Find the set of the solutions of each of the following absolute value inequalities. Check your answers. |(x+1)/2 - x/2|<1/2

Triangle UTS and triangle VTS are congruent using ASA criteria. Hence, SU = SV using CPCT.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

Although having the same form, each might have different sizes.

There are no matching angles that are not equal.

Similar equivalent side ratios exist.

Given: ST bisects ZUTV.

angle UTS ≅ angle VTS (as ST bisects ZUTV)

angle TUS and angle TVS are right angles as shown in the figure.

Thus, triangle UTS and triangle VTS are congruent using ASA criteria.

Hence, SU = SV using CPCT.

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After making the table using the given ratios we can conclude that Miguel will save $90 if he earns $120.00.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.

A proportion is an equation that equalizes two ratios.

For example, you might write the ratio as 1: 3 (there are 3 girls for every guy), which would suggest that there are 1 in 4 boys and 3 in 4 girls.

By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B).

So, the solution in the form of a table would be:

Money Earned    Money saved                  Ratio

10                              7.5                                3/4

50                            37.5                                3/4

120                             ?                                   3/4

150                          112.5                                3/4

? /120 =  3/4  => ? =   90

Miguel will save $90 if he earns $120.00.

Therefore, after making the table using the given ratios we can conclude that Miguel will save $90 if he earns $120.00.

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Correct question:

Miguel created the ratio table below to show how he uses the money he earns at work. Miguel’s Money Money Earned Money Saved $10.00 $7.50 $50.00 $37.50 $120.00? $150.00 $112.50 How much money will he save if he earns $120.00? $30.00 $45.00 $90.00 $75.00

Answer:

The given statement is False. When the interest is compounded half yearly the number of conversion periods will be two because a year comprises 12 months and has two periods of six months each.

Step-by-step explanation:

if it helped you please mark me a brainliest :))

Definitions: A definition is a statement that explains the meaning of a word or a concept. It clarifies what something is or what it means. For example, the definition of "circumference" is the distance around a circle.

examples of the question :-

Example: The definition of a polygon is a closed shape with straight lines.

Theorems: A theorem is a statement that has been proven to be true through a logical argument or a set of mathematical steps. Theorem is often used in mathematics, but it can also be used in other fields of study. For example, the Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Example: The theorem of the maximum value of a continuous function on a closed interval states that if f is a continuous function on the closed interval [a, b], then f attains a maximum value and a minimum value on that interval.

Formulas: A formula is a mathematical expression that shows the relationship between two or more variables. It can be used to solve problems or to make predictions. For example, the formula for the area of a rectangle is length times width.

Example: The formula for the circumference of a circle is C=2πr, where C is the circumference, r is the radius, and π is a mathematical constant.

Step-by-Steps: Step-by-step instructions are a series of directions or actions that need to be followed in order to complete a task or solve a problem. It is often used in math or science to explain a process or a procedure. For example, a step-by-step instruction on how to solve a quadratic equation might look like this:

Step 1: Write the equation in standard form.

Step 2: Identify the values of a, b, and c.

Step 3: Substitute these values into the quadratic formula.

Step 4: Simplify the equation and solve for x.

Example: A step-by-step instruction on how to find the derivative of a function might look like this:

Step 1: Identify the function.

Step 2: Use the power rule, product rule, or quotient rule to find the derivative.

Step 3: Simplify the derivative by combining like terms and simplifying fractions.

Step 4: Check your work by taking the derivative of the derivative to see if it matches the original function.

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Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the diameter of a circle is 13ft . We are interested in finding out the circumference of the circle.

Firstly we know that radius is half of the diameter . So we can calculate the radius as ,

[tex]\longrightarrow r =\dfrac{d}{2} \\[/tex]

Substitute the respective value ,

[tex]\longrightarrow r =\dfrac{13}{2} \ ft\\[/tex]

[tex]\longrightarrow r = 6.5 \ ft \\[/tex]

Secondly we can find the circumference as ,

[tex]\longrightarrow \boxed{\rm Circumference= 2\pi r } \\[/tex]

where "r" is the radius of the circle.

On substituting the respective values, we have;

[tex]\longrightarrow C = 2 \pi\times 6.5 \ ft \\[/tex]

[tex]\longrightarrow \boxed{\boldsymbol{ C = 13\pi \ ft }} \\[/tex]

Hence the circumference of the circle is 13π ft .

Answer:

f(g(x))

f(x+9)

5(x+9)-6

5x + 45-6

5x+39

and,

g(f(x))

g(5x-6)

5x-6+9

5x +3

The inequality or system of inequalities matched with the respective graphs are:


26) = Graph A
27) = Graph B
28) = Graph D

For y ≤ 3x² -
For any given value of x, the corresponding value of y can be found by squaring x and multiplying it by 3. Since the coefficient of x² is positive, the parabola represented by this inequality opens upward.

The graph of this inequality is a shaded region below or on the curve of the parabola. This means that any point (x, y) that lies on or below the curve satisfies the inequality, while any point above the curve does not.

For y ≥ - x²; y < x² + 3 -

The system of inequalities includes two quadratic functions in two variables, x and y. The first inequality y ≥ -x² represents a parabola that opens downward, while the second inequality y < x² + 3 represents a parabola that opens upward. The solution set for the system includes all points that satisfy both inequalities simultaneously. This solution set lies in the region above the first parabola and below the second parabola, and is bounded by the x-axis.

For y ≥ x²-5; y ≤ -2 x² + 3x + 3 -

The system of inequalities includes two quadratic functions in two variables, x and y. The first inequality y ≥ x² - 5 represents a parabola that opens upward, while the second inequality y ≤ -2x² + 3x + 3 represents a parabola that opens downward. The solution set for the system includes all points that satisfy both inequalities simultaneously. This solution set lies in the region between the two parabolas, and is bounded by the x-axis.


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It transform rectangle in  8 units left and then 7 units down then  x-axis and subsequently the y-axis were reflected and after this translated 7 units down

A set of translations, rotations, reflections, and dilations on a figure constitute a series of transformations in geometry. A composition of transformations is what results when two or more transformations are joined to create a new transformation. In a composition, one transformation creates a picture that serves as the foundation for the subsequent other transformation.

The possible transformations that rectangle ABCD could have undergone to become rectangle A′′B′′C′′D′′ are as follows: -

It was translated 8 units left, then 7 units down, for rectangle ABCD.

- First, the x-axis and subsequently the y-axis were reflected by the rectangle ABCD.

- Rectangle ABCD was translated 7 units down after being rotated 180 degrees around its origin.

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Answer: Since the parabola opens down and has a focus at (0, -12), its directrix is a horizontal line located 12 units above the vertex. Let the vertex of the parabola be (h, k).

Since the focal diameter is 20, the distance between the focus and the directrix is also 20. Therefore, the directrix is the horizontal line y = k + 12, and the distance from the vertex to the focus is equal to the distance from the vertex to the directrix, which is 10.

Using the definition of a parabola, we can write:

sqrt((x - h)^2 + (y - k)^2) = 10 + (y - k - 12)

Squaring both sides, we get:

(x - h)^2 + (y - k)^2 = (10 + y - k - 12)^2

Expanding the right-hand side and simplifying, we get:

(x - h)^2 + (y - k)^2 = (y - 2)^2

Simplifying further, we get:

x^2 - 2hx + h^2 + y^2 - 2ky + k^2 = y^2 - 4y + 4

Rearranging the terms, we get:

x^2 - 2hx + h^2 + 2ky - 4y + k^2 - 4 = 0

Since the parabola opens down, the coefficient of x^2 must be negative. Therefore, we can write:

-(x^2 - 2hx + h^2 + 2ky - 4y + k^2 - 4) = 0

Multiplying out the negative sign, we get:

-h^2 + 2hx - 2ky + 4y - k^2 + 4 = 0

Therefore, the equation of the parabola that opens down, has focus (0, -12), and a focal diameter of 20 is:

-h^2 + 2hx - 2ky + 4y - k^2 + 4 = 0

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

To determine whether the relation represented in the given table is a function, we need to check whether each input (x-value) in the table is associated with a unique output (y-value).

We can see that the input value "12" has two different output values, "16" and "19". This means that the relation is not a function since the same input is associated with multiple outputs.

Therefore, the relation represented in the given table is not a function.

Answer:

(6,0 ) is located in 1st quardrant o is x axis and 6 is y axix upuards

The intercepts of h(x) are (-1, 0), (4, 0), and (0, 4), and the asymptotes are x = 2 and y = 3. To find these intercepts and asymptotes using the graph, we need to look for the points where the graph intersects the x-axis and the y-axis, and where the function approaches infinity or a constant value as x approaches certain values.

From the graph, we can see that the function h(x) has a vertical asymptotes at x = 2, which means that as x approaches 2 from either side, the function approaches positive or negative infinity. We can also see that the function has a horizontal asymptote at y = 3, which means that as x approaches positive or negative infinity, the function approaches 3. To find the intercepts of h(x), we need to look for the points where the graph intersects the x-axis and the y-axis. From the graph, we can see that the function intersects the x-axis at x = -1 and x = 4, which means that these are the x-intercepts. The function intersects the y-axis at y = 4, which means that this is the y-intercept.

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No, we cannot prove that war is near based on these propositions only.

In logic and mathematics, a proposition is a statement or assertion that is either true or false. It is also referred to as a declarative sentence. Propositions are often used as the building blocks for logical reasoning and mathematical proofs.

Here,

The given propositions are a chain of conditional statements, also known as if-then statements. To prove that war is near, we would need a statement or evidence that directly supports this claim. None of the given propositions directly state or imply that war is near. Even if we assume that all the given propositions are true, the only thing we can conclude is that Notre Dame de Paris cathedral started burning. We cannot make any conclusions about whether war is near or not.

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By solving the ratio, we get the value of x is 3.

What is a ratio?

a ratio is a comparison of two quantities or values, often expressed as a fraction. Ratios can be used to express the relationship between two or more quantities.

Let the total number of tiles on the bathroom floor be represented by the variable "t".

Since 1/4 of the tiles are blue, we know that:

number of blue tiles = 1/4 * t

Similarly, we can find the number of green tiles:

number of green tiles = 3/4 * t

Now, we can use the given ratio of blue tiles to green tiles to create an equation:

(2x+1)/(4x+9) = (number of blue tiles) / (number of green tiles)

Substituting the values we found earlier, we get:

(2x+1)/(4x+9) = (1/4 * t) / (3/4 * t)

Simplifying this equation, we get:

(2x+1)/(4x+9) = 1/3

6x + 3 = 4x + 9

2x = 6

x = 3

Therefore, the value of x is 3.

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The perimeter of the given quadrilateral EGFH is 33 inches as shown in below figure.

A quadrilateral is a geometric shape with four angles and four straight sides. Quadrilaterals come in a wide variety of shapes, including squares, rectangles, trapezoids, and kites. Each kind of quadrilateral has its own set of characteristics and properties, but they all have four sides and four angles in common.

Draw two tangents from an outside point to the circle always in equal lengths;

So, the perimeter of quadrilateral EGFH = length of each tangents

the perimeter of quadrilateral EGFH = EG + GF + FH + HE

the perimeter of quadrilateral EGFH = 12 + (5+4) + (4+0.5) + (0.5+7)

the perimeter of quadrilateral EGFH = 12+ 21

Therefore, the perimeter of quadrilateral EGFH = 33 inches

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Complete question in figure-

True. In an indirect proof, also known as proof by contradiction, you start by assuming the opposite of what you intend to prove is true.

You then use deductive reasoning and logical steps to show that the assumption leads to a contradiction or an impossibility. This means that the assumption must be false and therefore the original statement you intended to prove must be true.

What is contradiction?

A contradiction is a situation where two or more statements, beliefs, or ideas are in direct opposition to one another, making them logically inconsistent or incompatible with each other. In other words, a contradiction occurs when there is a conflict between two or more pieces of information that cannot both be true at the same time.

For example, if someone says "I am currently in New York City," and then in the same conversation says "I am currently in Los Angeles," this is a contradiction because it is impossible to be in two different locations at the same time.

What is deductive reasoning?

Deductive reasoning is a method of reasoning in which specific conclusions are drawn from general principles or premises. It is a logical process that involves starting with a general principle or hypothesis, and then using specific observations or evidence to reach a specific conclusion.

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Complete question is: In an indirect proof, also known as proof by contradiction, you start by assuming the opposite of what you intend to prove is true.

After answering the provided question, we can conclude that The quadratic equation completed perfect square trinomial is (2c - 11)².

A quadratic equation is x[tex]ax2+bx+c=0[/tex], which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Fundamental Theorem of Algebra ensures that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. The formula "[tex]ax2 + bx + c = 0[/tex]" is a common solution for quadratic equations. where a, b, and c are numerical coefficients or constants. where the variable "X" is unidentified.

To make the trinomial [tex]4c² - 22c[/tex] + ... a perfect square, we need to add a constant term that will make it a perfect square trinomial.

Here are the steps to follow:

Therefore, the missing monomial is 121.

The completed perfect square trinomial is (2c - 11)².

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The slope of the line is 7/5 its y-intercept is (0,5) and x-intercept is (-25/7,0) when the equation of the line is 7x‐5y=‐25.

To write the equation of the line 7x-5y=-25 in slope-intercept form, we need to solve for y:

7x - 5y = -25

-5y = -7x - 25

y = (7/5)x + 5

Therefore, the equation of the line in slope-intercept form is y = (7/5)x + 5.

To find the slope, we can see that the coefficient of x is 7/5, so the slope is 7/5.

To find the y-intercept, we can see that the y-intercept is the value of y when x = 0. Plugging in x=0 into the equation, we get:

y = (7/5)(0) + 5 = 5

Therefore, the y-intercept is (0,5).

To find the x-intercept, we can set y=0 and solve for x:

0 = (7/5)x + 5

-5 = (7/5)x

x = -25/7

Therefore, the x-intercept is (-25/7,0).

To draw an accurate graph, we can plot the x- and y-intercepts and then use the slope to draw the line through those points. The slope of 7/5 means that for every 5 units to the right, the line goes up 7 units. We can use this to plot additional points and draw the line. The line should pass through the points (-25/7,0) and (0,5), and continue in both directions.

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The solution to the system of equations 3x - y = 4 and -2x + 7y = 20 is obtained as x = 48/19 and y = 68/19.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The system of equations is -

3x - y = 4

-2x + 7y = 20

The matrix for the system of equations is -

[tex]\left[\begin{array}{c c | c}3 & -1 & 4 \\-2 & 7 & 20\end{array}\right][/tex]

To solve the matrix, we can use row operations to get it into row echelon form -

The first row operation is -

[tex]R_1=\frac{1}{3}R_1[/tex]

On applying the first row operation we get -

[tex]\left[\begin{array}{c c | c}1 & \frac{-1}{3} & \frac{4}{3} \\-2 & 7 & 20\end{array}\right][/tex]

The second row operation is -

[tex]R_2=R_2+2R_1[/tex]

On applying the second row operation we get -

[tex]\left[\begin{array}{c c | c}1 & \frac{-1}{3} & \frac{4}{3} \\0 & \frac{19}{3} & \frac{68}{3}\end{array}\right][/tex]

The third row operation is -

[tex]R_2=\frac{3}{19}R_2[/tex]

On applying the third row operation we get -

[tex]\left[\begin{array}{c c | c}1 & \frac{-1}{3} & \frac{4}{3} \\0 & 1 & \frac{68}{19}\end{array}\right][/tex]

The fourth row operation is -

[tex]R_1=R_1+{\frac{R_2}{3}}[/tex]

On applying the fourth row operation we get -

[tex]\left[\begin{array}{c c | c} 1 & 0 & \frac{48}{19} \\0 & 1 & \frac{68}{19}\end{array}\right][/tex]

Therefore, the solution is x = 48/19 and y = 68/19.

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The value of x is 1.0 for the given triangle.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are:

The given triangle is a right triangle because it presents one of your angles equal to 90º. The figure shows:

Therefore, you have the opposite side of the angle u, the angle u and the variable x. Thus, you can apply the equation for sin (u) for finding x.

[tex]sin (x) = \frac{opposite\ side}{hypotenuse} \\ \\ sin (37) = \frac{0.6}{x}[/tex], knowing that sin37°=0.602

[tex]0.602=\frac{0.6}{x} \\ \\[/tex]

x=0.997, round to the nearest tenth

x=1.0

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The coefficient of x in the simplified form of the expression is -117.

The simplified form of an algebraic expression is the expression that has been reduced to its simplest possible form by combining like terms and performing any applicable operations, such as addition, subtraction, multiplication, and division.

Given that

= 3(x + 4)(x - 5)^2 - 6(x + 2)^3

Apply the distributive property.

= (3x + 3 × 4)(x−5)^2 − 6(x + 2)^3

Expand using the FOIL Method.

= (3x+12)((x−5)(x−5))−6(x+2)^3

= (3x+12)(x^2−10x+25)−6(x+2)^3

Expand ( 3 x + 12 ) ( x^2 − 10 x + 25) by multiplying each term in the first expression by each term in the second expression.

= (3x) × x^2 + 3x(−10x) + 3x × 25 + 12x^2 + 12(−10x) + 12×25 − 6(x+2)^3

= 3x^3 − 30x^2 + 75x + 12x^2 − 120x + 300 − 6(x+2)^3

= 3x^3 − 18x^2 − 45x + 300 − 6(x+2)^3

SImplify 6(x+2)^3 using Binomial expansion;

= −3x^3 − 54x^2 − 117x + 252

Therefore, we can conclude that the coefficient of x is - 117.

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To find the annual interest rate, we can use the formula:

simple interest = (principal x rate x time) / 100

where principal is the initial amount, rate is the annual interest rate, and time is the time period in years.

We know that the principal is $100, the simple interest is $3, and the time period is 6 months, which is half a year.

So, we can plug in these values and solve for the annual interest rate:

$3 = ($100 x rate x 0.5) / 100

$3 = $0.5 x rate

rate = $3 / $0.5

rate = 6

Therefore, the annual interest rate is 6%.

Answer:

To calculate the annual interest rate, we can use the simple interest formula:

I = P * r * t

Where:

- I is the interest earned

- P is the principal amount

- r is the annual interest rate

- t is the time period in years

In this case, we know that the principal amount is $100, the interest earned is $3, and the time period is 6 months, or 0.5 years. We can plug these values into the formula and solve for r:

3 = 100 * r * 0.5

r = 3 / (100 * 0.5)

r = 0.06, or 6%

Therefore, the annual interest rate is 6%.

I hope this helps!

10. Showing that ΔWVU ∼ ΔQRS, x = B. 5

11. Showing that ΔKML ∼ ΔEMD, x = A. 8.

A triangle is a geometric shape that is formed by connecting three straight lines to form a closed shape. It is a three-sided polygon and is one of the most basic shapes in geometry. The three lines that form a triangle are called sides, and the points where the sides meet are called vertices.

10. Showing that ΔWVU ∼ ΔQRS, we have:

WV/QR = VU/RS

⇒ (13x + 7)/45 = 88/55

Cross-multiplying, we have:

(13x + 7)55 = 45 x 88

= 715x + 385 = 3 960

= 715x = 3 960 - 385 = 3 575

∴ x = 3 575/715 = 5.

Thus, x = 5.

11. Showing that ΔKML ∼ ΔEMD, we have:

KM/EM = ML/MD = (3x - 2)/14 = 27/18

(3x - 2)18 = 14 x 27

= 54x - 54 = 378

= 54x = 378 + 54 = 432

⇒ x = 432/54 = 8.

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Answer:

8

Step-by-step explanation:

7+1

Answer:

x = 100 , y = 6

Step-by-step explanation:

[tex]\frac{x}{5}[/tex] = 20 ( multiply both sides by 5 to clear the fraction )

x = 5 × 20 = 100

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

8y - 6 = 9y - 12 ( subtract 9y from both sides )

- y - 6 = - 12 ( add 6 to both sides )

- y = - 6 ( multiply both sides by - 1 )

y = 6

Step-by-step explanation:

I think this is the way it has to be done (I added a photo)

Answer:

x=√715

Step-by-step explanation:

Using Pythagorean Theorem,,

(34) ^2= (21)^2+x^2

⇒x^2= 1156-441

⇒x^2= 715

⇒x= √715