Solve each equation.
log (7 x+1)=log (x-2)+1

The transformations needed to sketch the graph of [tex]h(x) = \sqrt[3]{1 - x}[/tex] are described as follows:

Starting with the graph of the basic function [tex]y = \sqrt[3]{x}[/tex], horizontally shift the graph right one unit, and then reflected the graph about the x-axis.

A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

The parent cube root function is given by:

[tex]y = \sqrt[3]{x}[/tex]

To have x -> x - 1, we reflect the function over the y-axis, hence:

[tex]y = \sqrt[3]{-x}[/tex]

To have -x -> 1 - x, we shift it one unit right, hence:

[tex]h(x) = \sqrt[3]{1 - x}[/tex]

The order of the transformations can be reversed, i. e., shift right then reflection.

Thus the correct statement to sketch the graph is given by:

Starting with the graph of the basic function [tex]y = \sqrt[3]{x}[/tex], horizontally shift the graph right one unit, and then reflected the graph about the x-axis.

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Taking into account the definition of probability, the probability for a customer to pick at least one item is 14/15.

Probability is the possibility that a phenomenon or an event will happen, given certain circumstances and it is expressed as a percentage.

The probability of any event A is defined as the ratio between the number of cases in which event A may or may not occur and the total number of possible cases. This is called Laplace's Law:

P(A)= number of favorable cases÷ total number of posible cases

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event is verified when one of the two, A or B, or both occurs and it is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B.

In first place, let's define the following events:

So you know:

In this case, considering the definition of union of events, the probability for a customer to pick at least one item is calculated as:

P(M∪F)= P(M) + P(F) -P(M∩F)

P(M∪F)= 17/30 + 5/6 -7/15

P(M∪F)= 14/15

Finally, the probability for a customer to pick at least one item is 14/15.

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A composite function exists as a function that depends on another function. The value for  (f⁰f)(0) = - 4/3

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the two functions be g(x) = 3x + 2 and f(x) = x - 2/3

Now, (f⁰f)(x) = f[f(x)]

f(x) = x - 2/3

(f⁰f)(x) = f( x - 2/3)

simplifying the above equation, we get

(f⁰f)(x) = (x - 2/3) - 2/3  

(f⁰f)(0) = - 2/3 - 2/3

(f⁰f)(0) = - 4/3

Therefore, the value of (f⁰f)(0) = - 4/3.

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The trace of water left on the floor is the circumference of 565.2 cm.

Water traces are seen on the floor from a wet bicycle tire.

The bicycle wheel makes three complete rotations before coming to a stop, circumference  and the tire has a radius of 30 cm.

The circle of the cycle is indicated by the water stain left on the floor.

Given the radius = 30 cm

So,

C = 2 × 3.14 × 30

C = 188.4

Given that a bicycle wheel turns three times before pausing to pick up a trace of water, the answer is,

3 x 188.4 = 565.2 cm

the floor has a 565.2 centimeter trace of water.

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Answer:

y-2 = -5(x-8)

Step-by-step explanation:

y-y₁=m(x-x₁)

Answer:

$29.40

Step-by-step explanation:

The exponential expression [tex]6^{-3}[/tex]/ [tex]3^{-2}[/tex] * 6² is equivalent to the exponential expression is 3² / [tex]6^{5}[/tex] which is option 2 and not option 1

The Exponential expression given to us is 6^-3/3^-2x6^2 or we can write it as

[tex]6^{-3}[/tex]/ [tex]3^{-2}[/tex] * 6²

There is a rule for solving exponents that when we reciprocate the fractions with exponential powers the signs of powers get changed from negative to positive and positive to negative

for example

[tex]x^{-2}[/tex] is written as [tex]\frac{1}{x^{2} }[/tex]

So, we can write the above  exponential expression as

3² / 6³ × 6²

Also, when two same numbers with different powers then the base remains same and powers get added.

3² / [tex]6^{3+5}[/tex]

3² / [tex]6^{5}[/tex]

So, the exponential expression [tex]6^{-3}[/tex]/ [tex]3^{-2}[/tex] * 6² is equivalent to the exponential expression is 3² / [tex]6^{5}[/tex] which is option 2 and not option 1

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Answer: 1/23

Step-by-step explanation:

x=multiplicative inverse of 23

23*x=1

23x=1

23x/23=1/23

x=1/23

Answer:The answer to your question is

I bought

12

hardcover books and

24

softcover books.

Explanation:

We shall represent the hardcover books purchased by

x

and the softcover books purchased by

y

. From the details we can write two equations:

x

+

y

=

36

8

x

+

2

y

=

144

From the first equation we can calculate the value of

y

.

x

+

y

=

36

Subtract

x

from each side.

y

=

36

−

x

Now, in the second equation, substitute

y

with

(

36

−

x

)

.

8

x

+

2

y

=

144

8

x

+

2

(

36

−

x

)

=

144

Open the brackets and simplify.

8

x

+

72

−

2

x

=

144

6

x

+

72

=

144

Subtract

72

from both sides.

6

x

=

72

Divide both sides by

6

.

x

=

12

Now in the first equation, substitute

x

with

12

.

x

+

y

=

36

12

+

y

=

36

Subtract

12

from both sides.

y

=

24

Step-by-step explanation:

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Answer:

He would have $100 in his bank account from the information provided

Step-by-step explanation:

The function that relates the sales and the number of muffins is :

S = 2.5 m

The sales amount can be find by the total sales. That is , if there are n products to sell and selling amount is x rs. then we can easily find the total sales by multiplying them and by this total sales we can easily find the number of items sold per units and vice versa.

In the question given,

amount (A) = $ 250.00

Now take any of two values from table ,

Choose any two points and calculate the slope:

slope = [tex]\frac{50 - 20}{20 - 8}[/tex] =  2.5

thus, y = 2.5x

Hence we can say the function that relates the sales and the number of muffins is :

S = 2.5 m

where, S = sales amount

           m = number of muffins to be sell

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The complete question is:

In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown.

a. What is a function that relates the sales and the number of muffins?

b. How many muffins would you have to sell to make at least $ 250.00 in sales?

Answer: D y=4x   3=4y+x

Step-by-step explanation:

[tex]y=4x\ \ \ \ m=4\\\\3=4y+x\\3-x=4y+x-x\\3-x=4y\\-x+3=4y[/tex]

Divide both parts of the equation by 4:

[tex]\displaystyle\\-\frac{x}{4} +\frac{3}{4}=y \\\\-\frac{1}{4} x+0.75=y\\\\y=-\frac{1}{4} x+0.75\ \ \ \ m_{\perp}=-\frac{1}{m}=-\frac{1}{4}[/tex]

Answer:

2x>8

Step-by-step explanation:

this should be right

Answer:

Step-by-step explanation:

Convert 9 feet into meters:

Round 2.7432 meters:

Answer:

Step-by-step explanation:

It’s the 3rd and last one 0.5 swim and 1.5 bike and 0 hours swim and 2 bike

I’ve done the test

Answer:

A) The original price of music player is $170.66

B) If the item was marked up by 1/2 before it was placed on the sales floor, what was that the store paid for the digital player.?

Step-by-step explanation:

A)you would divide $128 by 4, getting $32. then add that to the original price, being $160.

B) you would divide $160 by 2, getting $80, then add those two together in order to find what it was marked up to, being $240. hopefully this helps

The value of the expression,  5([tex]2^{-3}[/tex]) is expressed as: 5/8.

We are given the expression, 5([tex]2^{-3}[/tex]), to find the value of the expression, the steps explained below should be taken.

5([tex]2^{-3}[/tex]) [given expression]

Apply the negative exponents rule to evaluate the exponent in the expression

5([tex]2^{-3}[/tex]) = 5(1/2³)

5([tex]2^{-3}[/tex]) = 5/2³

Solve the exponent to eliminate the power of minus 3

5([tex]2^{-3}[/tex]) = 5/(2 × 2 × 2)

5([tex]2^{-3}[/tex]) = 5/8

Thus, the value of the expression,  5([tex]2^{-3}[/tex]) is expressed as: 5/8.

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Aqil have 88 stickers.

Let Ryan have x stickers initially. Then Aqil will have (352-x) stickers. Ryan lost 25% of his stickers i.e., x-(25% of x)

= x- 25x/100

= x-x/4

= 3x/4

After Ryan lost 25% of his stickers, the ratio of Ryan's stickers to Aqil's stickers was 9:4 i.e.,

3x/4 : (352-x) = 9 : 4

⇒ 3x/4/(352-x) = 9/4

⇒3x/4 x 4 = 9 x (352-x)

⇒3x = 3168-9x

⇒3x+9x = 3168

⇒12x = 3168

⇒x = 3168/12

⇒x = 264

∴ Ryan have 264 stickers of the total 352 stickers and Aqil will have (352-x) i.e., 88 stickers.

Hence, Aqil have 88 stickers out of the 352 stickers.

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The equation of the line is y = -(1/3)x + 5,

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

We have,

The line is perpendicular to y = 3x - 2 and passes through (3, 4).

The slope of the line and the slope of y = 3x - 2 is:

[tex]m_{1} m_{2}[/tex] = -1

Where [tex]m_{2}[/tex] = 3

[tex]m_{1}[/tex] = -1/3

The equation for the line that passes (3, 4) is given by:

y - 4 = -1/3 ( x - 3)

y = -1/3x + 1 + 4

y = -(1/3)x + 5

Thus the equation of the line is y = -(1/3)x + 5,

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The complete question is:

What is the equation of the line perpendicular to y = 3x − 2  and passes through point (3,4)?

Answer:

Step-by-step explanation: the five was never in bracket and -2 times 2 = -4

(5)^2 -2(5-3)

=(5)^2  -2(2)

=25  -2(2)

25 (-4)

-100

We can buy 9 programs after buying the laptop if we want to spend $ 500 at most on the laptop.

The cost of the laptop = $ 319

The maximum money we have = $ 500

Money left after purchasing the laptop will be calculated by using subtraction.

Money left = $ 500 - $ 319 = $ 181

Now, cost of each program = $ 20

The number of programs we can buy = $ 181 / $ 20

The number of programs we can buy = 9.05

That means 9 programs.

Therefore, we get that, we can buy 9 programs after buying the laptop if we want to spend $ 500 at most on the laptop.

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good luck buddy rip if you dont get the question

Answer:

square = width*height,

circle=pi*r^2

triangle = w * h * 0.5

Step-by-step explanation:

square = width*height,

circle=pi*r^2

triangle = w * h * 0.5

Answer:

14

Step-by-step explanation:

To solve [tex]\frac{ab^2-4}{10}[/tex]

We need to know what [tex]ab^2[/tex] is.

[tex]ab^2 = a*b^2 = 4 * 6^2 = 4*36 = 144[/tex]

[tex]\frac{144-4}{10} = 140/10 =14[/tex]

Hope this helps :)

Have a great day!

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(10,8)

Equation Form:

x=10,y=8

Step-by-step explanation:

The linear equation in slope intercept form is y = -2x + 1

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The table represents the given parameters

On the table, we have the following points

(x, y) = (0, 1) and (1, -1)

A linear equation is represented as

y = mx + c

Substitute (x, y) = (0, 1) and (1, -1) in y = mx + c

So, we have

1 = 0 * m + c

-1 = 1 * m + c

This gives

1 = c

-1 =m + c

Rewrite 1 = c as

c = 1

Substitute c = 1 in -1 =m + c

-1 =m + 1

Evaluate

m = -2

Substitute m = -2 and c = 1 in y = mx + c

y = -2x + 1

Hence, the linear equation in slope intercept form is y = -2x + 1

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The angle of A when the polygon slides 4 units left and 3 units up on the coordinate plane is 75°.

From the information, Polygon AVC’s slides 4 units left and 3 units up on the coordinate plane. If the original measure of angle A was 75 degrees.

It should be noted that translation doesn't change the angle. Therefore, the number will be the same as the translation is stationary.

Therefore, the angle of A when the polygon slides 4 units left and 3 units up on the coordinate plane is 75°

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The only graph that has a slope of -¹/₃ and a y-intercept of -4 that represents the inequality y > -¹/₃x - 4 is the graph represented by option C.

We want to find the graph that represents the inequality;

y > -¹/₃x - 4

Now, the general form of equation for a linear equation is;

y = mx + c

where;

m is slope

c is y-intercept

Now since the inequality is greater than, it means that it must be shaded at the top and must be a broken or dashed line. Thus, the only graph that has a slope of -¹/₃ and a y-intercept of -4 is the graph represented by option C.

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n-2 is the next larger odd integer if the number represented by n-3 is an odd number.

Parity, in mathematics, is the characteristic of an integer that determines whether it is even or odd. If an integer is a multiple of two, it is even; otherwise, it is odd. For instance, 4, 0, and 82 are even. 3, 5, 7, and 21 are odd numbers in comparison.

Whole numbers that cannot be divided perfectly into pairs are referred to as odd numbers. When two is divided by an odd number, one is left over.

based on the available facts;

Formulate based on the conditions stated:

(n-3)+1

Rearrange and group related terms:

n+(-3+1)

Calculate the sum or difference:

n-2

Answer is n-2

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