Last week, Russell bought 11 books and 12 movies for a total of

$245. Today, Russell bought 10 books and 26 movies for a total of $434. Assuming neither item has changed in price, what is the cost of a book in dollars?

Answer:

B)  (-∞, 2)

Step-by-step explanation:

Given functions:

[tex]f(x)=x-3[/tex]

[tex]g(x)=-0.5x[/tex]

To find the interval for which (f - g)(x) is negative, set (f - g)(x) less than zero and solve for x:

[tex]\begin{aligned}(f-g)(x)& < 0\\f(x)-g(x)& < 0\\(x-3)-(-0.5x)& < 0\\x-3+0.5x& < 0\\1.5x-3& < 0\\1.5x& < 3\\x& < 2\end{aligned}[/tex]

Therefore, the interval for which the composite function (f - g)(x) is negative is:

a = 14, b = 3.5

XZ = XY , then

2a + 3b = 11b ( subtract 3b from both sides )

2a = 8b ( divide both sides by 2 )

a = 4b

The perimeter is 91 , so

11b +2a + 3b + a = 91

14b + 3a = 91 ← substitute a = 4b

14b + 3(4b) = 91

14b + 12b = 91

26b = 91 ( divide both sides by 26 )

b = 3.5

and a = 4b = 4 × 3.5 = 14

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After it has been dilated with a scale factor of 2  the side lengths of AX'Y'Z is: a = 14, b = 3.5

XZ = XY , then

2a + 3b = 11b ( subtract 3b from both sides )

2a = 8b ( divide both sides by 2 )

a = 4b

The perimeter is 91 , so

11b +2a + 3b + a = 91

14b + 3a = 91 ← substitute a = 4b

14b + 3(4b) = 91

14b + 12b = 91

26b = 91 ( divide both sides by 26 )

b = 3.5

and a = 4b = 4 × 3.5 = 14

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The slope of the given equation is -3/2.

The equation of a line in the form 3x + 2y = 8 is not in the standard form of a linear equation, also known as slope-intercept form. In order to find the slope of the line, we need to express the equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

To do this, we can start by isolating y on one side of the equation. We can subtract 8 from both sides, resulting in 3x + 2y -8 = 0.

Next, we can divide both sides by 2, which gives us (3/2)x + y - 4 = 0. This is the equation in the slope-intercept form.

The slope of the line is represented by the coefficient of x, which in this case is (-3/2). It tells us that for every 1 unit increase in x, the value of y will decrease by 3/2 units.

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Answer:

75+(4²- 6²) +12= 67

15³- 16 × 2+28=3371

By using the area of the square formula, it can be concluded that the side of the square shed is 6 meters.

The area of a square or a rectangle can be defined as the number of square units needed to fill it.  

Area of a Square = side × side = side²

Area of a rectangle = width x length

Area of the square = area of the rectangle

Rectangle width = 3 meter

Rectangle length = 12 meter

To find the side of the square shed, we can do the following:

Area of the square = Area of the rectangle

                      side² = width x length

                               = 3 x 12

                               = 36

                       side = √36

                               = 6

Thus the side of the square shed is 6 meters.

Two storage sheds are to have the same area. One is square and one is rectangular. The rectangular shed is 3 meters wide and 12 meters long. How large is one side of the square shed in meters?

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Answer:

7/9=b/218

Step-by-step explanation:

The ordered pair which describes the location of M''M" is (4, -4).

In Geometry, a reflection over the y-axis is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of the image coordinates include the following:

(x, y)                               →              (-x, y)

Coordinate M = (-4, 4)   →  Coordinate M' = (-(-4), 4) = (4, 4).

Next, we would apply a reflection over the x-axis to the above coordinates as follows:

(x, y)                               →              (x, -y)

Coordinate M' = (4, 4)   →  Coordinate M" = (4, -(4)) = (4, -4).

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Answer:

= -13/6 OR -2.1667

Step-by-step explanation:

1 1/2 - 3 2/3

=3/2 - 11/3

LCM of 2 and 3 is 6

3/2 - 11/3

= 9 - 22

6

= - 13/6 OR -2.5

Answer: is it  

-2 1/6

Step-by-step explanation:

Rewriting our equation with parts separated

=1+12−3−23

Solving the whole number parts

1−3=−2

Solving the fraction parts

12−23=?

Find the LCD of 1/2 and 2/3 and rewrite to solve with the equivalent fractions.

LCD = 6

36−46=−16

Combining the whole and fraction parts

−2−16=−216

Simple bro

The value of angle x is 45°. Thus, option B is correct.

A corner is an angle if it forms a projecting part or a partially enclosed space. An angle is a figure made up of two lines that extend from the same point. a measurement of an angle or the amount of turning required to align or make parallel two lines or planes.

step1:

o is center

JK is a tangent

so <OKJ =90°

<OKM=90°-30°=60°

OM=OK=><OMK=60°

step2:

because LO=LO, LM=LK, ON=OK

So Triangle OLM ≅ Triangle OLK => <LOM=<LOK

so <LOM=150° => <LMO =15°

so  60° +15° =30°+x°=>x= 45

so the answer is B. 45°

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Answer:

The value of x is -19.

Step-by-step explanation:

Given that ZA and B are vertical angles and m/A = (2x +20)°, and m/B = (3x + 1)°, we know that ZA and B are congruent, meaning they have the same measure. We can set the two given equations equal to each other: m/A = (2x + 20)° = m/B = (3x + 1)°. Then, by isolating x on one side of the equation, we subtract 20 from both sides of the equation, then subtract 2x from both sides of the equation, which gives us x = -19, thus the value of x is -19.

Answer:

x = 19

Step-by-step explanation:

since vertical angles are equal we can set the value of angles A and B equal and solve for 'x'

2x + 20 = 3x + 1

20 = x + 1

19 = x

To show that one value is greater than another, use the "greater than" symbol (>). It can be used to express a comparison between two values in mathematical operations, programming, and other forms of notation.

   For instance, the "greater than" symbol can be used to compare integers in mathematical operations. For instance, you would write "x > y" to indicate that x is greater than y. This can alternatively be understood as "x exceeds y."

  Other comparison symbols, such as "less than," "greater than," and "less than or equal to," can be used in addition to the "greater than" symbol. These symbols can be used to describe many forms of value comparisons in programming and mathematical processes.

  The word "greater than" is represented by the symbol ">," therefore to write "greater than 4" you would write ">4".

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The required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

here,
The Sequences 8, 11, 14,...

first term a = 8
common difference = 11 - 8 = 3

Now,
The explicit formula is given as,
nth terms = a + (n - 1)d
nth term = 8 + (n - 1)3

Thus, the required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

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Answer:

so plot a 4 and the go up one over right one that way you have the linear equation graphed

A:Expression 3: 4(4x + 6) = 16x + 24 feet, B: No, he is incorrect

C: The perimeter of Carla’s room is 16x + 24, which is the same as Sam’s room.

An expression is a combination of numbers, symbols, and variables that represents a certain value otherwise set of values.

For example, 2x + 5 is an expression that represents any value that can be obtained by substituting any number for the variable x.

In this question

Part A:

The perimeter of Sam's bedroom can be expressed using the following equations:

1. P = 2(x+2) + 2(y+2)

2. P = 2x + 4 + 2y + 4

3. P = 2x + 2y + 8

Part B:

No, Sam is incorrect. The correct expression for the area of his bedroom is A = (x+2)(y+2). He is off by 8 square feet.

Part C:

The perimeter of Carla's room is 4x + 12, which is 4 more than the perimeter of Sam's room.

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Answer:

Area = 28

Area of cutout = 1/2 * 2 * 4 = 4

Area of entire rectangle without cutout = 32

(Also 4 * 4 + 2 * 4 + 1 * 4 = 28)

Answer:

The fractions which are equivalent to 1/2 are 2/4, 3/6, 4/8, 6/12 etc.

But there are more fractions that are equivalent to 1/2 such as 7/14, 8/16, 9/18, 10/20, 11/22, 12/24, 13/26, 14/28, 15/30, 16/32, 17/34, 18/36, 19/38, 20/40, 21/42, 22/44, 23/46, 24/48, 25/50, 26/52, 27/54, 28/56, 29/58, 30/60 and so on.

I might not get it but I tried :)

1/6 of the whole garden is planted in cucumber.

What is cucumber ?

Cucumber is a type of vegetable that belongs to the cucurbit family, which also includes melons, squash and gourds. They are typically long, cylindrical in shape, and have a green skin that is typically eaten raw.

The proportion of the garden planted in cucumber is 1/3 of the vegetable part of the garden. To find out what proportion of the entire garden is planted in cucumber, we can use this proportion and multiply it by the proportion of the garden that is planted in vegetables.

Half of the garden is planted in vegetables, so the proportion of the garden planted in vegetables is 1/2.

1/3 of the vegetable part of the garden is planted in cucumber, so the proportion of the garden planted in cucumber is ,

(1/2) x (1/3) = 1/6

So, 1/6 of the whole garden is planted in cucumber.

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Half of the garden is planted in vegetables, so the proportion of the garden planted in vegetables is 1/2.

1/3 of the vegetable part of the garden is planted in cucumber, so the proportion of the garden planted in cucumber is ,

(1/2) x (1/3) = 1/6

1/6 of the whole garden is planted in cucumber

The solution to the equation 7x - 9 = 16 is x = 25/7. This can be achieved by using the addition property of equality and simplifying the equation.

The equation 7x - 9 = 16 can be solved by using The equation's solution can be changed by adding the same amount to either side of the equation, according to the addition property.

To both sides of the equation, add 9.

7x - 9 + 9 = 16 + 9

Simplify the equation.

7x = 25

Divide both sides of the equation by 7.

7x/7 = 25/7

Simplify the equation.

x = 25/7

Therefore, the solution to the equation 7x - 9 = 16 is x = 25/7.

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Answer: 2/3

Step-by-step explanation:

To find the probability of A or B, we can use the formula: P(A or B) = P(A) + P(B) - P(A ∩ B)

Plugging in the given values:

P(A or B) = 1/2 + 1/3 - 1/4

To solve this, we must find a common denominator in order to add the fractions:

P(A or B) = 3/6 + 2/6 - 1/6

Simplifying:

P(A or B) = 4/6 = 2/3

So the value of P(A or B) is 2/3

Answer:

ff(x)=9x-48

Step-by-step explanation:

f(x)=3x-12

ff(x)=f(3x-12)

=3(3x-12)-12

= 9x-36-12

= 9x-48

The total amount Rita spend on the mall for 2 items is $77.12.

Given that,

The expression of amount spend on the first store = 13.06b + 29

The amount spend on the second store =  22

Total amount Rita spends=  13.06b + 29 + 22

= 13.06b + 51

Then to estimate the amount Rita spent if she had bought 2 items.

Now, we have the value of b = 2.

So by substituting,

= 13.06 x 2 + 51

= 77.12

Therefore the total amount Rita spend on the mall is $77.12.

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Answer:

V = 10 km/h

Step-by-step explanation:

Formula for speed --> V = X/t being X  equal to space and t the time wasted.

X = 30 km

t = 3 hours

then,

V = 30/3

V = 10 km/h

The statement about the relationship of the data in the table is indicated in the option;

A proportional relationship is one in which one variable (the output variable) is a constant multiple of the input variable, such that a point on the graph of ordered pairs of variable is the point (0, 0), which is the origin.

The points on the graph are; (1, 3.5), (2, 4.5), (3, 5,5)

The slope of the graph is therefore; (4.5 - 3.5)/(2 - 1) = 1

The equation in point-slope form is therefore; y - 3.5 = x - 1

y = x - 1 + 3.5 = x + 2.5

y = x + 2.5

The equation is a linear relationship. The equation is in the form; y = m·x + c, with the slope m = 1 and a y-intercept, c = 2.5

The y-intercept is 2,5, therefore, the graph does not pass through the origin.

The relationship of the line passing through the points, is a linear relationship. The line passing through the points does not pass through the origin, therefore the relationship is not a proportional relationship

The correct option is therefore; It cannot be a proportional because the straight line through the points does not go through the origin.

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Two term polynomial called as a binomial .

An algebraic equation that has more than two terms, particularly the accumulation of numerous phrases that each include a different power of the same variables known as polynomial.

But when we reduce more than two terms into only two terms we get binomial.

A formula in algebra that expresses the difference or sum of two terms is known as binomial.

For example:

[tex]x^{4} + x y^{2} +x^{2} + x[/tex] is polynomial because it has more than two separate terms which are [tex]x^{4}[/tex] , [tex]x y^{2}[/tex] , [tex]x^{2}[/tex] and [tex]x[/tex]

[tex]x^{2} + y^{2}[/tex] is binomial because it has only two separate terms which are [tex]x^{2}[/tex] and [tex]y^{2}[/tex].

[tex]4x+6y[/tex] is also binomial because it has also only two separate terms which are [tex]4x[/tex] and [tex]6y[/tex]

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Answer:

T is the cost

Step-by-step explanation:

by looking at the question you can see the answer.

Answer:

Answers in the attached photo.

Step-by-step explanation:

Steps are in the attached photo, do note this question is testing on the knowledge of Pythagoras' Theorem.

Yes, it is possible for a negative number to be an exponential function.

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Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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