please help quickly
If UY=13p-1 and VX=20p-95 than what is UY

Please Help Quickly If UY=13p-1 And VX=20p-95 Than What Is UY

Answers

Answer 1

Viewing the given triangle, the information given helped to determine side UY to be 90

What are similar triangles?

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

WX and WY, XV and YU

The solution is worked out using sides WX and XV, WY and YU

WX / WY = XV / YU

WX / WY = 1/2 since it is a mid segment

1 / 2 = (20p - 95) / (13p - 1)

13p - 1 = 2 * (20p - 95)

13p - 1 = 40p - 190

190 - 1 = 40p - 13p

189 = 27p

p = 7

solving for UY

= 13p - 1

= 13 * 7 - 1

= 90

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Related Questions

Its pre-algebra. I need it fast

Answers

Answer:

Obtuse and isosceles

Step-by-step explanation:

obtuse because an angle is more than 90* and isosceles because two sides are equal.

Hope this helps!

A gallon of gas cost $3.50 at the beginning of the month. At the e of the month it cost $3.75. What was the percent change in the price of a gallon of gas?
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ty:-;​

Answers

Answer:

7.14%

Step-by-step explanation:

Any comparison with the increase or decrease in price has to be compared to the ORIGINAL price. (at the beginning of the month.)

The price increased from $3.50 to $3.75, an increase of $0.25

To find what percent it is use:[tex]\frac{change}{original}[/tex]×100%

[tex]\frac{0.25}{3.50}[/tex]×100%

Answer:

7.1428571% increase

7  1/7 % increase

Step-by-step explanation:

To find the percent increase ( we know this is an increase since the amount went up), take the new amount and subtract the original amount

3.75 - 3.50 = .25

Divide by the original amount

.25 / 3.50

.071428571

Multiply by 100 %

7.1428571%

7 1/7 %

explain what the slope and intercept mean in each situation the amount of money y in a cash box after x tickets are purchased for carnival games. The slope of the line is 1/4 and the y intercept is 8

Answers

Answer:

The (1/4) slope is the prive per ticket.  The y intercept is the money in the cash box before any tickets were sold.

Step-by-step explanation:

Let y be the money and x the numbers of tickets sold, as requested.  We are told that the equation for this situation is:

   y = (1/4)x + 8

Let's assume the money is in units of dollars.  The slope of (1/4) would mean that each carnival game ticket cost $(1/4), or 25 cents.  The y-intercept is the value of y when x=0, which means zero tickets have been sold.  That means that the cash box had $8 before any sales were made.  [perhaps to use for making change].

The moon orbits earth at 384400km. The distance from earth to the sun is 149600000km. The diamiter of the sun is 1391000km. What would the diamiter of earth have to be to appear the same size as the sun from the moon if the celestial objects are in the order shown here : Sun, earth, moon.

Answers

Answer:

The diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers

Step-by-step explanation:

To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to know the distance from the Moon to the Sun and the distance from the Moon to Earth.

Since the distance from the Moon to the Sun is much greater than the distance from the Moon to Earth, the angle subtended by the Sun at the Moon will be much smaller than the angle subtended by Earth at the Moon.

Therefore, the size of Earth as seen from the Moon will be much larger than the size of the Sun as seen from the Moon.

To find the ratio of the size of Earth to the size of the Sun as seen from the Moon, we can use the formula:

size ratio = (distance to Earth / distance to Sun) x (Sun's diameter / Earth's diameter)

Substituting in the given values, we get:

size ratio = (384400km / 149600000km) x (1391000km / Earth's diameter)

Simplifying, we get:

size ratio = 0.00257 x (1391000km / Earth's diameter)

To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to solve for Earth's diameter. Dividing both sides of the equation by 0.00257, we get:

Earth's diameter = (1391000km / 0.00257) = 54304839.858km

Therefore, the diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers.

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Suppose that X ∼ Geom(p) and Y ∼ Geom(r) are independent. Find the probability P (X < Y )

Answers

The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent

What is probability ?

Probability could be defined as the ratio of number of favourable outcomes and total number of outcomes.

Given ,

X ∼ Geom(p) and Y ∼ Geom(r) are independent.

P(X<Y)=P(⋃1≤k<n,n∈N{X=k,Y=n})

=∑1≤k<n,n∈NP(X=k,Y=n)

=∑n=1∞∑k=1n−1P(X=k)P(Y=n)

=∑n=1∞∑k=1n−1p(1−p)k−1q(1−q)n−1

=pq∑n=1∞(1−q)n−11−(1−p)n−1p

=q∑n=1∞(1−q)n−1(1−(1−p)n−1)

=1−q / ∑n=1∞[(1−q)(1−p)]n−1

=1−q / 1−(1−p)(1−q)

=1−(1−p)(1−q)−q / 1−(1−p)(1−q)

=p(1−q) / p+q−pq.

Hence, The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent.

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54 is 72% of what number?

Answers

Using Y as the answer, 54/72% = Y/100%. 72Y = 54 x 100, 72Y = 5400 divided by 100 = 75.
54 is 72% of 75.

This problem requires simple division in which we will be dividing 54 by 0.72:

54 / 0.72 = 75

This can be checked through calculation of 72% of 75, which can be started with by dividing 75 by 10 to find 10% of 75:

75 / 10 = 7.5, and we can divide again by 10 to find that 0.75 is 1% of 75.

Now that we have 1%, we multiply it by 72 to find that:

0.75 • 72% = 54

Therefore, 54 is 72% of 75.

Is 7x and 7x2 are like terms?

Answers

7x and 7x2 are NOT like terms.

Terms with identical variables (like x or y) and any exponents (like the 2 in x2). Similar phrases can be combined. Similar or like terms are those that only differ in numerical coefficient but have the same literal coefficients raised to the same powers. Related terms are those that have the same exponent applied to similar variables. Dissimilar or unlike terms are those that do not have the same literal coefficients raised to the same powers. Only the numerical coefficients can change in terms similar to those of algebra.

However, because to the various exponents, 7x and 7x2 are NOT similar expressions.

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graphing piece wise functions

Answers

Answer:

thats by step overr.ic. yttt. .

which equation represents a line perpendicular to the given line x-4y=7

Answers

The equation of the line perpendicular to x - 4y = 7 can be written as:

y = 4*x + b

Where b could be any real number.

Which equation represents a line perpendicular to x - 4y = 7?

Two lines are perpendicular if the product between the slopes of the lines is equal to -1.

Where a general line in the slope-intercept form is written as:

y  =a*x +b

And the given line is:

x - 4y = 7

Writing this in the slope-intercept form we will get:

-4y = -x - 7

y = (-1/4)*x + 7/4

So the slope is -1/4, then the slope of our line must be such that:

a*(-1/4) = -1

a = -4*-1 = 4

a =4

So the line perpendicular to the given one is:

y = 4*x + b

Where b can be any real number.

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Which linear graph represents a proportional relationship?

A graph of a straight line that passes through the points 0 comma 2 and 1 comma 2.

A graph of a straight line that passes through the points negative 1 comma 0 and negative 1 comma 1.

A graph of a straight line that passes through the points 0 comma 0 and 1 comma negative 2.

A graph of a straight line that passes through the points 0 comma 2 and 2 comma 3.

Answers

Answer: The answer is C

Step-by-step explanation: i took the test and got it right

fraction bigger than 2 out of 5 and smaller than 2 out of 3. When i divided numerator by denominator , it will be 0.533.

Answers

The fraction that is bigger than 2/5 and smaller than 2/3 is 8/15.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3, 1/5 is a fraction.

We have,

Let the fraction be a/b.

2/5 < a/b < 2/3

Now,

a/b

= (2/3 + 2/5) / 2

= (10 + 6) / 30

= 16/30

= 8/15

= 0.533

Thus,

The fraction is 8/15.

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What is the coefficient of x3y4 in 2x 3y2 5?

Answers

The coeficient of x^3+y^4 in the algebraic expression is the number 2

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

2x^3+ 2y^4

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.

2 is the coefficient of x^3+y^4

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Stella took a taxi from her house to the airport. The taxi company charged a pick-up

fee of $1. 20 plus $1. 50 per mile. The total fare was $29. 70, not including the tip. How

many miles was the taxi ride?

09

Answers

Equivalent fractions are those that, despite their visual differences, reflect the same value. we consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces.

what is fraction?

Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.

If the denominators differ, similar fractions with a common denominator must be used. This requires figuring out the LCM of the two denominators. To be used as a denominator in fractions with various denominators, rename the fractions with a similar denominator.

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How do you write an x-intercept as a point?

Answers

The X-intercept is the point where the line crosses the x-axis. This happens where the Y is equals to zero.

The point slope form of a line is an equation of the line that takes on the form y - y1 = m(x - x1). In this equation, m is the slope of the line, and (x1, y1) is a point on the line. The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. This always happens at the point where y is equal to 0. Therefore, we find the x-intercept of a line in point-slope form by plugging y = 0 into the equation and then solving for x. The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. It is said to be as the x-coordinate of a point where a line, curve, or surface intersects the x-axis.

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plsss help

For the given polynomial, determine which of the binomials listed are factors. Pick two.


f(x) = 2x3 + 9x2 + 13x + 6



A.x + 1

B.x – 1

C.x + 2

D.x – 2

E.x + 3

F.x – 3

Answers

The factors for the Polynomial are (x+1) and (x+2).

What is Factor Theorem?

According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.

Given:

f(x) = 2x³ + 9x² + 13x + 6

Now, first (x+1) =0

x= -1

put x= -1 in f(x) as

f(-1) = 2(-1) + 9(1) + 13(-1) + 6

      = -2 + 9 - 13 + 6

      = 0

So, (x+1) is factor of f(x).

Now, second (x-1)= 0

x= 1

put x= 1 in f(x) as

f(1) = 2(1) + 9(1) + 13(1) + 6

      = 2 + 9 + 13 + 6

      = 31

So, (x-1) is not a factor of f(x).

Now, second (x+2)= 0

x= -2

put x= -2 in f(x) as

f(1) = 2(-2)³ + 9(-2)² + 13(-2) + 6

      = -16 + 36 - 26 + 6

      = 0

So, (x+2) is factor of f(x).

Now, second (x-2)= 0

x= 2

put x= 2 in f(x) as

f(1) = 2(2)³ + 9(2)² + 13(2) + 6

      = 16 + 36 + 26 + 6

      = 84

So, (x-2) is not a factor of f(x).

Now, second (x+3)= 0

x= -3

put x= -3 in f(x) as

f(1) = 2(-3)³ + 9(-3)² + 13(-3) + 6

      = -54 + 81 - 39 + 6

      = -6

So, (x+3) is not a factor of f(x).

Now, second (x-3)= 0

x= 3

put x= 3 in f(x) as

f(1) = 2(3)³ + 9(3)² + 13(3) + 6

      = 54 + 81 + 39 + 6

      = 180

So, (x-3) is not a factor of f(x).

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Find value of y

[tex] {y}^{2} - 58 = 25 \times 4 + 11[/tex]

Answers

Hello there!

Answer:

y = ± 13

Step-by-step explanation:

[tex]y {}^{2} - 58 = 25 \times 4 + 11 \\ y {}^{2} - 58 = 100 + 11 \\ y {}^{2} - 58 = 111 \\ y {}^{2} - 58 - 111 = 111 - 111 \\ y {}^{2} - 169 = 0 \\ (y + 13)(y - 13) = 0 \\ y = - 13 \: \: \: and \: \: \: y = 13[/tex]

Using the numbers 4. 3, -1. 07, and -2. 971,write an expression containing both addition and subtraction that simplifies to a negative number

Answers

Therefore , the solution of the given problem of expression comes out to be -1.07+(-2.917)-4.3=-8.287.

Define expression.

An expression is made up of a number, a variable, or a combination of both, along with certain operation symbols. Two expressions that make up an equation are separated by an equal sign. Example of a Word 8, 3, and the result is 11.

Here,

Given :  the numbers 4. 3, -1. 07, and -2. 971

Using the above given numbers we can construct

an expression which contain both

addition and subtract

thus ,

In order to form we use + sign and - sign

We get,

-1.07+(-2.917)-4.3=-8.287

Therefore , the solution of the given problem of expression comes out to be -1.07+(-2.917)-4.3=-8.287.

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Work out the equation of the line shown below.

Give your answer in the form y = mx + c, where m and c are

integers or fractions in their simplest forms.

Answers

to get the equation of any straight line, we simply need two points off of it, let's use those from the picture below.

[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{-100})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{140}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{140}-\stackrel{y1}{(-100)}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{(-10)}}} \implies \cfrac{140 +100}{30 +10} \implies \cfrac{ 240 }{ 40 } \implies 6[/tex]

[tex]\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}{(-100)}=\stackrel{m}{ 6}(x-\stackrel{x_1}{(-10)}) \\\\\\ y +100 = 6 ( x +10)\implies y+100=6x+60\implies {\Large \begin{array}{llll} y=6x-40 \end{array}}[/tex]

Is the interval 0 1 Infinite?

Answers

Therefore, the interval (0, 1) must be countless and infinite. Since the interval (0, 1) is as large as R, R is also infinite.

Interval:

In mathematics, a (real) interval is a set of real numbers containing all real numbers between any two numbers in the set. For example, the set of numbers x such that 0 ≤ x ≤ 1 is an interval containing (0, 1), and all numbers in between. Other examples of intervals are the set of numbers with 0 < x < 1, the set of all real numbers, the set of non-negative real numbers, the set of positive real numbers, the empty set, and any Singleton (a set of one element).

Real intervals play an important role in integral theory. This is because real intervals are the simplest set whose "length" (or "scale" or "magnitude") is easy to define. The notion of measure can be extended to more complex sets of real numbers, leading to the Boral measure and finally the Lebesgue measure.

Intervals are central to interval arithmetic, a general numerical technique that automatically provides guaranteed bounds for any mathematical expression, even in the presence of uncertainties, mathematical approximations, and arithmetic rounding.

Open Interval:

Open intervals do not include endpoints and are indicated by parentheses.  For example, (0, 1) means greater than 0 and less than 1. This is (0, 1) = {x | 0 This interval can also be expressed as ]0, 1[ . Please refer to the following.

Closed Interval:

A closed interval is an interval that contains all boundary points and is indicated by square brackets. For example, [0, 1] means greater than or equal to 0 and less than or equal to 1.

Half- Open Interval:

A half-open interval contains only one of its endpoints and is represented by a combination of open and closed interval notation. Example: (0, 1) means greater than 0 and less than or equal to 1, [0, 1) means greater than or equal to 0 and less than 1.

Complete Question:

II. Identify the following terms described in each item. Quantitative & Quaeritated. It can be separated into different categories that are distinguished by some nonnumeric characteristics. 2. It consists of numbers representing counts or measurements. Quantitative Quantitative 3. The result from either a finite number of possible values or countable number of possible values as 0, or 1, or 2, and so on 4. The result from infinitely many possible values that can be associated with points on a continuous scale in such a way that there are no gaps or interruptions 5. It is characterized by data that consist of names, labels, or categories only. 6. It involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless. 7. It involves meaningful amounts of differences between data. It has no true zero point or absolute zero. 8. It contains all the properties of the interval level but has true zero point or absolute zero. 9. It is a complete collection of all elements to be studied. 10. It is a branch of Mathematics that deals with the collection, organization presentation, analysis, and interpretation of data.​

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Graph the line that passes through the points (-3, -1) and (1, -1) and
determine the equation of the line.

Answers

Answer:

y = -1

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

To find slope we look for the rise/run or (y2 - y1) / (x2 - x1)

The slope here is 0, and the y-intercept is located at (0,-1), so the equation is

y = -1

Answer:

y = -1

Step-by-step explanation:

2. A square playground has a side which measures 40 metres. What is its area?​

Answers

The area of a square playground which has a side measures 40metres would be 100[tex]m^2[/tex].

How to calculate area?

step1

Perimeter of square = 40m

We have given that perimeter of square is 40m. To find its area, we have to calculate its side first.

Perimeter of square = 4× side

Substituting values in formula

Area of square = 4 × side

=> 40 = 4 × side

=> side = 40÷4

=> side = 10m

Side of square is 10m.

step 2

Calculating area of square :

We found that side of square is 10m. To find it area, required formula is:

Area of square = (side)²

To find area, substitute values in formula :-

Substituting values in formula :-

Area of square = (side)²

=> Area of square = (10)²

=> Area of square = 10 × 10

=> Area of square = 100m

so if the perimeter of square is 40m then the area is 100m.

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What are the 13 types of angles?

Answers

There are several types of angles, including: acute angles, right angles, obtuse angles, straight angles, reflex angles, complementary angles, supplementary angles, adjacent angles, linear pair, vertically opposite angles, alternate interior angles, alternate exterior angles, and corresponding angles.

Acute angles: angles measuring less than 90 degrees.

Right angles: angles measuring exactly 90 degrees.

Obtuse angles: angles measuring greater than 90 degrees but less than 180 degrees.

Straight angles: angles measuring exactly 180 degrees.

Reflex angles: angles measuring greater than 180 degrees but less than 360 degrees.

Complementary angles: two angles that add up to 90 degrees.

Supplementary angles: two angles that add up to 180 degrees.

Adjacent angles: two angles that share a common vertex and a common side but no common interior points.

Linear pair: two angles that add up to 180 degrees and share a common side.

Vertically opposite angles: two angles formed by two intersecting lines that are opposite to each other.

Alternate interior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and inside the parallel lines.

Alternate exterior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and outside the parallel lines.

Corresponding angles: two angles formed by two intersecting lines that are in the same relative position.

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the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³

Answers

[tex] \longmapsto \: 7x + 5x + 2x = 35820 \\ \\ x = \frac{35840}{14} = 2560[/tex] length equals to 7 into 2560 = 1792

slope intercept form of y + 6 = (x - 4)

Answers

y + 6 = (x - 4)

remove the parenthesis

y + 6 = x - 4

y + 6 + 4 = x

add 4 to both sides

y + 10 = x

simplify & switch sides to x being the solution

x = y + 10

and here’s your answer




look at picture please

Answers

The equivalent trigonometric identity to cot²θ + 1 is cot²θsec²θ

What are trigonometric identities?

Trigonometric identities are equations which contain the trigonometric ratios.

How to show the equivalent identity of cot²θ + 1?

Since we have the trigonometric identity cot²θ + 1,we need to find its equivalent expression.

So, we proceed as follows

Since cot²θ + 1 = 1/tan²θ + 1     (since cot²θ = 1/tan²θ)

Now taking the L.C.M, we have that

1/tan²θ + 1 = (1 + tan²θ)/tan²θ

We know that the trigonometric identity 1 + tan²θ = sec²θ

So, substituting this into the equation, we have that

(1 + tan²θ)/tan²θ =  sec²θ/tan²θ

Since cot²θ = 1/tan²θ, substituting the values of the variables into the equation, we have that

sec²θ/tan²θ = cot²θsec²θ

So, cot²θ + 1 = cot²θsec²θ

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Please help!!!! I'LL GIVE 5 STAR RATING AND A THANKS

Answers

Answer:

9.1

Step-by-step explanation:

For the first one, I just multiplied 4.55 and 0.5 by 2 somthey are proportional. Or divide distance by time!

Solve by factorising:
x^2+10x+21=0

Answers

Answer:

[tex]x = -7\\x = -3[/tex]

Step-by-step explanation:

The steps are in the image attached to this response.

The equation for this is ax^2+bx+ c. You get the answer by finding factors of A and C; multiply them to each other so example after you find a factors of A which would be D and E, and B which would be F and G; multiply D with F and E with G. After that see if the two answers you got add or subtract to get the same number as B. Find both of the factors like for this example the best factors to use for A well is 1•1 because thats the only factor possible and for C the best factor is 3•7 because since there both just multiply by one if you add them together you get 10. After you do all that this is the formula (Dx+/-G)(Ex+/-F) plug all the numbers in and then you get the answer (1x+7)(1x+3) more formal way:(x+7)(x+3)

P.S if you want to check its right make it back into a quadratic equation: (D•E)(D•F)+(G•E)+(G•F)=ax^2+bx+c

What is the formula for a isosceles triangle?

Answers

The formula for an isosceles triangle is A = (1/2) * b * h, where b is the base, h is the height, and A is the area.

The formula for an isosceles triangle is A = (1/2) * b * h. This formula is used to calculate the area of an isosceles triangle. To use the formula, you need to know the base, b, and the height, h, of the triangle. The base is the length of any one of the two equal sides of the isosceles triangle, and the height is the distance from the base to the opposite vertex. Once you have these measurements, you can plug them into the formula to calculate the area of the triangle. The formula multiplies the base, b, by the height, h, and then divides the product by two. This will give you the area of the triangle, A.

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Tamika is ordering a taxi from an online taxi service. The taxi charges $3. 50 just for the pickup and then an additional $0. 75 per mile driven. How much would a taxi ride cost if Tamika is riding for 5 miles? How much would a taxi ride cost that is m miles long?

Cost for 5 miles:

Cost for m miles:

Answers

If the pickup charge for taxi is $3.50 and additional charge of $0.75 per mile , then the cost for riding 5 miles is $7.25  and cost for riding m miles is $[tex]3.50+0.75m[/tex]   .

The pickup charge that taxi service charges is = $3.50  ;

the additional charge for per miles driven is = $0.75  ;

we have to find the cost for riding 5 miles ;

So , the total cost for riding 5 miles is = [tex]Pickup Charge + (Additional Charge)\times(Number Of Miles Driven)[/tex] ;

substituting the values , the total cost equation becomes ;

[tex]Total Cost = 3.50 + 0.75\times5[/tex]

= [tex]3.50+3.75[/tex]

= 7.25

So , the cost for 5 miles is = $7.25  ;

to find cost for driving "m" miles ,we substitute the number of miles = m;

[tex]Total Cost = 3.50+0.75\times m[/tex]

= [tex]3.50+0.75m[/tex]

Therefore , the cost for riding m miles is $ [tex]3.50+0.75m[/tex] .

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Given: AAED ≈ ABEC and
AC BD.
Prove: AABD≈ ABAC.
Note: quadrilateral properties are not permitted in this
proof.

Answers

The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.

What are the four traits of triangles that are similar?

The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.

According to given information:

Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.

Given that ΔAED ≈ΔBEC & AC = BD.

as  ΔAED ≈ΔBEC, AD = BC     .................(1)

Now in  ΔABD and ΔBAC,

     AD = BC        

(corresponding sides of similar triangles) [from (1)]

     AB = AB        

(common side)

     AC = BD      

   (given)

∴     ΔABD ≈ΔBAC  (By SSS criteria)    

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