f:x-2x+3 is a mapping defined on the set R of real numbers. Determine the pre-images of (a) 1 (b) -1 (c) 7 (d) -5​

The solution to the inequality is x = 0

The graph of x = 0 is a line that separates the plane into two half-planes

From the question, we have the following parameters that can be used in our computation:

|1/5x + 2| + 4 >= 6

This gives

|1/5x + 2| >= 2

Remove the absolute bracket

2 <= 1/5x + 2 <= 2

So, we have

0 <= 1/5x <= 0

Evaluate

0 <= x <= 0

This means that

x = 0

The graph of x = 0 is a vertical line in the coordinate plane that passes through the origin (0,0) and extends infinitely in both positive and negative directions along the y-axis.

It represents all points that have an x-coordinate of 0.

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Answer:

-1.5 and 1.5

Step-by-step explanation:

Let's call the maximum value of the function "c." The equation for the parabola is now y = x^2 + ax + (b - c).

Using the point (1,1), we can solve for "a" and "b":

1 = 1^2 + a(1) + (b - c)

1 - a + b - c = 1

c - a + b = 0

c = -a + b

And using the fact that the maximum value is -3:

-3 = -a + b

a - b = 3

Combining these two equations:

-3 = -a + b = a - b

-3 = 2a

a = -1.5

Plugging in "a" to either equation:

-3 = -(-1.5) + b

-3 = -1.5 + b

b = -1.5 + 3 = 1.5

So the values of "a" and "b" are -1.5 and 1.5, respectively.

Pls mark brainliest hope this helps :)

Answer:

Right isosceles

Step-by-step explanation:

AB = BC

∠ABC = 90°

An isosceles triangle with a right angle is known as an isosceles right triangle

Answer:

recipe should have 5.76 cups of sugar.

Step-by-step explanation:

To find out how many cups of sugar should be in Molly's apple recipe, you can use the proportion of sugar to apples in the recipe. Since the recipe is 36% sugary, that means for every 100 cups of apples, 36 cups of it is sugar. We can set up the proportion as:

Sugar / Apples = 36 / 100

To find the number of cups of sugar in 16 cups of apples, we can cross-multiply and divide:

Sugar = (36/100) * Apples

Sugar = (36/100) * 16

Sugar = 5.76 cups

So the recipe should have 5.76 cups of sugar.

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The inequality can be written as y < 1/4x + 3.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

The inequality can be written by finding the equation of the line. The two points on the line are ( 0,3) and ( 4,4).

The slope of the line is,

Slope = ( 3 - 4 ) / 9 0 - 4 )

Slope = 1 / 4

The y-intercept of the line will be calculated as:-

y = mx + c

3 = 0 +c

c = 3

The equation of the inequality can be written as:-

y < (1/4)x + 3

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Andrew invested $3520 at 7.5% and $19,480 at 13%.

Let's call the amount invested in the 7.5% bond "A" and the amount invested in the 13% bond "B".

We know that:

A + B = 23,000

0.075A + 0.13B = 2,880

We can use the second equation to solve for one of the variables, then substitute that value back into the first equation to solve for the other. For example:

0.075A + 0.13B = 2,880

0.13B = 2,880 - 0.075A

B = (2880 - 0.075A) / 0.13

Substituting this expression for B back into the first equation:

A + (2880 - 0.075A) / 0.13 = 23,000

0.875A + 2880 / 0.13 = 23,000 * 0.13

0.875A = 23,000 * 0.13 - 2880 / 0.13

0.875A = 3080

A = 3520

So Andrew invested $3520 at 7.5% and $23,000 - $3520 = $19,480 at 13%.

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Answer: [tex]y=10[/tex]

Step-by-step explanation:

Note that [tex]\angle ACB \cong \angle ACD[/tex] because diagonals of a rhombus bisect the angles from which they are drawn.

Now, because [tex]m\angle DEC=90^{\circ}[/tex] since diagonals of a rhombus are perpendicular, it follows that [tex]m\angle CDB+m\angle ABC=90^{\circ}[/tex].

[tex]6y+2y+10=90\\\\8y+10=90\\\\8y=80\\\\y=10[/tex]

Answer:

[tex]\sqrt{27}[/tex]

Step-by-step explanation:

because [tex]\sqrt{27} = 5.19[/tex]

so 5.19<5.34

Answer:

5.34

Step-by-step explanation:

Step 1:

First, we need to find the perfect square that is closest to but less than 27. The closest perfect square is 25 (5^2).

Step 2:

Now we need to divide the number we are trying to find the square root of (27) by the closest perfect square (25). In this case: 27/25 = 1.08

Step 3:

We can now find an approximate value for the square root of 27 by multiplying the closest perfect square (5) by the quotient obtained in step 2 (1.08). So, the approximate value of √27 is 5.40

Step 4:

In order to find a more accurate value of the square root, we can use the long division method.

Step 5:

We set up a long division problem with the dividend being 27 and the divisor being 5.

27 5

2 5

So, the quotient is 5 and the remainder is 2.

Step 6:

Now we bring down the next two digits (0) to get a new dividend of 20.

27 5

20

Step 7:

We divide 20 by 5 and get 4 as the quotient.

Step 8:

The final value of the square root of 27 is 5.4 (5 + 4/10)

Note: The process above is providing the approximate value of square root of 27, while the exact value of the square root of 27 is √27 = √(3^3) = 3.

That's why our answer is 5.34

The length of the longer ladder is 50 ft. Therefore, the answer is D.

Two ladders are leaning against the wall as shown below. The length of the longer ladder can be found as follows:

The triangles formed are right angle triangle. The triangles are similar to each other.

Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.

Therefore, using proportion,

15 / x = 3 / 10

cross multiply

150 = 3x

divide both sides by 3

x = 150 / 3

x = 50

Therefore,

length of the ladder = 50 ft

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The negative integer -4°F  represents the change in temperature for every thousand feet a person climbs.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

here,
As a person climbs a mountain, the temperature drops 4°F for every thousand feet climbed.

Change in temperature  = -4°F

Thus, the negative integer -4°F  represents the change in temperature for every thousand feet a person climbs.

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The solution to the expression is -41000

From the question, we have the following parameters that can be used in our computation:

calculate -1000 * 41 in long division​

The above expression is a product expression

This means that it cannot be evaluated using long division

When the expression is evaluated. we have

-1000 * 41 = -41000

Hence, the solution is -41000

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The initial speed of the uniform solid ball rolling smoothly along a floor inclined at 32° is 5.3 m/s.

We can use the conservation of mechanical energy to solve for the initial speed of the ball. The initial mechanical energy of the ball is equal to the final mechanical energy of the ball when it reaches the top of the ramp.

Initial mechanical energy = Final mechanical energy

1/2 mv^2 = mgh + 1/2 mv'^2

where

m = mass of the ball

v = initial speed

g = acceleration due to gravity (9.8 m/s^2)

h = height of the ramp (2.70sin(32°) = 1.43  m)

v' = final speed = 0 m/s

Solving for the initial speed, we get:

v = √(2gh) = √(2 * 9.8 * 1.43) = √(28.04) = 5.3 m/s.

So, the initial speed of the ball is 5.3 m/s.

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The area of the circle is  36π square meters. Option C is the correct option.

What is the area of an object?

Area is the total amount of space occupied by a flat (2-D) surface or an object's shape. On a piece of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

Given that the diameter of a circle is 12 meters.

The radius of a circle is half of its diameter.

The radius of the circle is 12/2 = 6 meters.

The area of a circle is πr², where r is the radius of the circle.

The area of the circle is π6² = 36π

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Answer:

The number of carrot sticks and apple slices is 16 + 48 = 64.

The percentage of carrot sticks is (16 / 64) * 100 = 25%.

Answer:

37.5% is the answer to this question

Answer:

37.5%

Step-by-step explanation:

General Explanation:

(1m = 100cm

2m = 200cm)

= (75cm ÷ 2m) × 100

= (75 ÷ 200 ) × 100

= 75 ÷ 2%

= 37.5%

_________________________________

Easier Explanation (Decimal to Percentage):

(1m = 100cm

2m = 200cm)

= 75cm ÷ 200cm

= 75 ÷ 200

= 0.375 (3/8 as a fraction)

= 37.5%

The inequalities that represent the constraints in this situation are r+c≥80 and 1.45R +0.75c≤200 respectively

The amount with victor = $200

Let the number of roses purchased by Victor be R,

Also, Rose cost $1.45 each

Therefore cost of rose = 1.45R

A;so, let the number of carby Victor be C at a cost of $0.65 each nation purchased by victor be $0.65 each

Therefore, cost of carnation = $0.65c

1) The inequality to represent the constraint that every person takes home at least one rose is r+c≥80 and

2) the inequality to represent the cost constraint is 1.45R + 0.65≤200

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Answer: The candle will take 16.5 cm of wax to burn out.

Step-by-step explanation:

The candle will take 22 - 5.5 = 16.5 cm of wax to burn out.

At the same rate, if the candle burned for 11 minutes and the remaining length was 5.5 cm, it will take 11 * (22/5.5) = 44 minutes to burn out.

The required coordinate of point H is given as (d+c, b), as per the given condition.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

Here,
As point H is collinear with point G so the y coordinate of the Point H is equal to y coordinate point G,
So
Y coordinate of point H = b

Now,
x coordinate of point H is given as,
Line GH is parallel with LINE FE
So, x-coordinate = FE = d-(-c) = d+ c

Thus, the required coordinate of point H is given as (d+c, b), as per the given condition.

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The statement "s1 ⊆ s2" means that every element in set s1 is also an element in set s2. In other words, set s1 is a subset of set s2.

To prove this, we can use a logical contrapositive argument. Assume that s2 is not a subset of s1, meaning there exists at least one element in set s2 that is not in set s1. Then, this means that s1 is not a subset of s2, which contradicts our original assumption that s1 ⊆ s2. Thus, we conclude that if s1 ⊆ s2, then s2 ⊆ s1.

Hence, if set s1 is a subset of set s2, then every element in set s1 is also in set s2. As a result, set s2 is also a subset of set s1.

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Addison's error is that the second equation should be 0.25x + 0.10y = 20.70, not 20.75.

An equation is a mathematical statement consisting of an expression and an equal sign. It is used to express a relationship between two or more variables, and is often used to solve mathematical problems. An equation can be written in a variety of forms, such as a single line, two lines, or a system of equations. An equation typically contains two elements: an expression and an equality sign. An expression is a combination of terms, such as numbers, variables, and operations.

Addison's error is that the second equation should be 0.25x + 0.10y = 20.70, not 20.75. This is because the total value of the quarters and dimes is $20.70, not $20.75. The second equation should also state that y is equal to x plus 10, not just x.

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There are total 35 students in the class.

Given that,

Vikas ranks 9th in the class,

Assume that there are 'n' number of students in the class  

Therefore,

There are 8 students who have scored better than him.

So, The total number of students with a rank better or equal to Vikas,

= 8 + 1 (Vikas himself)

= 9.

Now, his friend got the 35th rank which is the last rank

This means that there are a total of 35 students in the class.

Also, also given that,

Vikas's rank from the last is 27th,

This means that there are 26 students who have scored lower than Vikas.

So, the total number of students with a rank worse or equal to Vikas,

= 26 + 1 (Vikas himself)

 = 27.

Therefore, The total number of students in the class = 35.

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Answer:

12 and -6

-4 and 10

Step-by-step explanation:

The solution to the given system of inequalities is x belongs to (-1/3, 7).

The system of two inequalities represents two lines in a 2D plane and the solution is the common area between the two lines that satisfies both inequalities. Here's one way to solve this system:

Solve each inequality for x to get the equation of a line:

m<2: 4x - 26 < 2 -> 4x < 28 -> x < 7

m<3: 3x + 4 < 3 -> 3x < -1 -> x < -1/3

Plot both lines on a coordinate plane and shade the region where both inequalities are satisfied.

The solution is the set of all points that satisfy both inequalities and lies in the shaded region, which is x < 7 and x < -1/3. The solution is therefore x < min(7, -1/3) = -1/3 < x < 7.

So, the solution to the system of inequalities is x belongs to (-1/3, 7).

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By solving linear equations, we will see that Shanice and Brianna will have the same amount after 6 days.

We know that Shanice has $1,750 saved in her checking account for vacation. Each day, she withdraws $125 to pay for meals & entertainment expenses. Then the amount in her account after x days is modeled by the linear equation:

S = 1,750 - 125*x

And Brianna has $550 and adds $75 each day, so she as:

B = 550 + 75*x

Both of them will have the same amount when:

1,750 - 125*x = 550 + 75*x

1,750 - 550 = 75*x + 125*x

1200 = 200*x

1200/200 = x

6 = x

They will have the same amount after 6 days.

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The width of the wheel's face, measured from bead seat to bead seat, is known as the wheel diameter or rim diameter.The wheel's circumference is 81.64 inches as a result.

The width of the wheel's face, measured from bead seat to bead seat, is known as the wheel diameter or rim diameter.Considering that's where the tire and wheel meet, it's measured in this manner.

The diameter is 16 inches in our case.The equation for diameter can be solved by dividing both sides by since we already know that C (circumference) = x D (diameter). We discover that D = C/ after doing so.

The wheel's circumference is 81.64 inches.

A circle's circumference is determined by:

C is a circle's circumference.

A circle's diameter is given by d.

As stated in the sentence:

Bike wheels measure 26 inches in diameter.d equals 26 inches.

The wheel's circumference must be determined.

value used = 3.14

The wheel's circumference is 3.14 x 26 or 81.64 inches.

The wheel's circumference is 81.64 inches as a result.

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Therefore , the solution of the given problem of equation comes out to be x value is 79/19 and y = 18/19.

The equal symbol (=) is used in mathematical equations to denote equality between two propositions. Mathematical equations, which seem to be expressions of reality, are used to demonstrate how different numerical elements can be compared. For instance, the equal sign splits the integer 12 or the equation y + 6 = 12 into 2 different halves. One can compute how many characters each edge of a symbol has. Contradictory meanings are common in symbols.

Here,

Given :

=> x = 7 -3y

and

=> 4x -7y = 10

=> 4(7-3y) - 7y = 10

=> 28 -12y - 7y = 10

=> 28 - 19y = 10

=> 18 = 19y

=> y = 18/19

=> x = 7 - 3(18/19)

=> x =  133 - 54 / 19

=> x = 79 /19

Therefore , the solution of the given problem of equation comes out to be x value is 79/19 and y = 18/19.

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The domain is all integers, and the range is all integers that are multiples of 3.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=-3x

We need to find the domain and range.

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in

Domain is (-∞, -∞) and range is (-∞, -∞)

Hence, the domain is all integers, and the range is all integers that are multiples of 3.

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Answer:

540 minutes or 9 hours :)

Step-by-step explanation:

What I did is I multiplied 6 hours by 60 minutes. Or for the hours skip that step.

6x60=360       or     6/300=0.02

360/300=1.2    or     0.02x450=9

1.2 x450= 540  or         9 hours

540 minutes

540 minutes or 9 hours :D

Goodluck <3

Hope this helps!

A conditional statement is a logical statement that has two parts, a hypothesis [tex]p[/tex] and a conclusion [tex]q[/tex].

When a conditional independence statement is written in if-then form, the "if" part contains the hypothesis and the "then" part contains the conclusion.

The conditional probability of A given B is represented by [tex]P(\frac{A}{B} )[/tex] . The variables A and B are said to be independent if [tex]P(A) = P(\frac{A}{B} )[/tex] (or alternatively if [tex]P(A,B) = P(A) P(B)[/tex] because of the formula for conditional probability ).

In a situation in which we can compute all three probabilities [tex]P(A) , P(B)[/tex] and P(A∩B), it is used to check whether or not the events A and B are independent: If P(A∩B) = [tex]P(A)P(B)[/tex], then A and B are independent.

Conditional independence depends on the nature of the third event. If you roll two dice, one may assume that the two dice behave independently of each other. Looking at the results of one dice will not tell you about the result of the second dice. (That is, the two dice are independent.)

Therefore,

A conditional statement is a logical statement that has two parts, a hypothesis [tex]p[/tex] and a conclusion [tex]q[/tex].

When a conditional independence statement is written in if-then form, the "if" part contains the hypothesis and the "then" part contains the conclusion.

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Answer:

62 square units

Step-by-step explanation:

Area = 2(lb+lh+bh)

= 2(3×2+3×5+2×5)

= 62

The solid represented by the net is a rectangular prism.

And, The surface area of the solid is , 62.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The solid represented by the net.

Here, We know that;

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases.

Hence, The solid represented by the net is a rectangular prism.

Here, The length of the rectangular prism (l) = 5

The width of the rectangular prism (w) = 2

The height of the rectangular prism (h) = 3

We know that;

The surface area of the rectangular prism = 2 (wl + hl + hw)

Substitute all the values, we get;

The surface area of the rectangular prism = 2 (2×5 + 3×5 + 3×2)

The surface area of the rectangular prism = 2 (10 + 15 + 6)

The surface area of the rectangular prism = 2 × 31

The surface area of the rectangular prism = 62

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