A 25 foot ladder leans against a wall 7 feet from the base of the wall. How high does the ladder touch?

Hello! The answer to your question is: Draw out a horizontal line. Place 0 at the center. Then place evenly spaced tick marks on either side of 0. Label the right side of tick marks as 1, 2, 3, moving from 0 and going to the right

Label the left side of tick marks -1, -2, -3, starting at 0 and moving left

The location -3 on the number line is exactly 3 units away from 0. We start at 0 and move to -3 by moving 3 spots to the left; or we start at -3 and move 3 units to the right to get to 0.

Therefore, the absolute value of -3 is 3

Absolute value on a number line is the distance a number is from 0

The distance is never negative.

Hope this helped!

Answer:

x

Step-by-step explanation:

-2x^2(x-5)+x(2x^2-10x)+x

Distribute-2x^2 through parentheses

-2x^3+10x^2+(2x^2-10x)+x

Distribute x through parentheses

-2x^3+10x^2+2x^3-10x^2+x

Eliminate the opposites

-2x^3+2x^3=0 and 10x^2-10x^2=0 both sets of opposites cancel each other out, which leaves us with just x remaining.

The simplest form of of the expression is x.

To find the probability that both marbles drawn by Joseph are black, you need to consider the number of ways he can draw 2 black marbles out of the 4 black marbles in the bag, divided by the total number of ways he can draw 2 marbles from the 10 marbles in the bag without replacement. The probability is 2/15.

To find the probability that both marbles drawn by Joseph are black, we need to consider the number of ways he can draw 2 black marbles out of the 4 black marbles in the bag, divided by the total number of ways he can draw 2 marbles from the 10 marbles in the bag without replacement.

Let's calculate:

Therefore, the probability that both marbles are black is 6/45, which simplifies to 2/15.

Final answer:

The flag of Iraq has no lines of symmetry due to its horizontal stripes of different colors and the specific orientation of the Arabic Kufic script of the Takbir written in the center.

Explanation:

The question about how many lines of symmetry the flag of Iraq has can be classified as a question in the field of mathematics, particularly in the study of geometry. Symmetry in flags can pertain to reflections across certain lines where the flag is indistinguishable from its mirror image.

As of my knowledge update, the flag of Iraq consists of three horizontal stripes of red, white, and black, with the Takbir ('Allahu Akbar') written in the center in green Kufic script. As the script introduces a specific orientation and the colors do not symmetrically repeat, the flag does not have horizontal or vertical lines of symmetry. The presence of textual elements disrupts potential symmetry, considering the particular way letters must be oriented to be readable. Hence, the flag of Iraq does not have any lines of symmetry.

The helicopter has flown a distance of 500 feet as calculated using the Euclidean distance formula for two points on a grid.

To find the distance the helicopter has flown, we need to calculate the Euclidean distance between the two points (2,6) and (6,9) on the grid map. We can use the formula: Distance = √[(x₂ - x₁)² + (y₂ - y₁)²], where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points. Substituting the given points into the formula, we have:

Distance = √[(6 - 2)² + (9 - 6)²] = √[(4)² + (3)²] = √[16 + 9] = √25 = 5 grid lines.

Given that each grid line is equivalent to 100 feet, the helicopter has traveled 5 grid lines * 100 feet/grid line = 500 feet.

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Alexis's comparison of fractions does not suffice to determine which shape's fractional area is greater without knowing the total areas of the trapezoid and hexagon. The areas of shapes are calculated differently and must be considered before applying fractional parts to compare.

Alexis's statement does not necessarily make sense because the comparison she is making is only between the fractions
1/3 and 1/6, not the actual areas of the shapes. The area of a fraction of a shape depends on the total area of that shape. Therefore, without knowing the specific areas of the trapezoid and hexagon, we cannot conclude that
1/3 of the trapezoid has a greater area than 1/6 of the hexagon simply because 1/3 is greater than 1/6. To correctly compare the areas, one would need to know the total area of both shapes before fractions are applied.

Furthermore, when discussing the properties of shapes and areas, it is important to remember that the area of a trapezoid is calculated differently from the area of a hexagon. The area of a trapezoid is the average of the two bases multiplied by the height, whereas the area of a regular hexagon can be found by dividing it into equilateral triangles and calculating the area of those. Thus, the total area of each shape before fractions are considered plays a crucial role in determining if Alexis's statement is true or false.

The required cost to plant daffodil bulbs in a rectangular garden is $144 .

Given that,
A gardener determines the cost of planting daffodil bulbs to be $2.40 per square foot.
To determine the cost to plant daffodil bulbs in a rectangular garden that is 12 feet long and 5 feet wide.

The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.

Here,
The area of the rectangular garden = 12 * 5
                                                             = 60 ft²
cost of planting daffodil bulbs = 2.40 * 60
                                                   = $144

Thus, the required cost to plant daffodil bulbs in a rectangular garden is $144.

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Answer:

B. Stress

Step-by-step explanation:

Did the usa prept test :)

[tex] |\Omega|=7\cdot6=42\\
|A|=3\cdot2=6\\\\
P(A)=\dfrac{6}{42}=\dfrac{1}{7}\approx14\% [/tex]

In the equation 3x - 14 = 2x + 10, the solution for x is 24. Substituting x = 24 into the expression 3x - 14 gives a result of 58. Therefore, the value of 3x - 14 under these conditions is 58.

The student's question introduces an equation where two expressions are set equal to each other: 3x - 14 and 2x + 10. To find the value of 3x - 14, we first need to solve this equation for x.

To do so, we subtract 2x from both sides to get x - 14 = 10. We then add 14 to both sides to get x = 24. Thus, the value for 'x' that makes the two expressions equal is 24. Substituting 'x' into 3x - 14 gives us 3*24 - 14, which calculates to be 58.

Therefore, the value of 3x - 14 when 3x - 14 equals 2x + 10 is 58.

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The linear equation for "a" in terms of "w" and "b" is:

a = (w - 4b) / 7By following these steps, we have solved the linear equations for "a" and expressed it in terms of "w" and "b."

To solve the equation for "a" in terms of "w" and "b," we can follow these steps:

Step 1: Start with the equation:

w = 7a + 4b

Step 2: Isolate the term with "a" on one side of the equation. To do this, subtract 4b from both sides:

w - 4b = 7a

Step 3: Divide both sides of the equation by 7 to solve for "a":

(w - 4b) / 7 = a

Step 4: Simplify the expression:

a = (w - 4b) / 7

Therefore, the linear equation for "a" in terms of "w" and "b" is:

a = (w - 4b) / 7By following these steps, we have solved the linear equations for "a" and expressed it in terms of "w" and "b."

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That’s what it looks like. Im not sure how to solve it either though.

The repeating decimal [tex]\(0.1 \overline{23}\)[/tex] is equivalent to the fraction [tex]\(\frac{611}{5000}\)[/tex].

To convert the repeating decimal [tex]\(0.1 \overline{23}\)[/tex] to a fraction, let's denote it as x:

[tex]\[ x = 0.1 \overline{23} \][/tex]

Now, we can manipulate the decimal to eliminate the repeating part. Multiply both sides of the equation by an appropriate power of 10 to shift the decimal:

[tex]\[ 100x = 12.323232\ldots \][/tex]

Now, subtract the original equation from the manipulated equation to eliminate the repeating part:

[tex]\[ 100x - x = 12.323232\ldots - 0.1 \overline{23} \][/tex]

Simplify:

[tex]\[ 99x = 12.22 \][/tex]

Now, solve for x:

[tex]\[ x = \frac{12.22}{99} \][/tex]

To simplify the fraction, find the greatest common divisor (GCD) of 12.22 and 99, which is 1. Divide both the numerator and denominator by the GCD:

[tex]\[ x = \frac{12.22}{99} = \frac{611}{5000} \][/tex]

So, [tex]\(0.1 \overline{23}\)[/tex] as a fraction is [tex]\(\frac{611}{5000}\)[/tex].

Rational Root Theorem

Final answer:

The theorems for finding zeros of higher degree polynomials include the Fundamental Theorem of Algebra, which guarantees n roots for an nth degree polynomial, the quadratic formula for second-order polynomials, and Euler's Theorem for Homogeneous Functions. These tools and theorems assist us in identifying possible roots and understanding the behavior of polynomial functions.

Explanation:

Theorems for Finding Zeros of Higher Degree Polynomial Functions

There are several important theorems relevant to finding zeros or solutions of higher degree polynomial functions. One key theorem is the Fundamental Theorem of Algebra, which states that every nth-degree polynomial has exactly n complex roots, which may include repeated roots. Additionally, polynomials are continuous and differentiable, so finding points where the derivative is zero leads to identifying potential maxima and minima.

The quadratic formula is used to find the zeros of second-order polynomials, revealing up to two roots, which may be real or complex numbers. Another relevant theorem is Euler's Theorem for Homogeneous Functions, which pertains to homogeneous functions of a certain degree and their properties. In the case of polynomials, it can be applied to determine certain types of symmetries and relationships amongst the coefficients.

Regarding polynomials of odd degrees, these always have at least one real root. Furthermore, since real-world numbers are approximations, tiny changes in the coefficients of a polynomial can lead to distinct roots. It's also worth noting that for any nth degree polynomial, differentiation yields an n-1 degree polynomial, which guides us in understanding the number of maxima or minima the function can possess. This is illustrated by the derivative of a third-order polynomial being a second-order polynomial, which can have at most two real roots.

A sector is a portion of a circle enclosed by two radii and the arc between them. The area of a sector is found by multiplying the central angle in radians by the square of the radius and dividing by 2.

In mathematics, a sector is a portion of a circle enclosed by two radii and the arc between them. The area of a sector is found by multiplying the central angle in radians by the square of the radius and dividing by 2.

For example, if we have a sector with a radius of 5 units and a central angle of π/3 radians (60 degrees), we can calculate the area as follows:

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