How do you prove a trapezoid is isosceles?

If the length of two segments is equal then the two segments are congruent.

If l(AB) = l(CD) then seg AB ≅ seg CD.

Two line segments to be congruent if and only if they have the same length.

Two shapes are congruent if they are exactly the same shape and exactly the same size. In congruent shapes, all corresponding sides will be the same length and all corresponding angle will be the same measure.

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The values of a and b are;

⇒ a = 3

⇒ b = 3

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

An exponential function is,

⇒ f (x) = a bˣ

And, It passes through the points (0, 3) and (3, 81).

Now,

Since, It passes through the points (0, 3) and (3, 81).

Hence, Substitute x = 0 ,  f(x) = 3 in the function,

⇒ f (x) = a bˣ

⇒ 3 = a b⁰

⇒ a = 3

And, Substitute x = 3 ,  f(x) = 81 and a = 3 in the function,

⇒ f (x) = a bˣ

⇒ 81 = 3 b³

⇒ b³ = 27

⇒ b = 3

Thus, The values of a and b are;

⇒ a = 3

⇒ b = 3

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The algebraic expression √((x²-1)²) simplifies to x²-1

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Given: sqrt((x^(2)-1)^(2))=x^(2)-1

√((x²-1)²)

The square root will cancel out the square:

Thus, √((x²-1)²)  = x²-1

Therefore,  √((x²-1)²) simplifies to x²-1

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By using a linear combination, we can write our number using only hundreds and ones as:

2,857 = 28*100 + 57*1

To write the number using only hundreds and ones we need to write our number as a linear combination of ones and hundreds, so we can write:

2,857 = a*100 + b*1

There are multiple solutions for this, we can use b to cover the ones and the tens, so:

57 = b*1

57 = b

And we can use a to cover the hundreds and thousands, so:

2,800 = a*100

2,800/100 = a

28 = a

Then we can write our number using only hundreds and ones as:

2,857 = 28*100 + 57*1

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a) The function velocity of the particle is v(t) = 0.5 · t² + 6 · t + 7, b) The distance traveled by the particle is 467 feet.

In this problem we have the equation that represents the acceleration of a particle. The function velocity (v) is obtained by integrating the function acceleration (a) and the function position is obtained by integrating the function velocity. Now we present the definitions of each function:

Velocity

v(t) = ∫ a(t) + C

Position

s(t) = ∫ v(t) + C

Where C is the integration constant.

The distance traveled during the time interval is found means of definite integrals:

Δs = [tex]\int\limits^b_a {v(x)} \, dx[/tex]= s(b) - s(a)

a) First, determine the function velocity of the particle:

v(t) = ∫ (t + 6) dt + C

v(t) = 0.5 · t² + 6 · t + C

7 = C

v(t) = 0.5 · t² + 6 · t + 7

b) Second, determine the distance traveled in the given time interval:

Δs = s(10) - s(0)

Δs = 0.167 · 10³ + 3 · 10² + 7 - 0.167 · 0³ - 3 · 0² - 7

Δs = 467

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a. Angle g is corresponding to angle c.

b. Angle f is alternate to angle d.

c. Angle d is corresponding to angle h.

d. Angle c is vertically opposite to angle a.

e. Angle c is alternate to angle e.

f. Angle f is vertically opposite to angle h.

g. Angle e is corresponding to angle a.

h. Angle e is vertically opposite to angle g.

Please mark me BRAINLIEST if you like my answer

Answer:

27

Step-by-step explanation:

first you multiply 6x4 which is 24 the you divive 15 by 5 you'll get 3 then you add 24 + 3 and your answer is 27

Answer:

[tex]\begin{aligned}\textsf{(a)} \quad y&=-6x^2\\y&=4x^2-2\end{aligned}[/tex]

[tex]\textsf{(b)} \quad x=\dfrac{1}{4}y^2[/tex]

Step-by-step explanation:

A graph is symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph.

Linear functions are not symmetric with respect to the y-axis.

Quadratic functions are symmetric with respect to the y-axis if the y-axis is their axis of symmetry, so when the variable x is squared.

Cubic functions are not symmetric about the y-axis.

Square root functions are not symmetric about the y-axis.

There are two quadratic functions with x² in the given answer options.

Test to see if they are symmetric with respect to the y-axis.

Test for symmetry

To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.

Given function:

[tex]y=-6x^2[/tex]

Replace x with (-x):

[tex]\implies y=-6(-x)^2[/tex]

[tex]\implies y=-6x^2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.

Given function:

[tex]y=4x^2-2[/tex]

Replace y with (-y) and x with (-x):

[tex]\implies y=4(-x)^2-2[/tex]

[tex]\implies y=4x^2-2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.

A graph is symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, -b) on the graph.

Linear functions are not symmetric with respect to the x-axis.

Quadratic functions are symmetric with respect to the x-axis if the x-axis is their axis of symmetry, so when the variable y is squared.

Cubic functions are not symmetric about the x-axis.

Square root functions are not symmetric about the x-axis.

There is one quadratic functions with y² in the given answer options.

Test to see if it is symmetric with respect to the x-axis.

Test for symmetry

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

Given function:

[tex]x=\dfrac{1}{4}y^2[/tex]

Replace y with (-y):

[tex]\implies x=\dfrac{1}{4}(-y)^2[/tex]

[tex]\implies x=\dfrac{1}{4}y^2[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the x-axis.

The value of the variable x and the measures of each side of the triangle ΔDEF found using the definition of an isosceles triangle are;

x = 9

DE = 13

EF = 28

DF = 28

An isosceles triangle is a triangle that has two angles in the triangle that are congruent  and two congruent sides.

The specified parameters are;

∠D is congruent to ∠E in triangle ΔDEF

The length of the segments of ΔDEF are;

DE = x + 4

EF = 4·x - 8

DF = 7·x - 35

The (base) angles ∠D and ∠F of ΔDEF are congruent, therefore, ΔDEF is an isosceles triangle (definition)

Therefore;

EF = DF (Definition of an isosceles triangle)

4·x - 8 = 7·x - 35

7·x - 4·x = 3·x = 35 - 8 = 27

3·x = 27

x = 27 ÷ 3 = 9

x = 9

DE = x + 4

Therefore;

DE = 9 + 4 = 13

EF = 4·x - 8

Therefore;

EF = 4 × 9 - 8 = 28

DF = 7·x - 35

Therefore;

DF = 7 × 9 - 35 = 28

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An example of linear graph is y=2x+1

A linear equation is graphically represented by a linear graph.

For given real numbers A, B, and C, where A and B are not 0, a linear equation is one that can be expressed as Ax + By = C.It is a straight line graph.

Let's examine the graph.

A straight line is formed on the graph by the equation y=2x+1, which is a linear equation. When the value of x rises, the value of y eventually rises by the sum of the value of x plus two.

1). Determine the two changing quantities.

2).Let x and y be the first and second quantities, respectively.

3).Next, find out three ordered pairs (x, y) which satisfy the given equation.

4).Present these values in a tabular form.

5).Plot the points given in the graph.

6).Join the points.

This way we can form our graph

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Answer:

Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.

Step-by-step explanation:

Information—especially that which is slanted or deceptive—used to advance or publicize a specific political cause or point of view.

Glitzy Generalizations

Use expressions or words that sound appealing and are widely accepted.

Card Arranging

Using only those ideas and facts that support your argument.

Plain people

Tell voters that you are a normal person with same needs and beliefs as theirs.

Testimonial

Persuades people to do something by leveraging their popularity as a celebrity or athlete.

Bandwagon

Encourages a tendency to follow the crowd

Using names

Put a bad name on your opponent.

Glitzy Generalizations , Card Arranging , Plain people , Testimonial , Bandwagon , Using names are the six techniques used by propaganda.

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Answer:

75%

Step-by-step explanation:

First, you subtract 200 from 350 to get the difference, which is 150.

Then, you do 150 divided by 200 since 200 is the starting number and it is increasing by 150.

150/200 = 0.75

To convert the decimal into a fraction multiply by 100.

0.75*100 = 75

Answer:

Step-by-step explanation:

3< 0 + 2

3 < 2

the inequality is false because 3 is greater than 2, so the ordered pair (0,3) can’t be a solution of the inequality

Answer:

(0, 3) is not a solution to y < x + 2.

Step-by-step explanation:

Plug the given coordinates in to the inequality:

(0, 3)  →  x = 0,  y = 3

y < x + 2

3 < 0 + 2

3 ≮ 2

(0, 3) is not a solution to y < x + 2.

Answer:

x = 2y - 65

Step-by-step explanation:

During the time period of 20 years the percent decreases in the country's population is 3.28%.

Percentage is a number or ratio which is a fraction of hundred.

Given,

Population of the country in 1990 = 152 million

Population of the country in 2010 = 147 million

Percent decrease in the population will be ,

= [ (1990's population - 2010's population)/1990's population ]*100

= [ (152 - 147 )/152]*100

= [5/152]*100

= 3.28%

Hence , the decrease in the population will be 3.28%.

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The value of x in the Algebraic expressions is x = w / (56+r).

What is Algebra?

Algebra is a branch of mathematics focused on the study of mathematical symbols and the rules for manipulating those symbols. In algebra, letters and other symbols represent numbers, which can be manipulated and combined to solve equations and other mathematical problems. Algebra is used in a variety of different fields, from engineering to economics, and is essential for anyone studying mathematics. Algebra can be used to solve problems involving linear equations, quadratic equations, polynomials, and more. Algebra also provides an important foundation for more advanced fields of mathematics, such as calculus. By learning the basics of algebra, students can gain an understanding of key mathematical concepts and gain the skills necessary to solve complex problems.

The solution is,

given:        19x + rx  = -37x + w

            ( 19x + 37x) = w - rx

                56x + rx  = w

                 x(56+r )  = w

                             x = w / (56+r)

Therefore the value of x in the algebraic expression is  x = w / (56+r).

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Hence, yes we can solve the triangle with the help of Law of Cosines.

What is trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here given that,

Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible.

Yes, with the help of Law of Cosines we can solve the triangle and the formula for it is

[tex]c^2=a^2+b^2-2abcos(C)[/tex]

where, [tex]a,b,c[/tex] are the side lengths of the triangle and [tex]C[/tex] is the angle.

Hence, yes we can solve the triangle with the help of Law of Cosines.

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The formula for slope-intercept form is: y = mx + b

    m = the slope of the line

    b = the y-coordinate of the y-intercept, (0,b)

In this case, the slope is 3, since you go up 3 and to the right 1 to get from the point at (1,1) to the point at (2,4).  3/1 = 3

The line crosses the y-axis at (0,-2), so your b-value is -2.

The equation is y = 3x - 2.

In general, lines that increase (go uphill) from left-to-right have a positive slope.  Lines that decrease (go downhill) from left-to-right have a negative slope.  

The compound interest implies that Erica owes $10865 after 5 years

The given variables can be represented as:

The compound interest formula is given as

A = P(1 + r/n)^nt

Also from the question, we have

n = 12

This is so because the loan is compounded 12 times in a year as a result of being compounded monthly

Solving further, we replace the variables with their values in the above equation

A = 5300 * (1 + (8%/12))^(6*12)

Evaluate

A = 10865

Hence, the amount owed is $10865

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The two quantities have proportional relationship and it's slope is 333.33

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

In this case, we have to determine is there's a uniform increase or decrease of the quantity.

The formula of proportionality is often given as

y = kx

Let's take two points and check if they share the same constant of proportionality

2000 = k(6)

k = 333.33

1000 = k(3)

k = 333.33

The relationship between sales and day is proportional.

The slope of the graph is given as

m = y₂ - y₁ / x₂ - x₁

m = 2000 - 1000 / 6 - 3

m = 333.33

NB: The slope and constant of proportionality in this case are the same quantity.

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For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

Yes, whole numbers are closed under addition

It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

So the set of whole numbers are closed under addition

Addition of the set of positive integers is closed because the sum of any two integers is also an integer.

Consider subtraction. Positive numbers are not closed under subtraction because picking a larger number to subtract from a smaller one results in a negative number result.

Therefore,  For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

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The real zeroes of the given polynomial are located at (1, 2).

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

Given that, x⁴-2x³+x-2

Checking the real zeroes,

Considering point (1, 2)

y = 2 and x = 1

Putting the values,

x⁴-2x³+x-2 = 1-2+1-2 = 2

And, y = 2

Therefore, LHS = RHS

Hence, The real zeroes of the given polynomial are located at (1, 2).

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The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440

From the question, we have

⁸C₇ and ¹¹P₅

The combination expression: ⁸C₇

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 8 and r = 7

Substitute the known values in the above equation

Total = ⁸C₇

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

⁸C₇ = 8!/7!1!

Evaluate

⁸C₇ = 8

(b) The permutation expression: ¹¹P₅

The number of ways of selection could be drawn is calculated using the following permutation formula

Total = ⁿPᵣ

Where

n = 11 and r = 5

Substitute the known values in the above equation

Total = ¹¹P₅

Apply the permutation formula

ⁿPᵣ = n!/(n - r)

So, we have

¹¹P₅ = 11!/6!

Evaluate

¹¹P₅ = 55440

Hence, the values are 8 and 55440

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The answer to this Question is A we can use basic knowledge from linear equations to find the answer

What is Linear Equation?

Linear Equation is a equation in which degree of variables is 1 only

Yes the given case is possible only under some conditions that we can define as follows and as given in Linear Equations from Options

together cole and maggie have won 30 games and we are also given that  out of those 30 maggie has won 4 games

we should closely see at Linear Equations given in Options.

therefore cole has won 26 games which is more than 13

Hence the answer to the Question is Yes

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The equations are matched as below and the graph is plotted and attached

A log-log graph, also known as a log-log plot, is a two-dimensional graph of numerical data used in science and engineering that use logarithmic scales on both the horizontal and vertical axes.

The exponential graph is the opposite of logarithmic graph

In the given functions

log (x) is logarithmic function

10× is exponential function

Similarly, the natural exponent graph is the opposite of natural logarithm graph

in the given functions

e× is the natural exponential

ln (x) is the natural logarithm

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The number of distinguishable permutations in the given letters are:

a.) Bigger= 720

b.) Hollywood = 362,880

C.) possess = 5040

Permutation is defined as the arrangement of data set in a definite form which involves multiplication from the given number to 1.

The word 'bigger' contains 6 letters. Therefore the permutation of 6 = 6×5×4×3×2×1 = 720

For the word 'hollywood' contains 9 letters. Therefore the permutation of 9 =9×8×7× 6×5×4×3×2×1= 362,880

For the word 'possess' contains 7 letters. Therefore the permutation of 7 = 7× 6×5×4×3×2×1 = 5040.

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In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range.

The group of all outputs of a function is called its range. for example: Let's have a look at the function f: A→ B, where f(x) = 2x and A and B each represent a "collection of natural numbers. The domain in this case is A, and the co-domain is B. The range then appears as the function's output. so Set of all even natural numbers is the range.

A relation between a number of set of inputs with only one output corresponding to each of the input is called function.

Example:

Y = 2x

1. First, we have to write the function y=f(x) and then solve the equation for x and taking out equation of form x=g(y).

Suppose we have a function y=x2+1 and we have to find it range so,

we have to solve it for x to get

x=√y-1.

2. Now we have to find the domain of g(y), and this is simply the range of function f(x).

For our example,

y−1≥0, so [1,∞) is the range of f(x)=x2+1.

3. If we can't solve equation for x, then we can try it by drawing the graph of the function and find its range.

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