The rectangle shown has a perimeter of 64 cm and the given area. Its length is 8 more than five times its width. Write and solve a system of equations to find the dimensions of the rectangle.

Answer:

x = 0

Step-by-step explanation:

[tex]\frac{3}{2}(\frac{7}{3}x + 1) = \frac{3}{2}[/tex]

To start, let's multiply each side by the reciprocal of [tex]\frac{3}{2}[/tex].  Multiplying a fraction by its reciprocal gives us 1, which will make the left side of our equation simpler.

[tex]\frac{2}3} * \frac{3}{2}(\frac{7}{3}x + 1) = \frac{2}3} * \frac{3}{2}[/tex]

[tex]\frac{2}{3} * \frac{3}{2} = 1[/tex], so we have:

[tex]1(\frac{7}{3}x + 1) = 1[/tex] or [tex]\frac{7}{3}x + 1= 1[/tex]

Next, we can subtract 1 from both sides to further simplify the left side:

[tex]\frac{7}{3}x + 1 - 1= 1 - 1\\\frac{7}{3}x=0[/tex]

Finally, we can multiply by the reciprocal of [tex]\frac{7}{3}[/tex] on both sides in order to isolate x on the left.  Anything multiplied by 0 = 0, so now we have:

x = 0

7/2x + 3/2 = 3/2 <=> 7/2x = 0 <=> x=0

9 1/2 is the same as a number decreased by 15

I guess that's the right answer maybe i'm wrong if I am oh well

Answer:

$425000

Step-by-step explanation:

561000*100/132=425000

Answer:

-4 I believe is the answer

Step-by-step explanation:

Hope this helps:)

Answer:

77.14L

Step-by-step explanation:

20.3x3.8=77.14L

Answer:

16

Step-by-step explanation:

8x8 is 64, so half of 8 is 4 so 4x4 is 16

Step-by-step explanation:

Note: I'm only providing solutions for Problem 9.

Combining like terms involve performing the required mathematical operations (using the PEMDAS rule).  The terms must have the same degree (or exponents).  

Add the coefficients of both terms.  

3a + 7a  = 10a

Add the coefficients of both terms.  

4n + 3n = 7n

Subtract the coefficient of both terms.  

12y - 4y = 8y

Add the coefficients of all terms.  

5x + 2x + 4x = 11x  

The last term, "ba," can be rewritten as, "ab."  Remember that with algebraic expressions such as "ab," it essentially involves multiplication of both variables within the same term. Thus, ab = a × b. The variables ab also have a numerical coefficient of 1:  1a × 1b.

Now, we can perform the subtraction on all terms:

6ab - 2ab - ab = 3ab.  

Subtract 2mn from 2mn, which leaves you with 7mn:

7mn + 2mn - 2mn = 7mn  

For this algebraic expression, you could only combine the terms with the same variable and degree. Therefore, you'll have to subtract 3y from 4y, leaving the constant, 8, unaffected.  

4y - 3y + 8 = y + 8

Similar to question g, only combine the terms with the same degree and variable, leaving the constant unaffected.

7x + 5 - 4x = 3x + 5

You could only combine the terms with the same set of variables and degree, which are the first two terms on this given question. You cannot combine the last term, 4y, into the other terms.  

6xy + xy + 4y = 7xy + 4y

Using the same reasoning as in question e: the last term, 7ba, can be rewritten as 7ab, for which you could combine with the first term, 5ab.

5ab + 3 + 7ba = 12ab + 3  

Combine the like terms, which are the second and the last term.  

2 - 5m - m = 2 - 6m

Combine the like terms, which are the second and the last term.  

4 - 2x + x = 4 - x  

Answer:

Answer is A

Step-by-step explanation:

Subtract 47 from both sides to get 0

3x² - 18x - 42 = 0

Use Quadratic formula to get

[tex]3+\sqrt{23} \\3-\sqrt{23}[/tex]

Answer:

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

Because it moved 2 to the right.

Answer:

-8

Hope this helps :)

Since you have the answers, I'll just show the steps on how to get there.

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Problem 19

[tex](1+4i)^2\\\\(1+4i)(1+4i)\\\\1*1 + 1*4i + 4i*1 + 4i*4i\\\\1 + 4i + 4i + 16i^2\\\\1 + 4i + 4i + 16(-1)\\\\1 + 4i + 4i-16\\\\(1-16) + (4i+4i)\\\\(1-16) + (4+4)i\\\\-15 + 8i\\\\[/tex]

Keep in mind that [tex]i = \sqrt{-1}[/tex] by definition. Squaring both sides leads to [tex]i^2 = -1[/tex]

In the second step, I used the idea that x^2 = x*x. Right after that, I used the FOIL rule to expand everything out.

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Problem 21

We could follow the same idea as problem 19, but I'll use a different approach.

[tex](A+B)^2 = A^2+2AB+B^2\\\\(3+i)^2 = 3^2 + 2*3*i + i^2\\\\(3+i)^2 = 9 + 6i - 1\\\\(3+i)^2 = 8 + 6i\\\\[/tex]

The formula on the first line is the perfect square binomial formula.

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Problem 23

The FOIL rule can be used if you want, but I'll use the difference of squares rule instead.

[tex](m+n)(m-n) = m^2 - n^2\\\\(3+5i)(3-5i) = (3)^2 - (5i)^2\\\\(3+5i)(3-5i) = 9 - 25i^2\\\\(3+5i)(3-5i) = 9 - 25(-1)\\\\(3+5i)(3-5i) = 9 + 25\\\\(3+5i)(3-5i) = 34\\\\[/tex]

It turns out that multiplying any complex number of the form a+bi with its conjugate a-bi will result in a purely real number (that has no imaginary part). More specifically: [tex](a+bi)(a-bi) = a^2+b^2[/tex]

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Problem 25

We could use the difference of squares rule again, but I'll show a different approach. This time using the distribution rule. The FOIL rule could also be used if you wanted.

[tex](6+7i)(6-7i)\\\\x(6-7i)\\\\6x-7xi\\\\6(x)-7i(x)\\\\6(6+7i)-7i(6+7i)\\\\6(6)+6(7i)-7i(6)-7i(7i)\\\\36+42i-42i-49i^2\\\\36-49(-1)\\\\36+49\\\\85\\\\[/tex]

I used x = 6+7i and the substitution property to help distribute. Lines 3 and 6 are where distribution is applied.

Answer: point (60,0)

Step-by-step explanation: the x-intercept (60,0) shows that at 60 minuetes the balloon is 0 meter above the ground

The coordinates of the function of height and time are (210, 0) and (60, 10). The graph is attached below.

The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output. This means that if an object x is present in the set of inputs (also known as the domain), then a function f will map that object to exactly one object f(x) in the set of potential outputs (called the co-domain).

Given:

r(t) = 210 - 15t

Calculate the height after 10 minutes as shown below,

The height = 210 - 15 × 10

The height = 210 - 150

The height = 60

At time 0 the height will be,

The height = 210 - 15 × 0

The height = 210 - 0

The height = 210 meters,

Thus, the coordinates will be (210, 0) and (60, 10)

To know more about function:

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Answer:

The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.  The solution is the ordered pair(s) common to all lines in the system when the lines are graphed.

Lines that cross at a point (or points) are defined as a consistent system of equations. The place(s) where they cross are the solution(s) to the system.

Parallel lines do not cross. They have the same slope and different y-intercepts. They are an example of an inconsistent system of equations. An inconsistent system of equations has no solution.

Two equations that actually are the same line have an infinite number of solutions. This is an example of a dependent system of equations.

Step-by-step explanation:

Solve the system of equations graphically.

3x + 2y = 4

−x + 3y = −5

Solution

Graph each line and determine where they cross.

The lines intersect once at (2, −1).

A graphic solution to a system of equations is only as accurate as the scale of the paper or precision of the lines. At times the point of intersection will need to be estimated on the graph. When an exact solution is necessary, the system should be solved algebraically, either by substitution or by elimination.

Substitution Method

To solve a system of equations by substitution, solve one of the equations for a variable, for example x. Then replace that variable in the other equation with the terms you deemed equal and solve for the other variable, y. The solution to the system of equations is always an ordered pair.

Example

Solve the following system of equations by substitution.

x + 3y = 18

2x + y = 11

Solution

Solve for a variable in either equation. (If possible, choose a variable that does not have a coefficient to avoid working with fractions.)

In this case, it's easiest to rewrite the first equation by solving for x.

x + 3y = 18

x = −3y + 18

Next, substitute (−3y + 18) in for x into the other equation. Solve for y.

2(  3y + 12x + y = 11

2(−3y + 18) + y = 11-------Substitute -3y + 18 in for

   −6y + 36 + y = 11-------Distribute.

2(3y −5y + 36 = 11-------Combine like terms.

2(3y +  18−5y = −25-----Subtract 36 from both sides

2(3y + 18) +  y = 5----   -Divide both sides by -5.

Then, substitute y = 5 into your rewritten equation to find x.

x = −3y + 18

x = −3(5) + 18

x = −15 + 18

x = 3

Identify the solution.   A check using x = 3 and y = 5 in both equations will show that the solution is the ordered pair (3, 5).

Elimination Method

Another way to solve a system of equations is by using the elimination method.  The aim of using the elimination method is to have one variable cancel out. The resulting sum will contain a single variable that can then be identified. Once one variable is found, it can be substituted into either of the original equations to find the other variable.

Example

Find the solution to the system of equations by using the elimination method.

x − 2y = 9

3x + 2y = 11

Solution

Add the equations.

 x −  2y = 9

3x +  2y = 11

4x +  2y = 20

Isolate the variable in the new equation

4x = 20

 x = 5

Substitute x = 5 into either of the original equations to find y.

 x − 2y = 9

(5) − 2y = 9

     −2y = 4

        y = −2

Identify the ordered pair that is the solution.   A check in both equations will show that (5, −2) is a solution.

It may be necessary to multiply one or both of the equations in the system by a constant in order to obtain a variable that can be eliminated by addition. For example, consider the system of equations below:

3x + 2y = 6

 x − 5y = 8

Both sides of the second equation above could be multiplied by −3. Multiplying the equation by the same number on both sides does not change the value of the equation. It will result in an equation whereby the x values can be eliminated through addition.

Special Cases

In some circumstances, both variables will drop out when adding the equations. If the resulting expression is not true, then the system is inconsistent and has no solution.

4x + 6y = 13

6x + 9y = 17

3(4x + 6y = 13)

2(6x + 9y = 17)

12x + 18y = 39

12x + 18y = 34

             0 = 5

The equation is false.  The system has no solution.

If both variables drop out and the resulting expression is true, then the system is dependent and has infinite solutions.

6x + 15y = 24

4x + 10y = 16

2(6x + 15y = 24)

3(4x + 10y = 16)

12x + 30y = 48

12x + 30y = 48

             0 = 0

The equation is true.  The system has an infinite number of solutions.  (Notice that both of the original equations reduce to 2x + 5y = 8.  All solutions to the system lie on this line.)

Answer:

C must be acute, and ABC cannot be constructed

Step-by-step explanation:

24 degrees is under 90 degrees making angle c an acute angle.

ABC cannot be contructed because a triangle makes up of 180 degrees, and ABC does not make up 180 degrees.

Have a great day friend! :D

Answer:

C must be acute.

Step-by-step explanation:

The smaller the length of the side, the smaller is the angle opposite it, so C must be < 27.

Answer:

65 hard-shells

26 soft shells

Step-by-step explanation:

5 x 13 = 65

2 x 13 = 26

65 - 26 = 39

Answer:

-5/6

Step-by-step explanation:

1. Change 3/4 to 6/8 by cancelling the common factors.

2. Divide how you normally would

Answer:

- [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

-3[tex]\frac{1}{8}[/tex] ÷ 3[tex]\frac{3}{4}[/tex]

[tex]\frac{-25}{8}[/tex] ÷ [tex]\frac{15}{4}[/tex]

[tex]\frac{-25}{8}[/tex] × [tex]\frac{4}{15}[/tex]

[tex]\frac{-100}{120}[/tex]

[tex]\frac{-50}{60}[/tex]

- [tex]\frac{5}{6}[/tex]

* Keep in mind that - [tex]\frac{5}{6}[/tex], [tex]\frac{-5}{6}[/tex], and [tex]\frac{5}{-6}[/tex] mean the same thing!

First, I converted -3 1/8 and 3 3/4 to improper fractions. I then switched the sign of division to multiplication and changed 15/4 to 4/15. I then multiplied -25 with 4 and 8 with 15, resulting in -100/120. I simplified this to -5/6.

Hope this helps, and if you have any questions, let me know!

The demand is decreasing at the rate of 2units per week.

Given the price p (in dollars) and the demand x (in thousands of units) of a commodity satisfy the demand equation 6p+x+xp=94

Differentiating the function with respect to time will result in;

[tex]6\frac{dp}{dt}+\frac{dx}{dt} + x \frac{dp}{dt} + p\frac{dx}{dt} = 0[/tex]

Given the following paramters

p = $6

dp/dt = $2/wk

Substitute the given parameters into the formula to have:

[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0[/tex]

To get the demand x, we will simply substitute  p = 9 into the expression to have:

6(9)+x+9x=94

10x+54 = 94

10x = 94 - 54

10x = 40

x = 4

Substitute x = 4 into the derivative to have:

[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 2(4) + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 8 + 9\frac{dx}{dt} = 0\\20 + 10\frac{dx}{dt} =0\\10\frac{dx}{dt} =-20\\\frac{dx}{dt} =\frac{-20}{10}\\\frac{dx}{dt} =-\$2/wk[/tex]

Hence the demand is decreasing at the rate of 2units per week.

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Answer:

the answer is 12.2

[tex] \frac{b}{0.52} \\ we \: know \: b = 6.344 \\ then \\ \frac{6.344}{0.52} \\ = 12.2[/tex]

Answer:

42x-42

Step-by-step explanation:

(7x)(6x)+(6)(-7)=42x°-42°

Answer:

A. He can decrease the simple spacw

Answer:

D. He can increase the number of trials

A box=12 pencils

156 boxes =?

156÷12=13 boxes

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

5 + 3 = 8

-Lexi

Answer:

it would take 100 days for it to get better that just makes sense I think and for number two it would be 365% better

Step-by-step explanation:

Answer:

Can you provide how long it took to print per copy

Step-by-step explanation:

Answer:

it will take him 50 min because their are 730 and that is lot so it will take him 50min

Answer:

After reviewing the question you posted I have deduced that the correct answers are:

11) Max has $10.00. He earns $25.75 per lawn that he mows.

12) No. She is wrong. She did not group like terms correctly.

Step-by-step explanation:

11)

For 11) I first identified the independent variable of the equation, being "10".

And then the dependent variable of the equation, being "25.75". (The dependent variable of an equation will always be affected by the x)

I then looked at all the possible answers to see which one shared a independent variable of "10" and a dependent variable of "25.75".

The only possible answer that matches is Max has $10.00. He earns $25.75 per lawn that he mows.

This is because the only two possible answers that have "10" being a variable that does not change (independent variable) are:

--- "Max has $10.00. He earns $25.75 per lawn that he mows.

--- "Jon buys 10 toycars for $25.75 each"

However!

"Jon buys 10 toycars for $25.75 each" is an incorrect answer because it uses "10", although independent, as the x variable that affects the independent variable of "25.75".

12)

To find the correct answer for this question I simplified the equation from:

8t-15+3t   =   11m-15

Into:

8t+3t-15   =   11m-15

Which further simplifies into:

11t-15   =   11m-15

Which then you can notice that the two equations are similiar indeed, however they do not share like terms. One equation has "t" as their term, and the other as "m" as their term. Thus they do not share any like terms and are not equivalent.

Answer:

y = 10

Step-by-step explanation:

y = (-2)(x) + 4

y = (-2)(-3) + 4

y = 6 + 4

y = 10

Answer:

$154.96

Step-by-step explanation:

difference means to subtract so 879.95-724.99=154.96

Answer:

b

gnzjfzjgzjxjgzfjsngdjgsjfzgjskzjtztjsgjd5uduajai

Answer:

simply add what you got from your mother and father then subtract from what you spent then the remaining is the answer