Which expression has the smallest value?

a
|-34|
b
|-19|
c
|11|
d
|47|

Answer:

Step-by-step explanation:

You want the length of the minimum perimeter fence to enclose 3 sides of a rectangular area of 128 m² with one side of the enclosure provided by a river. You also want the enclosure dimensions.

If x represents the dimension of the enclosure parallel to the river, then the other dimension of the enclosure is found from ...

  A = LW

  128 = x·W

  W = 128/x

There will be two sides of this length, so the perimeter is ...

  P = L +2W = x +2(128/x)

  P = x + 256/x

This has an extreme value (minimum) where its derivative is zero:

  dP/dx = 0 = 1 -256/x²

Solving for x gives ...

  x² = 256

  x = √256 = 16

and the perimeter is ...

  P = 16 +256/16 = 32

The other dimension is 128/16 = 8.

The minimum perimeter is 32 meters; the enclosure is 16 by 8 meters.

__

Additional comment

This can be solved without using derivatives by working the reverse problem: the largest area for a given perimeter.

Using the same definition of x, the area in terms of perimeter is ...

  A = x · (P -x)/2

This is a quadratic equation with a maximum halfway between its zeros at x=0 and x=P. So, the value of x for maximum area is x = P/2. That area is ...

  A = (P/2)(P -P/2)/2 = (P/2)(P/4) = P²/8

Or, the minimum perimeter for a given area is ...

  P = √(8A)

In this problem, that is ...

  P = √(8·128) = √1024 = 32

The dimensions of the enclosure are (P/2)×(P/4) = 16×8.

Answer:

Step-by-step explanation:

5x - 9 ≤ 21

5x ≤ 30

x ≤ 6

The inequality x less-than-or-equal-to 6 represents the solution set of the inequality, the correct option is D.

An Inequality is the mathematical statement formed when two expressions are equated using an inequality operator.

The solution of the inequality  5x -9 ≤ 21 has to be determined

5x - 9 ≤ 21

Adding +9 on both the sides of the inequality

5x -9 +9 ≤ 21+9

5x ≤ 30

Dividing 5 on both the sides

x ≤ 6

Therefore, x less-than-or-equal-to 6 represents the solution set of the inequality, the correct option is D.

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For statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.

If the slope of the triangles is equal then triangle A is similar to triangle B.

In the statement  when we simplify

(5/3)=(15/9),

(5/3)=(5/3),

Then the reason for this statement is "If the slope of triangles are equal"

And the definition of slope in general is m = y/x.

Therefore, for statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

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Answer:

v = u​ - 9

Step-by-step explanation:

v + 9 = u​

v = u​ - 9

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Answer: True!

Explanation:

It is outside the triangle

I hope this helped!

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The order of operations (PEMDAS) states that we should perform multiplication and division before addition and subtraction. Using this order, we get:

244 - (33456 / 3456) * 345 + 13.55 - 2

= 244 - 97.02 * 345 + 13.55 - 2

= 244 - 33494.1 + 13.55 - 2

= -33238.55

Therefore, 244-33456/3456*345+13.55-2 = -33238.55.

Answer:

Step-by-step explanation:

(1+m)1+16=17²(1+1=2)=17²

Step-by-step explanation:

(1+m) 1+16=17

(1+16=17

Answer:

The exponential function is

\(y = {2}^{x} \)

Answer:

The test statistic for the hypothesis test is -1.202.

Step-by-step explanation:

We are given that a report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were burglarized and 23 out of 197 without pet dogs were burglarized.

Let \(p_1\) = population proportion of households with pet dogs who were burglarized.

\(p_2\) = population proportion of households without pet dogs who were burglarized.

SO, Null Hypothesis, \(H_0\) : \(p_1=p_2\)     {means that both population proportions are equal}

Alternate Hypothesis, \(H_A\) : \(p_1\neq p_2\)     {means that both population proportions are not equal}

The test statistics that would be used here Two-sample z-test for proportions;

                           T.S. =  \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }\)  ~ N(0,1)

where, \(\hat p_1\) = sample proportion of households with pet dogs who were burglarized = \(\frac{10}{129}\) = 0.08

\(\hat p_2\) = sample proportion of households without pet dogs who were burglarized = \(\frac{23}{197}\) = 0.12

\(n_1\) = sample of households with pet dogs = 129

\(n_2\) = sample of households without pet dogs = 197

So, the test statistics  =  \(\frac{(0.08-0.12)-(0)}{\sqrt{\frac{0.08(1-0.08)}{129}+\frac{0.12(1-0.12)}{197} } }\) 

                                     =  -1.202

The value of z test statistics is -1.202.

Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

90

Step-by-step explanation:

m² × m² is equal to m⁴.

w³ × w² is equal to w⁵.

5k³ × 4k⁴ × k is equal to 20k⁸.

The length of each side of the square is 9x.

A simplification of the expression 28x³ ÷ 4x is 7x².

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangle = (27x) × (3x)

Area of rectangle = 81x²

Note: Area of square = Area of rectangle

Area of square = (side length)²

81x² = (side length)²

Side length = √(81x²)

Side length = 9x

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Answer:

3

Step-by-step explanation:

9/4÷3/4

9/4 ×4/3

which would equal 3

The amount of Duane's first payment that goes to interest is approximately $26.47.

To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.

The formula to calculate the interest portion of a loan payment is:

Interest = Remaining Balance * Monthly Interest Rate.

Let's calculate the interest for the first payment using the given information:

Loan Amount = $5,000.00

Monthly Payment = $118.57

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

= 6.5% / 12

= 0.00542

Next, we need to calculate the remaining balance after the first payment:

Remaining Balance = Loan Amount - Principal Paid

= $5,000.00 - $118.57

= $4,881.43

Finally, we can calculate the interest portion of the first payment:

Interest = Remaining Balance * Monthly Interest Rate

= $4,881.43 * 0.00542

= $26.47

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Answer:

x=3+ay/4a

Step-by-step explanation:

4(x-3)/a=y

a*4(x-3)/a=a*y

4a(x-3)=ay

4a(x-3)/4a=ay/4a

x-3=ay/4a

x-3+3=3+ay/4a

x=3+ay/4a

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

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Based on the intersecting secants theorem:

a. CG*CE = CH*CD

b. length of DH = 10 in.

When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.

a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:

CG*CE = CH*CD

b. Given the following lengths:

CG = 3 in, CH = 2 in, and GE = 5 in

CE = CG + GE = 3 + 5 = 8 in.

CD = CH + DH = 2 + DH

Substitute into CG*CE = CH*CD:

3*8 = 2*(2 + DH)

24 = 4 + 2DH

24 - 4 = 2DH

20 = 2DH

20/2 = DH

DH = 10 in.

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The relation between this two functions is g(x) = -f(x)

This means that g(x) is a reflection of f(x) about the x-axis, that is, a reflection about a horizontal line

The image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).

First, we apply the translation T-1,0, which moves every point 1 unit to the right (since the x-coordinate is decreased by 1) and leaves the y-coordinate unchanged. Therefore, the image of (-7,-8) under T-1,0 is (-7-1,-8) = (-8,-8).

Next, we apply the dilation D1/2, which scales every distance from the origin by a factor of 1/2. Therefore, the image of (-8,-8) under D1/2 is (-8/2,-8/2) = (-4,-4).

Thus, the image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).

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Given the point ( -1, -8 )

The x-coordinate of the point = -1

The y-coordinate of the point = -8

So, x < 0, y < 0

So, the point lies in the third quadrant

So, the answer will be Quadrant 3

We will use the solutions to the absolute value functions to determine the function's description as follows:

The two solutions to the absolute value function are given as follows:

We will investigate each description as follows:

A) The distance of x from -3 is 8.

We will use the number line and determine the distance from ( x = -3 ) to the other solution ( x = 5 ). The number of units along the x-axis from point ( x = -3 ) to ( x = 5 ) would be:

Hence, option A is correct!

B) This option describes the absolute value function as follows:

We will solve the above absolute value function as follows:

The above solution to the absolute value function is not equal to the solution presented in the number line. Hence, option B is incorrect!

C) The distance of x from 1 is 4

The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 1 ) as follows:

We see that the distance from each solution ( x = -3 ) AND ( x = 5 ) from point ( x = 1 ) is 4 units along the x axis. Hence, option C is correct!

D) The distance of x from 4 is 1

The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 4 ) as follows:

The above statement is true for the solution ( x = 5 ); however, incorrect for solution ( x = -3 ). Hence, we will reject this option D as it is not true in entirety!

E) This option describes the absolute value function as follows:

We will solve the above absolute value function as follows:

The above solution to the absolute value function is not equal to the solution presented in the number line. Hence, option E is incorrect!

F) This option describes the absolute value function as follows:

We will solve the above absolute value function as follows:

The above solution to the absolute value function is not equal to the solution presented in the number line. Hence, option F is incorrect!

G) The distance of x from -3 is 5

The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 4 ) as follows:

The above statement is not true for the solution ( x = 5 ). Hence, we will reject this option G as it is not true in entirety!

H) This option describes the absolute value function as follows:

We will solve the above absolute value function as follows:

The above solution to the absolute value function is equal to the solution presented in the number line. Hence, option H is correct!

The correct statements are:

The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 4 ) as follows:

The answer for it is diagram B because it does not cross or have parallel lines

Answer:

POINTFARMER.EXE=EZ

Step-by-step explanation:

The equation that shows how many more packs of erasers she needs is 38/6.

The form of the equation that can be used to determine how many more erasers Miss Jones needs is :

Number of more erasers needed = (total erasers needed - erasers in her desk) / number of erasers sold in a pack

Where:

Total erasers needed =  50

erasers in her desk = 12

number of erasers sold in a pack = 6

= (50 - 12) / 6

= 38 / 6

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Answer:

that would be 6

x = 6

Step-by-step explanation:

Answer: x=14 y=10

Step-by-step explanation:

The number of gallons of water are wasted in a year is: 684.375 gallons and the additional money that is being spent on the water bill is: $6.23.

a. Number of gallon of water wasted

365 days=365 days×24

365 days = 8760 hours

Number of gallons wasted=8760 × 60 minutes

Number of gallons wasted = 525,600 minutes

525,600 oz wasted

1 gallon = 128 oz

6 gallon= 128 oz × 6 oz

6 gallon= 768 oz

so,

Amount of water wasted=525,600 oz /768 oz

Amount of water wasted=684.375 gallons

b. Additional money:

Additional money=$9.11/1000×684.375 gallons

Additional money= $6.23

Therefore the number of gallons of water are wasted in a year is: 684.375 gallons and the additional money that is being spent on the water bill is: $6.23.

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Answer:(2I3O-9247)

Step-by-step explanation:

Answer:

27.57 degree

Step-by-step explanation:

shown in the diagram

The measurement of the smallest angle, of Δ ABC, is 27.57°

A triangle is a polygon with three edges and three vertices and three angles.

Given that, a triangle has sides 17, 29 and 16, we need to find the measurement of the smallest angle,

We know that, In any triangle, the largest side and largest angle are opposite one another, the smallest side and smallest angle are opposite one another, the mid-sized side and mid-sized angle are opposite one another. (please refer to the figure attached)

Therefore, the smallest angle, is opposite to side 16,

Using the cosine law of the triangle,

c² = a²+b²-2abcosC

C = cos⁻¹(a²+b²-c²) / 2ab

C = cos⁻¹(29²+17²-16²) / 2(29)(17)

C = cos⁻¹(874/986)

C = cos⁻¹(0.886409736)

C = 27.57°

Hence, the measurement of the smallest angle, of Δ ABC is 27.57°

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