For what value of x is the rational expression below equal to zero? 2-x+x/2+x

The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).

given

slope = y2- y1 / x2 - x1

= -120/8  = -15

( 6 , 120 )

( 14 , 0 )

The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.

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Answer:

Step-by-step explanation:

2n -3 =-21

2n-3+3=-21+3

2n=-19

n=-9.5

The distance between point G and H is 4√2 units51.96 unit²

An equation is a expression that shows the relationship between numbers and variables.

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the origin is:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Let us take point G as out reference point (origin)

Hence:

G = (0, 0) and H = (4, -4)

[tex]GH=\sqrt{(-4-0)^2+(4-0)^2}=4\sqrt{2}\ units[/tex]

The distance is 4√2 units

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The given function has one root i.e. -3.

The Synthetic approach can speed up polynomial division, especially when the result needs to be divided by a linear factor. It is often used to find polynomial roots or zeroes rather than dividing components.

In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

We've f(x) = x³-4x+15

               = (x+3) ( x²-3x+5) + 0

which implies that it has remainder as 0, So -3 is a root of given f(x).

Since x²-3x+5 can't be factorized more, the given function has only one root i.e. -3.

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The total amount Derek repaid after 5 years of quarterly payments at 10% per annum is $12,829.40.

The quarterly payments represent periodic payments made every three months to offset the credit.

The periodic payments can be computed using an online finance calculator.

Where the periodic payment is given, the total payment made can be determined as the product of the periodic payments and the number of periods involved.

N (# of periods) = 20 quarters (5 years x 4)

I/Y (Interest per year) = 10%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $-641.47

Results:

FV = $-0.03

Sum of all periodic payments = $-12,829.40

Total Interest = $2,829.43

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Derek borrowed $10,000 at 10% per annum compounded quarterly and repays $641.47 quarterly.  How much money did he repay after 5 years?

Answer: put the dot on the positive 6 vertical line. Then put a point on the point (4,5) and the point (8,4)

Step-by-step explanation:

Answer:

20 Stickers

Step-by-step explanation:

Set up for the problem

22+16= 38

38-18=20

So, Overall=20...

Oki and Stephen can only produce 0.75 bags of trail mix in total.

Two numbers can have a division symbol (") added between them to indicate that they have been divided. Therefore, we can write 36 6 if we need to demonstrate the division of 36 by 6. A fractional representation is 366, which we can also use.

Compared to multiplication, division is the opposite. When you divide 12 into three equal groups, you get four in each group if three groups of four add up to 12, which they do when you multiply.

The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a fair distribution.

According to question:-

3/3 : 4/2 =1:2

90/120 = 0.75.

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Table 1 represents a positive correlation. As the temperature rises, the number of customers also increases.

What is a correlation?

A positive correlation is a relationship between two variables in which an increase in one variable is associated with an increase in the other variable.

Table 1 represents a positive correlation. As the temperature rises, the number of customers also increases.

To plot the set of data points from Table 1, we can use a scatter plot. Each data point in the table would be represented by an (x,y) coordinate, where x is the increase in temperature and y is the number of customers. So, in this case, we would have 8 points in the scatter plot, one for each pair of data in table 1.

The plot would look like a group of points in the coordinate plane with a general upward trend, as the x-values (increase in temperature) increase, the y-values (number of customers) also increase. It's possible to observe a pattern in the points, this pattern confirms that there is a positive correlation between temperature and the number of customers.

Hence, Table 1 represents a positive correlation. As the temperature rises, the number of customers also increases.

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Answer: 1. 7a 2. 5r 3. 8y+4 4. 12m-7 5. 7u+5 6. 8q+6 7. 3w+5x 8. 4j + 4k 9. 5d+6

Step-by-step explanation: Add the coefficients of the terms with same variables. ex. 5a+4a+7... 5a and 4a have same variable which is a so add the 5 and 4 and you get 9a and the 7 doesn't match so leave it out and you get 9a + 7

Answer:

1) 7a

2) 5r

3) 8y +4

4) 12m-7

5) 7u+5

6) 8q+6

7) 3w+5x

8) 4j +4k

9) 5d+6

Step-by-step explanation:

you just add or subtract the number with the same letter after it (if there is no letter just leave it as is, unless there are two or more numbers with no letter after, then add or subtract as normal)

The triangles ∆AEC ≅ ∆AFC by Side-Angle-Side theorem

The complete question is added as an attachment

With the given information and the image attached below, we can state that the two triangles are congruent by SAS,

Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.

The proof is given as:

Statement Reason

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Answer: 28%

Step-by-step explanation: So, if we know that Mia's team won 18 of the 25 games they played, we need to subtract 18 from 25. We get 7. So, now we need to use this formula to solve:

Part percent / Whole number * 100

Let's plug in the numbers:

7 / 25 * 100

0.28 * 100

= 28

Therefore, they lost 28% of their games. I hope this helped!

Answer:

28%

Step-by-step explanation:

To find percentages, we need to know the number of games lost out of 25, then multiply it by 4 to get our percentage. We know that she won 18 of 25. 25 - 18 =7, so she lost 7 games. This gives us the fraction:

[tex]\frac{7}{25}[/tex]

Then, we will multiply this fraction by 4 to get it out of 100:

[tex]\frac{28}{100}[/tex]

This gives us 28/100, to find the percentage out of a fraction with a denominator of 100, we multiply by 100 and add a % symbol. This gives us:

[tex]\frac{28}{100} * 100 = 28%[/tex]

Then, we add our percent symbol, meaning Mia's soccer team lost 28% of their games.

Hope this helped!

Answer:

[tex]j = \dfrac{9}{2} = 4,5 \\\\\\k = 2[/tex]

Step-by-step explanation:

I am working on the assumption that the figure shown is a parallelogram, otherwise my answer will not be valid

The diagonals of a parallelogram bisect each other

In the above figure, the top left-bottom right diagonal is bisected by the top right  - bottom-left diagonal

This means

[tex]3j = 5j - 9[/tex]

Subtract 5j from both sides:

[tex]3j - 5j = -9[/tex]

[tex]-2j = -9[/tex]

[tex]j = \dfrac{-9}{-2} = \dfrac{9}{2} = 4,5 \\[/tex]
I am not sure if you want it in fraction or decimal

Similarly

[tex]k + 10 = 6k\\\\[/tex]

Subtract k from both sides:
[tex]10 = 6k-k\\\\\\10 = 5k\\\\\\\textrm{Switching sides,}\\5k = 10\\\\k = \dfrac{10}{5} = 2\\\\[/tex]

Answer:

521621

Step-by-step explanation:

38600=7.4

x=100

*cross multiply*

100x38600/7.4

=521621.6216

nearest whole number: 521621

The exponential function that models this situation is given as follows:

y = 3(5)^x.

The y-intercept of the exponential function represents the number of people that were called by the administrators.

The graph of the exponential function is given by the image presented at the end of the answer.

The general format of an exponential function is given as follows:

y = a(b)^x.

In which:

First, the 3 school administrators decide when an announcement is needed, hence the parameter a, representing the y-intercept, is given as follows:

a = 3.

In each round, each person inserted into the conversion calls 5 more people, hence the parameter b is given as follows:

b = 5.

Meaning that the function is defined as follows:

y = 3(5)^x.

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Answer:

Rectangle, parallelogram, trapezoid, quadrilateral

Step-by-step explanation:

because the properties of the rhomboid(that is what it is called) match with those different shapes listed above

B1 should be smaller in order to spread out the explanatory components in order to test a B1 hypothesis or generate confidence intervals around a B1 hypothesis.

Though an explanatory variable is a hypothesis that is predicted to be able to explain the research outcomes, a response variable demonstrates the impact that is anticipated to come from the explanatory variable. The regression line has a slope that is B1.

In other circumstances, the alternative hypothesis is compared against the null hypothesis to determine whether the assertion that the population slope is not equal to Zero is valid. The value of b1 is to be construed as the average result altering when the explanatory variable is increased by one unit.

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The measure of the smaller complementary angles is 40°

When two angles add up to 90°, we say they complement each other in terms of mathematics. Hence in geometry, complementary angles are defined as two angles whose sum is 90 degrees.

The larger angle = 50°

we shall represent the smaller angle with the letter x so that;

x + 50° = 90°

subtract 50° from both sides of the equation

x + 50° - 50° = 90° - 50°

x = 40°

Therefore, the smaller complementary angle has a measure of 40°.

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C = 12k, where C represents the cost on the electrical bill and k represents the electricity used is a relationship that varies directly. Option C is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,
A standard directly proportional relationship is given as,
y = kx

Now,
comparing the above equation with the equation among the option,
If the equation in options matches with the above equation, so that equation will be a relationship that varies directly.

Thus, C = 12k, where C represents the cost on the electrical bill and k represents the electricity used is a relationship that varies directly. Option C is correct.

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Answer: x = -8/3

Step-by-step explanation:

7 = 3(5+x)

3(5+x)=7

apply the distributive property

15+3x=7

rearrange the variables to  the left side of the equation

3x=7-15

3x=-8

divide on both sides

x=-8/3

Answer:

x = -8/3

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 7 = 3(5 + x)

Then the value of x will be,

→ 7 = 3(5 + x)

→ 7 = 3(5) + 3(x)

→ 7 = 15 + 3x

→ 7 - 15 = 3x

→ -8 = 3x

→ 3x = -8

→ [ x = -8/3 ]

Hence, the value of x is -8/3.

Answer:

86

Step-by-step explanation:

let the numbers be x,x+2,x+4,x+6

Then x+x+2+x+4+x+6=332

4x=332-12=320

x=320/4=80

so numbers are 80,82,84,86

Answer:86

Step-by-step explanation:

If Catarina’s boat has come untied and floated away on the lake. She is standing atop a cliff that is 35 feet above the water in a lake. Approximately the distance from the cliff is Catarina’s boat is : 63.6ft.

Distance can be defined as how far an object is from another object.

Now let find the distance:

AE/CD = BC/DE

Hence,

5.5/3.5 = 10/DE

Cross multiply

AE = 350/5.5

AE = 63.6ft

Therefore we can conclude that the distance is 63.6ft.

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Answer:

it's a function

Step-by-step explanation:

to test if it's a function or not you do the vertical line test if it intersects the function at more than one point then it's not a function,, but here in the given function when you do the vertical test it'll only intersect it at one point so it's a function

Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6

The study of numbers, their variations, mathematics and the regional tissue, structures, and both their actual and imagined locations, is known as mathematics. A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input. Each function is given a city, town, or scope, which is frequently referred to as a realm.

Here,

Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).

Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).

The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).

Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).

=> f(x) = (x-h)² + k

The outcome of translating a unit to the right with b unit up is

=>f'(x) = (x-h-a)² + k + b

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Answer:

22

Step-by-step explanation:

as you can see at the bottom, they have added up all of the tallies. so all you need to use addition to add 10 + 12 which is equal to 22.

2x-1 with a translation 1 unit left followed by a reflection in the x-axis is -2x -1.

What is translation and reflection?

Flipping an object across a line without causing it to change in size or shape is called reflection. An object can rotate around a fixed point without changing its size or shape. Changing a figure's size, shape, or orientation does not constitute translation.

Reflections and translations are two of the most popular types of transformations. An object moves from one location to another through translation, remaining the same size and orientation.

One unit left means  -1 shift on x-axis leads to F(x+1)

Reflection on x-axis means rotating the graph upside down on x-axis which leads -F(x+1)

-F(x + 1) = -2(x + 1) + 1 = -2x - 2 + 1 = -2x -1

Hence, 2x-1 with a translation 1 unit left followed by a reflection in the

x-axis is -2x -1.

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The solution is

a) The motor boat traveled a displacement of

b) The velocity of the tugboat

c) The negative distances and velocities means the boat is traveling down a river

Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time. It is a vector quantity. Velocity is the change in displacement of an object with respect to time

Velocity = Displacement / Time

Given data ,

Some boats are traveling up and down a river

So , when the boat is traveling up a river , the velocity will be positive and when the boat is traveling down a river , the velocity will be negative

a)

The velocity of motor boat = - 3.4 mph

The time taken by the boat = 0.75 hours

Velocity = Displacement / Time

Substituting the values in the equation , we get

Displacement = Velocity x Time

Displacement D = - ( 3.4 ) x 0.75

On simplifying the equation , we get

Displacement D = -2.55 miles

Therefore , the boat traveled -2.55 miles down

b)

The displacement of the tugboat D = -1.5 miles

The time taken by the tugboat T = 0.3 hours

So , velocity of the tugboat V = ( -1.5 ) / 0.3

On simplifying the equation , we get

Velocity V = -5 mph

Therefore , the velocity of the tugboat is -5 miles per hour

c)

When the boat is traveling down a river , the velocity will be negative

Hence , the equations are solved

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