Write an algebraic expression to represent each statement.
the number, b, divided by thirty-six

The system of linear inequalities as shown in the given graph is:

y < 1/3x + 2

y ≤ -2x + 2

Depending on the inequality sign, we can express the linear inequality in slope-intercept form as, y = mx + b. The sign "=" would be placed by the appropriate inequality sign, the m represents the slope and b represents the y-intercept of the line.

One of the lines is dashed, and the shaded part is beneath it, therefore, the inequality sign for the dashed line would be "<".

For the solid line, the inequality sign to use would be "≤" because the shaded part is also beneath it.

Both lines intercept the y-axis at y = 2, therefore, the y-intercept (b) for both lines would be: b = 2.

Slope of the dashed line (m) = rise/run = 1/3

Slope of the solid line (m) = rise/run = -2/1 = -2

The inequality for the dashed line would be written by substituting m = 1/3 and b = 2 into y < mx + b:

y < 1/3x + 2

The inequality for the solid line would be written by substituting m = -2 and b = 2 into y ≤ mx + b:

y ≤ -2x + 2

The system would be:

y < 1/3x + 2

y ≤ -2x + 2

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The inequality is given below

What is an inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two digits on the number line were made. Different types of inequalities are represented by a variety of different notations.

The inequality the represents the given problem is 138 + x ≤ 230.]

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1) The roots of the equation are x = -7/3 and 5/2

And the correct options are option (A) and option (B)

2) Amber needs to draw the straight line y = 4x. And the point of intersection of both the graphs (y = 3x² and y = 4x)would give the solutions to given equation i.e., x = 1.33 and x = 0

Consider the first question,

We need to find the roots of given equation (3x + 7)(2x - 5) = 0

From above equation we can say that either 3x + 7 = 0 or 2x - 5 = 0

If 3x + 7 = 0

3x = -7

x = -7/3

And is 2x - 5 =0

2x = 5

x = 5/2

So, the roots of the equation are x = -7/3 and 5/2

Hence, the correct options are option (A) -7/3 and option (B) 5/2

Consider 2nd question,

Amber is trying to solve 3x² - 4x = 0 using graphical method.

She drew the graph of y = 3x² which is parabolic in nature.

we need to draw the straight line to solve the given equation.

If we draw the line y = 4x and then subtract it from y = 3x², then we get the original equation 3x² - 4x = 0

So, we need to draw the straight line y = 4x

Therefore, Amber needs to draw the line y = 4x the point of intersection of both the graphs would be the solutions to given equation.

i.e., x = 1.33 and x = 0

The graph is as shown below.

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To translate figure ABCD into A'B'C'D' rotate 90° about D and then reflect across AB.

When a figure is relocated from one place to another without changing its size, shape, or orientation, a transition known as translation takes place.

If we know which way the figure is moving and how much, we can draw the translation in the coordinate plane.

Every point of the object must be translated by the same amount and in the same direction.

To translate figure ABCD into A'B'C'D' rotate 90° about D and then reflect across AB.

option (d)

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Chee will have $100 after 6 weeks by saving $ 5 per week , it is solved by forming the equation:

70 + 5w

Steps for converting word problems to equations

Here in the question,

So we already know chee has $70. This is a constant for us.

We also know she saves $5 per week with. In other words, her total cash after w weeks is:

70 + 5w

This is how we express ourselves. The 70 represents $70 the money she already has, and the 5w represents how much she will have saved after w weeks.

Substitute 6 for w to find chee's total financial situation after 6 weeks.

= 70 + 5(6)

∴Multiply:

= 70 + 30

then add:

$100

So, Chee would have $100 after 6 weeks.

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The ratio of pints in case of red to green is 4:1 and that of sidelengths is 2:1 and in case of blue to green the ratio of pint is 6:1 and that of sidelengths is 3:1.

The Total surface area of a cuboid (TSA) is equal to the sum of the areas of it’s 6 rectangular faces, which is given by:

Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units

The above formula gives the total surface area of a cuboid having all six faces.

Since all the pedestial are in the form of cuboid and we have to paint its all  6 faces and we need 0.5 pint to paint the red pedestal

So, given the side lengths of green pedestal are half that of red one.

So,

TSA of red pedestal= 2 (lw + wh + lh)

So,

TSA of green pedestal

[tex]2 (\frac{l}{2} \frac{w}{2} +\frac{w}{2}\frac{h}{2}+\frac{l}{2}\frac{h}{2})\\2 (\frac{lw}{4} +\frac{wh}{4}+\frac{lh}{4})\\\frac{2(lw + wh + lh)}{4}[/tex]

TSA of green pedestal = TSA of red pedestal/4

So, pint needed for green = 0.25 * pint for red = 0.125 pint

Similarly, for Blue pedestal it is given that the sidelengths are thrice that of green pedestal .

TSA of blue pedestal = 1.5(TSA of red pedestal)

So, pint needed for blue pedestal = 1.5 * pint for red = 0.75

Ratio of pints need red to green = 0.5:0.125 = 4 :1

Ratio of sidelength of red to green =  2 :1

Ratio of pints need blue to green = 0.75:0.125 = 6:1

Ratio of sidelength of blue to green =  3 :1

The ratio of pint amount is twice the ratio of sidelengths.

Therefore, ratio of pints in case of red to green is 4:1 and that of sidelengths is 2:1 and in case of blue to green the ratio of pint is 6:1 and that of sidelengths is 3:1.

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The above graph represents Baile's Distance-Time Graph. The data on the graph came from her trip which is explained below.

A distance-time graph can be used to show the distance traveled by a straight-line moving object.

In a distance-time graph, the gradient of the line matches the item's speed. The gradient increases as the thing go faster (and the steeper the line).

So Bailey took off from her home on a power bike at the rate of 7.5 miles per hour. After 4 hours, she got to the bank to carry out an important transaction.

At the bank, she ended up spending two hours. Feeling frustrated for having wasted a lot of time at the bank, she took off to the Baseball game at a whopping 30 miles/hour.

As soon as she got to the game, she recalled that she forgot her ticket and turn back immediately traveling back home at the rate of 15 miles per hour.

Unfortunately, she decided to watch the rematch of the game online

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Answer:

10.48 miles ran in one hour .

Answer:

[tex]\frac{1.08}{0.027}=40[/tex]

Step-by-step explanation:

Multiply the Numerator and Denominator by 1000

[tex]\frac{1080}{27}[/tex]

Write the Problem in Long division format

[tex]\begin{matrix}27\overline{|\smallspace1080}\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

Divide 108 by 27 to get 4

[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 27\overline{|\smallspace1080}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace1\emptyspace0\emptyspace8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

Divide 0 by 27 to get 0

[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\emptyspace4\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ 27\overline{|\smallspace1080}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace1\emptyspace0\emptyspace8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

The answer is 40.

The first five terms of the sequence are 1, 1, 2, 3, 5.

An arithmetic progression is sequence of numbers in which the difference between the consecutive terms is constant.  

[tex]a_{1} = 1 = a_{2}[/tex]              ( first two terms given)

[tex]a_{n} = a_{n-1} +a_{n-2}[/tex]     ( given sequence formula)

[tex]a_{3} = a_{2}+a_{1}[/tex]            

= 1+1

= 2                           ( third term)

[tex]a_{4} = a_{3}+a_{2}[/tex]

= 2 + 1

= 3                           (fourth term)

[tex]a_{5} =a_{4} +a_{3}[/tex]

= 3 + 2

= 5                            (fifth term)

Therefore, we conclude that  the first 5 terms for the sequence

[tex]a_{n} = a_{n-1} +a_{n-2}[/tex] are 1, 1, 2, 3 and 5.

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Answer:57/100

Step-by-step explanation:

You just take 57 and add it to 100

Answer:

Step-by-step explanation:

the distance between two points is 3.5 cm

The length of the line segment bridging two locations in a plane is known as the distance between them. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to determine the separation between any two locations on an x-y plane or coordinate plane.

(1,-2) (1,1.5)

distance between two points is

= [tex]\sqrt{(1-1)^{2} + (1.5+2)^{2}[/tex]

= 3.5 cm

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Answer:   A)   (f + g) (x)

Step-by-step explanation:  Use substitution  (f + g) (x) = f (x) + g (x)  

Transform the expression   (f + g) (x) =  x+3/x+2 + x+1/x-1  

Simplify   (x-1) *(x+3) + (x + 2) * (x + 1)/(x +2) *(x -1)

Remove the opposites and calculate   x^2 +3x - x - 3 + x^2 + x + 2x + 2 /

x^2 - x + 2x -2  

Solution     (f + g) (x) = 2x^2 + 5x -1 / x^2 + x - 2

Exponents are the powers that are added to numerals. Exponents are a different approach to express multiplication, which involves multiplying the same integer again. You can find out how many times your number has been multiplied by itself using the exponent. This shows how it's connected to other maths areas.

The number of times a quantity is multiplied by itself can be used to define an exponent. For instance, the result of multiplying 2 by itself three times is 2 2 2 = 2³

Exponents, which are superscript numbers, tell you how many times to multiply a number by itself. Understanding scientific scales like the pH scale or the Richter scale, utilizing scientific notation to represent very large or very small numbers, and taking measurements are some examples of real-world applications.

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Answer:

[tex]{ \tt{f(x) = - 3x + 8}} \\ \\ { \tt{f( - 4) = - 3( - 4) + 8}} \\ \\ { \tt{f( - 4) = 12 + 8}} \\ \\ { \tt{f( - 4) = 20}}[/tex]

For the function f(x) = -3x + 8, f(-4) is 20.

Given,  f(x) = -3x + 8 and f(-4)

Put the value -4, wherever x is present,

f(x) = -3x + 8

f(-4) = (-3 × -4) + 8

f(-4) = 12 + 8

f(-4) = 20

∴ The value of f(-4) is 20 for function f(x) = -3x + 8

This function connects an input to an output. "f(x) = ..." is the classic way to write a function. We will see different ways of thinking about functions, but there are always three main parts: input, relation, and output.

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Answer:

712.4

Step-by-step explanation:

X + (X × P%) = Y

X(1 + P%) = Y

Solving our equation for Y

Y = X(1 + P%)

Y = 260(1 + 174%)

Converting percent to decimal:

p = 174%/100 = 1.74

Y = 260(1 + 1.74)

Y = 260(2.74)

Y = 712.4

The 174% added was 452.4

260 × 174% = 452.4

the answer is 712.4 I believe

The number of the smaller squares which would be shaded to represent 0.75% as given in the task content is; 75.

The number of squares to correctly represent 245% on the grid is; 245.

It follows from the task content that; To represent the percent, Don uses a 10 × 10 grid and divides one of the squares in the grid into 100 smaller squares.

Since each Square in the 10 × 10 grid represents 1%, it follows that on division of one of the squares in the grid into 100 smaller squares;

The percentage, 0.75% can be represented by shading 75 smaller squares.

Also, the number of squares to be shaded on 10 × 10 grids to represent 245% according to the task content is; 245. This follows from the fact that, all 100 squares on the on 10 × 10 grids represent 100%.

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The graph is a linear function on a coordinate plane that passes through (-5, 4), (0, 2), and (5, 0) and the solution is below the graph. The correct option is D

From the question, we are to determine the graph that best models the given inequality

The given inequality is y ≤ -2/5x + 2

First, we will graph the line of y = -2/5x + 2 by determining the x-intercepts and y-intercepts

Determining the x-intercepts

y = -2/5x + 2

Set y = 0

0 = -2/5x + 2

2/5x = 2

2x = 10

x = 10/2

x = 5

(5, 0)

The line passes through the points (5, 0)

Determining the y-intercepts

y = -2/5x + 2

Set x = 0

y = -2/5(0) + 2

y = 2

(0, 2)

The line passes through the point (0, 2)

Using the x-intercepts and y-intercepts, the graph of the line is shown below

Since the inequality sign is less than or equal to, ≤, the line is a solid line and the solution is below the graph

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The quadratic function that best fit the given data is y = 2x² - 5/2x - 8.

In algebra, quadratic function is defined as a function in the second degree or power. It can be expressed as y = f(x) = ax² + b x + c, where a, b, and c are constants.

Using only three points from the given data, we can determine the quadratic equation that fits the data.

Let P1 = (-2 , 5)

P2 = (0 , -8)

P3 = (2 , -5)

Substitute the points in the expression f(x) = y = ax² + b x + c.

5 = a(-2)² + b(-2) + c     ⇒     5 = 4a - 2b + c     (equation 1)

-8 = a(0)² + b(0) + c     ⇒     -8 = c     (equation 2)

-5 = a(2)² + b(2) + c     ⇒     -5 = 4a + 2b + c     (equation 3)

Substitute equation 2 in equation 1 and 3.

5 = 4a - 2b + -8     ⇒     13 = 4a - 2b     (equation 4)

-5 = 4a + 2b + -8     ⇒     3 = 4a + 2b     (equation 5)

13 = 4a - 2b     (equation 4)

-(3 = 4a + 2b)    (equation 5)

10 =       -4b

b = -5/2

Substitute the value of b in equation 4.

13 = 4a - 2(-5/2)

4a = 13 - 5

a = 2

If a = 2, b = -5/2 and c = -8, then the quadratic equation should be y = 2x² - 5/2x - 8.

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Answer:

y - 6 = 4/3(x - 6)

Step-by-step explanation:

Given line: y= -3/4 + 1

So if a line is perpendicular to another line, then its slope will be the negative reciprocal of the other line slope (reciprocal of a fraction is the inverse of it's fraction example: reciprocal of 10/6 is 6/10). So for this problem the given line's slope is -3/4. But since the equation that has (6, 6) is perpendicular, the slope will be 4/3.

Now that we know the slope we can put the number's in the point slope form. Point slope formula: y - y1 of point = m(x - x1) (y1 = y of point, x1= x of point and m= slope)

So the equation will be y - 6 = 4/3(x - 6)

hope this helps :)

Note: If your problem needs it in slope-intercept form, it will be:  y = 4/3x - 2

Expected Return is usually based on anticipated income and anticipated capital appreciation of the companies performance..

Portfolio is simply defined as a list of securities showing how much is (or will be) invested in each of them.

The expected return on a portfolio is calculated as the weighted average of the expected returns on the securities that the portfolio involves. The weight of each security is the a Portion or a fraction of wealth invested in that security. Expected return on a portfolio of N securities is: rp= sum (Xr).

Expected Return is usually based on anticipated income and anticipated capital appreciation.

The expected return on a portfolio is defined as the expected amount of returns that a portfolio may generate. And it is established on the weighting of assets in a portfolio and their anticipated capital appreciation and must be equal to or greater than the expected return of the worst-performing security in the portfolio.

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The required ratio of actual length of tunnel to that of construction is 64:1.

Fraction is written as a ratio of two integers. Given the following parameters:

length of construction plan = 21/2 feet long

length of actual tunnel = 53 1/3 yards long

Determine the ratio

Ratio = actual/construction

Ratio = 160ft/2.5ft

Ratio = 64/1

Hence the ratio of the actual to the construction plan is 64:1

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Answer: $275.50

Step-by-step explanation:

5% = 0.05

So we take 290.00 time 0.05 and get `14.50. Then we 290.00 - 14.50= 275.50.

So the answer is $275.50

The proportion that can be used to show that AC and CE has equal slope is: 2 - 0/3 - 0 = 4 - 2/6 - 3.

Using any two points on a given line, the formula to find the slope of the line is given as:

Slope (m) = change in y / change in x = rise/run or the line.

Given that triangles ABC and CDE are two similar right triangles, find the slope of AC and CE as explained below:

Point A is at (0, 0)

Point C is at (3, 2)

Point E is at (6, 4)

Slope of AC = change in y / change in x = 2 - 0/3 - 0 = 2/3

Slope of CE = 4 - 2/6 - 3 = 2/3

Thus, the proportion showing that the slope of AC and the slope of CE are the same would be expressed as:

2 - 0/3 - 0 = 4 - 2/6 - 3.

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The most appropriate choice for Conjecture and Counter examples will be given by

There is atleast one zoo, may be in Africa or any other countries,  where the number of elephants is more than the number of giraffes. This is the required counterexample of this conjecture.

What is Conjecture and Counter examples?

Suppose an information is provided where the information is incomplete or insufficient, then any conclusion formed based on that information is called Conjecture.

Suppose, a statement  have been given a statement. If one can provide an example where the conditions of the statement are satisfied but the conclusion is false, then that example is called counter example.

Here,

Counterexample of "There are always more elephants in a zoo than giraffes."

There is atleast one zoo, may be in Africa,  where the number of elephants is more than the number of giraffes.

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Answer:

x=6

Step-by-step explanation:

we know that

slope formula is,

m=(y2-y1) / (x2-x1)

where m=-3

x1=x,y1=-4 and x2=2,y2=8,

-3=(8-(-4))/(2-x)

Now solving the expression

we get,

-6+3x=12

3x=18

x=6