Find the x-intercept of the line 18x–5y=12.
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

Answer:

50

Step-by-step explanation:

10 x 5 = 50

Answer:

Just add each one and you will get the answer

Step-by-step explanation:

For example 7+9+18+24 = 58

There is no solution for the given system of inequalities there is no point that satisfies both inequalities.

The following system of inequalities is given as:

a.

y ≥ x + 1

y ≤ -x - 2

b.

y ≥ x + 1

y ≥ - x - 2

The system of the given inequalities represents a region in the x-y plane that is the solution set for the inequalities. To find the solution set, we can graph the inequalities on the same coordinate plane and find the region where they overlap.

The inequality y ≥ x + 1 represents the line y = x + 1 and all the points above it. Similarly, y ≤ -x - 2 represents the line y = -x - 2 and all the points below it.

When we graph these two lines on the same coordinate plane, we find that the lines intersect at the point (-1.5,-0.5) which means that the common region of the two lines(the region where they overlap) is the empty set. This means that there is no point that satisfies both inequalities and therefore there is no solution for the given system of inequalities.

Similarly, therefore there is no solution for the system of inequalities y ≥ x + 1 ; y ≥ - x - 2.

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Answer:

B

Step-by-step explanation:

[tex]-2<x+3<2 \implies -5<x<-1[/tex]

Answer:

q = 40 degrees

r = 60 degrees

p = 100 degrees

Step-by-step explanation:

before we start we need to know that angles on a straight line equal 180 and angles in a triangle add up to 180.

by knowing this we can workout

q= 180 - 140 = 40 therefor q = 40 degrees

r= 180-120=60 therefor r = 60 degrees

p = 180 - q - r

180 - 40 - 60 = 100 therefor p = 100 degrees

[-5, 3) is the interval of all real numbers greater that or equal to -5 but less than 3

A number system is defined as a system of writing to express numbers.

We need to write all real numbers greater that or equal to -5 but less than 3

[-5, 3)

-5 is included in the interval because it is greater than or equal to.

But the 3 is not included in the interval because it is strictly less than

Hence, [-5, 3) is the interval of all real numbers greater that or equal to -5 but less than 3

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Answer:

  (d)  no, there is not a proportional relationship because 58 over 14 does not equal 38 over 3.

Step-by-step explanation:

You want to know if there is a proportional relationship between °C and °F, given the relation (°F, °C) = (58, 14) or (38, 3).

The relationship is proportional if the ratio of input and output is the same in all cases. Here, we see that ...

  58/14 ≠ 38/3 . . . . . . . the relationship is not proportional

<95141404393>

The Restaurant feet  IS 13

step1:

The area of the walls can be written as:

Aw=h(2i+2w)

We can plug in given values:

Aw=2(2(.5)+2(5.5)=13

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Complete the Venn diagram using Potatoes only = 48, sugar beets only = 12, the intersection of P and S = 6 and the box outside the P and S = 34

Given: ξ = 100 farms

60 farms only grow potatoes or sugar beets.

4/5 of these 60 farms grow only potatoes.

The number of farms that grow potatoes are 3 times the number that grow sugar beets

Potatoes only = 4/5 × 60 = 48

sugar beets only = 60 - 48 = 12

Let the intersection of P and S be x

Since P = 3S, we have:

48 + x  =  3 (12+x)

48 + x = 36 + 3x

12 = 2x

x = 6

Since we have 100 farms, we can write:

48 + 6 + 12 + y = 100  (y represents the box outside the circles of P and S)

66 + y = 100

y = 100 - 66

y = 34    

Complete the Venn diagram according

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The following formula may be used to calculate the measure of an angle: angle measurement = (intercepted arc size of angle) / (360 degrees)

Where the size of the intercepted arc of the angle equals the radius of the circle produced by the angle.

If we know the ratio of the sides of a triangle, we may use trigonometry to get the measure of an angle.

The sine of an angle, for example, is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse, and the tangent of an angle is the ratio of the length of the hypotenuse to the length of the adjacent side.

As a result, we might use sin(theta)=opposite/hypotenuse.

cos(theta)=adjacent/hypotenuse

tan(theta)=opposite/adjacent

Using inverse trigonometric functions, calculate the angle in radians or degrees.

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Answer:

y = [tex]\frac{6}{5}[/tex] x

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, - 6 ) and (x₂, y₂ ) = (5, 6 )

m = [tex]\frac{6-(-6)}{5-(-5)}[/tex] = [tex]\frac{6+6}{5+5}[/tex] = [tex]\frac{12}{10}[/tex] = [tex]\frac{6}{5}[/tex] , then

y = [tex]\frac{6}{5}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation.

using (5, 6 ) , then

6 = 6 + c ⇒ c = 6 - 6 = 0

y = [tex]\frac{6}{5}[/tex] x ← equation of line

Answer:

See attached graph

Graph is not continuous

Step-by-step explanation:

The function is not continuous as you can see from the break in the graph

It is discontinuous at x = -2

Answer:

See attachment for graph.

The function is not continuous.

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases} x-3 \;\;\;\;\: \text{if}\;\;\;x \leq -2\\4x+5 \;\;\; \text{if}\;\; \;x > -2 \end{cases}[/tex]

Therefore, the function has two definitions:

When graphing piecewise functions:

First piece of the function

Substitute x = -2 into the first function:

[tex]\implies f(-2)=-2-3=-5[/tex]

As the interval for the first equation is x ≤ -2, it includes the value of x = -2.  Therefore, place a closed circle at point (-2, -5).

To help graph the line, find another point on the line by inputting another value of x that is less than -2 into the same function:

[tex]\implies f(-5)=-5-3=-8[/tex]

Plot point (-5, -8) and draw a straight line from the closed circle at (-2, -5) through (-5, -8).  Add an arrow at the other endpoint to show it continues indefinitely as x → -∞.

Second piece of the function

Substitute x = -2 into the second function:

[tex]\implies f(-2)=4(-2)+5=-3[/tex]

As the interval for the second equation is x > -2, it does not include the value of x = -2.  Therefore, place an open circle at point (-2, -3).

To help graph the line, find another point on the line by inputting another value of x that is more than -2 into the same function:

[tex]\implies f(1)=4(1)+5=9[/tex]

Plot point (1, 9) and draw a straight line from the open circle at (-2, -3) through (1, 9).  Add an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attachment for the graph.

[tex]\boxed{\begin{minipage}{8cm}\underline{Determining if a function is continuous at $x=a$}\\\\Condition 1: $f(a)$ exists\\\\Condition 2: $\displaystyle \lim_{x \to a}f(x)$ exists at $x=a$\\\\Condition 3: $\displaystyle \lim_{x \to a}f(x)=f(a)$\\\end{minipage}}[/tex]

If all three conditions are satisfied, the function is continuous at x = a.

If any one of the conditions is not satisfied, the function is not continuous at x = a.

To determine whether or not the given piecewise function is continuous, find if the function is continuous at x = -2.

Condition 1

Does f(-2) exist?  Yes → f(-2) = -5

Condition 2

[tex]\textsf{Does}\;\;\displaystyle \lim_{x \to -2} f(x)\;\; \sf exist\;at\;\;x=-2?[/tex]

To the left of  x =- 2, f(x) = x - 3

To the right of  x = -2 , f(x) = 4x + 5

Evaluate the left and right limits as x approaches -2:

[tex]\displaystyle \lim_{x \to -2^-}f(x)=\lim_{x \to -2^-} -2-3=-5[/tex]

[tex]\displaystyle \lim_{x \to -2^+}f(x)=\lim_{x \to -2^+} 4(-2)+5=-3[/tex]

[tex]\textsf{As}\;\;\displaystyle \lim_{x \to -2^-} f(x) \neq \lim_{x \to -2^+} f(x), \;\; \lim_{x \to -2} f(x)\;\; \textsf{does not exist}.[/tex]

As condition 2 fails, there is no need to proceed to condition 3.

Therefore, the function is not continuous.

Answer:

{(1, 2), (2, 3), (3, 4), (4, 5)}

Step-by-step explanation:

Given:

Which relation is a function?

{(1, 2), (2, 3), (3, 4), (4, 5)}

{(1, 2), (2, 1), (1, 3), (3, 1)}

{(0, 2), (0, 4), (0, 6), (0, 8)}

{(1, 2), (3, 4), (5, 6), (1, 8)}

Solve:

To know which relation is a function, we must know how it a function.

There are two ways to figure out.

One way is by looking at a graph - Vertical Line Test : Draw a vertical line and if the line hits the graph one time, the graph is a function.

Another way is by looking at the function : In a function there can be only one  x- value(Input) for every y- value(Output). Meaning that there can be duplicate y-value but can't have any in x - value. If there is duplicate x-value meaning it not a function.

Thus, now let's look at each answer choice.

-------------------------------------------------------------------------------------------------------------

Starting with :  {(1, 2), (2, 3), (3, 4), (4, 5)}

Input (x) | Output (y)

1                     2

2                    3

3                    4

4                    5

There is only one x- value. Therefore, it a function.

-------------------------------------------------------------------------------------------------------------

Next : {(1, 2), (2, 1), (1, 3), (3, 1)}

Input (x) | Output (y)

1                     2

2                    1

1                     3

3                    1

There are two 1's in x-value(Input). Therefore, it isn't a function

-------------------------------------------------------------------------------------------------------------

Then: {(0, 2), (0, 4), (0, 6), (0, 8)}

Input (x) | Output (y)

0                    2

0                    4

0                    6

0                    8

All of the x-value(Input) are the same. Therefore, it isn't a function

-------------------------------------------------------------------------------------------------------------

Lastly: {(1, 2), (3, 4), (5, 6), (1, 8)}

Input (x) | Output (y)

1                     2

3                    4

5                    6

1                     8

There are two 1's in x-value(Input). Therefore, it isn't a function

-------------------------------------------------------------------------------------------------------------

RevyBreeze

These conversions can be carried out for any amount of mass given in grams.

0.379 g = 379 mg

787 g = 0.787 Mg

74.3 g = 0.0743 kg

1. To convert 0.379 g to mg, multiply 0.379 by 1000. 0.379 x 1000 = 379 mg.

2. To convert 787 g to Mg, divide 787 by 1000. 787 / 1000 = 0.787 Mg.

3. To convert 74.3 g to kg, divide 74.3 by 1000. 74.3 / 1000 = 0.0743 kg.

The 0.379 g was converted to 379 mg, 787 g was converted to 0.787 Mg, and 74.3 g was converted to 0.0743 kg.

The conversion of 0.379 g to mg is done by multiplying 0.379 by 1000. The result is 379 mg. To convert 787 g to Mg, divide 787 by 1000. The result is 0.787 Mg. To convert 74.3 g to kg, divide 74.3 by 1000. The answer is 0.0743 kg. In summary, 0.379 g was converted to 379 mg, 787 g was converted to 0.787 Mg, and 74.3 g was converted to 0.0743 kg. This demonstrates how to convert mass from grams to different derived units. These conversions can be carried out for any amount of mass given in grams.

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The amount of water needed for 90 mL concentrate is 225 mL

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

2 parts concentrate to 5 parts of water

The above parameter can be expressed using the following ratio expression

Ratio = Concentrate : Water

Substitute the known values in the above equation, so, we have the following representation

Concentrate : Water = 2 : 5

From the question, we have

Concentrate = 90 ml

Substitute the known values in the above equation, so, we have the following representation

90 : Water = 2 : 5

Multiply the second ratio by 45

This gives

90 : Water = 90 : 225

By comparison, we have

Water = 225

Hence, the amount of water  is 225 mL

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The equation of the variation based on the information will be y = 6x.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

From the information, it was stated that y varies directly as x. When y = 9, x is 1.5. This will be Illustrated as:

y = kx

9 = 1.5k

Divide

x = 9 / 1.5

x = 6.

The equation of the variation will be y = 6x.

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A fraction is a numerical expression that represents a part of a whole using two numbers separated by a fraction bar .Fractions can be used to describe how much of a quantity is being referred to. Examples of fractions include 1/2, 3/4, 5/8, 7/10, and 11/12.

1. 1/2 (one half)

2. 3/4 (three fourths)

3. 5/8 (five eighths)

4. 7/10 (seven tenths)

5. 11/12 (eleven twelfths)

Fractions are numerical expressions used to represent parts of a whole. To express a fraction, two numbers are separated by a fraction bar. The top number (numerator) represents the number of parts taken from the whole, and the bottom number (denominator) represents the total number of parts in the whole. For example, if a pizza is divided into four equal slices, each slice can be described as being "1/4" of the pizza. Other examples of fractions include 3/4, 5/8, 7/10, and 11/12. Fractions can help to quickly and accurately describe how much of a quantity is being referred to.

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A fraction is a mathematical phrase that uses two integers and a fraction bar to indicate a portion of a whole. The fractions 5/7, 9/11, 23/53, 35/37, and 43/51 are a few examples.

Parts of a whole can be represented numerically using fractions. Two numbers are separated by a fraction bar to represent a fraction. The total number of pieces in the whole is represented by the bottom number (denominator), while the number at the top (numerator) indicates how many parts were picked from the whole. As an illustration, if a pizza is cut into four equal pieces, each piece might be referred to as "1/4" of the pizza. The fractions 9/11, 23/53, 35/37, and 43/51 are other examples. Fractions make it easier to express a quantity's size succinctly and precisely.

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Answer:

The slope of the line parallel is 5/2

Step-by-step explanation:

Parallel lines have the same slope as the given slope.

So to find the slope of 5x - 2y = 2, we need to change it into slope intercept form, y=mx+b:

First, subtract 5x to both sides,

5x - 2y = 2

-5x          -5x

----------------------

-2y = 2 - 5x

Then divide each side by -2

[tex]\frac{-2y}{-2} = \frac{2}{-2} - \frac{5x}{-2}[/tex]

Which will be,

[tex]y = -1 - (-\frac{5}{2}x)\\[/tex] or [tex]y = \frac{5}{2}x -1[/tex]

So, m = 5/2, making the slope 5/2.

Hope this helps!

Answer: A line that is parallel to a given line will have the same slope as the given line.

The slope of a line can be found by rearranging the equation of the line into slope-intercept form (y = mx + b) where m is the slope.

To find the slope of the line 5x - 2y = 2 , we can rearrange the equation to:

5x - 2y = 2

5x = 2y + 2

y = (5/2)x - 1

So the slope of the line is m = 5/2.

So a line parallel to the given line will have a slope of 5/2 as well.

Step-by-step explanation:

lol they used art how do u not know this

Answer:

25

Step-by-step explanation:

[tex]0<5x-35<90 \\ \\ 0<x-7<18 \\ \\ 7<x<25[/tex]

Janelle can buy either 1 or 2 snacks.

Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. Here are the steps for solving inequalities:

Step - 1: Write the inequality as an equation.

Step - 2: Solve the equation for one or more values.

Step - 3: Represent all the values on the number line.

Step - 4: Also, represent all excluded values on the number line using open circles.

Step - 5: Identify the intervals.

Step - 6: Take a random number from each interval, substitute it in the inequality and check whether the inequality is satisfied.

Step - 7: Intervals that are satisfied are the solutions.

Given inequality: 20 ≥ 8 +4.99x

We solve this inequality:

20 = 8 + 4.99x

12 = 4.99x

∴ x = 2.40

Number of snacks is between   0 < x < 2.40.

Also, the snacks purchased should be integer form.

∴ The value of x is 1 and 2.        

Thus, Janelle can buy either 1 or 2 snacks.

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Yes, the relation is a function. No, this is not a one-to-one function. Yes, the inverse of the relations is also a function.

A function is a relation that states that there should only be one output for each input, or we could say that a particular kind of relation (a set of ordered pairs) that abides by the rule that every X-value should be connected to only one y-value is referred to as a function.

The Cartesian product is a subset of it. Also known as a collection of points (ordered pairs). Or, to put it another way, the relationship between the two sets is described as a collection of ordered pairs, where each ordered pair is made up of an object from a different set.

Examples include the notation (-2, 1), (4, 3), and (7, -3), which is typically written in set notation form.

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Answer: dimensions of the two rectangles are 6x4 and 6x2

Answer:

200+200=400+600=1000

Step-by-step explanation:

Answer:

Use the given functions to set up and simplify x % . 200 m l = 15 % = 0.15 200 m l = 0.15 x % = 0.15 mL = 0.15

i may be wrong if so sorry.

The domain of  f(x , y) = √(y - x²) / (1 - x²) is

D ∈ [0, 1).

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

[tex]\frac{.30}{.48}[/tex] x [tex]\frac{100}{100}[/tex] = [tex]\frac{30}{48}[/tex] ÷ [tex]\frac{6}{6}[/tex] = [tex]\frac{5}{8}[/tex]

The least possible value of p+n+d+q would be 6 + 3 + 3 + 3 = 15. So, the least possible value of p+n+d+q is 15.

To solve this problem, we need to use the concept of prime factorization. First, we need to find the least common multiple of the four numbers, p, n, d, and q. To do this, we can factor each of the numbers into their prime factors:

[tex]p = 2^a * 3^b * 5^c * 7^d \\n = 2^e * 3^f * 5^g * 7^h\\d = 2^i * 3^j * 5^k * 7^l\\q = 2^m * 3^n * 5^o * 7^p[/tex]

The least common multiple (LCM) of p, n, d, and q is the product of the highest power of each prime factor that appears in any of the numbers. For example, the LCM would be 2^i * 3^j * 5^k * 7^l, because that is the highest power of each prime factor that appears in any of the numbers.

Now that we have the LCM of the four numbers, we need to find out how much money that is worth. Since we know that the total value is $1.08, we can divide both sides by the LCM to find out how much each factor is worth:

[tex]1.08/2^i * 3^j * 5^k * 7^l = x[/tex]

x = 0.01102

So, each factor of the LCM is worth 0.01102. Now, we just need to add up the total number of factors that appear in p, n, d, and q. The least possible value of p+n+d+q would be the sum of the number of powers of each prime factor in p, n, d, and q. For example, if[tex]p = 2^2 * 3^3 * 5^1 * 7^0, n = 2^1 * 3^2 * 5^0 * 7^2, d = 2^0 * 3^1 * 5^2 * 7^1,[/tex] and [tex]q = 2^2 * 3^0 * 5^2 * 7^1.[/tex]

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Answer: It would be 6/35

To determine if two triangles are congruent, the following conditions must be met:

To determine if triangle HL is congruent, you must first compare the lengths of each side. If the lengths of each side are equal, then the triangles are similar. Next, you must compare the angles of each triangle. If the angles of each triangle are equal, then the triangles are congruent. Finally, you must compare the pairs of vertical angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. If all of these pairs are equal or supplementary, then the triangles are congruent. If all three conditions are met, then it can be concluded that triangle HL is congruent.

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The proof of the statement given in the question that the "that the given function has an x-intercept that is equal to its y-intercept" is shown below.

The given function is , y = x/(x²-4)

To find x-intercept of the function, we will find the value of x for which y=0. Thus , we will get the result as,

0 = x/(x²-4)

Then we will multiply both sides of the equation by (x²-4), to get

    0 × (x²-4) = x

=> 0 = x

Thus, the x-intercept of the function as calculated is 0.

Now, for y intercept,

y = 0/(0²-4)

=> y = 0

y-intercept of the function is also 0.

Now, as the value of both the intercepts are same i.e., 0 therefore, the given statement is proved.

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The x-intercept and y-intercept of the given function y = x are both 0, so the x-intercept is equal to the y-intercept.

Given function: y = x

Since the given function is y = x, we can determine its x-intercept and y-intercept by setting y and x equal to 0.

To find the x-intercept, set y = 0:

0 = x

Therefore, the x-intercept of the given function is 0.

To find the y-intercept, set x = 0:

y = 0

Therefore, the y-intercept of the given function is 0.

Since the x-intercept and y-intercept of the given function are both 0, the x-intercept is equal to the y-intercept.

The x-intercept and y-intercept of the given function y = x are both 0, so the x-intercept is equal to the y-intercept.

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