Select the correct answer. what is the height, x, of the equilateral triangle? an equilateral triangle with the angles labeled as 60 degrees and a side length of 8 inches, the height labeled as x
a. in.
b. in.
c. in.
d. in.

Answer:

3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18.

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Answer:

Step-by-step explanation:

Depreciation means wearing and tearing in the value of an asset over the years

(a) Given:

p = initial value of an asset

i% = depreciation per year

n = number of years

Depreciation after n years (d) = [tex]p(1-\frac{1}{100} )^{n}[/tex]

Value of machine after n years = p-d

(b) Given:

p = RM100000

i% = 5

n = 10
Depreciation after 10 years = [tex]100000(1-\frac{5}{100} )^{10} = 59873.69392[/tex]

Value of machine after 10 years = p-d = RM100000 - RM59873.69392 = RM 40123.30608

Value of machine after 10 years to nearest ringgit = RM40123

Answer: 1/7

Step-by-step explanation: Find the GCD (Greatest Common Denominator) of the numerator and denominator. The GCD of 22 and 154 is 22. Divide both the numerator and denominator by the GCD = 22 ÷ 22; 154 ÷ 22. Reduced fraction: 1/7. Therefore, 22/154 simplified to lowest terms is 1/7.

Answer:

Parallelogram formula- 1/2 x base xheight

Step-by-step explanation:

The translation of the coordinate points on the graph by linear displacement in comparison of original points ( x , y ) get translated to     ( x + h,  y + k ) where h ∈R , k ∈R.

As given in the question,

Let us consider original coordinate point on a given graph be ( x ,y ).

Translation represents the change in the linear displacement or the location without changing the shape and size.

Shift of the point may be horizontally or vertically.

Let 'h' and 'k' be the horizontal and vertical shift.

If the horizontal shift is right then it is represented by x + h

If the horizontal shift is left then it is represented by x - h

If the vertical shift is up then it is represented by y +k

If the vertical shift is down then it is represented by y - k.

Therefore, the translation of the coordinate points on a given graph represented by original points ( x , y ) get translated to ( x + h,  y + k ) where h ∈R , k ∈R.

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The measure of convex arc upper Z is 243⁰ Option D

We should be aware that a convex angle is the angles that are irregular in nature

Assume that  the radius of the given circle is r.

The central angle of the lower arc ZWX = 41+180 = 221⁰

Note that then central angle of the upper arc ZWX = 360- 221⁰

This implies that the central angle of the upper arc ZWX = 360-221 = 139⁰

Recall that Lenght of arc = A/360 *2*π*r

Where A is the angle made by the radii, r= radius of the circle

Arc length of upper ZWX:

Arc length of upper ZWX = 139π/180*r

Arc length of upper ZWX = 139πr/180

The lenght is (139*22)/ 180*7

= 3058/2360

= 245⁰

In conclusion the measure of the convex upper is 245⁰

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AC = 25 units is the length of AD.

The Geometric Mean (Altitude) Theorem (9.7) The hypotenuse of a right triangle is split into two pieces by the height from the right angle. The geometric mean of the lengths of the two hypotenuse segments determines how long the altitude is.

Length of BC = 10 units

Length of DC = 4 units

We will use geometric mean theorem in the given right triangle to get the length of side AC.

[tex]hypotenuse/leg=leg/projection\\AC/BC=BC/DC\\x/10=10/4\\x=25[/tex]

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The average speed of Luna I is 1.78 x 10^-3 kilometers/minute.

To find the average speed of Luna I, we need to divide the total distance traveled (3.8 x 10^5 kilometers) by the total time it took to travel that distance (2.16 x 10^4 minutes). The quotient of these two numbers is 1.78 x 10^-3 kilometers/minute.

It's the ratio of distance covered to the time taken to cover that distance. The unit of speed is distance/time, which in this case is kilometers/minute. The speed of Luna I is in scientific notation, which is a way to express very large or very small numbers in a more manageable form.

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C) there is a 5% probability of rejecting a false null hypothesis

Simply put, probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Testing hypotheses is a crucial component of empirical research and evidence-based medicine. A well-developed hypothesis is only half the solution to the research problem. Working understanding of fundamental statistical principles is preferred for this, as well as subject-specific knowledge gleaned through a thorough survey of the literature.

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Factor -20 x-5 y, where x+y=4 and x+y=5. Our prime numbers become much, much harder to factor as we add a few extra digits.

When you factor in mathematics, you divide a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of an amount into its factors or divisors. The factorization of the integer 12, for instance, might be 3 times 4 or something similar. [tex]N = X^{a} * Y^{b} * Z^{c}[/tex] is used to represent the general factorization formula. In this instance, X, Y, and Z stand for a number's factors. Get a polynomial's GCF (Greatest Common Factor).

GCFs of polynomials should be factored out. By grouping the terms, factor a polynomial with four terms. trinomial of the form, and factor it. The size of our goods and the size of the data we use to check mean that each check takes an average amount of time longer. It is clear from this that factoring the product becomes significantly more difficult when we add a few digits to our prime integers.

Therefore the correct answer is option A)5(4x+y)

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The equation for dimensions of the rectangle is x(x - 3) = 10 and the width is 2 meters and the length is 5 meters.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

x(x-3)=10

x²-3x=10

x²-3x-10=0

x²-5x+2x-10=0

(x-5)(x+2)=0

x=-2,5

x=5 units

x-3=5-2

=2 units

The rectangle's dimensions are x(x - 3) = 10, with a width of 2 meters and a length of 5 meters.

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The measure of ∠S is 59.4° for trignometric identities

What are trigonometric identities?

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

ΔSTU:

s = 50 inches

t = 58 inches

u = 630 inches

Applying the cosines rule on ΔSTU.

s² = t² + u² - 2 x t x u x cos S

cos S = (t² + u² - s²) / 2tu

cos S = (58² + 27² - 50²) / (2 x 58  x 27)

cos S = (3364 + 729 - 2500) / 3132

cos S = 0.5086.

∠S = (0.5086)

∠S = 59.4°

Thus,

∠s angle value is  59.4°.

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The number of units that tile will he need to surround his pool is 19.82units.

this question is of quadratic equation ,

The number of units of tile simply refers to the perimeter.

So, we need to find all the sides of the rectangle.

Now, we have,

AB = 4.24 units

BD = 7.07 units.

So, we can find AD using pythagoras theorem.

So,

(AD)² + 4.24² = 7.07²

(AD)² + 17.978 = 49.985

(AD)² = 49.985 - 17.978

AD = √32.007

AD = 5.66 units

AD = BC = 5.66 units

Likewise, AB = DC = 4.24 units

Thus,

perimeter = 2(5.66) + 2(4.24) = 19.8 units.

The number of units that tile will he need to surround his pool is 19.82units.

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We found that translations have the following three properties: line segments are taken to line segments of the same length;

angles are taken to angles of the same measure; and. lines are taken to lines and parallel lines are taken to parallel lines.

Properties of Translations

- Distance Where the lengths of the segments stay the same.

-Angle Measures These remain the same.

-Parallelism Where the parallel lines will stay parallel.

-Collinearity The points will stay on the same line.

-Orientation The order of the letters will stay the same.

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]5x+4y=16\implies 4y=-5x+16\implies y=\cfrac{-5x+16}{4} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{4}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is -5/4 and it passes through (8 , -7)

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{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}{(-7)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{8}) \implies y +7= -\cfrac{5}{4} (x -8) \\\\\\ y+7=-\cfrac{5}{4}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{5}{4}x+3 \end{array}}[/tex]

Answer for the given problem,

a.  Percentage of 160 in number 40 is, 400%

b. The number for which 40 is 160% of that number is,  25

c.  The number which is 40% of 160 is, 64

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

a.   present quantity = 160

     whole quantity  = 40

    Percentage = 400 %

b.  present quantity = 40

    Percentage = 160

    Whole quantity  = 25

c.   whole quantity  = 160

     Percentage = 40%

     Present quantity = 64

Hence, Answers are respectively,  400%,  25,  64

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The GCF of the given expressions is 4x⁷⁶

The greatest common factor, abbreviated as GCF, of two numbers is the largest number that is a factor of, or divides evenly into, both of the numbers. When two numbers are relatively small, we have a quick and simple way to calculate their greatest common factor. We do this by listing all of the factors of each number, and then identifying the largest number that is in both lists.

Given here, The expressions 20x⁷⁶ and 8x⁹² and GCF(20,8)=4

and x⁷⁶ is a factor of  8x⁹²

∴ GCF(20x⁷⁶ , 8x⁹²) =4x⁷⁶

Hence, The GCF of the given expressions is 4x⁷⁶

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It is not possible to find the height of an isosceles triangle when only the base is given. To find the height, you would need to know at least one other side length, in addition to the base.

The height of an isosceles triangle can be found using the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the two shorter sides. To use the Pythagorean Theorem, you must first know the length of at least two sides of the triangle. Since only the base is given, it is not possible to calculate the height of the isosceles triangle. In order to find the height, you would need to know either the length of the other two sides, or the angle of one of the two equal sides. Once you have this information, you can use the Pythagorean Theorem to calculate the height of the triangle.

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Answer: −2<x<0

Step-by-step explanation: 2<x+4<4 2+−4<x+4+−4<4+−4 −2<x<0

Answer:

Depending of the figure that you are trying to find perimeter on, you just add up all the sides of that figure.

Answer:

The perimeter is the distance around a figure.

Step-by-step explanation:

For example, if I have a square where each side is 5 inches.  The perimeter would be 20 inches.  5 + 5+ 5 + 5, a square has four sides and each side length is 5 inches.

The description for the problem involving the linear function is given as follows:

The time it will take to make a total of 20 parts is of 6 minutes.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

In this problem, the function is defined as follows:

y = 2x + 8.

In which the variables are given as follows:

Hence the time needed to make 20 pieces is given as follows:

20 = 2x + 8

2x = 12

x = 12/2

x = 6 minutes.

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Logarithms are used for a variety of purposes in mathematics, science, engineering, and other fields. Some common uses of logarithms are mentioned below:

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

They are used for:

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The graph of the inverse variation equation is called a rectangular hyperbola.

A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.

An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.

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The answers to all the subparts are shown:

(1) The numerator is simply added. The denominator is copied.

(2) Yes, it has; yet, we include them since that is what needs to be done.

In a fraction, the number above the line is the numerator.

For instance, the numerator of the fraction 3/5 is 3.

A fraction's numerator displays the number of pieces that make up the whole while the denominator, or a number of equal parts, is displayed below the line.

So, we have the equation:

2x² + x/2x - 2 + x - 4/ 2x - 2

Now, answering questions taking the above-given equation into consideration:

(1) The numerator is simply added. The denominator is copied.

(2) Yes, it has; yet, we include them since that is what needs to be done.

(3) We complete the square, but we can also use the straightforward factoring approach.

(4)  We eliminate or simply cancel the factors in the numerator that are also present in the denominator to simplify the sum.

Therefore, the answer to all the subparts are shown:

(1) The numerator is simply added. The denominator is copied.

(2) Yes, it has; yet, we include them since that is what needs to be done.

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The polynomials which, when added to the polynomial 3x²+3x-1, is equivalent to the following expressions: 1, 2x²-3, and x+5 include the following below:

This is referred to as algebraic expressions that consist of variables and coefficients.

For 1; it is calculated as:

3x²+3x-1 + P = 1.

P = 2 - 3x² -3x.

For 2x²-3, it is calculated as:

3x²+3x-1 + P = 2x²-3

P = -2 -x² -3x

For x +5; it is calculated as:

3x²+3x-1 + P = x +5

P = 6 -2x -3x².

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The full question is:

Find a polynomial which, when added to the polynomial 3x^2+3x-1, is equivalent to the following expressions: 1, 2x^2-3, and x+5

An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a contradiction.

a fact or assertion that contradicts what someone else said or that differs from another fact or assertion to the point where one of them must be incorrect.

A situation or set of ideas that contradict one another is called a contradiction. A contradiction would be saying out loud that you support the environment while never remembering to empty the recycling. A statement that contains opposing ideas is frequently referred to as a "contradiction in terms."

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Answer:

N > -2/21

Step-by-step explanation:

Move -4/7 to the other side

n - 4/7 > - 2/3

n > - 2/3 + 4/7

Find a common denominator

n > - 14/21 + 12/21

Add

n > - 2/21

Answer:

Intial money=Rs 3300

final money=3300-(70×5)-(2×125)-2500

=3300-350-250-2500

=3300-3100=RS 200

Now,

share of each of them= 200/2=Rs100

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Answer: Probably negative 69