer is 5 seconds.

The coat will cost $54

He would have played the cello for 7 hours and 30 minutes because 4 hours would be 6 hours of the cello and then he only did one more hour so you split 3 in half and that makes it an hour and a half. So the answer is 7 hours 30 minutes

Given that the ratio of piano practice to cello practice for Chase is 2:3, if he practiced the piano for 5 hours, he would have practiced the cello for 7.5 hours.

To find out how many hours Chase spent practicing the cello, we first need to assess the ratio of piano to cello practice. The problem tells us that for every 2 hours practicing the piano, Chase spends 3 hours practicing the cello. So, the ratio of piano to cello practice is 2:3.

If he practiced the piano for 5 hours, the equivalent time spent practicing the cello can be found by setting up a proportion like: (2 hours piano / 3 hours cello) = (5 hours piano / x hours cello), where x is the number of cello practicing hours. Solving this proportion for x gives us x = (5 * 3) / 2 = 7.5 hours.

An interpretation of this result is that for every hour Chase spends practicing the piano, he spends 1.5 hours practicing the cello. Therefore, Chase spent 7.5 hours practicing the cello last week, given that he practiced the piano for 5 hours.

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Answer:

A) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3.

Step-by-step explanation:

The answer choice speaks for itself.

The legs of a 45-45-90 triangle have the ratios 1 : 1 : √2.

The legs of a 30-60-90 triangle have the ratios 1 : √3 : 2.

Clearly, the given leg lengths match the second set of ratios more closely:

10 : 17.32 : 20 ≈ 1 : √3 : 2.