george places a mirror on the ground 45ft from the base of building. He walks backward until he can see the top of the building in the middle of the mirror. At that point, George’s eyes are 6th above the ground and he is 7.5ft from the mirror. Use similar triangles to find the height of the building.

Answer:

Side length of square = -10b³ + 12

Step-by-step explanation:

Forming the equation,

→ P = 4 × side

→ P = 4a

→ [ a = P/4 ]

Now the side length of square is,

→ a = P/4

→ a = (-40b³ + 48)/4

→ a = (-40b³ ÷ 4) + (48 ÷ 4)

→ a = (-10b³) + (12)

→ [ a = -10b³ + 12 ]

Hence, side length is -10b³ + 12.

Answer:

-10b³ + 12

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

As a square has four sides of equal length, the perimeter of a square is four times the length of one side.

Therefore, to find the expression for the side length of a square, simply divide the expression for the perimeter by 4.

[tex]\begin{aligned}\textsf{Side length of a square}&=\dfrac{\textsf{perimeter}}{4}\\\\\implies \textsf{Side length of the square}&=\dfrac{-40b^3+48}{4}\\\\&=\dfrac{-40b^3}{4}+\dfrac{48}{4}\\\\&=-10b^3+12\end{aligned}[/tex]

Answer: Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Step-by-step explanation:

The length of the rectangle is 18 feet and width is 8 feet .

The perimeter of a rectangle is the sum of the lengths of all four sides of the rectangle. It is calculated by adding twice the length and twice the width. The formula to calculate the perimeter of a rectangle is

P = 2(L + W), where P is the perimeter, L is the length and W is the width of the rectangle. In simpler terms, it is the total distance around the rectangle.

The perimeter of rectangle is given by  2 ( l + b)

where l is length of rectangle and b is width of the rectangle

given that perimeter of rectangle is 52

so 2 (l+b)= 52

=>  l+b=26  ---(i)

given l = b +10

=> l -b = 10 ---(ii)

adding equation (i) and (ii) we get :

2l = 36

=> l =36/2

so length = 18 and breadth = 18 - 10 =8

so the length is 18 and breadth is 8.

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A graph of the solution of the inequality is: graph F.

In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would solve the given inequality by making x the subject of formula as follows;

x - 5 < 14

By adding 5 to both sides of the inequality, we have the following:

x - 5 + 5 < 14 + 5

x < 19

Note: The line on a number line should be open when the inequality symbol is greater than (>) or less than (<).

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A parallelogram does not comprise the characteristics of having all congruent angles, Therefore, option B: "All angles are congruent." is the correct answer.

A parallelogram is a quadrilateral with opposite sides parallel and therefore opposite angles equal.  Examples of parallelograms include rhombuses, rectangles, and squares.

So common characteristics of a parallelogram are:

While all angles in parallelogram are not congruent, so this is not a property of a parallelogram.

"

Complete question

Which property is not a characteristic of a parallelogram?

O A. Opposite sides are congruent.

B. All angles are congruent.

O C. Opposite sides are parallel.

D. Opposite angles are congruent.

"

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n +2 represents that number is increasing by 2.

A horizontal line with evenly spaced numerical increments is called a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Given, n + 2

to put something with something else to increase the number or amount or to improve the whole: Beat the butter and sugar together and slowly add the eggs. She's added a Picasso to her collection.

that means the number is increasing by 2

Therefore, n +2 represents that number is increasing by 2.

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The rectangular pool has a width of 80 feet and a length of 68 feet. The area is 640 square feet and the length is 12 feet shorter than the width.

1. 640 divided by 12 = 53.33

2. 53.33 + 12 = 65.33

3. Width = 65.33 feet

4. Length = Width - 12 = 65.33 - 12 = 53.33 feet

The area of the rectangular pool is 640 square feet. To find the width, we divide 640 by 12 because the length is 12 feet shorter than the width. 640 divided by 12 gives us 53.33. We add 12 to this number to get the width of the pool, which is 65.33 feet. To find the length, we subtract 12 from the width, which gives us 53.33 feet. Therefore, the width of the pool is 65.33 feet and the length is 53.33 feet. The area of the pool is 640 square feet and the length is 12 feet shorter than the width.

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Answer: 1240

l gty ytdv tvt tbsaw vfffhv rÉÆêÄ Âerô

A triangle def is called a "midsegment triangle" and it is formed by connecting the midpoints of the sides of a triangle ABC.

The midsegment triangle is always parallel to the original triangle and has half the area. The three sides of the midsegment triangle are called the "midsegments" of the original triangle, and they are always parallel to the corresponding sides of the original triangle and have half the length.

A triangle defined by connecting the midpoints of the sides of triangle ABC is called a "midsegment triangle" or "medial triangle." The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and is parallel to the third side. The three sides of the medial triangle are the midsegments of the original triangle, and the three angles of the medial triangle are equal to one-half of the angles of the original triangle.

A triangle is a geometric shape that has three sides and three angles. It is a fundamental shape in Euclidean geometry and is one of the basic shapes in geometry. Triangles are classified based on their angles and sides, such as acute, right, and obtuse triangles. The sum of the angles in a triangle is always 180 degrees. Triangles can also be classified as equilateral, isosceles, or scalene based on the lengths of their sides. They are used in a variety of fields such as construction, engineering, and physics.

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The third stanza of Wilfred Owen's poem "Dulce et Decorum Est" is only two lines long, but it creates a gripping and powerful emotional impact.

Through the use of enjambment, the abrupt transition of the first line to the second creates an unsettling feeling, as if the speaker is struggling to express their thoughts and emotions. The imagery of the gas masks and the vivid depiction of the soldiers' "blood-shod" feet further amplify this emotion, providing a stark contrast to the ideals of glory and honor that the poem's title alludes to. This imagery also serves to evoke a feeling of despair and hopelessness, as the reader is confronted with the harsh realities of war. By using such a minimal amount of words, Owen is able to create an intense emotional effect that resonates with the reader and communicates a powerful message about the horrors of war.

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An earthquake with a Richter scale value of 4.0 is 10 times more powerful than one with a value of 3.0.

On the Richter scale, every whole-number rise in magnitude corresponds to a 10-fold increase in observed amplitude.

In order to evaluate the size of different earthquakes, the Richter scale was initially developed to quantify the magnitude of earthquakes of moderate size (i.e., magnitude 3 to magnitude 7). The scale was created for earthquakes that occurred in southern California, were detected by the Wood-Anderson seismograph, and had epicenters that were less than 600 km (373 miles) away from the seismograph's position.

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The coordinates of point M after a 90° clockwise rotation about P is (0, -3).

Thus, by applying the rule of 90° clockwise rotation-

M = (3,0) taking P as reference point .

M' = (0, -3) after 90° clockwise rotation.

Thus, the coordinates of point M after a 90° clockwise rotation about P is (0, -3).

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A circumference is not, first of all, calculated in square units. Square measurements can only be made for areas.

figuring out the circle's area:

find the circle's radius first

A circle's circumference is determined by

C = 2πr

Given that a circle has a 14π cm circumference

by entering C's value in the formula above, we obtain

14π = 2πr

Divide both sides by 2π

r = 7

Therefore, value of radius ( r ) is 7 cm

The circle's area is defined as :

A = π r^(2)

A = π ( 7 )^2

A = π ( 49 )

Consequently, the circle's area is

49π cm^2

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4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).

[tex]p(x)=2x^3-7x^2+2x\\g(x)=2x-3\\dviding. p(x) by g(x),\\ we get2x-3)2x^3-7x^2+2x(x^2-2x2x^3-3x^2- +0 -4x^2+2x-4x^2+6x+ -0 -4xq(x)=x^2-2xand, r(x)=-4x\\Now,\\According to division algorithmp\\(x)=g(x)*q(x)+r(x)2x^3-7x^2+2x=(2x-3)(x^2-2x)+(-4x)\\adding 4x-2 on both side,\\ we get\\2x^3-7x^2+2x+4x-2=(2x-3)(x^2-2x)+(-4x)+4x-22x^3-7x^2+6x-2=(2x-3)(x^2-2x)+(-2)[/tex]

4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

what number must be added to[tex]2x^3-7x^2+2x[/tex] so that the resulting polynomial leaves the remainder -2 when divided by 2x-3​

The three fundamental trigonometric ratios, namely sine, cosine, and tangent, each yield the ratio of the lengths of the two sides of a right-angled triangle.

We are aware that the sides of a right-angled triangle are called the "legs" and the "hypotenuse," respectively. Thus, the longest side of a right-angled triangle is still referred to as the "hypotenuse" in trigonometry, while the other two legs are referred to as the "opposite side" and "adjacent side."

The opposite, adjacent, and hypotenuse sides of a right-angled triangle are used to define the sin, cos, and tan functions in trigonometry. These are the sin, cos, and tan formulae.

sinФ = OppositeHypotenuse

cos Ф = AdjacentHypotenuse

tan Ф = OppositeAdjacent

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Answer:

The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value "5" is the Y Coordinate.

The cost of the shoes is $19.

Here are the system of equations that represent the question:

x + y = 46 equation 1

y = x - 8 equation 2

The substitution method would be used to solve these equations

Substitute for y in equation 1

x + x - 8 = 46

Combine similar terms: x + x = 46 - 8

Add similar terms together: 2x = 38

Divide both sides of the equation by 2: x = 38/2

x = 19

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Answer:

Follow the equations from the person above me, but instead the cost of the shoes is 27.

Step-by-step explanation:

We can see here that the different orders that she can wear the shorts is 25.

In mathematics, an order refers to the degree or highest exponent of a term in a polynomial equation. For example, the equation y = 3x^2 + 2x + 1 is a polynomial of order 2, because the highest exponent of x is 2.

In computer science, an order is a set of instructions for a computer to perform a specific task. For example, an order can be used to sort a list of numbers in ascending or descending order.

We see here that if the 5 pairs of basketball will go round on every day of the five days. Thus, it is: 5 x 5 = 25.

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By taking the quotient between the distance and the time, we will see that the speed is 16 miles per hour.

Remember that the speed is defined as the quotient between the distance traveled and the time in which that distance is traveled.

Such that:

speed = (distance)/(time)

Here we know that the ship can travel 48 miles in 3 hours, so:

distance = 48 mi

time = 3 hours

Then the speed is:

S = 48mi/3h

S = 16 mi/h

So the speed of the ship is 16 miles per hour.

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The area over which the signal is transmitted are: a.[tex]\pi[/tex] b. [tex]25\pi[/tex] c. CB transmits 25 times more signal to walkie talkie.

When two quantities of the same units are compared, the ratio shows how much of one quantity is included in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, while part to part ratio is the other.

The area of the circle is given by the formula:

[tex]A = \pi r^2[/tex]

For the walkie-talkie the signal is received up until 1 mile. Substitute the value of r = 1.

[tex]A _1= \pi (1)^2\\\\A_1 =\pi[/tex]

For the CB radio the signal is received up until 5 miles. Substitute the value of r = 5.

[tex]A_2 = \pi (5)^2\\\\A_2= 25 \pi[/tex]

a. The area over which a walkie-talkie can transmit its signal is [tex]\pi[/tex] miles.

b. The area over which a CB radio signal can transmit its signal is [tex]25\pi[/tex] miles.

c. The ratio of the transmitted signals are:

[tex]\frac{CB}{WT} = \frac{25\pi}{\pi} \\\\CB = 25 (WT)[/tex]

Hence, the CB signal transmits 25 times more than the signal transmitted by the walkie-talkie.

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The equation Y = x + 95 shows that for each year increase in age, the systolic blood pressure increases by 15 mm hg.

1. Plot the data points on a scatter plot.

2. Draw a line of best fit that passes through as many data points as possible.

3. Calculate the slope of the line of best fit using the formula

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

4. For example, if the line of best fit passes through two points with coordinates (x1, y1) and (x2, y2), calculate the slope as:

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

5. The slope represents the increase in systolic blood pressure for each year of age.

The equation Y = x + 95 is a linear model that represents the relationship between age and systolic blood pressure. To calculate the increase in systolic blood pressure for each year of age, we can plot the data points on a scatter plot and draw a line of best fit that passes through as many data points as possible. The slope of this line of best fit is then used to calculate the increase in systolic blood pressure for each year of age. For example, if the line of best fit passes through two points with coordinates (x1, y1) and (x2, y2),

the slope can be calculated as

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

This slope represents the increase in systolic blood pressure for each year of age.

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The given statement that "unpaid volunteer selling or serving alcohol at an event does not hold the volunteer to be civilly or criminally liable for selling/serving alcohol to an intoxicated person as far as the volunteer is TABC certified" is false because, under the TABC program, alcohol is prohibited to be served or sold to the intoxicated person.

The Texas Alcoholic Beverage Commission (TABC) does not prohibit alcohol to be served at private, invitation-only events in private residences, where there is no direct or indirect charge for that alcohol. However, TABC certification disallows to serve of alcohol to already dru-nk persons.

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No, All 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles.

No, not all right triangles are 30-60-90 triangles. A right triangle is a type of triangle that has one right angle (90 degrees) and two acute angles. The other two angles in a right triangle can have any measurement, they don't have to be 30-60-90 degrees.

A 30-60-90 triangle is a special type of right triangle that has specific angle measurements: one angle is 90 degrees (the right angle), one angle is 30 degrees, and one angle is 60 degrees. The ratio of the sides in a 30-60-90 triangle is also fixed, the longest side is opposite the 90-degree angle and it is always twice the length of the shortest side and the medium side is opposite the angle of 60 degrees and it's always the square root of 3 times the length of the shortest side.

For example, if a right triangle has angles of 45 degrees, 45 degrees, and 90 degrees, it is not a 30-60-90 triangle. The angles do not fit the pattern of 30-60-90 degrees.

Therefore, In short, all 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles. A 30-60-90 triangle is a special type of right triangle with specific angle measurements and side ratios.

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The domain and range are described for a relation, and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively. For example, if the relation is R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then: Domain = {1, 2, 3, 4} and Range  = {2, 3}.

The domain and range of a function are the elements of a function. The domain is the set of all the input elements of a function, and the range is the possible outcome given by the function.

Domain→ Function →Range. If there exists a function f: α → β such that every element of α are mapped to elements in β, then α is the domain, and β is the co-domain.

The image of an element 'p' under a relation R is given by 'q', where (p,q) ∈ R. The function's range is the set of images. The domain and range of a function are denoted in general as follows:

Domain(f) = {x ∈ R} and range(f) = {f(x): x ∈ domain(f)}.

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Answer:

200 students vote in the election

Step-by-step explanation:

We know

120 votes = 60%

1% = 2 votes

To find how many students vote in the election, we take

2 x 100 = 200 votes

So, 200 students vote in the election

The simplified form of the given expression is [tex]4x^2y^3[/tex].

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the abilities they possess, many rules of exponents are given.

Adding exponents while maintaining the same base is the rule for multiplying similar bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing similar bases, maintain the base constant and deduct the exponential of the denominator from the exponential of the numerator.

The given expression is:

[tex]\sqrt[4]{256x^8} * \sqrt[4]{y^{12}}[/tex]

The first term can be separated and written as follows:

[tex]\sqrt[4]{256} * \sqrt[4]{x^8} * \sqrt[4]{y^{12}}[/tex]

Using the identity [tex]\sqrt[n]{x^a} = x ^{\frac{a}{n} }[/tex] we can write the expression as:

[tex]4 * x ^{\frac{8}{4} } * y^{\frac{12}{4} }\\\\4x^2y^3[/tex]

Hence, the simplified form of the given expression is [tex]4x^2y^3[/tex].

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Answer:

Circumference = 56.55

Area=254.47

Answer:

x=1/10

Step-by-step explanation:

2x+3 = 4-8x

2x+8x=4-3

10x=1

x=1/10