Cara wants to build an 80 foot long rectangular sheep pen in back of her barn. If she bought 180 feet of fencing and used her barn wall as one side of the pen equaling the width, what would be the area of the sheep pen?.

Answer:

x=64/39

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 2/13 from both sides.

Step 3: Multiply both sides by 2/(-1).

Answer:

1 25/39

Step-by-step explanation:

on my test

x = 9 or -7 is the solution of the quadratic equation

Given: the quadratic equation (x−1)²−20 = 44

(x−1)²−20 = 44

Add 20 to both sides:

(x−1)² = 44+20

(x−1)² = 64

Take the square root of both sides:

(x−1)² = 64

x-1 = ±√64

x = 1±√64

x = 1±8

x = 1+8 or 1-8

x = 9 or -7

Therefore, the solution of the equation is x = 9 or -7

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0.0227 is the probability that a randomly selected bolt will have a diameter greater than 0.604 inches.

What is probability explained with an example?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

                           The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

The probability that randomly selected bolt will have a diameter grater than  

0.60x inches.

P(x > 0.604 ) = P( x - 0.600/0.002 > 0.604 - 0.600/0.002 )

                      = P( Z > 2 )

                       = 0.02275

     P(x > 0.604 ) = 0.0227

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The solution of the system of equations y = x + 2 and x - y = -2 is (c) infinite many solutions

From the question, we have the following parameters that can be used in our computation:

y = x + 2

x - y = -2

Substitute the equation y = x + 2 in the equation x - y = -2

So, we have the following representation

x - (x + 2) = -2

Open the bracket in the above equation

So, we have the following representation

x - x - 2 = -2

Evaluate the like terms in the above equation

So, we have the following representation

-2 = -2

Both sides of the above equation are the same

This means that the equation has a lot of solution

In other words, the equation has infinite many solutions

Hence, the solution is (c) infinite many solutions

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Answer:

48

Step-by-step explanation:

If the area of each square is 16, then each side length has side length of 4 because the area of a square is:

[tex]s^2=A[/tex]

[tex]s^2=16\\s=4[/tex]

Each of the outer edges has 4+4+4 and there are four of them so:

[tex](4+4+4)*4=48[/tex]

Applying the corresponding angles theorem, the measure of angle 3 is: C. 121°.

Using the figure below that shows that line a is parallel to line b, where angle 1 and angle 2 are corresponding angles, based on the corresponding angles theorem, the measure of angle 1 is equal or congruent to angle 2.

Given the following:

Measure of angle 1 = 9x - 4

Measure of angle 2 = 13x - 32

m<1 = m<2 [corresponding angles theorem]

Substitute

9x - 4 = 13x - 32

Solve for the value of x

9x - 13x = 4 - 32

-4x = -28

x = 7

Measure of angle 3 = 180 - (13x - 32)

Plug in the value of x

Measure of angle 3 = 180 - (13(7) - 32)

m<3 = 121°

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The zeroes of the polynomial in discuss whose factors are; ( 3x - 2), ( x² - 1 ), and ( x + 4 ) are; 2 / 3, +1, -1 and -4.

To determine the zeroes of a polynomial, the factors of the polynomial must be equated to zero.

On this note, since the given factors of the polynomial are; (3x-2), (x^2-1), and (x+4).

The zeroes are determined as follows;

3x - 2 = 0; 3x = 2; Therefore; x = 2 /3.

x² - 1 = 0; x² = 1; Therefore, x = ±1.

x + 4 = 0; Therefore; x = -4.

Consequently, it can be concluded that the zeroes of the polynomial as determined from its factors are; 2 / 3, -1, +1, -4.

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The rearranged equation for V is V = E - F

From the question, we have the following parameters that can be used in our computation:

E=F+V

Rewrite the above equation properly

So, we have the following representation

E = F + V

The variable expense is V

So, we have

E = F + V

Subtract F from both sides

V = E - F

hence, the equation is V = E - F

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Answer:

∠BFC ≅ ∠DFE and DFC (BFC IS CONGRUENT TO DFE AND DFC)

Step-by-step explanation:

∠BFC and DFE are vertical angles which are equal ( OR CONGRUENT)

∠BFC and DFC are supplementry meaning the angles add upp to 180°. The square in ∠BFC shows that it is 90°. So then, angle DFC must be 90° because 180°-90° is 90°.

So ∠DFC and ∠DFE ≅ to ∠BFC

The equation of the line that passes through the points (2, 15) and (5, 21) is y = 2x + 11

The coordinates of the first point = (2, 15)

The coordinates of the second point = (5, 21)

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (21-15) / (5-2)

= 6 / 3

= 2

The slope intercept form is

y = mx + b

Substitute the values

15 = 2(2) + b

15 = 4 + b

b = 15 - 4

b = 11

Substitute the values in the equation

y = 2x + 11

Therefore, the equation of the line in slope intercept form is y = 2x + 11

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Perpendicular bisector passes through midpoint of the line joining the given two points so the equation for this perpendicular bisector of the line segment whose endpoint are (7,-1) and (-9,-5) is 4x-y=29.

To divide a segment or an angle into two congruent sections is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.

A straight line called a bisector divides an angle or a line into two equal pieces. The bisector of a segment always travels through the middle of the segment.

For this problem you have to find the mid point of the line joining

the given points and also the slope of the perpendicular line.

Here, A(7,-1) and B(-9,-5) are the given two points.

let

C is the mid point and CD is the perpendicular through C

Midpoint of AB=[x1+x2)/2,(y1+y2)/2]

C=((7-9)/2,(-1-5)/2)

C=(-1,-3)

Slope of AB=(y2−y1)/(x2−x1)

=(-5+1)/(-9-7)

=4/16

=1/4

Slope of CD=4

Equation of line;

(y−y1)=m(x−x1)

(y+1)=4(x−7)

Y+1=4x-28

4x-y=29

this is our required solution.

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The equation that is used to prove 1 + tan²(x) = sec²(x) is Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x)  , the correct option is (d) .

In the question ,

a trigonometric equation is given as 1 + tan²(x) = sec²(x) ,

we have to find the equation that will be used in proving .

the equation is 1 + tan²(x) = sec²(x)

rewriting the equation ,

we get ,

1+Sin²(x)/Cos²(x) = 1/Cos²(x)...because tan(x) = Sinx/Cosx and Secx = 1/cosx

taking the LCM as Cos²(x) , and solving further ,

we get ,

Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x)

that is option (d) .

Therefore , the equation is Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x) .

The given question is incomplete , the complete question is

Which equation can be used to prove 1 + tan²(x) = sec²(x) from the options given in the image below  ?

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The polynomial x³ - 2x² - 13x - 10 divided by x + 2 will have quotient of x² - 4x - 5x and a remainder of zero.

The polynomial x³ - 2x² - 13x - 10 divided by x + 2 as follows;

We divide the first of the polynomial x³ by x to give x²

multiply x - 1 by x² to get x³ + 2x²,

then subtract x³ + 2x² from x³ - 2x² - 13x - 10 to get -4x² - 13x - 10

divide -4x² by x to get -4x

multiply x - 1 by -4x to get -4x² - 8x

then subtract -4x² - 8x from -4x² - 13x - 10 to get -5x - 10

divide -5x by x to get -5

multiply x - 1 by -5 to get -5x - 10,

then subtract -5x - 10 from -5x - 10 to get a remainder of zero.

Therefore, the division of the polynomial x³ - 2x² - 13x - 10 by x + 2 using long division give us the quotient x² - 4x - 5x and a remainder of zero.

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Answer: x= 23/18

Step-by-step explanation:

4(3x-1) =-3(2x-6) + 1

12x - 4 = -6x + 18 + 1

12x -4 = -6x + 19

18x -4 = 19

18x = 23

x = 23/18

The function y=540(1.04)^x represents exponential growth. The rate of increase can be determined by finding the value of 1.04^x.

For example, if x=1, then the value of 1.04^1 is 1.04, which represents a 4% increase. If x=2, then the value of 1.04^2 is 1.0816, which represents an 8.16% increase. If x=3, then the value of 1.04^3 is 1.1265, which represents a 12.65% increase.

In general, as the value of x increases, the value of 1.04^x increases at a faster rate, resulting in an exponential growth curve. The percentage rate of increase is determined by the value of 1.04. In this case, the percentage rate of increase is 4% per unit increase in x.

Answer:

Yes, the runners number of strides will fit evenly into the length of the race.

Step-by-step explanation:

The bridge is 138,435 feet. You would divide this to get 46,145 as a whole number.

Answer:

Step-by-step explanation:

You are dividing 138435 by 3.

The quotient would be 46145 with no remainder. So the answer would be yes.

A 2nd way to do this is to see if 183435 is a multiple of 3.

Hope this helps!

Have a great day!

The profit won by Hahid is 28 rupees

Profit is the term used to describe the financial gain experienced when the revenue from a business activity outweighs the costs, costs, and taxes incurred to maintain the activity in question.

There are three main measures of profit. These are gross profit, operating profit and net profit.

According to given question:-

The total amount with which Hahid bought the bananas are

(5/4)*80=100

The total amount with which Hahid sold the bananas are

(8/5)*80=128

The profit got by Hahid is 128-100=28

Hence the solution is 28

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The required bearing angle of town B from Thomas is 65°.

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 125° clockwise, then he faces towards town B,

The bearing angle will be 300+125 = 425°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 425 - 360 = 65

The bearing angle of town B from Thomas is 65°.

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The least common factor of 3 and 5 was chosen as the first step in order to combine the fractions 2/3 + 4/5, leading to option (A) Finding the least common denominator.

The smallest multiple that any two numbers have in common is called the lowest common multiple.

It implies that we can divide both numbers by that and that this is the lowest number by which both numbers may be divided.

The LCM of 2 and 8 is 8, for instance.

So, using the two fractions provided:

2/3 + 4/5

15 is the least frequent factor between 3:

(10 + 12)/15

Thus, we used LCM in the first phase.

Therefore, the least common factor of 3 and 5 was chosen as the first step in order to combine the fractions 2/3 + 4/5, leading to option (A) Finding the least common denominator.

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Complete question:
When adding 2/3 + 4/5, what step must be completed first?

A)Finding the least common denominator.

B)Reducing the fractions.

C)Adding the numerators, but keeping the denominators.

D)Adding the denominators, but keeping the numerators.

Applying the definition of supplementary angles, the reasons that complete the two-column proof that proves x = 15 are:

a. Substitution property

b. Combine like terms

c. Division property of equality.

Two angles are supplementary angles if their sum is equal to 180 degrees when they are added together.

Given that m∠RST = 5x° and m∠UVW = 7x°, and both angles are supplementary angles, the two-column proof that proves x = 15 is shown below.

Statement                                  Reason                                            

m∠RST = 5x°; m∠UVW = 7x°    Given

∠RST and ∠UVW are

supplementary angles.

m∠RST + m∠UVW = 180          Definition of supplementary angles

5x + 7x = 180                             Substitution property

12x = 180                                   Combine like terms

x = 15                                         Division property of equality

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The probability that the student answers exactly 1 question is 0.166.

What is the binomial coefficient?

In combinatorics, the binomial coefficient is used to denote the number of possible ways to choose a subset of objects of a given numerosity from a larger set.

There are [tex]3^5 = 243[/tex] possible ways that the student can answer the quiz.

To answer exactly 1 question correctly, the student must answer 4 questions incorrectly and 1 question correctly. There are 5 ways to choose which question the student gets correct, and for each of these ways, there are [tex]3^4 = 81[/tex] ways for the student to answer the remaining questions. Therefore, there are a total of 5*81 = 405 ways for the student to answer exactly 1 question correctly.

Thus, the probability that the student answers exactly 1 question correctly is 405/243 = approximately 0.166.

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Step-by-step explanation:

Tha answer in standard form is x + 4y = -1

The required equation of line is  y = -5x + 2.

The equation of a line in slop intercept form is an equation of the form

y = mx + c . Where m is the slope of the line and c is the intercept of the line on the Y-axis.

Given,

Line passes through (0,2)

Therefore, (2) = m(0) + c

  or               2 = c

Also, the line passes through (1,-3)

Therefore, (-3) = m(1) + 2

or                  m = -3 - 2

                    m = -5

Hence, the required line is y = -5x + 2.

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The function y = (x + 2)^(1/2) + 3 belongs to the family of square root functions. A square root function is a type of function in which the independent variable (in this case, x) is under the radical sign.

In mathematics, a function is a relationship between a set of potential inputs and an equally likely set of outputs, with the condition that each input is associated to just one possible outcome. In other terms, a function is a category of mathematical action that accepts one or more parameters for input and generates a return result. Equations or graphs are frequently used to depict functions, which are useful for both modeling and solving mathematical issues.

In computer programming, a function is a block of code that completes a particular task and can be used repeatedly throughout a program. Programmers have the option of creating their own functions or using ones that are already included in the language.

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The rate of change of y with respect to x will be;

⇒ 10

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The table is shown in figure.

Now,

Since, The table is shown in figure.

Let two points from the table as;

(x, y) = (- 8.5 , - 92)  (- 6.5, - 72)

We know that;

⇒ Rate of change = dy/dx = (y₂ - y₁) / (x₂ - x₁)

Substitute all the values we get;

⇒ Rate of change = (- 72 - (-92)) / (- 6.5 - (-8.5))

                            = 20 / 2

                            = 10

Thus, The rate of change of y with respect to x will be;

⇒ 10

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Equation in slope intercept form and in standard form for (-2,6) and parallel to x3y=5 will be x + 3y = 10

Given equation =>  x + 3y = 5

3y = -x + 5 so, we have to write it in the equation form,

y = -(1/3)x + 5/3

slope = -1/3     Parallel lines have the same slope.

Now, you have a point and a slope, so use the Point-Slope form of the equation of a line.

y - y1 = m(x - x1) , by using the equation of line

y - 6 = (-1/3)(x - 2), then we get

y - 4 = (-1/3)x + 2/3

y = (-1/3)x + 3 1/3   Slope-intercept Form

(1/3)x + y = 10/3     Multiply both sides by 3.

x + 3y = 10    Standard form

So, the equation is x + 3y = 10

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Answer:

2

Step-by-step explanation:

log_4 (16) is a tiny math problem. It is asking 4^? = 16

See, a log is an exponent. So what power of 4 makes 16? Well, 4^2 = 16. So that means that the log_4(16) = 2

Answer:

I believe the answer is D. 3/8

Therefore ,A pink gold bracelet weight 60 g has 45.6g of gold .

A fraction of 100 is a percentage, also known as percent. Percentage, which is defined as "per 100," represents a fraction of a total sum. 45 out of 100 is what is meant by 45%, for instance. The share of a whole expressed in terms of 100 is discovered when a percentage is calculated. Calculators online or on paper can be used to determine it.

In addition to "out of 100" and "for every 100," the word "percentage" can also be used. You could, for instance, say "it snowed 20% of the time" or "it snowed 20 days out of every 100 days."

Here,

We know that,

A pink gold bracelet weight 60 g has 76% gold, 18% copper and 6% aluminum.

Therefore,

In order to calculate the weight of gold

First we obtain its percentage in bracelet

It's percentage given in question is 76%

Thus,

mass of gold will be 76% of 60g which is 0.76 * 60=45.6g

Therefore ,In pink gold bracelet has a weight of 60 g has 45.6g of gold .

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Answer: No, the ratio between AD and DE is 3:1.

Step-by-step explanation:

The centroid splits the median in a 2:1 ratio from vertex to side.

Answer:

It is letter D; No, the ratio between AD and DE is 3:1.

Step-by-step explanation: