What are the rules of inequalities?.

The x intercept of f(x) is same as x intercept of g(x) and the statements the y intercept of f(x) is same as y intercept of g(x) are true.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The function  f (x) = x² -7x

when we translate the graph f(x) to g(x) it can be seen that g(x) is a translation of f(x) by left and upwards.

So the statements the x intercept of f(x) is same as x intercept of g(x) and the statements the y intercept of f(x) is same as y intercept of g(x)

Hence, the x intercept of f(x) is same as x intercept of g(x) and the statements the y intercept of f(x) is same as y intercept of g(x) are true.

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The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

How is inequity resolved?

Luis has $420 to spend at a bicycle shop on new accessories and clothing.

He spends $209.67 on a brand-new bicycle.

He spends $6.04 apiece on two bicycle reflectors and $25.77 on a pair of cycling gloves.

He intends to use all or part of the remaining funds to purchase new riding clothing at $37.16 apiece.

Therefore,

x is the maximum amount of clothes Luis can buy on a tight budget.

In order to illustrate the scenario, the inequality that may be employed is as follows:

209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420

235.44 + 12.08 + 37.16x ≤ 420

247.52 +  37.16x ≤ 420

37.16x ≤ 420 - 247.52

37.16x ≤ 172.48

divide both sides by 37.16

x ≤ 4.64155005382

x ≤ 4

Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

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The total discount tickets sold are 8460 tickets.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.


The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.


We have that,
94% = 94/100
       = 0.94

By multiplying the tickets sold by the factor of 0.94, we get

0.94 × 9000
8460 tickets

The total discount tickets sold are 8460 tickets.

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The formula is a fact or a rule written with mathematical symbols. It usually connects two or more quantities with an equal sign.

In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.

Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.

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Answer:

x=7 because scince it got dilated by 7

No, "FG)(x)" and "g/f)(x)" are not inverse of each other."FG)(x)" refers to the composition of two functions, "F" and "G", where the output of "G" is used as the input for "F".

The notation for this is represented as "F(G(x))", where "x" is the input for both functions.

The function "F" is applied to the output of the function "G", meaning that the output of the function "G" is used as the input for the function "F".

On the other hand, "g/f)(x)" is not a standard notation in mathematics. It could be interpreted as applying the function "g" to the input "x", and then applying the function "f" to the result of "g". But it could also be interpreted as applying f to the input x and then applying g to the result of f.

Inverse functions are related to the idea of reversing the effect of a function. For example, if "f" is a function that maps a set of inputs to a set of outputs, then the inverse function "f^-1" maps the set of outputs back to the original set of inputs. The notation for an inverse function is typically represented as "f^-1(x)" or "f^(-1)(x)". It's important to note that not all functions have inverses, and the inverse of a function is also a function.

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To find the median of grouped data if (n) is odd the median is (n+1)/2 and if (n) is even the median will be average of n/2th and the (n/2)+1.

Data that is written continuously and is sorted in ascending order is the median of a bunch of data. The information is presented as a frequency distribution table that separates higher level information from lower level information. Using the formula is one of the simplest ways to determine the median of grouped data.

We can employ the procedures and formula below to determine the median for grouped data:

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Answer:

d) x[tex]\geq 4[/tex]

Step-by-step explanation:

Answer:

option d is correct ok hope it helps

A rotation of 270° counterclockwise will map the blade formed by ΔFEG onto the blade formed by ΔHGI

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the first triangle be represented as ΔFEG

Let the second triangle be represented as ΔHGI

Now , for both the triangles to be similar , the mapping of the rotation of the blade should be rotated once in the clockwise or three times in the counterclockwise direction

So , for a rotation of 90° clockwise rotation: (x,y) becomes (y,-x)

So , for a rotation of 270° counterclockwise rotation: (x,y) becomes (y,-x)

The ΔFEG of the blade will map itself onto the ΔHGI of the blade after a rotation of 270° counterclockwise rotation

Hence , the rotation is 270° counterclockwise rotation

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Answer:

6 12 18 24

Step-by-step explanation:

i think you mean finding a multiple of 6 in between 1 and 25. how it will work is times 6 until you get out of the 25 range 1x 6 = 6 2x6 = 12 3x6 = 18 and 4x6 = 24 5x 6 = 30 which is not between 1 and 25. pick any of these four to  answer with

Answer:

15:17

Step-by-step explanation:

We know

Fifteen of the 32 students in the class own a dog, so the ratio of students who have a dog to students who do not is

15:17

The angle 180  is not an acute angle.

We know that an angle is the figure, in which two rays meet at a common point (vertex).

The types of angles (based on their magnitude) are:

Acute Angle (angle measuring greater than 0° and less than 90°)

Obtuse Angle, (an angle which is less that 180° and greater than 90°)

and Right Angle (an angle that measures 90°)

There are some types of angle based on their rotation:    

Straight Angle, (an angle measuring 180 degrees)

Reflex Angle, (an angle which is greater than 180 degrees but less than 360 degrees )

and Full Rotation (an angle measuring 360 degrees)

From the definition of acute angle,

acute angle measures greater than 0° and less than 90°

So, 180 degrees can not be an acute angle.

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The ratio of comparision of the cup is given as 4:2

A mathematical comparison of two or more values or quantities is called a ratio. It can be used to compare the relative sizes or amounts of various items since it expresses the relationship between the values in terms of a proportion or a fraction.

let the number of cups of strawberries required be x. and the number of cups of whipped cream required be y

given that x=4 and y=2

so the ration of comparision is given by:

x:y

=>4:2

so 2:1

so the ratio of comparision is given as 4:2

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The solution to the system of inequalities given by x + y > −2 and −x + y < 1 is the ordered pair that lies under the conditions x > -3/2 and y > -1/2. One of which is (1, 0).

An inequality is a statement about the relative size or order of two values. It's a statement that one value is greater than, less than, greater than or equal to, less than or equal to, or not equal to another value. It's represented using mathematical symbols such as <, >, ≤, ≥, ≠.

To find the solution to a system of inequalities, rewrite any of the two inequalities as y in terms of x.

x + y > -2 can be rewritten as y > -x - 2

Substitute the value of y into the other inequality.

-x + y < 1 will become -x + (-x - 2) < 1

Solve for the value of x.

-x + (-x - 2) < 1

-2x -2 < 1

-2x < 1 + 2

-2x < 3

2x > -3

x > -3/2

Plug in the value of x into the equation of y and solve for y.

y > -x - 2

y > -(-3/2) - 2

y > -1/2

So, the solution of the system of inequalities will be the region where both of these conditions, x > -3/2 and y > -1/2, are true, which is the area where the graph of y > -x - 2 and y < x + 1 overlap.

One ordered pair (1 , 0) is a solution to the system of inequalities x + y > -2 and -x + y < 1.

We can check it by plugging in the ordered pair into the inequalities.

x + y > -2 becomes 1 + 0 > -2 which is true

-x + y < 1 becomes -1 + 0 < 1 which is true

So (1,0) satisfies both inequalities.

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The 4 inverse operations in math are addition, multiplication, square root and cube root.

The term inverse in math is referred to as the opposite of another operation and for example, the inverse of the number 2 is written as 1/2.

Here we need to identify the four inverse operations in math.

Here we also need to know that a function or operation which reverses the order or operation of another function or operation

According to the definition of the term inverse, the type of inverse operation in math is defined as follows:

=> addition and subtraction,

=> multiplication and division,

=> squares and square roots only for positive numbers,

=> cubes and cube roots.

And basically these inverse operations are used in solving algebraic equations

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Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

This would then result in the answer of t = 5/4.

Emma's first mistake was when she set up the equation. She started with:

−

3

5

=

4

5

t

−

3

5

This equation does not make sense mathematically, as it cannot be solved. The equation should have been set up as:

3

5

=

4

5

t

By setting up the equation correctly, Emma could have proceeded to solve the equation. To solve the equation, she would have needed to subtract 3/5 from both sides of the equation, resulting in

3

5

−

3

5

=

4

5

t

−

3

5

This would then result in the answer of t = 5/4.

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Answer:

calculating

Step-by-step explanation:

In the given arithmetic series, the third, fifth, and tenth terms are, respectively, 20, 36, and 76.

The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the. sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d

Given, Term sequence described by each rule

A(n)=4+(N-1)(8)

thus,

Third term A(3) = 4 + (3 -1)8

A(3) = 20

Fifth term A(5) = 4 + (5 -1)8

A(5) = 36

tenth term A(10) = 4 + (10 - 1)8

A(10) = 76

Therefore, the third fifth and tenth terms of the given arithmetic series are 20, 36, and 76 respectively.

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Answer:

√50 must lie between 7 and 8

Step-by-step explanation:

To some extent you have to know the squares of integers

7² = 49

8² = 64

So √50 must lie between 7 and 8

The graph of an inverse proportion is a curved graph.

When two variables are related in a way where their product is always constant, that relationship is called an inverse proportion. Y = k/x or xy = k, where k is a constant, are two ways to express it mathematically. Hyperbolas which are curved graphs are formed with inverse proportions. Collecting all points in the plane where the gap between two fixed points and a fixed point is constant is known as a hyperbola.

With the foci on the y-axis and the x-axis serving as the hyperbola's centre, the graph of the equation y = k/x is a hyperbola. The y-axis serves as the hyperbola's centre of gravity, with the x-axis serving as its foci, on the graph of the equation xy = k.

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Answer:

I hope this is helpful. I had to crop it slightly to insert it.

Answer:  See the graph image attached

Step-by-step explanation:

x   y

0  -3

1   -4

Answer: 370 cubic centimeters

Step-by-step explanation:

They're just boxes stack on top of another. Find volume of both box and add together.

Use the cuboid formula to find volume of each box:

[tex]Volume = length *width * height[/tex]

Bottom box volume: [tex]10cm*5cm*5cm=250^3cm[/tex]

Top box volume: [tex]8cm*5cm*3cm=120^3cm[/tex]

Total volume = [tex]250^3cm+120^3cm=370^3cm[/tex]

The value of k is 7

Consider the given equations are:

2x+3y=7

(k−1)x+(k+2)y=3k

The general equations

[tex]a_{1} x+b_{1} y =c_{1}[/tex]

[tex]a_{2} x+b_{2} y =c_{2}[/tex]

substituting the values,

[tex]a_{1} = 2, b_{1} y=3,c_{1}=7[/tex]

[tex]a_{2}=(k-1) ,b_{2} =( k+2), c_{2}= 3k[/tex]

An equation can have infinitely many solutions when it should assure some conditions. The system of an equation has infinitely numerous solutions when the lines are coincident, and they have the same y-intercept.

We know, the condition of infinite solutions

[tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]

Therefore,

[tex]\frac{2}{k-1} = \frac{3}{k+2} =\frac{7}{3k}[/tex]

⇒[tex]\frac{2}{k-1} =\frac{3}{k-2}[/tex]

⇒ 2k -4 = 3k-3

⇒ k = 7

Hence, the value of k is 7.

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The complete question is:

Find the value of k, infinitely many solutions

2x+3y=7,(k−1)x+(k+2)y=3k

She must use 187.5 ounces of water and 62.5 ounces of salt solution for her experiment.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

The smallest equivalent fraction of the number is the form that is the simplest. How to find the most basic form: In the numerator and denominator, look for shared factors. Examine the fraction to see if one of the numbers is a prime number.

Say w= the amount of water in oz, then the 60% of the solution is 250 - w

Set up the equation:

Use distributive property first

0.60(250-w) = 0.15 x 250

Isolate to solve for w

150- 0.60w= 37.5

-0.60w= 37.5-150

0.60w= -112.5

w= 187.5 ounces

250-187.5= 62.5 ounces salt solution

Therefore, she must use 187.5 ounces of water and 62.5 ounces of salt solution for her experiment.

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Write down the set of numbers for which you want to find the GCF.

Starting from 1, check if each number in the set is divisible by it. If all the numbers are divisible by it, mark it as a common factor.

Repeat step 2, incrementing the number by 1, until you reach the smallest number in the set.

The largest common factor that you marked in step 2 is the GCF.

This method is based on the idea of checking each number starting from 1 till the smallest number in the set and checking if it is divisible by all numbers in the set. It's a simple method that can be applied to find GCF of any set of numbers.

It's worth noting that this method may not be the most efficient way to find GCF of set of numbers, as it involves checking each number starting from 1 till the smallest number in the set. In cases where the numbers are large, more efficient methods like prime factorization and Euclidean algorithm are preferred.

When you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole.

It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.

The top number in a fraction is referred to as the numerator, while the bottom number is referred to as the denominator.

4/5, for instance, is a fraction.

What happens to the denominator of a fraction when you divide it by a negative number is unimportant because the entire result, or quotient, is the opposite of whatever the original fraction was.

Therefore, when you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

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Answer:

y = 7x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = 7 , then

y = 7x + b ← is the partial equation

to find b substitute (1, 8 ) into the partial equation

8 = 7(1) + b = 7 + b ( subtract 7 from both sides )

1 = b

y = 7x + 1 ← equation of line

Answer:

51.1 (degrees)

Step-by-step explanation:

Use the tangent function to solve for the angle x since we have the opposite and adjacent sides of the angle x:

[tex]tan(x)=\frac{9.3}{7.5} \\x=tan^{-1}(\frac{9.3}{7.5}) \\x=51.11550356[/tex]

Rounding gives:

[tex]x=51.1[/tex]

Answer:

Approximately 2.3 hours after 12 noon

Step-by-step explanation:

We are given
Stock A price at 9AM = $13.45
It increases by $0.08 per hour

Stock B at noon = $14.20
It decreases by $0.14 each hour

We have to find when the two prices will be the same.

Since the base time references are different - 9am for A and noon for B, we have to establish the same time reference

Let's do this by finding the price of stock A at noon, then we have the same time base reference of noon

9am - noon = 3 hours

In 3 hours stock A would have risen by 0.08 x 3 = $0.24

Price of stock A at noon is 13.45 + 0.24 = $13.69

Thereafter stock A continues to increase by the same rate of $0.08 per hour
The equation to model stock A price starting at noon is
13.69 + 0.08x where x is the number of hours elapsed after 12 noon

Stock B price is $14.20 at 12 noon and decreases by $0.14 per hour
Equation to model stock B price after 12 noon is

14.20 - 0.14x where x is the elapsed time after 12 noon

For both prices to be the same after the same x hours, we have
13.69 + 0.08x = 14.20 - 0.14x

Solving for x will tell us how many hours it will take for both stock prices to be the same

Solving
13.69 + 0.08x = 14.20 - 0.14x

So the two stock prices will be the same 2.3 hours after 12 noon or about 2 hours and 18 minutes after 12 noon or roughly around 2:18pm

I got 18 minutes by multiplying 0.3 x 60 = 18