Find the value of x .

Answer:

When solving a compound inequality, you can express the solution in two different ways: using a union or intersection.

Using a union:

A union represents the solutions that belong to either one inequality or the other, or both. You can express a union using the symbol "or," or by writing the solutions for each inequality separately and combining them using a "union" symbol (∪). For example, if you have the compound inequality "x > 2 or x < -3," you can express the solution as "x ∈ (-3, 2) ∪ (-∞, -3) ∪ (2, ∞)."

Using an intersection:

An intersection represents the solutions that belong to both inequalities. You can express an intersection using the symbol "and," or by writing the solutions for each inequality separately and combining them using an "intersection" symbol (∩). For example, if you have the compound inequality "x > 2 and x < -3," you can express the solution as "x ∈ (-3, 2) ∩ (-∞, -3) ∩ (2, ∞)."

Which method you use to express the solution will depend on the specific inequalities and the type of solutions you are looking for. It is important to carefully consider the inequality symbols (>, <, ≥, ≤) and the use of "and" or "or" in order to determine the correct solution.

When solving a compound inequality, the solution can be expressed in one of two ways: as an interval or as a union of intervals.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

An interval is a set of all real numbers between two given numbers, and is written in the form (a, b) or [a, b], where a and b are real numbers, and a < b. If a and b are included in the interval, then the interval is written as [a, b]; if a and b are not included in the interval, then the interval is written as (a, b).

A union of intervals is a combination of two or more intervals, and is written in the form (a, b) ∪ (c, d) or [a, b] ∪ [c, d], where a, b, c, and d are real numbers, and a < b and c < d.

When solving a compound inequality, it is important to first simplify the inequality by combining like terms, isolating the variable on one side of the inequality, and combining any separate inequalities into a single inequality. Then, the solution can be found by graphing the inequality on a number line, and shading the portion of the number line that represents the solution.

Once the solution is found the solution can be expressed either as an interval or as a union of intervals depending on the inequality. For example, if the inequality is x>1 and x<3, then the solution would be expressed as (1,3) and this is an example of an interval. If it's x>1 and x≥3 then the solution would be expressed as (1,3] U [3,∞) and this is an example of union of intervals.

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Answer:

Answer: £272.51

Step-by-step explanation:

First, we need to determine how much money Selma needs to have in her account in order to pay the bill and still have £10 left over. The bill is for £465.20, so Selma needs to have £475.20 in her account in order to pay it.

Next, we need to determine how much money Selma needs to pay into her account in order to reach this total. She starts with £202.69 on Monday, so she needs to pay £475.20 - £202.69 = £<<475.20-202.69=272.51>>272.51 into her account on Tuesday. Answer: £272.51

The slope of the line is 1.25 and the value of x is 12.

A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate. A line's slope provides information on the steepness and direction of the line. the angle at which two straight lines intersect.

Given that:

rise =10

run = 8

The slope is determined by the following formula:

Slope = Rise / Run

[tex]Slope = \frac{10}{8} = 1.25[/tex] .

The slope of a line equation is given by:

[tex]y_2 - y_1 = m (x_2-x_1)[/tex]

Here, m is the slope of the equation.

Substitute the value of [tex]m= \frac{10}{8}, y_2=21 , y1= 6, x_2 =x, x_1= 0[/tex] in the equation.

[tex]21-6 = \frac{10}{8}(x-0)\\ \\15= \frac{10}{8} (x)\\\\(15)(8) = 10x\\\\120=10x\\\\x=12[/tex]

Hence the value of x is 12.

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Answer:

The slope of the line is 1.25 and the value of x is 12.

Step-by-step explanation:

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{ 1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{2}) \\\\\\ y-7=- \cfrac{ 1 }{ 2 }x+1\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 2 }x+8 \end{array}}[/tex]

Answer:

28°, 62°

Step-by-step explanation:

As 8,15,17 is a Pythagorean Triple, the triangle must be a right triangle. Hence, we can use our common trig ratios to solve the problem. Let's assume our right triangle has a base of 8, a height of 15, and a hypotenuse of 17.

Here are all the acute angles in order:

[tex]\cos^{-1}(\frac{15}{17})\approx28^\circ[/tex]

[tex]\sin^{-1}(\frac{15}{17})\approx62^\circ[/tex]

so, if we take 40(origin amount) to be the 100%, what is 26 off of it in percentage anyway?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 40 & 100\\ 26& x \end{array} \implies \cfrac{40}{26}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 20 }{ 13 } ~~=~~ \cfrac{ 100 }{ x }\implies 20x=1300\implies x=\cfrac{1300}{20}\implies x=65[/tex]

The student that has the highest reading rate is Student C who has the highest rate of change of the number of words read of 158 words per minute.

The rate of change of a function is the rate at which the output value changes per unit change in the input value.

The possible data and table obtained from a similar question on the website are presented as follows;

Student A

Number of minutes;         [tex]{}[/tex]1              2             3              4

Number of words read; 150        [tex]{}[/tex]300          450          600

Student B

y = 158·x

Where;

x = The time duration in minutes

y = The number of words read by the student

Student C

The points on the graph representing the reading rate of student C are; (2, 280), (3, 420), (5, 700)

The first difference of the number of words read by Student 1 is constant, indicating that the relationship is a linear relationship, with the reading rate obtained by the rate of change of the number of words read as follows;

Reading rate for Student A = (300 - 150)/(2 - 1) = 150

The reading rate for Student A is 150 words per minute

The equation for the reading rate of Student B; y = 158·x, indicates that Student B reads 158 words per minute

The of the straight ling graph for the reading rate of Student C is found as follows;

Slope = (420 - 280)/(3 - 2) = 140

The slope indicates that the number of words read by Student C increases by 140 words every minute, therefore, the reading rate for Student C is 140 words per minute

The student that reads fastest is therefore, Student C who has a reading reading rate of 158 words per minute

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Step-by-step explanation:

think of it as a ruler the small dashes represents the 16ths and the big dashes represents the 4ths. They are on the same line therefore they are equal.

The equation of the trend line will be : Y = (1/4)x - 1.

Given is a scatter plot a shown in the image.

The general equation of a straight line is -

y = mx + c

{m} - slope

{c} - intercept along the y - axis

We can find the slope as follows. The line passes through the points -

(4, 0) and (0, - 1). We can write -

m = (- 1 - 0)/(0 - 4)

m = - 1/-4

m = 1/4

and

[c] = - 1

So the equation of the trend line will be -

Y = (1/4)x - 1

Therefore, the equation of the trend line will be : Y = (1/4)x - 1.

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Answer: The correct interpretations about the graph of r(t) are B, D, and E.

Interpretation B is correct because the graph shows that the average mortgage rate fell to a relative minimum between 2002 and 2003.

Interpretation D is correct because the graph shows that the average mortgage rate was highest between 2006 and 2007, based on the absolute maximum.

Interpretation E is correct because an appropriate domain for this function would be 0≤t≤10, as t represents time and the graph shows data for the period between 2002 and 2010.

Interpretation A is not correct because the graph does not show that the average mortgage rate increased continuously between 2003 and 2005.

Interpretation C is not correct because the y-intercept does not represent the average mortgage rate in 2010. The y-intercept represents the value of the function when t = 0, which does not correspond to any time in the given data.

Step-by-step explanation:

To find the cost of each pound of almonds, we need to find the difference in the cost of the almonds between the two purchases and divide it by the difference in the number of pounds of almonds. In this case, the difference in the cost of the almonds is $31 - $12 = $19 and the difference in the number of pounds of almonds is 3 - 5 = -2 pounds. Dividing the difference in the cost by the difference in the number of pounds gives us $19/-2 = $-9.50 per pound. This means that the cost of each pound of almonds is $-9.50.

To find the cost of each pound of jelly beans, we can use a similar process. In this case, the difference in the cost of the jelly beans is $31 - $12 = $19 and the difference in the number of pounds of jelly beans is 8 - 2 = 6 pounds. Dividing the difference in the cost by the difference in the number of pounds gives us $19/6 = $3.17 per pound. This means that the cost of each pound of jelly beans is $3.17.

Therefore , the solution of the given question of equation come out to be

x = 1/3 tablespoon .

Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.

Here,

Given : 2/3 cup Tablespoons

We have to find the half Tablespoons

So,

In order to find the half Tablespoons

Thus,

=> 1 Tablespoon = 2/3Tablespoons + x

where x is the half Tablespoons

=> x = 1/3 tablespoon

Therefore , the solution of the given question of equation come out to be

x = 1/3 tablespoon .

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Answer: 10:30 am

Step-by-step explanation: If you need to seat a passenger every 30 seconds, (half of a minute, which is 60 seconds), for every minute, 2 passengers will be seated. So, if you seat 2 passengers for a min each until you have seated 110 people, you will have taken up 55 minutes in total. (110 divided by 2 passengers a min). And finally, 55 minutes past 9:35 am would be 10:30 am. Hope this helps!

The total length is 2.077m (2177 cm).

Length is a measurement of size, distance, or duration. It can refer to physical size (length of a field, length of an object, etc.), distance (length of a journey, length of a river, etc.), or duration (length of a movie, length of a school day, etc.). Length can also refer to the duration of time it takes to complete something (length of a task, length of a process, etc.). Length is typically measured in units such as meters, feet, inches, miles, kilometers, and seconds.

The given measurements can be added together to calculate a total length. The addition of 1.8m, 77cm, and 210mm can be expressed in the form of a sum equation. The equation would be 1.8m + 77cm + 210mm = ?.

To solve this equation, the measurements need to be converted to the same unit of measurement. In this case, all measurements can be converted to cm. 1.8m is equal to 1800cm, 77cm is equal to 77cm, and 210mm is equal to 21cm.

Therefore, the sum equation becomes 1800cm + 77cm + 21cm = ?. To find the total length, the numbers can be added together.

The total length is 1977cm. However, since the measurements are expressed in decimals, the answer must also be expressed in decimals. Therefore, the total length is 2.077m (2177 cm).

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Answer: obtuse

Step-by-step explanation:

64+47=111

111>39

Answer:

[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex]  meters

[tex]r=10.24[/tex]  meters

Step-by-step explanation:

Here is the equation for the volume of a sphere

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

Lets solve for [tex]r[/tex].

Multiply both sides of the equation by [tex]\frac{1}{\frac{4}{3}\pi}[/tex].

[tex]\frac{1}{\frac{4}{3}\pi}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]

Simplify the left side.

Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].

[tex]\frac{1}{\frac{4\pi }{3}}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]\frac{3}{4\pi } (\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]

Cancel the common factor of [tex]\pi[/tex] by factoring it out of the first term.

[tex]\frac{3}{4} (\frac{4}{3}*r^3)=\frac{1}{\frac{4}{3}\pi}V[/tex]

Combine [tex]\frac{4}{3}[/tex] and [tex]r^3[/tex].

[tex]\frac{3}{4}*\frac{4r^3}{3}=\frac{1}{\frac{4}{3}\pi}V[/tex]

Multiply the numerators on the left side of the equation. Then multiply the denominators.

[tex]\frac{12r^3}{4*3}=\frac{1}{\frac{4}{3}\pi}V[/tex]

[tex]\frac{12r^3}{12}=\frac{1}{\frac{4}{3}\pi}V[/tex]

Cancel the common factor of 12.

[tex]r^3=\frac{1}{\frac{4}{3}\pi}V[/tex]

Simplify the right side.

Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].

[tex]r^3=\frac{1}{\frac{4\pi }{3}}V[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]r^3=\frac{3V}{4\pi }[/tex]

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

[tex]r=\sqrt[3]{\frac{3V}{4\pi } }[/tex]

Now we have an equation to find the radius.

Substituting our number for volume gives us

[tex]r=\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]

Enter this into a calculator

[tex]\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]

You can leave the answer in simplest radical form or as a decimal.

[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex]

[tex]r=10.24[/tex]

A rating/review would be much appreciated. Hope this helps!

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{3}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +4= -\cfrac{3}{4} (x +4) \\\\\\ y+4=-\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-7 \end{array}}[/tex]

Answer:

y = -3/4x - 7

Step-by-step explanation:

Given: slope = m = -3/4

Plug this value into the standard slope-intercept equation of y = mx + b.

y = -3/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, point (-4, -4). Plug in the x and y values into the x and y of the standard equation.

-4 = -3/4(-4) + b

To find b, multiply the slope and the input of x(-4)

-4 = 3 + b

Now, subtract 3 from both sides to isolate b.

-7 = b

Plug this into your standard equation.

y = -3/4x - 7

This is your equation.

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Answer:

1/2

Step-by-step explanation:

Slope(m)

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

= (8 - 1)/(7+7)

= 7/14

= 1/2

Answer: 125y³

To rise a product to a power, rise each factor to that power:

(5y)³ = 5³y³ = 125y³

Answer: C

Step-by-step explanation: it says that it's smaller or equal to x and x is smaller than 17

Answer: It's closer to 1/2

Step-by-step explanation: It's closer to 1/2 and here's why:

So, 1/2 (exact) is 8/16

0 = 0

1 = 16/16

Since 9/16 is the closest to 8/16 or around 1/2 in this case, it'd be about 1/2. I hope this helps!

Answer: the bottom two graphs show continuous data

Step-by-step explanation:

Answer:

  $202.30

Step-by-step explanation:

You want to know the value of a 20% tip on a bill of $1011.50.

The tip amount can be found by multiplying the bill amount by the tip percentage:

  20% · $1011.50 = $202.30

Lucas tipped the server $202.30.

__

Additional comment

You know that 10% of the amount can be found by moving the decimal point one place: $101.15.

20% of the amount will be double this value: $202.30. You can do this math mentally.

The required measure of the value of x is given as 2√3. Option A is correct.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

here,
Consider the given triangle,

perpendicular = 6
base = x

Applying trigonometric operation,
tan30 = perpendicular/base
tan30 = 6/ x
x = 6/√3
x = 2√3

Thus, the required measure of the value of x is given as 2√3. Option A is correct.

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Answer:

x ≤ −2 or x ≥ 5

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The total length needed in inches will be 490.5 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long  The total length needed in inches will be:

= (3 ft 4 7/8 inch × 12)

Note that 1 feet = 12 inches

= (12 × 3) + (4 7/8) × 12

= (36 + 4.875) × 12

= 490.5 inches

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