Solve. Check for extraneous solutions. (7 x+6)¹/₂-(9+4 x)¹/₂=0

The dimensions of the fencing is 28 ft and 37 ft respectively.

He use 130 feet of fencing to go around a rectangular pool and patio.

The length of the area is 9 more than the width.

The dimension of the fence can be found as follows:

Therefore,

perimeter of the rectangular fence = 2(l + w)

where

Hence,

l = 9 + w

perimeter of the rectangular fence = 2(w + 9 + w)

perimeter of the rectangular fence = 2(2w + 9)

130 = 4w + 18

130 - 18 = 4w

112 = 4w

w = 112 / 4

w = 28 ft

l = 9 + 28 = 37 ft

Therefore, the width and length of the fencing is 28 ft and 37 ft respectively.

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Answer:0.16=16%

Step-by-step explanation:    [tex]\frac{0.16}{100}[/tex]

the 100 is directly under the point so the zero will cancel out leaving= [tex]\frac{16}{100}[/tex]

And  [tex]\frac{16}{100}[/tex] equals to 16%

if we had a value "z", and we'd like to know how much is 16% of "z", well

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of z}}{\left( \cfrac{16}{100} \right)z}\implies 0.16z[/tex]

so we can use the "factor" of 0.16, to get the 16% of any value,

since 0.16   is the decimal representation of the percentage of 16.

hmmm what is 16% of 50 anyway?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of 50}}{\left( \cfrac{16}{100} \right)50}\implies 8[/tex]8 out of 50

how much is 16% of 25 anyway?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of 25}}{\left( \cfrac{16}{100} \right)25}\implies 4[/tex]4 out of 25

Descriptive statistics is the correct answer.

Descriptive statistics are numbers that are used to summarize and describe data. The word "data" refers to the information that has been collected from an experiment, a survey, a historical record, etc. (By the way, "data" is plural. One piece of information is called a "datum.") If we are analyzing birth certificates, for example, a descriptive statistic might be the percentage of certificates issued in New York State or the average age of the mother. Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed. Several descriptive statistics are often used at one time to give a full picture of the data.

Descriptive statistics are just descriptive. They do not involve generalizing beyond the data at hand. Generalizing from our data to another set of cases is the business of inferential statistics, which you'll be studying in another section. Here we focus on (mere) descriptive statistics.

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The solution to the system of equations using substitution is: x = 3 and y = -4.

Given the system of equations:

-7x - 2y = -13 -----> equation 1

x - 2y = 11 -----> equation 2

Rewrite equation 2

x - 2y = 11

x = 11 + 2y

Substitute x = (11 + 2y) into equation 1

-7(11 + 2y) - 2y = -13

-77 - 14y - 2y = -13

-77 - 16y = -13

-16y = -13 + 77

-16y = 64

y = -4

Substitute y = -4 into equation 2

x - 2(-4) = 11

x + 8 = 11

x = 11 - 8

x = 3

Therefore, the solution to the system of equations using substitution is: x = 3 and y = -4.

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Answer:

65%

Step-by-step explanation:

To find percentage, we take the fraction of the total and multiply it by 100.

[tex]\frac{325}{500} \times=\frac{325}{5}=65[/tex]

Answer:

[tex]153.84\%[/tex]

Step-by-step explanation:

[tex] 1. \: \frac{500}{3.25} \\ 2. \: 153.84\%[/tex]

10 order of small popcorn Should be made to keep  the cost same at both the theaters

The theater P charges Admission fee of $10 and small popcorn order of $4.55

The theater Q charges Admission fee of $8 and small popcorn order of $4.75

We need to find the number of order of small popcorn so that the cost remain same

Let the number of small popcorn order be x

Then we can form the algebraic equation as

10 + 4.55x = 8 + 4.75x

now we should simplify the equation

10- 8 = 4.75x-4.55x

2= .2x

x = 2/0.2

x = 10

Hence , 10 order of small popcorn Should be made to keep  the cost same at both the theaters

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Answer:

20000fish deeen of fatherlaal yyyeeeeepee classes link hahahaha nnooooo bb bot play fff 15 sec wait ok now ans free fire max ok u noobbot

The domain for g (x) + f (x) = x² + x - 20 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.

We are given the two functions as:

f (x) = x - 4

g (x) = x² - 16

Now, first, we need to add f (x) from g (x).

So, we get that:

g (x) + f (x) = x² - 16 + (x - 4)

g (x) + f (x) = x² - 16 + x - 4

g (x) + f (x) = x² + x - 20

Now, the domain of the function will be all real numbers as it will be defined for all the real numbers.

Therefore, we get that the domain for g (x) + f (x) = x² + x - 20 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.

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Answer:

-207

Step-by-step explanation:

38x - 17

38(-5) - 17

-190 - 17

-207

*Please mark brainliest answer

Answer:-173

Step-by-step explanation:

38x - -17

38 multiplied by -5 equals -190

-190 - -17 equals -173

Answer:

Odd

Step-by-step explanation:

The answer to the equation is 1,859, making the answer odd.

One pair of vertical angles are ∠1 and ∠4.

One pair of angles that are congruent are ∠3 and ∠6.

One pair of angles that are congruent are ∠3 and ∠6.

Vertical angles are the angles opposite each other when two lines cross.

Vertical angles are congruent. This means vertical angles are equal to each other.

Therefore, one pair of vertical angles are ∠1 and ∠4.

Linear pair of angles are formed when two lines intersect each other at a single point.

Therefore, one pair of linear pair angles are ∠6 and ∠8.

Angles are congruent when they are the same. Congruent angles includes corresponding and alternate angles.

Therefore, one pair of angles that are congruent are ∠3 and ∠6.

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The function f(x) = ( x + 7)³ - 8 will shift left 7 units along x axis and will shift down 8 units along y axis to its parent function g(x) = x³.

By translation, we can stretch, shrink and shift graphs along the x-y coordinate.

We know a parent function is a function that is in its simplest form without any translation.

Given f(x) = (x + 7)³ - 8 and its parent function is g(x) = x³.

Now let us break this function f(x),

f(x) = ( x+ 7)³ implies x + 7 = 0 ⇒ x = -7.

So, x will shift 7 units to the left along the x-axis.

f(x) = ( x + 7)³ - 8, This will shift the function down 8 units along y-axis.

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(-2, -3) represents the coordinate of point B from the given expression.

The formula for calculating the midpoint of coordinates is expressed as shown below:

Midpoint = {(x₁+x₂)/2, (y₁+y₂)/2}

Given the following parameters

Midpoint = (3, -4)

A = (8,-5)

Required

Coordinate point B

Substitute the given parameters

3 = (8+x₂)/2

3(2) = 8+x₂

6 = 8+x₂

x₂ = -2

Similarly

-4 = (-5+y₂)/2

-4(2) = -5+x₂

-8 = -5 +y₂

y₂ = -3

Hence the coordinate of point B from the given expression is (-2, -3)

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Answer:

X" (and any subsequent words) was ignored because we limit queries to 32 words.

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Pakistan

The solution to the given equation -1 = -1 + (p/8) is p = 0.

Given the data in the question;

Solve for p to determine the solution to the equation.

-1 = -1 + (p/8)

Rewrite the equation as;

-1 + (p/8) = -1

Next, move all terms containing p to the left side and all constants to the right side of the equation.

-1 + (p/8) = -1

(p/8) = -1 + 1

Add -1 and 1

p/8 = -1 + 1

p/8 = 0

p = 0 × 8

p = 0

The solution to the given equation -1 = -1 + (p/8) is p = 0.

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Answer:

- 2(x - 3zy)

Step-by-step explanation:

The value of the expression 3√70 to the nearest integer will be 25.10.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 3√70

We know that the value of √70 will be 8.3666. Then the value of the expression will be given as,

⇒ 3√70

⇒ 3 x 8.3666

⇒ 25.0998 ≈ 25.10

The value of the expression 3√70 to the nearest integer will be 25.10.

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The answer is 190m.

The faster train is 160 m long and crosses a lamp post in 12 seconds.

The speed of the faster train = 16012 = 403 m/s

Given that, the speed of the other train is 6 km/hr (53 m/s) less than the faster one. [we can convert speeds from km/h to m/s by multiplying with 5/18]

The speed of the slower train = 353 m/s.

Given that, the two trains cross each other in 14 seconds when running in opposite directions along parallel tracks.

tracks.

Relative speed =  total length of two trains  time taken to cross each other

25m/s = 160+ length of second train 14

Length of the second train = 190m.

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2.89 is the value of x in equation [tex]e^x[/tex] = 18 solved by using natural logarithms.

We have been asked to find x in [tex]e^x[/tex] = 18 using natural logarithms

⇒  [tex]e^x[/tex] = 18

⇒  x = ㏑ (18)

⇒ x = 2.89

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

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Use natural logarithms to solve each equation.

[tex]e^x[/tex] = 18

Answer:

Comparamos los dos números decimales anteriores, y podemos ver que 2.5 es mayor que 1.75. Por lo tanto, 5/2 es mayor que 7/4

Step-by-step explanation:

Answer:

7/4 because if you divide them both, 7/4's decimal will be greater                                                                      

The velocity of the spacecraft is 7.7025 km/s as calculated with the help of mass ratio.

Given:

To find: Velocity of the spacecraft (v) = ?

Finding:

Here, c = 2.7 km/s, t = 30s, R = 20

On substituting the values of 'R', 't', 'v', we get:

v = -0.0098 ( 30) + 2.7 ( ln (20))

=> v = - 0.294 + 2.7 (2.995)

=> v = 7.7025 km/s

Hence, the velocity of the spacecraft is 7.7025 km/s as calculated with the help of mass ratio.

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The problem that can be defined by the function is:

A cat breeding company has 20 cats initially. The number of cats increases by 10% each year. Write a function for the exponential growth of the number of cats over the years. How many cats will the company have after 10 years?

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount and x is the number of time periods.

Consider the modeled function y = 20(1.1)ˣ.

Now, y = 20 × ( 1 + r)ˣ

f(x) = 20 × ( 1 + r)ˣ

Comparing the above equation with A(x) = a( 1 + r)ˣ

The initial amount is 20 and it increases 1 + r = 1.1.

Therefore, r = 0.1 = 10 %

Let's say we are starting a cat breeding company. Initially, we have 20 cats.

So, the problem for the function is:

A cat breeding company has 20 cats initially. The number of cats increases by 10% each year. Write a function for the exponential growth of the number of cats over the years. How many cats will the company have after 10 years?

So, a = 20, x = 10, and r = 10% = 0.1

Therefore,

A(x) = a( 1 + r)ˣ

y = a( 1 + r)ˣ

y = 20( 1 + 0.1 )ˣ

y = 20( 1.1)¹⁰

y = 20 × 2.594

y = 52

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According to the question, to calculate the relationship model of the given equations which are as follows:

[tex]z=30[/tex] when [tex]x =3 ; y=2[/tex]

And the condition is z varies jointly with x and y which can be represented as: [tex]z = \frac{k}{xy}[/tex]

Substituting the values to get the final expression:

[tex]30 = \frac{k}{(3)(2)} =\frac{k}{6}[/tex]

[tex]k=180[/tex]

Substitute the value of 'k' in the original equation. And the final expression is: [tex]z = \frac{180}{xy}[/tex]

What is function?

In mathematics, function can be defined as an expression or the rule or the law. It defines the relationship between dependent variable and the independent variable.

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Answer:

here to try to help!

Step-by-step explanation:

346.96 why? Kerry was not payed at the overtime for extra hours hope it helped!

The solution of x , y , z are 3 , -3 , 9 respectively using matrix.

We have given three equations -x+2 y+z=0 , y =-2 x+3 , z = 3 x

This can be written as AX=B

Where [tex]A=\left[\begin{array}{ccc}-1&2&1\\2&1&0\\-3&0&1\end{array}\right][/tex]    and [tex]X=\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]    [tex]B=\left[\begin{array}{ccc}0\\3\\0\end{array}\right][/tex]  

A is the coefficient matrix, X the variable matrix and B the constant matrix.

       [tex]|A|=-1(1)-2(2)+1(3)\\|A|=-1-4+3=-2[/tex]

Since , [tex]|A|\neq 0[/tex]

Hence, the system of equations is consistent and has a unique solution

A inverse is given by [tex]\frac{adjA}{|A|}[/tex]     .....(2) and adj(A) is given by [tex]AdjA=C^T[/tex]   ...(3)

Minor of matrix A will be

                          [tex]M_{11}=1\\M_{12}=2\\M_{13}=3\\M_{21}=2\\M_{22}=2\\M_{23}=6\\M_{31}=-1\\M_{32}=2\\M_{33}=-5[/tex]

Then Co - factor will be

           [tex]C_{11}=1\\C_{12}=-2\\C_{13}=3\\C_{21}=-2\\C_{22}=2\\C_{23}=-6\\C_{31}=-1\\C_{32}=-2\\M_{33}=-5[/tex]

Matrix C will be represented by

   [tex]C=\left[\begin{array}{ccc}1&-2&3\\-2&2&-6\\-1&-2&-5\end{array}\right][/tex]

Transpose of matrix C will be represented by

[tex]C^T=\left[\begin{array}{ccc}1&-2&-1\\-2&2&-2\\3&-6&-5\end{array}\right][/tex]

Then , putting this value in equation (3) , we get

     [tex]adjA=C^T\\adjA=\left[\begin{array}{ccc}1&-2&-1\\-2&2&-2\\3&-6&-5\end{array}\right][/tex]

Putting the value of |A|=-2 and adjA in equation (2) , we get

   [tex]A^{-1}=\frac{1}{-2}\left[\begin{array}{ccc}1&-2&-1\\-2&2&-2\\3&-6&-5\end{array}\right][/tex]

Putting the value of A inverse in equation (1) , we get

         [tex]X=\frac{1}{-2}\left[\begin{array}{ccc}1&-2&-1\\-2&2&-2\\3&-6&-5\end{array}\right]\left[\begin{array}{ccc}0\\3\\0\end{array}\right]\\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\frac{-1}{2} \left[\begin{array}{ccc}-6\\6\\-18\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}3\\\ -3 \\9\end{array}\right][/tex]

On comparing , we get x = 3 , y = -3 , z = 9

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The inverse of the function y=4 x²+5  is y = √((x-5)/4).

Inverse functions are those that cancel one another out. In other words, if g(x) is f's inverse, then f(g(x)) = g(f(x)) = x. (x). Given an equation for which we want the inverse, we have a fantastic method we can utilize to do this.

Not every function has a counterpart. If f(x) has an inverse, it is clear to see that it will never again have the same value. We give this resource a special name.

A function (f(x)) is said to be one-to-one if each member of the range corresponds to exactly one element of the domain.

Given,

We have a function,

y=4 x²+5

subtracting 5 from each side.

⇒ y - 5 = 4 x²

Divide by 4 and then either

⇒ x² = (y - 5) / 4

⇒ x = √((y-5)/4)

Just change the labels now, x to y.

⇒ y = √((x-5)/4)

So, the inverse of given function is y = √((x-5)/4)

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Solution of this polynomial equation is x = 3

In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Types of polynomial equations :

Some examples of polynomial equation are :

According to question,

3x = 9

=> 3x / 3 = 9 /3

=> x = 3

Thus solution for given equation is x = 3.

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