A rectangular dog pen is constructed using a barn wall as one side and 120m of fencing for the other three sides. a) give a sketch of the situation. b) express the area in terms of x. c) sketch the graph. d) find the value of x that gives the greatest area. e) find the dimensions of the pen. f) state the domain.

The error that the customer made was that he subtracted 3 from 10 instead of dividing 3 by 10.

It is given in the question that at the clothing store T-shirts are on sale, 3 for $10. A customer at the store says that one T-shirt should cost $7 at this rate.

We have to find the error made by the customer while calculating the rate of a T- shirt.

To find the rate of a shirt we will divide the number of shirts by the total amount.

Hence, the rate of a shirt will be $  10/3

But the customer subtracted 3 from 10 to get $ 7 as the rate of a T-shirt.

Hence, the customer subtracted 3 from 10 instead of dividing 3 by 10.

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Answer:

8%3-29xy

Step-by-step explanation:

thats the answer

The inequality that can be used to find the domain of f(x) is x - 3 ≥ 0.

The correct answer is the second one i.e.x minus three over or equal to zero.

Given:

Function f(x) = √x-3

The fact that a negative number cannot be used as the term in the root square, so

x - 3 ≥ 0  which implies that, x ≥ 3.

From the inequality, we can tell that the domain of the function is the interval [3,∞).

Hence the inequality is x - 3 ≥ 0.

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Using the exterior angle theorem, the value of x in the triangle is: x = 8.

The exterior angle theorem states that the measure of the angle formed outside a triangle when a side is extended through one of the points of the triangle is equal to the sum of the remote interior angles of the triangle.

Triangle LMN is shown in the diagram attached below, where:

The measure of angle MNO = (5x + 2)°

The measure of angle NLM = (x + 10)°

The measure of angle LMN = (x + 16)°

Therefore:

Measure of angle MNO = measure of angle NLM + measure of angle LMN [based on the exterior angle theorem]

Substitute

(5x + 2)° = (x + 10)° +  (x + 16)°

Solve for x

5x + 2 = x + 10 +  x + 16

Combine like terms

5x + 2 = 2x + 26

5x + 2 - 2x = 2x - 2x + 26 [subtraction property of equality]

3x + 2 = 26

3x + 2 - 2 = 26 - 2  [subtraction property of equality]

3x = 24

3x/3 = 24/3 [division property of equality]

x = 8

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A rough sketch of the rectangular plot is

The perimeter of the rectangle is given by the formula:

Where,

and,

i

The perimeter is 320, so we can write:

Total fencing cost $3120 and this is 1 length side and 2 width side.

The fencing on length side is $24 per foot and width side is $4 per foot.

e can write an equation:

Now, we have to solve the 2 simultaneous equations,

Let's solve with elimination >>>>

We can substitute this value of "l" into the first equation and solve for "w". This is shown below:

Thus,

     The number that produces zero when multiplied by an is known as the additive inverse of a number, or a, in mathematics. The opposite (number),[1] sign change,[2] and negation are other names for this number. [3] The additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive, when applied to a real number. The additive inverse of zero is zero.

   Subtraction, which can be seen as adding the opposite, is closely related to additive inverse:

   a − b  =  a + (−b).

On the other hand, additive inverse can be compared as subtracting from zero:

−a = 0 − a.

As a result, the unary minus sign can be used to represent subtraction without using the "0" symbol, even though there shouldn't be a space after the unary "-" in proper typography.

 Negation has the following algebraic characteristics in addition to the identities mentioned above:

It is an Involution operation when (a) = a.

−(a + b) = (−a) + (−b)

−(a − b) = b − a

a − (−b) = a + b \s(−a) × b = a × (−b) = −(a × b)

(−a) × (−b) = a × b

Particularly, (a)2 = a2.

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The two distinct lines, line l and line m, have the following relationship with line n

A. The measure of the angle where line | meets line n is 90 degrees

B. The measure of the angle where line meets line n is 90 degrees

This is a term used to refer to lines that intersect at angle 90 degrees. perpendicular lines are also found in right angle triangle. Hence it is right to say that two sides of a right angled triangle are perpendicular to each other.

The features of perpendicularity also helps in defining a squire and rectangles. This is true because the sides meet at angle 90 degrees

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Reason:

87.5% of the students take the bus to school

100% - 87.5% = 12.5% of the students do not take the bus to school

The info about the "18 boys and 46 girls" is put there as a distraction since it's never used.

Since the two triangles in the given are similar triangles, we now know that they both have the same angle, but scaled, meaning they have different side lengths.

Base on the given, XA = 15, while XZ = 27

We can now assume that if XA : XZ, BA : YZ

We can rewite this as:

Now, plugging in the values of XA, XZ, and BA, we can now solve for YZ.

We now see that the length of YZ is 36 inches.

Next, to solve for XY, we will use the same method, but this time we will be using XB instead of BA.

Therefore, XY is 18 inches long.

The mean of the sampling distribution of sample means when 35 random components are tested will be 4.05 years.

From the information, it should be noted that the journalist believes that, in reality, these components have a shorter lifespan than what the company is reporting.

He then tests a random group of 35 of these components and finds a mean lifespan of 4.05 years.

Therefore from the information, we acne see that the mean lifespan has already been given.

Therefore, the mean lifespan is 4.05 years.

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The amount of money earned by each person will be;

Savannah = $190

Greg = $180

Kevin = $165

From the information, the following can be deduced:

Savannah works $9.50 per hour.

Greg works $9 per hour.

Kevin works $8.25 per hour

Therefore, they all work for 20 hours. The amount for each person will be:

Savannah works $9.50 per hour. = $9.50 × 20 = $190

Greg works $9 per hour. = $9 × 20 = $180

Kevin works $8.25 per hour = $8.25 × 20 = $165

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Savannah works $9.50 per hour.

Greg works $9 per hour.

Kevin works $8.25 per hour

If all tree friends worked 20 hours during the week, how much does each person earn?

we have the function

h(x)=-3x-1

this is the equation of a line

To graph a line we need at least two points

so

Find out the intercepts

step 1

Find out the x-intercept (value of x when the value of y=0)

For h(x)=0

substitute

0=-3x-1

3x=-1

x=-1/3

the x-intercept is (-1/3,0)

as the value is a fraction, take another point

For x=2

h(x)=-3(2)-1

h(x)=-7

we have the point (2,-7)

step 2

Find out the y-intercept (value of h(x) when the value of x=0)

For x=0

h(x)=-3(0)-1

h(x)=-1

the y-intercept is (0,-1)

step 3

we have the points

(2,-7)

(0,-1)

To graph, the line, plot the given points and join them

using a graphing tool

The amplitude is determined as the distance from the midline of the cosine function.

From the graph provided, the depth is shown as 3 units (between 5 units and 2 units) which puts the midline at 3.5 units. The amplitude therefore is 1.5

ANSWER:

80°

STEP-BY-STEP EXPLANATION:

Since the sides XZ and YZ are equal, the angle We know that the sum of all the angles is equal to 180 °, therefore:

Answer:

(3,2)

Step-by-step explanation:

The equation of the line graphed is

y = 2/3x + 2

Parallel lines have the same slope.

y = mx + b

y = 2/3x + 0  P tells me that the y-intercept is 0

y = 2/3 x  Which point would make this true?

Point (3,2)  We plug in 3 for x and 2 for y

2 = 2/3(3)

2 = 2 This is a true statement, so the point (3,2) is on the line.

Answer:33/4

Step-by-step explanation: its hard to explain but thats the correct answer 33/4 decimal form is 8.25 and mixed number is 8 1/4

If $44,900 is invested at an interest rate of 7% per year,investment at the end of 5 years is

1)Annual =61712.27

2)Semiannual=62066.34

3)monthly= 62375.51

4)daily = 62287.59

Over a specific time period, compound interest builds up on both the principal and interest. A principal is also included when accounting for interest that has accrued on it over time. The cumulative principal value is used to calculate interest for the upcoming period as well.

Given that : If $44,900 is invested at an interest rate of 7% per year .

p =44,000

R = 7%

t =5

(2)Semiannual means  compounding is in a year done means two times hence, n = 2

We know

A(t) =p[tex][1 +\frac{r}{n} ]^{nt}[/tex]

A(5) = 44000[tex][1+\frac{0.07}{2} ]^{2(5)}[/tex]

A(5)=62066.34

(1) Annual means. compounding is done 1 time for  a year

So, n = 1

A (5) = 44000[tex][1 + 0.07]^{(5)}\\[/tex]

A(5)= 61712.27

(3)Monthly means compounding is done 12 times in a year.

So, n = 12

= 44000[tex][1 + \frac{0.07}{12} ]^{60}\\[/tex]

= 62375.51

(4)For daily put n = 365

A(5) = 44000[tex][1 + \frac{0.07}{5} ]^{5(5)}\\[/tex]

= 44000[tex][1 + \frac{0.07}{5} ]^{25}\\[/tex]

=62287.59

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The solutions to the questions are

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The area expression is given as

Area = ▢ × 102 + ▢ × 101 + 6

From the question, we can use any number

However, this number must be positive

Assume the number is 5

So, we have

Area = 5 × 102 + 5 × 101 + 6

In (a), we have:

Area = 5 × 102 + 5 × 101 + 6

Evaluate

Area = 1021

The perfect square number closest to this is

Closest = 1024

In (b), we have

Closest = 1024

Rewrite as

Area = 1024

Take the square roots

Length = 32

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The monthly deposit that Florence must make in order to reach her goal is  $366.74.

The series of payments that must be made is known as an annuity. An annuity is a series of payment made over a period of time. The amount that is invested monthly would grow at an exponential rate. This is because both the amount invested and the interest that has been accrued grows at each compounding period.

The formula to determine the monthly deposit is:

Monthly deposit = future value / annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

(65 - 22) x 12

43 x 12 = 516

1,200,000 ÷ [((1.00583)^516]}- 1 / 0.00583] = $366.74

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this is transformations or enlagement of triangle by a certain scale factor.

which simply means it can either be double, or shortened .

solution

a. angle T is the preimange of angle T'

b. line RS and RS'

c. line RT and RT'

line ST and ST'

extra note: this is ∆RST filled over but shortened by x factors to mirror image ∆RST

The transformations are

Transformation 1

Here, we have

The coordinates are given as

P(-5, 4), Q(2, 8), R(6, 1) and S(-1, -3)

The transformation is given as

<2, -4>

This is represented as

(x, y) ⇒ (x + 2, y - 4)

This means that the translation is (x + 2, y - 4)

When this rule is applied on the coordinates, we have

P'(-3, 0), Q'(4, 4), R'(8, -4) and S'(1, -7)

Next, we plot the image of the transformation on a coordinate plane

See attachment for the image of the transformation

Transformation 2

Here, we have

The coordinates are given as

E(-7, -7), F(-2, -3), G(-1, -6)

The transformation is given as

<8, 3>

This is represented as

(x, y) ⇒ (x + 8, y + 3)

This means that the translation is (x + 8, y + 3)

When this rule is applied on the coordinates, we have

E'(1, -4), F'(6, 0) and G'(7, -4)

Next, we plot the image of the transformation on a coordinate plane

See attachment for the image of the transformation

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The order from smaller to greatest is -11.5, -11, -10, 12, 12.5.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold math Z.

The value of a continuous quantity that can represent a distance along a line is a real number. René Descartes first used the word "real" in this meaning in the 17th century when he made a distinction between the real and imaginary roots of polynomials.

Given numbers are -11.5, -11, -10, 12.5, 12

The order from smaller to greatest is -11.5, -11, -10, 12, 12.5.

Real numbers: -11.5, -11, -10, 12, 12.5.

Rational numbers: -115/10, 125/10

Integer numbers: -11.5, -11, -10, 12, 12.5.

Whole numbers: 12, 12.5, 26

Therefore, the order from smaller to greatest is -11.5, -11, -10, 12, 12.5.

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FOR ARITHMETIC

[tex]lhs = 9 - 4 \\ lhs = 5 \\ rhs = 4 - 1 \\ rhs= 3 \\ \\ lhs \: not = rhs[/tex]

SINCE THERE IS NO COMMON DIFFERENCE LET US TEST FOR A GEOMETRIC SEQUENCE.

[tex]lhs = \frac{9}{4} \\ \\ rhs = \frac{4}{1} \\ rhs = 4 \\ \\ lhs \: not = rhs[/tex]

THERE IS NO COMMON DIFFERENCE NOR A COMMON RATION THIS MEANS THAT THE SEQUENCE IS NEITHER AN ARITHMETIC NOR A GEOMETRIC SEQUENCE.

THE OPTION IS A.NEITHER.

Answer: 14

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The amount in pounds of water that's been carried by Devin as described by the ratio given in the task content is; 10.5 pounds.

It follows from the task content that the amount of water Devin is carrying is to be determined.

On this note, since the backpack contains food, water, bedding, and emergency supplies are in the ratio; 2 : 3 : 1 : 4.

It therefore follows from proportion that the ratio representation of total of all supplies is; (2 + 3 + 1 + 4) = 10.

Therefore, since the total weight is; 35 pounds, it follows that the amount of water Devin is carrying can be of help as follows;

w/35 = 3/10.

w = (3 × 35)/10

w = 105/10

w = 10.5 pounds.

Ultimately, the total weight of water Devin is carrying is therefore; 10.5 pounds.

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We are asked to determine the value of the variation of the angle with respect to "x". To do that we will determine an equation that relates "x" and the angle using the following right triangle:

We can use the function tangent since this is defined as:

Now, we plug in the values:

Now, we will determine the angle when "x = 2000". We substitute 2000 in the equation:

Now, we take the inverse function of the tangent:

Solving the operations we get:

Therefore, the angle is 56.31 degrees or 0.983 radians.

We are asked to determine the value of the derivative of "x" with respect to "t". Since this is equivalent to the velocity of the plane we have that:

Now, we are asked to determine the derivative of the angle with respect to time. To do that we will determine the derivative with respect to time on both sides of the equation:

For the derivative on the left side, we know that the derivative of the tangent is the secant squared, therefore, we have:

Now, we determine the derivative on the right side using the following formula:

Applying the rule we get:

Now, we solve for the derivative of the angle with respect to time:

Now, we substitute the values:

Solving the operations:

Therefore, the variation of the angle with respect to time is 0.047 rad/s.

This means that the dish is rotating at a speed of 0.047 rad/s.

Answer: We are asked to determine the value of the variation of the angle with respect to "x". To do that we will determine an equation that relates "x" and the angle using the following right triangle:We can use the function tangent since this is defined as:Now, we plug in the values:Now, we will determine the angle when "x = 2000". We substitute 2000 in the equation:Now, we take the inverse function of the tangent:Solving the operations we get:Therefore, the angle is 56.31 degrees or 0.983 radians. We are asked to determine the value of the derivative of "x" with respect to "t". Since this is equivalent to the velocity of the plane we have that:Now, we are asked to determine the derivative of the angle with respect to time. To do that we will determine the derivative with respect to time on both sides of the equation:For the derivative on the left side, we know that the derivative of the tangent is the secant squared, therefore, we have:Now, we determine the derivative on the right side using the following formula:Applying the rule we get:Now, we solve for the derivative of the angle with respect to time:Now, we substitute the values:Solving the operations:Therefore, the variation of the angle with respect to time is 0.047 rad/s.This means that the dish is rotating at a speed of 0.047 rad/s.

Step-by-step explanation:

We want to know which values of m satisfy ≤

5m + 1 4

Substracting 1 both sides:

-1 - 1

+03

5m ≤ 3

Dividing by 5 both sides

/5/5

m ≤ 3/5

m ≤ 0.6

Since 1 and 2 are higher than 0.6 and 0 ≤ 0.6

Then if m=0 it is satisfied

1) When q = 13, the expression q - 10 is; 3

2)  When x = 4.2, the expression 34.5x is; 144.9

3) The simple interest you would earn in 2.5 years is;  $5.25

1) We want to evaluate the following expression;

q - 10 when q = 13.

Thu, we will plug in 13 for q to get;

13 - 10 = 3

2) We want to evaluate the following expression;

34.5x when x = 4.2

Plug in 4.2 for x to get;

34.5 * 4.2 = 144.9

3) The formula for simple interest is;

I = PRT/100

Where;

P is principal

R is rate

T is time

We are given;

P = $70

R = 3% = 0.03

Time; T = 2.5 years

Thus;

I = 70 * 0.03 * 2.5

I = $5.25

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