Wally Beige has painted a rectangular mural that is 7 ft tall and 11 ft wide. He plans to paint a border of equal width all the way around the outside of the mural. To end up with a border that has an area of 88 square ft, find the width of the border.

The nonlinear- function which represents b(9)=4 is given by b(x)=72/x - 4 .

In mathematics and physics, a nonlinear system is one in which the change in the output is not proportional to the change in the input. Engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems since the majority of systems are inherently nonlinear.

Nonlinear function graphs don't resemble lines at all. It contains the formula f(x) = ax + b. Its equation can take any form, with the exception of f(x) = ax + b. The slope of the curve is the same between any two points. The point pairs on the graph do not all have equal slopes.

Of all the given options: the only equations which imply that b(9)=4  are :

i) b(x)=72/x - 4 and  (iv) b(x)=4

Of this two options only the first option is non-linear.

Hence the required option is  b(x)=72/x - 4 .

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Disclaimer:

The missing options are:

i)   b(x) = 72/x - 4

ii) b(x) = √x + 7

iii)b(x)  = 2x+1

iv) b(x) = 4

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Where the conditions above are given with regard to the above triangle, the ratio AD:DB is 1:1.

Since D is the midpoint of AB, we have:

AD = DB

Let M and N be the midpoints of OA and OB, respectively. Then we have:

AM = MO = x/2

BN = NO = y/2

Also, from the given information, we have:

OD = 3/7x + 4/7y

Since D is the midpoint of AB, we have:

AD + DB = AB

Substituting AD = DB, we get:

2AD = AB

Therefore:

AD = AB/2

We can express AB in terms of x and y using the law of cosines:

AB^2 = OA^2 + OB^2 - 2(OA)(OB)cos(BOA)

Since M and N are midpoints, we have:

OM = OA/2 and ON = OB/2

Therefore, using the law of cosines, we have:

MN^2 = OM^2 + ON^2 - 2(OM)(ON)cos(MON)

Substituting OM = OA/2 and ON = OB/2, we get:

MN^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

But MN = OD, so we can also express this as:

OD^2 = (3/7x + 4/7y)^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

Substituting OD^2 = (3/7x + 4/7y)^2 and simplifying, we get:

9x^2 + 16y^2 = 49(OA^2 + OB^2) - 42(OA)(OB) cos(BOA)

Substituting AB^2 = OA^2 + OB^2 - 2(OA)(OB) cos(BOA) and simplifying, we get:

9x^2 + 16y^2 = 49AB^2

Substituting AD = AB/2, we get:

9x^2 + 16y^2 = 49(2AD)^2

Simplifying, we get:

x^2 + 4y^2 = 28AD^2

We want to find the ratio AD:DB, which is the same as the ratio AD:(AB - AD). Substituting AB = 2AD, we get:

AD:(AB - AD) = AD:AD = 1:1

Therefore, the ratio AD:DB is 1:1.

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Answer: x=4

Step-by-step explanation:

The solutions for the given system of equations are (-9, 33) and(-2, 12).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are y=x²+8x+12 -----(i) and 3x+y=-6 -----(ii).

Here, y=-6-3x in the equation (i), we get

-6-3x=x²+8x+12

x²+8x+12+6+3x=0

x²+11x+18=0

Splitting middle term method, we get

x²+9x+2x+18=0

x(x+9)+2(x+9)=0

(x+9)(x+2)=0

x=-9 or x=-2

Substitute x=-9 in the equation (ii), we get

y=-6-3(-9)

y=33

Substitute x=-2 in the equation (ii), we get

y=-6-3(-2)

y=12

So, solutions are (-9, 33) and(-2, 12)

Therefore, the solutions for the given system of equations are (-9, 33) and(-2, 12).

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Answer:

4   1/21 is the answer

Answer:

20% of the Congress is made of Senators.

Step-by-step explanation:

Our whole here is 500, since the House of Representatives and Senate combined would have 500 members in this case. So, we now need to find out how many senators there are.

\(2\) x \(50\) = \(100\)

Now, since we know the fact that there are 100 senators in Congress, we will find out what percent of 500 is 100.

100 = 20% of 500. To check, we will multiply 5 by 100. We get 500.

Therefore, the answer is 20%.

Explanation

when a line intersect a pair of parallel lines, diverse angles are formed

As we can see, angles 1 and angle 2 are supplementary , ( the sum equal 180)

the same for angles 3 and 4,

also angle1 is congruent to angle 3

and

angle 3 and 4 are supplementary ,so

I hope this helps you

Answer:

43.6 has 3 significant figures.

Answer:

height = 4 in

base = 5 in

Step-by-step explanation:

The area of a triangle can be found using the equation:

\(A = \frac{1}{2} bh\)

where \(b\) is the base of the triangle and \(h\) is the base.

In order to plug into this equation, we need to use the relationship between the base and height. It is given that the base is 3 inches shorter than twice the height. Converting this to a mathematical equation:

\(b = 2h-3\)

Since we are given that the area is 10 inches squared, we can now plug into the area equation to solve for the height (using the quadratic formula):

\(10 = \frac{1}{2} (2h-3)(h)\\2h^2 - 3h -20 = 0\\h = 4\)

** We reject the negative solution of -5/2, since the triangle's height cannot be negative.

Now, we can simply plug in this height to solve for the base:

\(b = 2(4) - 3\\b = 5\)

The complete statement is 5 + 7

The commutative property of addition is a mathematical rule stating that a change in the order or arrangement of the numbers being added does not affect the sum.

It is also important to note the following sign changes;

(-) (-) = +

(+) (+) = +

(-)(+) = -

(+)(-) = -

Given the expression;

5 - ( -7)

We know that the signs (-)(-) is equivalent to (+) sign

Substitute into the expression;

5 + 7

Thus, the complete statement is 5 + 7

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By multiplying the surface area of one face by six, 54 cm2 is obtained as the area of six faces.

By multiplying the surface area of one face by six, 54 cm2 is obtained as the area of six faces.

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The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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Sathish will be going to pay a total of $64.8 for the gas.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

The First 150 and last 150 km will cover by Satish only

Since 6 liters covers 100 km

So,

Cost of 300 km (18 liters) ⇒ 18×1.2 = 21.6

Now,

The journey 2100 - 300 = 1800 km has been covered by all three

Split 1800/3 = 600 km of money Satish will pay

So,

Cost of 600km(36 liters) ⇒ 36 × 1.2 = 43.2

Total paid = 21.6 + 43.2 = 64.8.

Hence "Satis will be going to pay a total of $64.8 for the gas".

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Answer:

the answer to the question is -25/27

In response to the given question, we can state that Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.

Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

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You would have 19 degrees of freedom in an independent-groups design and 20 degrees of freedom in a correlated-groups design..

In an independent-groups design, you would have 19 degrees of freedom. This is because the degrees of freedom for an independent-group design is equal to the number of participants minus one. Therefore, in this example, 20 participants minus one equals 19 degrees of freedom.

In a correlated-groups design, you would have 18 degrees of freedom. This is because the degrees of freedom for a correlated-groups design is equal to the number of participants minus two. Therefore, in this example, 20 participants minus two equals 18 degrees of freedom.

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Therefore, the population of seabirds 6 years ago was approximately 11,745.5.

Percent is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". For example, if there are 25 students in a class and 20 of them passed the test, the percentage of students who passed the test is 80%. This is calculated by taking the number of students who passed (20) and dividing it by the total number of students (25), then multiplying by 100.

Here,

3. The amount of the radioactive element can be modeled by the equation:

\(A(t) = A(0) *e^{rt}\)

where A(t) is the amount of the element at time t, A(0) is the initial amount at time t=0, r is the continuous rate of decrease, and e is the mathematical constant approximately equal to 2.71828.

In this problem, we know that the initial amount A(0) is 4500 nanograms, the continuous rate of decrease r is 15% per hour, and we want to find the amount of the element at 6 p.m., which is 6 hours after noon.

First, we need to convert the continuous rate of decrease from hourly to continuous, using the formula:

r = ln(1 - p)

where p is the hourly rate of decrease, expressed as a decimal. In this case, p = 0.15, so:

r = ln(1 - 0.15)

≈ -0.1707

Substituting the given values into the equation for A(t), we get:

\(A(t) = 4500*e^{-0.1707t}\)

where t is the time in hours since noon. To find the amount of the element at 6 p.m. (t = 6), we plug in t = 6 and evaluate:

\(A(6) = 4500*e^{-0.1707*6}\)

≈ 2595.5

Therefore, there will be approximately 2595.5 nanograms of the element at 6 p.m.

4a. The population of seabirds can be modeled by the equation:

\(P(t) = P(0)*e^{rt}\)

where P(t) is the population at time t, P(0) is the initial population at time t=0, r is the continuous rate of growth, and e is the mathematical constant approximately equal to 2.71828.

In this problem, we know that the initial population P(0) is 16,000, the continuous rate of growth r is 4% per year, and we want to find the population 6 years from now.

We need to convert the continuous rate of growth from years to continuous, using the formula:

r = ln(1 + p)

where p is the annual rate of growth, expressed as a decimal. In this case, p = 0.04, so:

r = ln(1 + 0.04)

≈ 0.0392

Substituting the given values into the equation for P(t), we get:

\(P(t) = 16000*e^{0.0392t}\)

where t is the time in years since the initial time. To find the population 6 years from now (t = 6), we plug in t = 6 and evaluate:

\(P(6) = 16000*e^{0.0392*6}\)

≈ 20661.7

Therefore, the population of seabirds will be approximately 20,661.7 in 6 years.

4b. To find the population 6 years ago, we can use the same equation but with t = -6 (since we are going back in time):

\(P(6) = 16000*e^{0.0392*-6}\)

≈ 11745.5

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Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

The solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

To determine which value is included in the solution set for the inequality statement -3(x-4) > 6(x-1), we need to solve the inequality for x.

Starting with the given inequality:

-3(x - 4) > 6(x - 1)

First, distribute -3 and 6 to the terms inside the parentheses:

-3x + 12 > 6x - 6

Next, combine like terms by subtracting 6x from both sides and adding 6 to both sides:

-3x - 6x > -6 - 12

-9x > -18

To isolate x, divide both sides of the inequality by -9. Remember that when dividing by a negative number, we need to reverse the inequality sign:

x < (-18) / (-9)

x < 2

Therefore, the solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

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Answer:

1287

Step-by-step explanation:

93.22-16=77.22

77.22 devided by 0.06=1287

Answer:X=17

Step-by-step explanation:

Im not 100% sure

Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.

Isaiah's Ratio:

Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:

Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%

Casho's Ratio:

Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:

Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)

Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).

Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

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Answer:

Engineers use limits in real life.

Step-by-step explanation:

Limits are also used as real-life approximations to calculating derivataves. So to make calculations, engineers will approximate a function using small differences in the function and then try and calculate the derivative of the function by having smaller and smaller spacing in the function sample intervals.

Answer:

Step-by-step explanation: its b

The value of the expression -x³ + 3x² - x + 20 when x = -1 is 23.

Given the expression in the question;

-x³ + 3x² - x + 20

To determine the value of the expression,

First, we substitute -1 for x in the expression:

-( -1 )³ + 3( -1 )² − ( -1 )) + 20

Next, we simplify each term using the order of operations (also known as PEMDAS):

-( -1 )³ = -( -1 ) = 1

(recall that the exponent is evaluated first, then the negative sign is applied)

3( -1 )² = 3(1) = 3

(recall that the exponent is evaluated first)

-( -1 ) = 1

(recall that subtracting a negative is the same as adding a positive)

Now, putting these simplified terms back into the original expression, we get:

1 + 3 + 1 + 20

Finally, we add these terms together to get the final answer:

23

Therefore, the value of the expression is 23.

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Answer:

The second box plot represents the data

Step-by-step explanation:

A box and whisker plot gives you the five-number summary of the data, which includes:

the minimum (lowest value of the data)

the maximum (highest value of the data)

Q1 (25% of the data lies below this point)

Q3 (75% of the data lies below this point), and

the median (the middle of the data).

The two ticks at the far left and far right of the box-and-whisker plot are the minimum and maximum respectively.  From the data, we see that the minimum is 5 and the maximum is 10.

Although both plots have a minimum value of 5, only the second plot has the accurate maximum at 10.