4
BOOKMARK
Simplify each of the following expressions:
-5 - 2 + 8 =

We take the inverses of the function and get the results as follows:

[tex]f(1)=1+1=2\\f^{-1}(1)=\sqrt{1-1}=0\\f^{-1}(f(1))=\frac{\sqrt{\sqrt{4(1)+1} -3}}{\sqrt{2} } \\f(f^{-1} (1))=1[/tex],  [tex]f(2)=4+1=5\\f^{-1}(2)=\sqrt{2-1}=1\\f^{-1}(f(2))=\frac{\sqrt{\sqrt{4(2)+1} -3}}{\sqrt{2} } \\f(f^{-1} (2))=2[/tex], [tex]f(3)=9+1=\sqrt{10} \\f^{-1}(3)=\sqrt{3-1}=\sqrt{2} \\f^{-1}(f(3))=\frac{\sqrt{\sqrt{4(3)+1} -3}}{\sqrt{2} } \\f(f^{-1} (3))=3[/tex]

What are the inverses of a function?

A function that can change into another function is referred to as being inverse or anti. In other words, the inverse of any function "f" will take y to x if it takes x to y in the first place. The inverse function is indicated by  F^-1 if the function is denoted by F.

Given C={1,2,3}, and

[tex]f(x)=x^{2} +1\\ f^{-1}(x)=\sqrt{x-1} \\f^{-1}(f(x))=\frac{\sqrt{\sqrt{4(x)+1} -3}}{\sqrt{2} } \\f(f^{-1} (x))=x[/tex]

Now,

For C=1,

[tex]f(1)=1+1=2\\f^{-1}(1)=\sqrt{1-1}=0\\f^{-1}(f(1))=\frac{\sqrt{\sqrt{4(1)+1} -3}}{\sqrt{2} } \\f(f^{-1} (1))=1[/tex]

For C=2

[tex]f(2)=4+1=5\\f^{-1}(2)=\sqrt{2-1}=1\\f^{-1}(f(2))=\frac{\sqrt{\sqrt{4(2)+1} -3}}{\sqrt{2} } \\f(f^{-1} (2))=2[/tex]

For C=3

[tex]f(3)=9+1=\sqrt{10} \\f^{-1}(3)=\sqrt{3-1}=\sqrt{2} \\f^{-1}(f(3))=\frac{\sqrt{\sqrt{4(3)+1} -3}}{\sqrt{2} } \\f(f^{-1} (3))=3[/tex]

Hence, the solution is provided.

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The equation that represents the the total amount he paid, y, for x pounds of potatoes is y = 0.64x.

Dontrelle bought [tex]5\frac{1}{2}[/tex] pounds of potatoes for $3.52.

The equation that can be used to represent the the total amount he paid, y, for x pounds of potatoes is as follows:

rate = amount paid / weight in pounds

amount paid = $3.52

weight of potatoes = 11 / 2 pounds

rate = 3.52 ÷11 / 2

rate = 3.52 × 2  / 11

rate = 7.04 / 11

rate = 0.64 dollars per pound.

Therefore, the equation is y = 0.64x

where

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The smallest to largest test values of the inequality (x-4)(x-5)<0 are  

(-infinity,4) , (4,5) & (5,+infinity)

What is a inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.

"A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">," "," "," or "."

(x-4)(x-5)<0

x-4<0             or             x-5<0

x<4                or              x<5

1)

for False the test values of the inequality (x-4)(x-5)<0  from smallest to largest Lies in between (-infinity,4)

2)

for True the  test values  of the inequality (x-4)(x-5)<0 from smallest to largest Lies in between (4,5)

3)

for True the  test values of the inequality (x-4)(x-5)<0  from smallest to largest Lies in between (5,+infinity)

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Answer:

a

Step-by-step explanation:

Answer:a

Step-by-step explanation:

[tex]x = \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]   ,   [tex]x = -\sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]

Step-by-step explanation:

[tex]z= -9+3x^{2} +3y^{2} : x= \sqrt{\frac{z-3y^{2}+9 }{3} } ,x = - \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]

[tex]z= -9+3x^{2} +3y^{2}[/tex] :   [tex]-9+3x^{2} +3y^{2} =z[/tex]

[tex]-9+3x^{2} = z- 3y^{2}[/tex]

[tex]3x^{2} = z - 3y^{2} +9[/tex]

[tex]\frac{3x^{2} }{3} = \frac{z}{3} - \frac{3y^{2} }{3} + \frac{9}{3}[/tex]

[tex]x^{2} = \frac{z-3y^{2}+9 }{3}[/tex]

for [tex]x^{2} =[/tex][tex]f(a)[/tex] the solutions are [tex]x= \sqrt{f(a)} , -\sqrt{f(a)}[/tex]

[tex]x = \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]  ,  [tex]x = -\sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]

[tex]x = i \sqrt{\frac{z+2y^{2}-5 }{2} } , x = -i \sqrt{\frac{z+2y^{2}-5 }{2} }[/tex]

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I'm here trying to help my 12 yr old

Answer:

the fraction 5/7 is equivalent to approximately 71.4%

Step-by-step explanation:

if you divide 5/7, you'll get an answer like 0.71428

to convert decimals to fractions, you have to multiply by 100 to get 71.428

to round to the nearest tenth, round the 2 up to 3

71.43

and then, round 4 down

71.4%

hope this helped!

Answer:

JN

Step-by-step explanation:

By solving the given equation, we know that Courtney withdrawals $25.75 each time from her bank account.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the value of the variable x is 7.

So, we have the equation:

400-3x=322.75

Now, solve the equation for x to get the amount Courtney withdrawals each time:

400-3x=322.75

-3x = 322.75 - 400

-3x = -77.25

x = -77.25/-3

x = $25.75

Therefore, by solving the given equation, we know that Courtney withdrawals $25.75 each time from her bank account.

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Complete question:
Courtney made 3 withdrawals of equal amounts from her savings account. The equation below can be used to determine x, the amount in dollars of each withdrawal.

400-3x=322.75

What was the amount in dollars of each of Courtney's withdrawals?

answer choices

a. $24.09

b. $25.75

c. $74.25

d. $77.25

Answer:

Step-by-step explanation:

In order for the ratio of volumes of a cylinder, cone, and sphere to be true, the radius of each solid would have to be equal. This is because the radius is a factor in the volume formulas for all three solids:

Volume of cylinder: πr^2h

Volume of cone: (1/3)πr^2h

Volume of sphere: (4/3)πr^3

If the radius is equal in all three solids, then the volumes will be in the same ratio as the given ratio, regardless of the values of h or the surface area. Therefore, the correct answer is : The radius and the height.

Answer:  

~ Sarah = b

!!!Michael = 1/2*b + 3

~~David = b/2 + 8

!!!Hannah = 3b + 28

~~~~~Sarah = 3b/2 + 14

The flow chart to prove m∠3≅m∠4 is given below.

What is the vertical angle theorem?

The Vertical Angle Theorem states that when two straight lines cross, they create two linear pairs. Due to the fact that their angles add up to 180 degrees, the adjacent angles created when two lines intersect are known as supplementary angles.

Given, m∠1≅m∠2

Then, m∠1≅m∠3 ( vertical angles theorem)

m∠2≅m∠3 (Given)

Then, m∠2≅m∠4 (vertical angle theorem)

Hence, m∠3≅m∠4 (transitive property of congruence) proved

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After solving the equation we can say that Plan A will cost $10 more than Plan B. So, D is the Correct answer

What is an Equation?

A statement that affirms the equality of two expressions connected by the equals sign "=" is known as an equation.

For illustration, 2x - 5 = 13.
The two most well-known groups of equations in algebra are the linear

equations and the polynomial equations.
P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations.

Here, the parameters a and b. To solve these equations, we can use geometric or computational techniques from linear algebra or mathematical analysis. There are several sorts of equations

as well, including:

linear algebra quadratic formulas cube-based equations linear equations Equations that differ Statistical equations

Plan A:- $135 + $15(no. of premium channel)
Plan A for 5 premium channels will be
=$135 + $15(5)
= $135 + $75
=$210

Plan B:-
equation
C=$(5p+180)  
p = no. of premium channel
Plan B for 5  premium channels will be equation
C = $25 + $180
= $205

Thus,
Plan A will cost $5 more than Plan B
As Plan A cost $210 and Plan B cost $205

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Answer:

Step-by-step explanation:

0

Answer: 6

Step-by-step explanation: you can ask siri

The ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.

What is the constant of variation?

The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.

We have,

         x         y

         2         10

         4         24

         6         36

To determine whether y varies directly with x, you need to see if the ratio of y to x is constant for all the data points.

If y varies directly with x, then the ratio y/x will be constant for all the data points. In this case, you can write an equation for the direct variation in the form y = kx, where k is the constant of variation, which is equal to the ratio y/x.

If the ratio y/x is not constant for all the data points, then y does not vary directly with x.

so, let's see the k constant of variation,

k =  y/x

k = 2/10 =1/5

k = 4/24 = 1/6

k = 6/36 = 1/6

so,  k = 1/5, k=1/6, k=1/6.

Hence, the ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.

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The solution to the system of equations is (y,z) = (-23/11, 33/11).

What is the system of equations?

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.

To eliminate the z-terms in this system, you can multiply the first equation by 3 and the second equation by -1 and then add the resulting equations together. This will give you an equation in terms of only y, which you can then solve for y.

The resulting equation will be:

(4y + 3z) * 3 + (y - z) * -1 = (-6) * 3 + (-5) * -1

12y - 3z - y + z = -18 - 5

Combining like terms, we get:

11y = -23

Dividing both sides by 11, we get:

y = -23/11

Now that we have solved for y, we can substitute this value back into one of the original equations to solve for z. For example, substituting -23/11 for y in the first equation gives us:

4(-23/11) + 3z = -6

Solving for z, we get:

z = 33/11

Hence, the solution to the system of equations is (y, z) = (-23/11, 33/11).

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The annual interest rate of the bank account is 2.3%

Let's check the equation for each year.

Compound Interest earned amount

A = P( 1 + r/n)ⁿˣ

A = accumulated amount

P =  original amount deposited

r =  interest rate

n = times it compounds per year

x = years

when Amount = $736.80, x = 4 years and r% → r/100

736.80 = P(1 +[(r/100)/1] ¹×⁴

736.80 = P(1 + r/100)⁴

when Amount =$788.82 , x = 7 years and r% → r/100

788.82 = P(1 +[(r/100)/1] ¹×⁷

788.82 = P(1 + r/100)⁷

using the 1st equation:

736.80 = P(1 + r/100)⁴

P = 736.80 /[(1 + r/100)⁴]

Substitute on the Using 2nd equation

788.82 = P(1 + r/100)⁷

788.82 =  736.80 /[(1 + r/100)⁴] * (1 + r/100)⁷

788.82 =  736.80 * [(1 + r/100)⁷/(1 + r/100)⁴]

788.82 = 736.80 * (1 + r/100)³

788.82/736.80 = (1 + r/100)³

∛788.82/736.80 = ∛ (1 + r/100)³

∛788.82/736.80 = (100 + r)/100

100 ∛788.82/736.80 = 100 + r

100 ∛788.82/736.80 - 100 = r

r ≈ 2.3%

Hence, the annual interest rate of the bank account is 2.3%

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Every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.

Given that,

Show that each component of isom (r²) is either a translation or a rotation using the findings from section 3.7.

An isometry of R² is a mapping T:R²⇒R² which preserves distance.

The formula for the distance between x and y is

d(x,y)=|y-x|=√(y₂-x₂)²+(y₁-x₁)²

The preservice means,

d(x,y)=d(T(x),T(y))

A translation is an isometry.

Since,

d(Tv(x),Tv(y))=|(xv)-(y-v)|=d(x,y)

The rotation matrix, for rotating by an angle Θ, is defined as,

cosΘ     -sinΘ

sinΘ       cosΘ

Therefore, every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.

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Matching the equation to choices

equation                                                classifications

2x = y + 3 and y = - 2x + 1                       consistent and independent

2x = y + 3 and 2y - 4x = -6                     consistent and dependent

2x = y + 3 and 2y - 4x = 6                       inconsistent

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.

2x - y = 3... equation * 2

4x - 2y = 6

-4x + 2y  = 6

subtracting gives

8x - 4y = 0

no solution  

A system is deemed consistent if it has at least one solution.

A consistent system is independent if it only has one solution.

y = 2x - 3

y = -2x + 1

subtracting gives

0 = 4x - 4

x = 1

substituting x to get y

y = -1

A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them.

-y + 2x =  3 .... equation * 2

-2y + 4x =  6

2y - 4x = -6  

subtracting gives

-4y + 8x = 12 - none cancels out meaning infinite number of possible solutions

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The solution of the expression will be;

⇒ x = - 88

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

'' one eighth times quantity x plus 32 end quantity equals negative 7.''

Now,

Since, The algebraic expression is,

'' one eighth times quantity x plus 32 end quantity equals negative 7.''

Hence, We can formulate;

⇒ 1/8 (x + 32) = - 7

⇒ x + 32 = - 56

⇒ x = - 56 - 32

⇒ x = - 88

Thus, The solution of the expression will be;

⇒ x = - 88

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Answer:

9203 in.³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3) × 3.14159 × (13 in.)³

V = 9203 in.³

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

According to the statement, the value of Z-Stat is +2.10. And we must find the P value when H0 is rejected only in the upper tail. The Z-stat is defined as the Z-score, which indicates how much a given value differs from the standard deviation.

The Z-score, also known as the standard score, is the number of standard deviations a given data point is above or below the mean.

And we know that the P-Value is calculated by converting your statistic into a Z-Score.

As a result, the p value is 0.0179.

So, When ZSTAT = +2.10, the resulting P-Value is 0.0179.

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Answer:

[tex]\huge\boxed{\sf \$ 7.50}[/tex]

Step-by-step explanation:

Given that,

6 inches of sandwich = $2.50

Multiply 3 to both sides

6 × 3 inches of sandwich = $2.50 × 3

[tex]\rule[225]{225}{2}[/tex]

Based on the information in the fragment, it can be inferred that Josiah's mistake is that he did not multiply the numerator and denominator by the correct number to equal 1,500 (option B). So, the correct statements are A, C, and D.

To find the proportion in this problem we have to do the following procedure:

Once we have carried out the previous steps we must continue the procedure rewriting the equation with the data obtained previously. With this information we can conclude that Josian had the necessary information to discover how many songs of each genre were played during an hour on his MP3, however he performed the wrong procedure so his result was wrong.

According to the above, we can infer that the products are not well carried out. So, Josiah's mistake is no multiplying the numerator and denominator by the correct number to equal 1,500 (option B).

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