What is the area of the shaded region to the nearest tenth of a foot?

Part a) Explain what formulas you will use to find the area of the shaded area.

Par b) Explain how you find the area of the shaded region. What was your thought process?

Step-by-step explanation:

[tex]-4x-7+10x=-7+6x\\\\(-4x+10x)-7=-7+6x\\\\6x-7=-7+6x\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-7=-7\qquad\bold{TRUE}\\\\Answer:\ \text{Infinitely many solutions}[/tex]

Final answer:

By simplifying the given linear equation and combining like terms, we find that the single solution is x = 0. Verification confirms that this solution is valid as it satisfies the original equation.

Explanation:

The equation presented by the student is a linear equation with the variables on both sides. To solve this equation, we will combine like terms and isolate the variable x on one side of the equation.

First, let's simplify the equation by combining like terms:

-4x - 7 + 10x = -7 + 6x

Combine x terms on the left side and numerical terms on the right:

6x = 0

Finally, divide by the coefficient of x to solve for x:

x = 0

This value of x is the single solution to the equation. It's important to note that there are no other solutions in this case, as it's a simple linear equation and not a quadratic or higher-order polynomial equation.

Verification

To verify that x = 0 is indeed a solution, we can substitute it back into the original equation:

-4(0) - 7 + 10(0) = -7 + 6(0)

All terms involving x drop out, confirming that -7 = -7 is an identity, making x = 0 a valid solution.

The height of the wall if A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall, is 5.81 feet.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine, cosine, and tangents are their names and acronyms (tan).

Given:

A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall,

Calculate the height of the wall as shown below,

Assume the height of the wall is x then,

x² + base² = ladder height²

x² + 5.5² = 8²

x² = 64 - 30.25

x² = 33.75

x = √33.75

x = 5.81 ft

Thus, the height of the wall is 5.81 feet.

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The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y.

The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y. For example, if we substitute x = 1, we get y = 3(1)^2 - 18(1) + 15 = 0. So, when x = 1, y is 0.

To find more values, we can create a table of values by substituting different x values into the equation. The resulting values of y can be plotted on a graph to see the pattern and shape of the equation.

Table of Values:

This equation represents a quadratic function in the form of y = ax^2 + bx + c, where a = 3, b = -18, and c = 15.

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The probability of Max winning the first three games while losing the rest two is 0.023.

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

As it is given that the probability of winning the game is 2/5. Since the sum of all the probability of an event is 1, therefore, the probability of losing the game can be written as,

Sum of all probability = Probability of winning + Probability of losing

[tex]1 = \dfrac25+\text{(Probability of losing)}\\\\\text{(Probability of losing)}=\dfrac35[/tex]

Thus, the probability of losing the game is 3/5.

As we need to calculate the probability of Max winning the first three games while he losing the rest two. Therefore,

[tex]P = \dfrac25 \times \dfrac25 \times \dfrac25 \times \dfrac35 \times \dfrac35 = \dfrac{72}{3125} = 0.023[/tex]

Hence, the probability of Max winning the first three games while losing the rest two is 0.023.

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Step-by-step explanation: We are given three rectangular figures A, B and C.

We need to determine which polygons are similar and which are not.

Note: The sides of similar figures are in proportion.

Let us check first A and B figures.

150/108 = 50/36

100/72 = 50/ 36.

We can see 150/108 = 100/72 = 50/ 36.

Sides are in proportion of Polygons A and B.

Let us check first A and C figures.

150/132 = 25/22

100/80 = 5/4.

We can see 150/132 ≠ 100/80.

Sides are not in proportion of Polygons A and C.

Let us check first B and C figures.

108/132 = 9/11.

72/80 = 9/10.

We can see 108/132 ≠ 72/80.

Sides are not in proportion of Polygons B and C.

To find the combined width of the three tables, add up their individual widths.

To find the combined width of the three tables, we need to add up their individual widths.

The first table is 3 feet 11 inches wide, which is equivalent to 3 feet 11 inches + 0 feet 11 inches = 3 feet 22 inches.

The second table is 6 feet 10 inches wide, which is equivalent to 6 feet 10 inches + 0 feet 10 inches = 6 feet 20 inches.

The third table is 3 feet 7 inches wide, which is equivalent to 3 feet 7 inches + 0 feet 7 inches = 3 feet 14 inches.

Adding up the widths: 3 feet 22 inches + 6 feet 20 inches + 3 feet 14 inches = 12 feet 56 inches.

Therefore, the combined width of the three tables is 12 feet 56 inches.

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Option D, which is x + 2y^2 - 7, is a trinomial as it contains exactly three terms.

A trinomial is an algebraic expression with three terms.

These terms are usually separated by '+' or '-' signs. Let's examine the options given to identify a trinomial:

Therefore, Option D is the correct answer as it is the expression that contains exactly three terms, making it a trinomial.

The exponential function will be written as:

y = 12 (0.56) ^ (t/4)  

y=12 (0.56^ (1/4)) ^t

but

0.56^ (1/4) = 0.8651

thus plugging the value in y we get:

y=12 (0.8651) ^t

in two decimal places we get:

y=12 (0.87) ^t

The value of b in the  equation is [tex]b=\frac{2A}{h}[/tex].

Simplification of an equation is the process of writing an equation in the most efficient and compact form without affecting the value of the original equation.

For the given situation,

The equation is [tex]A=\frac{bh}{2}[/tex]

The equation can be simplified as

⇒ [tex]A=\frac{bh}{2}[/tex]

⇒ [tex]2A=bh[/tex]

⇒ [tex]b=\frac{2A}{h}[/tex]

Hence we can conclude that the value of b in the  equation is [tex]b=\frac{2A}{h}[/tex].

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The range of the numbers 3, -97, -15, -42 is 100.

The range of a set of numbers is the difference between the largest and smallest numbers in the set. To find the range of the numbers 3, -97, -15, -42, we first need to find the largest and smallest numbers. The largest number is 3 and the smallest number is -97. Subtracting the smallest number from the largest number gives us a range of 100.

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The equation q^2=36 has two solutions because both a positive and a negative number squared can result in a positive number. The solutions are q=6 and q=-6, illustrating the concept of integer powers and square roots.

To solve the equation q squared equals 36 (q2 = 36), we look for the number that, when multiplied by itself, gives the product of 36. In mathematics, finding a value that satisfies this condition involves taking the square root of both sides of the equation. Thus, we have two potential solutions since both positive and negative values can be squared to yield a positive result.

The square root of 36 is 6, so our equation gives us two possible solutions: q = 6 or q = -6. This demonstrates the concept of integer powers, where for instance, raising 4 to the power of 3 (43) means multiplying 4 by itself three times. When dealing with the square root, we are essentially doing the opposite: we are asking what number multiplied by itself gives us the original number under the square power.

Answer: The answer is B) 11.25

Step-by-step explanation: I got it right

Answer:

The area of the circle is equal 28.3 cm² to the nearest tenth.

Step-by-step explanation:

To find the area of the circle that has a radius of 3, we will simply use the formula;

Area of a cirle = π r²

where π is a constand and r is the radius.

From the question given π = 3.14   and r=3

We can now proceed to insert the value into the formula;

Area of a cirle = π r²

                        =3.14×3²

                         =3.14×9

                           =28.26

                            ≈28.3 cm²

Therefore, the area of the circle is equal 28.3 cm² to the nearest tenth.

The statements that are true about the intersecting rays are

A) m∠3 = m∠1

B) m∠2 = 60°

D) m∠3 = 120°

Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.

Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.

When lines intersect, two angle relationships are formed:

Opposite angles are congruent

Adjacent angles are supplementary

Given data ,

Let the two intersecting lines be m and n

Now , the angles formed are shown in the diagram

where the measure of ∠1 = ∠3 ( Opposite angles are congruent )

Now , the measure of ∠2 = 180° - ( 65° + 55° ) ( angles in a triangle = 180° )

The measure of ∠2 = 60°

So , the measure of ∠3 = 180° - ∠2 ( Adjacent angles are supplementary = 180° )

And , the measure of ∠3 = 120°

Hence , the angles in the intersecting lines are solved

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