If g(x) = -f(x), across which axis is f(x) reflected to obtain g(x)?

The value of the logarithm expressions  [tex]log_{2} 8 - log_{2} 4[/tex] is 1.

Using only two logarithms at a time, from left to right, use the product property or quotient property of logarithms to rewrite logarithms of the form [tex]log_{b} A - log_{b} B = log_{b} (\frac{A}{B} )[/tex]

The logarithm expressions is [tex]log_{2} 8 - log_{2} 4[/tex].

Use the properties to rewrite logarithm expressions as a single logarithm

Using only two logarithms at a time, from left to right, use the product property or quotient property of logarithms to rewrite logarithms of the form [tex]log_{b} A - log_{b} B = log_{b} (\frac{A}{B} )[/tex]

= [tex]log_{2} 8 - log_{2} 4 = log_{2} (\frac{8}{4} )[/tex]

=[tex]log_{2} 2[/tex]=1

thus the expressions value is 1.

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Answer:

8/2 or 4

Step-by-step explanation:

y^2 - y^1 / x^2 - x^1

Answer:

x = -1

y = -2

Step-by-step explanation:

We are given the following equations:

[tex]y = -2x - 4[/tex]

[tex]y = 3x + 1[/tex]

As we can see, the expressions [tex]{-2x - 4}[/tex] and [tex]3x + 1[/tex] are both equal to [tex]y[/tex]. Therefore, we can equate them:

[tex]-2x - 4 = 3x + 1[/tex]

Now we can solve for [tex]x[/tex] by making [tex]x[/tex] the subject of the equation:

⇒ [tex]-2x - 4 -3x = 3x + 1 - 3x[/tex]      [Subtracting [tex]3x[/tex] from both sides]

⇒ [tex]-5x - 4 = 1[/tex]

⇒ [tex]-5x - 4 + 4 = 1 + 4[/tex]                 [Adding 4 to both sides of equation]

⇒ [tex]-5x = 5[/tex]

⇒ [tex]\frac{-5}{-5}x = \frac{5}{-5}[/tex]                                     [Dividing both sides by -5]

⇒ [tex]x = \bf -1[/tex]

Now that we know the value of [tex]x[/tex], we can calculate the value of [tex]y[/tex] by replacing the [tex]x[/tex] with -1 in any of the equations for  [tex]y[/tex] given above:

[tex]y = 3x + 1[/tex]

⇒ [tex]y = 3(-1) + 1[/tex]

⇒ [tex]y = -3 + 1[/tex]

⇒ [tex]y = \bf -2[/tex]

Therefore, the solution to the system of equations is : x = -1, y = -2.

Answer:

x = -1

y = -2

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y = -2x - 4\\y= 3x + 1\end{cases}[/tex]

Use the method of substitution to solve for x:

[tex]\begin{aligned}& \textsf{Substitute}: & 3x+1 & = -2x-4\\& \textsf{Add $2x$ to both sides}: & 3x+1+2x & = -2x-4+2x\\& \textsf{Combine like terms}: & 5x+1 & = -4\\& \textsf{Subtract $1$ from both sides}: & 5x+1 -1& = -4-1\\& \textsf{Simplify}: & 5x & = -5\\& \textsf{Divide both sides by $5$}: & \dfrac{5x}{5} & = \dfrac{-5}{5}\\& \textsf{Simplify}: & x & = -1\end{aligned}[/tex]

Substitute the found value of x into one of the equations and solve for y:

[tex]\begin{aligned}& \textsf{Equation}: & y& = 3x+1\\& \textsf{Substitute in $x=-1$}: & y & = 3(-1)+1\\& \textsf{Multiply the numbers}: \quad & y & = -3+1\\& \textsf{Simplify}: & y & = -2\\\end{aligned}[/tex]

Therefore, the solution to the given systems of equations is (-1, -2).

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The statements that describe the graph of f(x) are (a) the vertex of f(x) is located at (−3,−1) and (c) there is a y-intercept located at (0,2).

The equation of the function is given as

f(x) = |x + 3| - 1

The above function is an absolute value function.

An absolute value function is represented as

f(x) = a|x - h| + k

Where

Vertex = (h, k)

This means that the vertex of f(x) is located at (−3,−1)

To calculate the y-intercept, we set x = 0

So, we have

f(0) = |0 + 3| - 1

Evaluate

f(0) = 2

This means that there is a y-intercept located at (0,2).

To calculate the x-intercept, we set y = 0

So, we have

|x + 3| - 1 = 0

Evaluate

x = -2

This means that there is a x-intercept located at (-2, 0).

Hence, the statements that describe the graph of f(x) are (a) the vertex of f(x) is located at (−3,−1) and (c) there is a y-intercept located at (0,2).

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The amount of sugar that the two companies charge the same is 20 tons

The cost when the two companies charge the same is $5,015

What is breakeven amount of sugar for the two companies?

The amount of sugar that the two companies charge the same is derived at the point when the total cost of both companies are the same, bearing in mind that the total cost in this case is made of fixed cost to rent truck and variable cost, which is additional fee for each ton of sugar moved.

First company:

TC=3005+100.50x

Second company:

TC=250.75x

3005+100.50x=250.75x

3005=250.75x-100.50x

3005=150.25x

x=3005/150.25

x=20 tons of sugar

Total cost of 20 tons=250.75*20=$5,015

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Full question:

The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $3005 to rent trucks plus an additional fee of $100.50 for each ton of sugar. The second company does not charge to rent trucks but charges $250.75 for each ton of sugar

For what amount of sugar do the two companies charge the same?

What is the cost when the two companies charge the same?

Answer:

7 miles

Step-by-step explanation:

hey

minus 1.30 from 31.05 because that is the pickup fee, so 31.05-1.30= 29.75

and then divide 29.75 by 4.25 therefore 29.75/4.25=7

The peak wavelength that Earth emits as a blackbody is approximately equal to 9.657 × 10⁻⁶ m.

The Wien's displacement law is a consequence of Planck's radiation law, that states the brightness of a radiative body is a function of wavelength at a given temperature. Wien's displacement law states that peak wavelength is inversely proportional to the temperature (T), in Kelvin. The Wien's displacement law is represented by the following formula:

λ' = b / T

Where:

If we know that b ≈ 2.897 × 10⁻³ m · K and T ≈ 300 K, then the peak wavelength of the Earth is:

λ' = (2.897 × 10⁻³ m · K) / (300 K)

λ' ≈ 9.657 × 10⁻⁶ m

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The cubic equation  y³ = -8 has the value of y = -2 which is first option.

The cubic equation given to us is y³ = -8

We can shift the power from left hand side to right hand side but the cubic power would turn cube root of -8

We know that square root of any negative number is not a real number but in case of Cube roots , This is possible and the root with negative sign and simple root

Also, when we square root any number we add ± sign but in case of cube root we only add the sign of number whose cube root is taken

y³ = -8

y = ∛-8

y = ∛(-2)(-2)(-2)

y = ∛(-2)³

y = -2

So, The cubic equation  y³ = -8 has the value of y = -2 which is first option.

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Considering the definition of an equation and the way to solve it, for 25 words the charges will be the same.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Number of words

Being "x" the number of words, and knowing that:

If the charges are the same, the equation in this case is:

Boat Mart= Boat Bargains

1.30 + 0.12x= 1.80 + 0.10x

Solving:

0.12x - 0.10x= 1.80 - 1.30

0.02x= 0.5

x= 0.5 ÷ 0.02

x= 25

Finally, for 25 words the charges will be the same.

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Answer:

C The total cost, in dollars, for all binders and notebooks purchased

Step-by-step explanation:

x = the cost of a binder

y =  the cost of a notebook

Mario purchased 4 binders that cost x dollars each and 3 notebooks that cost y dollars each.

4x + 3y = 24

If the given equation represents this situation, which of the following is the best interpretation of 24 in this context?

The total cost, in dollars, for all binders and notebooks purchased.

The value of r² is 0.8673.

Given that x and y are two variables as listed below

We have to find r² the coefficient of determination

x         y         xy          x²        y²

3        2          6           9          4

4        4         16         16        16

5        5         25         25        25

7        6         42         49        36

10      20      200       100      400

------------------------------------------

29     37       289       199      481

Mean x = ( 29 / 5 )

Var X= ( 199 / 5 ) - 29 =10.8,

Mean Y = 7.4, Var Y = ( 481/5 ) - 37 = 96.2 - 37 = 59.2

Now,

r = { n(∑xy ) - (∑x)(∑y) } / √ { n( ∑x²) - (∑x )² ) × [ n(∑y²) - (∑y)² ] }

r = { 5 × 289 - 29 × 37 } / √ { ( 5 ( 199 ) - (29)² ) × [ 5( 481 - ( 37 )² ] }

r = { 1445 - 1073 } / √ { ( 995 - 841 ) × [ 2405 - 1369 ] }

r = 372 / √ { ( 154 ) × [ 1036 ] }

Therefore,

r² = ( 372 )² /  ( 154 ) × [ 1036 ]

r² = 0.8673

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Answer:

J.o.i.n p.l.z zfd-isvq-wrr

Answer=0.027777777777778

Step-by-step explanation: = 6−2

=162

=16×6

=136

Answer:  B

Step-by-step explanation:

Answer:

B is your answer

Step-by-step explanation:

Hope its right

The height of the stack of shim stocks will be  6 1/4 inches.

A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is 1 3/5. A whole number is a number that is not made up of a decimal or a fraction.

In order to determine the height of the stack, multiply the width of each shim stock by the total number of pieces. Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign used to represent multiplication is x.

Height of the stock = width of one stock x number of pieces

50 x 1/8 = 50 / 8 = 6 2/8 = 6 1/4 inches

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The angles in the picture are calculated and their values are as follows:

Given data

a = 3

b = 3.2

c = 5

using cosine rule for <ABC

b^2 = a^2 + c^2 - 2ac cos B

2ac cos B = a^2 + c^2 - b^2

cos B = (a^2 + c^2 - b^2) / 2ac

cos B = (3^2 + 5^2 - 3.2^2) / 2*3*5

cos B = 23.76/30

B = arc cos (0.792)

B = 37.63 degrees

using sine rule for <BCA

sine B / b = sin C / c

sin 37.63/ 3.2 = sim C / 5

C = arc sin (0.954)

C = 72.55

solving for <CAB

< CAB = 180 - 72.55 - 37.63

< CAB = 69.82 degrees

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If a number, a, rounded to 1 decimal point is 49.3. A number, b, rounded to 1 decimal point is 7.6 the upper and lower bounds of a-b is: 41.66; 41.79.

Given:

A= 49.3

B=7.6

Now let find the lower bounds and the upper bounds

Lower bounds is calculated as:

Lower bounds=a-b

Lower bounds=49.35-7.69

Lower bounds=41.66

Upper bounds is calculated as:

Upper bounds=a-b

Upper bounds=49.34-7.55

Upper bounds=41.79

Therefore If a number, a, rounded to 1 decimal point is 49.3. A number, b, rounded to 1 decimal point is 7.6 the upper and lower bounds of a-b is: 41.66; 41.79.

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Answer:

The answer is 0.00007

Step-by-step explanation:

Because the number behind the 7 was a 1 and not 5 or more, you could not round the 7 up, so it stayed the same.

The angle number represents an angle adjacent to  ∠DGA is angle 2.

∠DGB.

When two angles share a shared vertex and side, they are said to be neighboring. The terminus of the rays that create the sides of an angle is referred to as the vertex of an angle. Adjacent angles can be complimentary or supplementary if they have a shared vertex and side.

Adjacent angles seem to be two angles that share a shared vertex and then a common side but do not overlap. Angles 1 and 2 in the figure are adjacent. They have the same vertex as well as a common side. In the diagram, angles 1 and 3 are not contiguous.

When two angles have a common side as well as a common vertex (corner point) but do not overlap, they are said to be adjacent.

Adjacent angles comprise two angles with the same arm and vertex. When two lines meet at the vertex as well as form a pair of opposite angles, vertical angles are formed. They share an arm and a vertex. They share a vertex of the arm but no arm.

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The equivalent temperature range of the expression is -80 < x < 100.

Inequality are expressions not separated by an equal sign. Inequality expressions can be written as a range in an interval form a<x<b.

According to the given question, we are told that the lowest temperature ever recorded in Alaska is -80 degree F and the highest temperature ever recorded is 100 degrees F.

The range of the temperature expressed as inequality expression is -80<x<100

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34 cartons were delivered by the Yellow Bell Farm to various stores in the Hudson Valley.

Let the farm deliver 408 eggs to various stores around the Hudson Valley.

According to the question, a carton contains a dozen eggs.

A dozen is a grouping of twelve objects. It is abbreviated as doz or dz.

1 dozen = 12 eggs

So one carton contains a dozen eggs, or 12 eggs and

12 eggs needs 1 cartoon.

408 eggs needed = 408÷12 = 34 cartons

So 34 cartons were delivered by the yellow farm.

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The common difference of Uth term is 0

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

The nth term of the sequence () is given by: If the first term of an arithmetic progression is and the common difference between succeeding members

Formula

a_n=a_1+(n-1)d

a_n = the nth term in the sequence

a_1 = the first term in the sequence

d = the common difference between terms

we gives

a_n=a+(n-1)d

a_11=a+(n-1)d

a_11=a+(11-1)d

a_11=a+10d

a_11=3+10d

10d=-3

d=(-3)/10,  a=3

To find the Uth term of sequence

U_n=a+d(n-1)

U_11=a+d(11-1)

apply the value of a=3,d=(-3)/10

U_11=3+((-3)/10 (11-1) )

U_11=3+((-3)/10 (10) )

U_11=3+(-3)

U_11=0

Therefore, Uth term of arithmetic progression is 0.

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Answer: The difference of the amounts after practice and before practices = 11/24

Step-by-step explanation:

Given data,

Initial quantity of drink = 5/6

After practice quantity = 3/8

difference of the amounts after practice and before practices

difference of amount = Initial quantity of drink - After practice quantity

                                   = (5/6) - (3/8)

                                   = (20-9)/24

 difference of amount = 11/24

Therefore,

The difference of the amounts after practice and before practices = 11/24

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The fraction that needs to be mowed is 2/3, The fraction division for the condition is x = 1 - 1/3.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

Given that,

Michael mows = 1/3 of the yards.

Let's say the remaining fraction is x

Remaining fraction = Total fractions - a fraction of the mowed.

x = 1 - 1/3

x = 2/3

Therefore 2/3 fraction still needed to mow.

Hence "The fraction that needs to be mowed is 2/3, The fraction division for the condition is x = 1 - 1/3".

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Answer:

(a) 9

(b) -2

Step-by-step explanation:

it is very important to start by finding the equation of the line then substitute in some values.

Answer:

11.25

Step-by-step explanation:

x/3 = 3.75
x = 11.25

Work has been corrected:

If x - 3.75 = 2/3, then x/3 = 3.75 (3.75 is 1/3 of the total money, X.)

We can find the value of x by isolating the variable:

x/3(3) = 3.75(3)
x = 11.25

Thus the total money, x, is 11.25

Solve this problem by setting up ratios with the information you know.

You know:

With this information, you can assume that he used 1/3 of his money.

With this set up a ratio comparing the numerical amount he spent to the ratio of his total money that he spent:

[tex]\frac{1}{3} =\frac{3.75}{x}[/tex]

x= the total amount of money he started with.

Now cross multiply to come up with a final equation:

x = 3.75 × 3

Solve: x = 11.25

The original amount of money he started with was $11.25

Answer:

1. 5x - 15

2. 5x - 3

Step-by-step explanation:

The first one is f(g(x)), which means that you substitute g(x) into f(x).

5(x - 3)

5x - 15

Vice versa for the 2nd one.

(5x) - 3

5x - 3

Hope this helps! :)