The area of a bulletin board is 52 square feet the length is three feet less than four times the width find the length and width of the bulletin board

Answer:

(-2, 4)

Step-by-step explanation:

One of the equations is already solved for y, so let's solve the other one for y and by the transitive proprerty of equality, if y = y, then what those y's are equal to are equal to each other.  Solving the first equation for y:

x + y = 2 so

y = -x + 2

Let's fill that in for y in the second equation.  Where

[tex]y=\frac{1}{2}x+5[/tex], making the substitution,

[tex]-x+2=\frac{1}{2}x+5[/tex]

Combining like terms and getting the x on one side and the constant on the other side of the equals sign:

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

The product of a fraction and its reciprocal is 1 so we will multiply both sides by

[tex]-\frac{2}{3}[/tex] to get:

[tex](-\frac{2}{3})(-\frac{3}{2})x=(3)(-\frac{2}{3})[/tex]

and we end up with x = -2.

Now that we know that, we can sub that in for x in either one of the original equations.  I chose the first one:

If x + y = 2, then -2 + y = 2

and y = 4

Therefore, the solution set is (-2, 4)

Answer:

144, 36, 9, 2 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

The recursive formula allows us to find a term in a sequence from the previous term.

Given

[tex]a_{n}[/tex] = [tex]\frac{a_{n-1} }{4}[/tex]

Given the fourth term we require to work back to the third term , second and so on. Rearrange the formula to give

Multiply both sides by 4, then

[tex]a_{n-1}[/tex] = 4[tex]a_{n}[/tex]

Given a₄ = 2 [tex]\frac{1}{4}[/tex], then

a₃ = 4 × a₄ = 4 × 2[tex]\frac{1}{4}[/tex] = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144

The first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied with that constant term to form a geometric progression.

The recursive formula allows us to find a term in a sequence from the previous term.

Given

[tex]a_n=\dfrac{a_n-1}{4}[/tex]

Given the fourth term, we require to work back to the third term, second, and so on. Rearrange the formula to give.

Multiply both sides by 4, then

a[tex]_{n-1}[/tex] = 4a[tex]._n[/tex]

Given a₄ = 2, then

The first four terms will be calculated as given below:-

a₃ = 4 × a₄ = 4 × 2 = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144

Therefore, the first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.

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Answer:

Step-by-step explanation:

No solution

Answer:

First, before I answer, he or she forgot the n/3.

So the problem is n/3 + (-4) = 2

The answer is 6

Step-by-step explanation:

First, simply + -4 to -4, because different signs subtract

Second subtract -4 + 2 which equals 2

Now multiply 3 ( came from n/3) with 2

And its 6

I hope I helped you!!!

ANSWER

[tex]x = 140 \degree[/tex]

EXPLANATION.

The two tangents each meet the radius at 90° each.

This implies that,

[tex]x + 40 + 90 + 90 = 360[/tex]

The sum of interior angles of a Quadrilateral is 360°

We simplify to get

[tex]x + 40 = 180[/tex]

[tex]x = 180 - 40[/tex]

[tex]x = 140 \degree[/tex]

I'm only doing these because it's about a pet pig named Hammy.

5.

rate = distance / time

a.

rate: 36 inches per 3 seconds

b

unit rate: 12 inches per second

c

5 seconds × 12 inches per second = 60 inches

d

144 inches / 12 inches per second = 12 seconds

6.

a.

[tex] \frac 4 7 \div \frac 3 5 = \frac 4 7 \times \frac 5 3 = \dfrac{20}{21}[/tex]

b.

[tex]2 \frac 2 5 \div 1 \frac 7 9 = \frac{12}{5} \div \frac{16}{9} = \frac{12}{5} \times \frac{9}{16} = \dfrac{27}{20} [/tex]

c

[tex]3.24 \div 1.5 = 3.24 \div \frac 3 2 = 3.24 \times \frac 2 3 = 6.48/3 = 2.16[/tex]

d

[tex] \frac 8 9 \div 3\frac 1 3 = \frac 8 9 \times \frac{3}{10} = \dfrac{4}{15}[/tex]

Answer:

Step-by-step explanation:

(a) Hammy's rate is 36 inches in 3 sec.

(b) Hammy's unit rate is (36 inches) / (3 sec) = 12 in/sec

(c) In 5 sec Hammy can run (12 in/sec)(5 sec) = 60 in

(d) time = distance/rate, so here the time is (144 in) / (12 in/sec) = 12 sec

(6a) 4/7 divided by 3/5 is equivalent to 4/7 times 5/3, which comes out to 20/21.

(6b) Convert 2  2/5 to 12/5 and 1  7/9 to 16/9.  Then invert the second improper fraction and multiply:  12/5 times 9/16 = 108/80, or 27/20.

(6c)  3.24 divided by 1.5 is equivalent to 3.24 times 2/3:  2.16, or 2  4/25

(6d) 8/9 divided by 3  1/3 is equivalent to 8/9 times 3/10, or 24/90, or 4/15.

Hi!

To solve this, first let's decide what quadrant the 135 degrees lies in. Starting in quadrant one, it would end up landing in quadrant 2.

Coordinates:

(cos, sin)

In quadrant 2, the y value (sin) as a coordinate would be positive, therefore our final answer should be positive.

180 - 135 = 45

Therefore our reference angle will be sin45.

We should know that sin45 is equal to [tex]\cfrac{\sqrt{2} }{2}[/tex]

Now, remember that our final answer should be positive. We don't have to change this because it's already positive, so your final answer is:

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

The exact value of sin 135 degrees is - (√2)/2.

The unit circle and trigonometric identities can be used to calculate the sine of 135 degrees.

We can determine the location of the point on the unit circle that corresponds to an angle of 135 degrees by utilizing the unit circle. It is located in the third quadrant.

In the first and second quadrants, the sine function is positive; however, the third and fourth quadrants are where it is negative.

We can use the fact that the sine of an angle equals the y-coordinate of the point on the unit circle corresponding to that angle to determine the precise value.

The sine of 135 degrees is negative because the third quadrant's y-coordinate is negative.

We can determine the precise sine value of 135 degrees by using a reference angle.

In the third quadrant, the reference angle for 135 degrees is 45 degrees (180 degrees - 135 degrees).

The sine of a 45-degree angle is (2)/2 or 1/sqrt(2).

The sine of 135 degrees is a negative number because the reference angle is in the third quadrant.

Consequently, (2)/2 is the precise value of sin 135 degrees.

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Answer:

Step-by-step explanation:

1. Each term has an even coefficient, so a factor of 2 can be removed:

  2(3x^2 +7x -15)

The remaining quadratic factor is prime.

__

2. Each of these two terms is a square, so this is the difference of two squares.

__

3. This cubic has one irrational negative real root. It is prime.

__

4. This trinomial factors in the usual way: (x +15)(x -2). It is factored by "factoring trinomials."

__

5. The magnitude of the x-coefficient is double the square root of the (positive) constant, so this is a perfect square trinomial.

Answer:

Step-by-step explanation: You are given the equation of -7x+6y=9 and -2x-5y=16 and you are asked to find what x=? and what y=?

First step is to write down the problem

-2x-5y=16

next add 5y over the equal sign.

-2x=5y+16

Next is too divide by -2

-2x/-2=5y+16/-2

after solving you get

x=-2.5y-8

now you substitute the equation into the other formula to get

-7(-2.5y-8)+6y=9

then solve by doing -7*-2.5y and -7*-8 to get 17.5y and 56 which will give you

17.5y+56+6y=9

Next you subtract 56 to the other side to get 9-56 or -47 now you have

17.5y+6y=-47

next is too add the 17.5y and 6y together to get 23.5y

23.5y=-47

next is too divide by 23.5

23.5y/23.5=-47/23.5

solve to get y=-2, now this is half you the problem

Step two is too substitute what y=-2 into the equation of x=-2.5y-8 to get

x=-2.5(-2)-8

Solve to get

x=5-8

Solve again to get

x=-3

Your answers are x=-3 and y=-2

Answer:

x = -3 and y = -2

Step-by-step explanation:

It is given that,

-7x + 6y = 9

   ----(1)

-2x - 5y = 16    -------(2)

To find the solution of given equations

eq(1) * 2 ⇒

-14x + 12y = 18 ------(3)

eq(2) * 7 ⇒

-14x - 35y = 112   ---(4)

eq (3) - eq(4) ⇒

-14x + 12y = 18 ------(3)

-14x - 35y = 112   ---(4)

    0   4y = -94

y = 94/(-47) = -2

Substitute the value of y in eq (2)

-2x - 5y = 16    -------(2)

-2x - 5*-2 = 16

-2x +10 = 16

-2x = 6

x = 6/-2 = -3

Therefore x = -3 and y = -2

Step-by-step explanation:

This equation is written in standard form, y = ax² + bx + c.

a = 1 , b = -2 , c = -4

First, the x² tells you that this is going to be a parabola. Since the a is positive, the parabola will be facing up (with the ends pointing up).

Next, you find the axis of symmetry, or vertex, which is where the middle of the parabola is. The formula for this is [tex]\frac{-b}{2a}[/tex].

[tex]\frac{-(-2)}{2(1)}[/tex]   Simplify

[tex]\frac{2}{2}[/tex]   Simplify

1

So, the middle of your parabola will be at x = 1.

Now, find the x-intercept. Since the x-intercept of a graph is where y = 0, just plug 0 into the equation for y.

y = x² - 2x - 4   Plug in 0

0 = x² - 2x - 4   Factoring won't work, so use the Quadratic Formula.

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]   Plug in[tex]$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-4)}}{2(1)}$[/tex]   Simplify

[tex]$x=\frac{2\pm\sqrt{4+16}}{2}$[/tex]   Simplify

[tex]$x=\frac{2\pm\sqrt{20}}{2}$[/tex] The square root of 20 is about 4.47.

[tex]$x=\frac{2+4.47}{2}$[/tex] and [tex]$x=\frac{2-4.47}{2}$[/tex]   Simplify

x = 3.235 and -1.235

These are your x-intercepts, where your parabola crosses the x-axis.

Now, just put all of this information together on a graph!

Answer:

The true statements are:

The y-variable will be eliminated when adding the system of equations

There is only one solution to the system of equations is

Step-by-step explanation:

* Lets explain how to solve the problem

- We use the elimination method to solve the system of the

  linear equation

- The solution is one of three cases

# Exactly one solution ⇒ the 2 lines which represented the equations

  intersect each other at one point

# No solution ⇒ the 2 lines which represented the equations are

  parallel to each other

# Infinite solutions ⇒ the two lines are coincide

- In the system of the linear equations of the problem we have two

 linear equations  -x + 6y = 16 and 8x - 6y = -2

- To solve we must to eliminate one of the two variables

∵ The y's in the two equations have the same coefficients and

   different signs

∴ We add the equations to eliminate y

∴ (-x + 8x) + (6y - 6y) = 16 + -2

∴ 7x = 14 ⇒ divide both sides by 7

∴ x = 2

- Substitute the x in any one of the two equations by 2

∴ -2 + 6y = 16 ⇒ add 2 to both sides

∴ 6y = 18 ⇒ divide both sides by 6

∴ y = 3

∴ The solution of the system of the equations is (2 , 3) ⇒ only one

   solution

- Lets check the statements to find the true statements

# The x-variable will be eliminated when adding the system of

   equations is not true

# The y-variable will be eliminated when adding the system of

   equations is true

# The sum of the system of equations is - x + 6y is not true

# There is only one solution to the system of equations is true

Statements 1 and 2 are true, while statements 3 and 4 are false.

Let's analyze each statement:

1. The x-variable will be eliminated when adding the system of equations.

  - When adding the equations, the x-variables are eliminated because (x) in one equation cancels with (-8x) in the other equation. So, this statement is true.

2. The y-variable will be eliminated when adding the system of equations.

  - When adding the equations, the y-variables are also eliminated because (6y) in one equation cancels with (-6y) in the other equation. So, this statement is true.

3. The sum of the system of equations is -x + 6y.

  - The sum of the two equations is indeed (-x + 6y). Adding the equations directly gives ( -x + 6y = 14), not ( 16). So, this statement is false.

4. There is only one solution to the system of equations.

  - Since the system of equations represents two equations with two variables, the solution can either be a unique solution, no solution, or infinitely many solutions. To determine this, we need to solve the system of equations. We can do this by eliminating one variable and solving for the other. However, from the given equations, we can't determine the nature of the solution without further analysis. So, this statement is indeterminate based solely on the provided equations.

Therefore, statements 1 and 2 are true, while statements 3 and 4 are indeterminate based on the given information.

Answer:

So a point is (-3,-5) and the vertex is (-4,-3)

Step-by-step explanation:

This is in vertex form. Vertex form is y=a(x-h)^2+k where (h,k) is the vertex.

The vertex here is (-4,-3)... now just use a value of x to plug in (any value besides -4)

I will choice -3.  This gives -2(-3+4)^2-3

f(-3)=-2(1)^2-3

f(-3)=-2-3

f(-3)=-5

So a point is (-3,-5) and the vertex is (-4,-3)

Answer:(-4,-3)

Step-by-step explanation:

The answer is:

The correct answer is c.

[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]

To calculate the slugging average or slugging percentage, we need to divide the number of total bases by the total times at bat.

[tex]SluggingAverage=\frac{TotalBases}{TimesAtBat}[/tex]

We know that:

A single means 1 base.

A double means 2 bases.

A triple means 3 bases.

A homerun means 4 bases.

So, we know that:

[tex]Singles=25=25bases\\Doubles=2*10=20bases\\Triples=3*3=9bases\\Homeruns=10*40=40bases\\TimesAtBat=140[/tex]

Then, substituting and calculating we have:

[tex]SluggingAverage=\frac{25bases+20bases+9bases+40bases}{140}[/tex]

[tex]SluggingAverage=\frac{94bases}{140times}=0.671[/tex]

Hence, the correct answer is c.

[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]

Have a nice day!

Answer:

  congruent triangles

Step-by-step explanation:

The complete reason is, "corresponding parts of congruent triangles are congruent." This reason is sometimes abbreviated CPCTC.

It can be helpful to note that the previous step concluded that the relevant triangles are congruent.

Answer:

5. Congruent triangles

Step-by-step explanation:

Congruent Triangles : When two triangles are congruent, all its three sides are equal and have the same angles.

So in conguent traingles,

ΔADB ≅ BDC

Therefore, AB = DC and AD = BC

Thus this completes the missing information that proves that the quadrilateral ABCD ia a parallelogram, then its opposite sides are congruent.

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-4}{2(1)}~~,~~6-\cfrac{(-4)^2}{4(1)} \right)\implies (2~~,~~6-4)\implies (2~,~2)[/tex]

Answer:

B. (2,2).

Step-by-step explanation:

Convert to vertex form y = a(x - b)^2 + c where (b, c) is the vertex.

y =x^2 - 4x + 6

y = (x - 2)^2 - 4 +6

y = (x - 2)^2 + 2.

Therefore the vertex is (2, 2).

Step-by-step explanation:

A number cubed is equal to the product of 52 and the square of the number.

Answer:

  (x, y, z) = (1, -1, -4)

Step-by-step explanation:

A suitable graphing or scientific calculator can find the reduced row-echelon form for you. There are on-line calculators that will do that, too.

_____

In general, if you want to do this by hand, you want to use row operations on the augmented matrix to make the diagonal elements 1 and the off-diagonal elements 0 as shown in the attached result.

If a[i,j] represents the element at row i, column j, you do that by dividing row i by a[i, i] (to make a[i, i] = 1), then subtracting the product of row i and a[k,i] from row k. (for all rows k ≠ i) For this 3-row matrix, repeat these steps for i = 1 to 3.

In the general case of an n by n+1 augmented matrix, you will be doing n^2 row operations, each one involving evaluation of n+1 expressions. The work rapidly grows with matrix size, so readily justifies use of a calculator.

As with many "elimination" problems, appropriate choice of sequence can reduce the work. The above algorithm always produces the reduced row-echelon form, but may result in messy arithmetic along the way.

Answer: A

Step-by-step explanation: edge 2021

Answer:

  (x, y) = (-3, 5)

Step-by-step explanation:

There are many ways to solve a system of two equations with two unknowns. Almost all of them involve reducing the system to one equation in one unknown. (Graphical solution, as in the attachment, bypasses that algebraic manipulation.)

In general, the first step is to look at the equations to see if ...

If the first condition is true, then the system may be easily solved by "substitution." The expression you have for one of the variables can be substituted for that variable in the other equation.

If the second condition is true, you can add the equations to eliminate the variable with opposite coefficients. (Opposites add to give zero.)

Here, the third condition holds: the coefficient of x in the first equation (4) is simply related to the coefficient of x in the second equation (8) by a factor of 2.

___

So, we can eliminate the x-variable from the system of equations by multiplying the first equation by -2 and adding that result to the second equation:

  -2(4x +2y) +(8x +5y) = -2(-2) +(1)

  -8x -4y +8x +5y = 4 +1 . . . . eliminate parentheses

  y = 5 . . . . . . . . . . . . . . . . . . . collect terms

Now, we can substitute this value into either equation to find the value of x. Using the first equation, we get ...

  4x +2(5) = -2

  4x = -12 . . . . . . . subtract 10

  x = -3 . . . . . . . . . divide by 4

The solution to the system of equations is (x, y) = (-3, 5).

Answer:

[tex](p - 19) \geqslant 47[/tex]

[tex]p \geqslant 66[/tex]

Answer: The required interval notation of the solution is [66, ∞).

Step-by-step explanation:  We are given to translate and solve the following inequality :

"Nineteen less than p is no less than 47".

Also, to write the solution in interval notation.

According to the given information, the inequality can be written as follows :

[tex]p-19\geq47.[/tex]

The solution of the above inequality is as follows :

[tex]p-19\geq47\\\\\Rightarrow p\geq47+19\\\\\Rightarrow p\geq 66.[/tex]

Thus, the required interval notation of the solution is [66, ∞).

Answer:

  Wet Suit Willy

Step-by-step explanation:

To find boxes per dive, divide boxes by dives:

  Sam: 33/11 = 3 . . . boxes per dive

  Willy: 81/18 = 4.5 . . . boxes per dive

  Dan: 104/26 = 4 . . . boxes per dive

Wet Suit Willy found the most treasure boxes per dive: 4.5.

Answer:

45.71 - 6x

Step-by-step explanation:

If Heather bought markers to donate, the amount she donates is subtracted from her balance of 45.71.  We know she bought 6 packs of markers, but we do not know how much each pack cost.  We will make this our unknown "x".  The expression for  packs of markers costing "x" is 6x.  Because she buys them from her account, which takes aways from her balance, the expression that represents this donation is:

45.71 - 6x

(Notice that the question asks for the EXPRESSION after she buys the markers, not the EQUATION.  The difference between an expression and an equation is the lack of an equals sign in the expression.)

Answer:

M= 45.71 - 6x

Step-by-step explanation:

M represents money and x is how much each pack of markers cost. 45.71, which is the original amount, minus 6x will give the correct amount.

Answer:  272

Step-by-step explanation:

f(x) = 4x         g(x) = 3x - 5

(g × f)(x) = (4x)(3x - 5)

             = 12x² - 20x

(g × f)(-4) = 12(-4)² - 20(-4)

               = 12(16) + 80

               = 192 + 80

              = 272

Answer:

sqrt of 2/2

Step-by-step explanation:

Answer:

The exact value of cos 45° is: [tex]\frac{\sqrt{2} }{2}[/tex].

Step-by-step explanation:

The equation of Bunny hill ski resort is z = 10x + 35 while z = 5x + 40  for the Black diamond ski resort at the point and at point (1,45) the cost of both will be the same.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say x number of hours a men sky

Then,

Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour

So,

Total cost

z = 35 + 10x

Now,

Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski

So,

Total cost

z = 40 + 5x

Now point where the cost of both resorts will same is

35 + 10x = 40 + 5x

x = 1

So,

z = 40 + 5(1) = 45

Hence, at point (1,45) the cost of both will be the same.

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Final answer:

To find when the costs are the same for both ski resorts, set up an equation based on their rates and solve for the number of hours, which in this case is 1 hour.

Explanation:

To determine at what point the cost of both Bunny Hill Ski Resort and Black Diamond Ski Resort is the same, we can set up an equation based on the given rates.

Let x be the number of hours spent skiing. Then the total cost at Bunny Hill Ski Resort is $35 (ski rental) plus $10 per hour (hourly rate), which is expressed as 35 + 10x.

Similarly, the cost at Black Diamond Ski Resort is $40 (ski rental) plus $5 per hour (hourly rate), or 40 + 5x. To find when the costs are equal, we set the two expressions equal to each other:

35 + 10x = 40 + 5x

Now we can solve for x:

35 + 10x = 40 + 5x
10x - 5x = 40 - 35
5x = 5
x = 1

Thus, after 1 hour of skiing, the cost of skiing at both resorts becomes the same.

Answer:

  {4}

Step-by-step explanation:

It is helpful to let a calculator or spreadsheet perform the function evaluations for you. The two functions have the same value only for x=4 in the domain.

  f(4) = 13 = g(4)

_____

The functions also have the same value for x=-2, but that is not in the domain given.

Answer:

  y = 3

Step-by-step explanation:

The solution is the point where the lines intersect, (x, y) = (6, 3). The y-coordinate of that point is 3.

Answer:

y = 3

Step-by-step explanation:

You must count the lines from the intersection to the Ox axis down.

Answer:

Step-by-step explanation:

Add all the students: 4+6+2+2+3+4+6+3 = 30

Add all the male students = 14

divide : 14/30=0.466666

multiply by 100

0.466*100=4.66

round

Answer = 5

Answer: A C and E

Step-by-step explanation:

-4+6 (x-2x)^2 36x^2yz-3

(A) (C) (E)

There's a screenshot of the answers below

Answer:

A. 6i

Step-by-step explanation:

Apply by the radicial rule.

[tex]\sqrt{-36}=\sqrt{-1}\sqrt{36}[/tex]

[tex]\sqrt{-1}\sqrt{36}[/tex]

Imaginary number.

[tex]\sqrt{36 i}[/tex]

Square root the numbers from left to right.

[tex]6^2=36[/tex]

[tex]\sqrt{6^2}=6[/tex]

6i is the correct answer.

I hope this helps you, and have a wonderful day.

Answer:

A

Step-by-step explanation:

It is best to graph the function when searching for the range.

For the function f(x) = (x + 5)(x + 1), the range is ALL REAL NUMBERS when y is greater than or equal to -4.

Get it?