Answers
If DBC = 90° what is the relationship between AD and CD?
_____________________________________
Answer
AD=CD
_____________________________________
The sum of supplementary angles is 180º
If ∠ DBC = 90°
∠ DBC = 90° so then ∠ DBA = 90º
DB is the same for the two triangles
and AB = BC
By the side angle side congruence theorem, we can conclude AD=CD
Related Questions
Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it.
can u also do the which rule part in addition to the proofs? thanks !
and u get brainliest if you make a proof chart
Answers
For the given parallelogram;
ΔESN ≅ ΔSNA (By ASA congruence).
What is meant by the term ASA congruence?According to the ASA congruence rule, if two angles of one triangle and the side provided between these two angles are equal to two angles of another triangle as well as the side provided between them, therefore the two triangles are congruent.In parallelogram ESAN
Given: SA || NE
SE || NA
Thus, it form parallelogram ESAN (apposite pair of sides parallel)
So,
∠ESN = ∠SNA (alternate interior angle)
∠ENS = ∠NSA (alternate interior angle)
SN = SN common
Thus, ΔESN ≅ ΔSNA (By ASA congruence).
To know more about the ASA congruence, here
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-Quadratic Equations-The sum of two integers is 42 and their product is 432. Write and solve an equation to find the two integers.
Answers
numbersThe first thing to do is to write the exact relations from the question, as follows:
[tex]\begin{gathered} x+y=42 \\ x\times y=432 \end{gathered}[/tex]Where X and Y stand for the unknown integer numbers.
Now, we will isolate Y in the first equation and substitute in the second one. This way, we will be able to find the value of X. From this strategy, we perform the calculation that follows:
[tex]\begin{gathered} y=42-x\to x\times(42-x)=432 \\ 42x-x^2=432\to0=x^2-42x+432 \\ x^2-42x+432=0 \end{gathered}[/tex]Now, it is important to remember the Bhaskara relation. But first, let's remember that any quadratic equation attends to the following generic form:
[tex]y=ax^2+bx+c[/tex]And we use the Bhaskara relation to find the values of X where Y is 0. In the present question, the constants are the following:
[tex]\begin{gathered} a=1 \\ b=-42 \\ c=432 \end{gathered}[/tex]And the Bhaskara relation is:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Now, we will substitute the values and perform the calculation.
[tex]\begin{gathered} x_{1,2}=\frac{-(-42)\pm\sqrt[]{(-42)^2-4\times1\times432}}{2\times1} \\ x_{1,2}=\frac{-(-42)\pm\sqrt[]{1,764-1,728}}{2}=\frac{42\pm\sqrt[]{36}}{2}=\frac{42\pm6}{2} \\ x_1=\frac{42+6}{2}=\frac{48}{2}=24_{} \\ x_2=\frac{42-6}{2}=\frac{36}{2}=18 \end{gathered}[/tex]As you can see, both numbers, 24 and 18, if summed will result in the number 42. For this reason, we found here, not only the value of X but also the value of Y. Because there is no distinction between X and Y, you say that:
The two number which are integers, their sum is 42 and their multiplication is 432 are the numbers 24 and 18.In an experiment, the probability that event B occurs is, and the probability that event A occurs given that event B occurs is 5 6 What is the probability that events A and B both occur? Simplify any fractions.
Answers
We are given the following information:
The probability that event B occurs is:
[tex]P(B)=\frac{3}{5}[/tex]And the probability that event A occurs given that event B occurs is:
[tex]P(A|B)=\frac{5}{6}[/tex]And we need to find the probability that both A and B occur.
To solve this problem, we have to use the conditional probability formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Where
P(A|B) is the probability of A given that B occurred.
P(B) is the probability of B.
And P(A∩B) is the probability of A and B occuring.
Thus, we solve for P(A∩B) in the previous equation:
[tex]P(A\cap B)=P(A|B)\cdot P(B)[/tex]And substitute the known values:
[tex]P(A\cap B)=\frac{5}{6}\cdot\frac{3}{5}[/tex]We multiply the fractions and get the following result:
[tex]\begin{gathered} P(A\cap B)=\frac{5\cdot3}{6\cdot5} \\ P(A\cap B)=\frac{15}{30} \end{gathered}[/tex]Finally, we simplify the fraction by dividing both numbers in the fraction by 15:
[tex]P(A\cap B)=\frac{1}{2}[/tex]Answer: 1/2
Complete the table below. Provide an answer for each integer division problem, and write a related equation using integer multiplication.
Answers
You need to remember the Sign Rules for Division:
[tex]\begin{gathered} \frac{-}{-}=+ \\ \\ \frac{+}{+}=+ \\ \\ \frac{-}{+}=- \\ \\ \frac{+}{-}=- \end{gathered}[/tex]And the Sign Rules for Multiplication:
[tex]\begin{gathered} -\cdot-=+ \\ +\cdot+=+ \\ -\cdot+=-_{} \\ +\cdot-=- \end{gathered}[/tex]Then, knowing those rules, you can solve the operations given in the exercise:
1. For the Integer Division:
[tex]-36\div(-9)=4[/tex]The result is positive because both numbers have the same sign.
Now, knowing that result, you can set up the following Related Equation using Integer Multiplication:
[tex](-9)(4)=-36[/tex]2. For the second Division, you get:
[tex]24\div(-8)=-3[/tex]Then, its corresponding Related Equation using Integer Multiplication can be:
[tex](-8)(-3)=24[/tex]3. For the next one, you get:
[tex]50\div10=5[/tex]So, its corresponding Related Equation using Integer Multiplication can be:
[tex]10\cdot5=50[/tex]4. For the last Division, you get:
[tex]42\div6=7[/tex]Hence, its corresponding Related Equation using Integer Multiplication can be:
[tex]7\cdot6=42[/tex]Therefore, the answer is:
Research shows that 9% of 6th graders in K-6 schools have tried cigarettes and 59% of 7th graders in 8-9 or 7-9 middle schools have tried cigarettes. What is the relative percentage increase, rounded to the nearest percent?
Answers
The initial percentage is 9%
Then, the final percentage is 59%.
Then, the relative percentage increase;
[tex]\begin{gathered} C=\frac{x_2-x_1}{x_1}\times100 \\ C=\frac{59-9}{9}\times100 \\ C=\frac{50}{9}\times100 \\ C=5.555\times100 \\ C=556\text{ \%} \end{gathered}[/tex]You buy a square lot that is 330 ft. on each side. What is its size in acres?
Answers
Given in the question:
a.) A square lot is 330 ft. on each side.
To be able to determine the size of the lot in acres, let's first recall how many sq. ft. are there in 1 acre.
[tex]\text{ 1 acre = 43,560 ft.}^2[/tex]Step 1: Let's determine the area of the lot.
[tex]\text{ Area = s}^2\text{ ; Formula in getting the area of a square}[/tex]We get,
[tex]\text{ Area = 330}^2[/tex][tex]\text{ Area = }108,900ft.^2[/tex]Therefore, the area of the lot is 108,900 sq. ft.
Step 2: Let's convert the area in sq. ft. to an acre.
[tex]\text{ 1 acre = 43,560 ft}^2[/tex][tex]\text{ = 108,900 (ft}^2)\text{ x }\frac{1\text{ acre}}{43,560(ft^2)}[/tex][tex]\text{ = }\frac{108,900}{43,560}\text{ acre}[/tex][tex]\text{ = 2.5 acres}[/tex]Therefore, the size of the lot in acres is 2.5
If a coffee table was originally priced at $64 but was on sale for 75% off the original price. What is the sale price?
Answers
Answer:
$16
Explanation:
Original Price of the table =$64
There is a sale for 75% off the original price.
75% of the original price = 75% x 64
=0.75 x 64
=$48
Therefore, the sales price will be:
[tex]\begin{gathered} Original\; Price-Amount\text{ off} \\ =64-48 \\ =\$16 \end{gathered}[/tex]The sale price of the table is $16.
evalute 2×[4×(2+1)×3]
Answers
Given the expression:
[tex]2\times\mleft[4\times\mleft(2+1\mright)\times3\mright][/tex]The answer will be as follows:
[tex]\begin{gathered} 2\times\mleft[4\times\mleft(2+1\mright)\times3\mright] \\ =2\times\mleft[4\times3\times3\mright] \\ =2\times36 \\ =72 \end{gathered}[/tex]so, the answer will be 72
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
Answer:
13
Step-by-step explanation:
The value of x is 13. This can be shown thus:
(x - 7)² = 36
(x - 7)² = 6²
Therefore, x - 7 = 6
Collect like terms
x = 6 + 7
x = 13
To find the solution when adding vectors, simply draw and label the given information. Answer here
Answers
the answer to the statement is
To find the __________solution when adding vectors simply draw and label the given information.
is
To find the resultant solution when adding vectors simply draw and label the given information.
then the answer is
resultant
This is a 30-60-90 triangle.What is the measure of x?Rationalize the denominator.x = [?]?12
Answers
The value of x is:
[tex]x=4\sqrt[]{3}[/tex]To solvbe this, we need to use the tan function. The 60º is at the top left of the triangle, and the 30º angle is on the bottom right.
Then we know, the angle bottom right = 30º, the opposite leg = x and the adjacent leg = 12
The trignometrical function that relates those 3 things is tangent:
[tex]\tan (\theta)=\frac{\text{opposite leg}}{\text{ adjacent leg}}[/tex]In this case:
[tex]\begin{gathered} \tan (30º)=\frac{x}{12} \\ x=12\cdot\tan (30º) \end{gathered}[/tex]Thus:
[tex]\tan (30º)=\frac{1}{\sqrt[]{3}}\Rightarrow x=12\cdot\tan (30º)=\frac{12}{\sqrt[]{3}}[/tex]Now we need to rationalize the answer. To do it, we multiply and divide by the denominator:
[tex]x=\frac{12}{\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{12\sqrt[]{3}}{3}=4\sqrt[]{3}^{}[/tex]And that's the answer
Kevin rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 95 cents for each mile driven, Kevin had to payS1850 when he returned the truck or how many miles did he drive the truck?
Answers
To answer this, first subtract $ 18.99 from the total ( $ 1850 )
$1850 - $
2. The distance-time graph shows two cars that are traveling at the same time. Which car has the greater speed, and by how much? DA Car B Car A Distance (km) 480 420 3601 300 2401 1801 120 60 0 2 3 4 5 6 7t Time (h) 12
Answers
The speed of the car = distance/time
Let us find the speed of each car
Car A starts from (0, 0) to (6, 360)
Its speed is
[tex]SA=\frac{360-0}{6-0}=\frac{360}{6}=60[/tex]The speed of car A is 60 km/h
car B starts at (1, 0) to (6, 480)
Its speed is
[tex]SB=\frac{480-0}{6-1}=\frac{480}{5}=96[/tex]The speed of car B is 96 km/h
Therefor car B is faster than car A
Since the difference between their speeds = 96 - 60 = 36 km/h
Car B is faster by 36 km/h
suppose y varies directly with x, and y=21 when x=140. What is the value of y when x=36
1= 140
2= 165
3= 201.6
4= 176
Answers
The value of y when x = 36 is 5.4 as y varies directly with x.
What is the value of y when x equal 36?The proportional relationship is simply the relationships between two variables where their ratios are equivalent.
For a direct variation, the equation is a linear equation in two variables.
This is expressed as;
y varies directly with x ⇒ y ∝ x
y = kx
Where k is the proportionality constant.
First, we determine the proportionality constant k when y = 21 and x = 140
y = kx
k = 21 / 140
k = 3/20
Now, when x = 36, the value of y will be;
y = kx
y = 3/20 × 36
y = 108/20
y = 5.4
Therefore, the numerical value of y is 5.4.
Learn more about proportionality here: brainly.com/question/11202658
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Write the coordinates of the vertices after a rotation 270° clockwise around the origin.-10-8-6-4-2246810-10-8-6-4-2246810xyFGHF'=,G'=,H'=,SubmitQuestions
Answers
So,
Here we have the following vertices:
[tex]\begin{gathered} F(-9,-1) \\ G(0,-1) \\ H(-9,-2) \end{gathered}[/tex]We're going to rotate these vertices 270° clockwise around the origin.
Remember that a 270° clockwise rotation around the origin follows the rule:
[tex](x,y)\to(-y,x)[/tex]So, if we apply this rule to our points, we obtain:
[tex]\begin{gathered} F(-9,-1)\to F^{\prime}(1,-9) \\ G(0,-1)\to G^{\prime}(1,0) \\ H(-9,-2)\to H^{\prime}(2,-9) \end{gathered}[/tex]Sydnie has an online biology quiz due every 4 days and an online math quiz 3 days. If both quizzes are due onDue on December 7, when is the next day both quizzes will be due again?DECEMBER 2020STMO20RNNA. December 11B. December 18C. December 19D. December 25tes
Answers
In order to find the next day that the quizzes will be due again, we first need to find the least common multiple (LCM) of the numbers 4 and 3.
To do so, we first need to factorate each number:
[tex]\begin{gathered} 4\to2\cdot2 \\ 3\to3 \end{gathered}[/tex]Then, we multiply each factor the maximum number of times they appear. In this case, we need to multiply 2 two times and 3 one time:
[tex]2\cdot2\cdot3=12[/tex]So the LCM is 12. Now, we just need to add 12 days to the last due date, which was 7 December. Adding 12 days, the next due date will be 19 December.
So the answer is C.
Drag a number next to the correct description in the chart. Not all answer choices will be used
Answers
a) The distance between 4 and -24 on a number line.
A distance in one dimension can be calculated as:
[tex]D=|x_1-x_2|=|4-(-24)|=|4+24|=|28|=28[/tex]b) The distance between -12 and 5 on a number line.
[tex]D=|-12-5|=|-17|=17[/tex]c) The distance between -14 and -6 on a number line.
[tex]D=|-14-(-6)|=|-14+6|=|-8|=8[/tex]Note: when calculating distances, it doesn't matter which of the two numbers we put first in the substracion. It will yield the same result.
Answer: A) 28, B) 17 C) 8
need help asappppppp
Answers
Ok, so:
Let me draw the situation here below:
We're going to use the pythagorean theorem:
If 9² + 12² = 15², then, the triangle is a right triangle.
So, 81 + 144 = 225
So, the relation is good.
Then, the statement is true.
I need help can someone help me with the geometry question?
Answers
We are given the coordinates of the vertices of a quadrilateral. When we plot the points we notice the following figure:
Now, we will prove that this figure is a rectangle. First, for the figure to be a rectangle we need to prove that opposite segments are parallel, this means that their slopes are equal.
First, to determine the slope of a line segment we use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]Are points in the segment.
First, we will determine the slope of the segment that has endpoints (-1,3) and (-5,-3), this means that:
[tex]\begin{gathered} (x_1,y_1)=(-1,3) \\ (x_2,y_2)=(-5,-3) \end{gathered}[/tex]Substituting in the formula for the slope we get:
[tex]m=\frac{-3-3}{-5-(-1)}[/tex]Solving the operations:
[tex]m=-\frac{6}{-4}=\frac{3}{2}[/tex]Now we will determine the slope of the side opposite to this. The end-points are:
[tex]\begin{gathered} (x_1,y_1)=(2,1) \\ (x_2,y_2)=(-2,-5) \\ \end{gathered}[/tex]Substituting in the formula for the slope we get:
[tex]m=\frac{-5-1}{-2-2}=-\frac{6}{-4}=\frac{3}{2}[/tex]Since the slopes are both equal to 3/2, this means that the lines are parallel.
Now we determine the slope of the line with end-points (-1,3) and (2,1). This means:
[tex]\begin{gathered} (x_1,y_1)=(-1,3) \\ (x_2,y_2)=(2,1) \\ \end{gathered}[/tex]Substituting in the formula for the slope we get:
[tex]m=\frac{1-3}{2-(-1)}=-\frac{2}{3}[/tex]Now we use the segment in front of this one, we have the end-points:
[tex]\begin{gathered} (x_1,y_1)=(-2,-5) \\ (x_2,y_2)=(-5,-3) \end{gathered}[/tex]Now, we substitute in the formula for the slope:
[tex]m=\frac{-3-(-5)}{-5-(-2)}=\frac{2}{-3}=-\frac{2}{3}[/tex]Since the slopes are the same this means that pairs of opposite sides are parallel.
Now we will prove that pairs of adjacent sides are perpendicular. They are perpendicular if the product of their slopes is -1.
Since pairs of opposite sides have the same slope It will be enough to prove that the product of the different slopes we found is euqal to -1. The first slope we determine is:
[tex]m_1=\frac{3}{2}[/tex]And the third slope we found is:
[tex]m_2=-\frac{2}{3}[/tex]Now we determine their product:
[tex]m_1m_2=(\frac{3}{2})(-\frac{2}{3})=-1[/tex]Since the product is -1, this means that adjacent sides are perpendicular and therefore, we have proved that the figure is a rectangle.
In the image shown, Line n is a transversal cutting parallel lines and m.< 3 = x + 50< 7 - 2x + 20What is the measure of < 3?A)70°B)75°C)80°D)85
Answers
The angle 3 and angle 7 are corresponding angle. So,
[tex]\angle3=\angle7[/tex]Subtitute the measure of angles and obtain the value of x.
[tex]\begin{gathered} x+50=2x+20 \\ 2x-x=50-20 \\ x=30 \end{gathered}[/tex]Determine the measure of angle 3.
[tex]\begin{gathered} \angle3=20+50 \\ =70 \end{gathered}[/tex]So measure of angle
what is a factor of the expression 250 x cubed - 16 y ^ 3
Answers
Consider the given expression as,
[tex]250x^3-16y^3[/tex]The equation can be written as,
[tex](\sqrt[3]{250}x)^3-(\sqrt[3]{16}y)^3[/tex]Use the algebraic identity,
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]Substitute the values and simplify,
[tex](\sqrt[3]{250}x)^3-(\sqrt[3]{16}y)^3=(\sqrt[3]{250}x-\sqrt[3]{16}y)\mleft\lbrace(\sqrt[3]{250}x)^2+(\sqrt[3]{250}x)(\sqrt[3]{16}y)+(\sqrt[3]{16}y)^2\mright\rbrace[/tex]Thus, the factors of the given expression are,
[tex](\sqrt[3]{250}x-\sqrt[3]{16}y)\text{ and }\lbrace(\sqrt[3]{250}x)^2\text{ and }(\sqrt[3]{250}x)(\sqrt[3]{16}y)+(\sqrt[3]{16}y)^2\rbrace[/tex]How do I simplify rational expressions in algebra 2
Answers
Given:
The expression is given as,
[tex]\frac{x^3-7x+12}{9-x^2}[/tex]The objective is to simplify the expression,
Explanation:
Rearrange the given expression as,
[tex]\frac{x^3+0x^2-7x+12}{-x^2+9}[/tex]Now, divide the polynomials using long division method.
To find the quotient divide only the first term of the dividend and the first term of the divisor.
[tex]\frac{x^3}{-x^2}=-x[/tex]To perform division:
Now, the division can be calculated as,
Thus, the result can be written as,
[tex]-x+\frac{2x+12}{9-x^2}[/tex]Hence, the simplified expression is obtained.
What is the area of the acute triangle given below? A. 36 sq. units O B. 26 sq. units O C. 18 sq. units D. 72 sq. units
Answers
Solution
From the info given we have this:
h= 6ft
b = 12ft
And we can use the following formula:
[tex]A=\frac{b\cdot h}{2}=\frac{12\cdot6}{2}=36ft^2[/tex]then the answer would be:
a ) 36 ft^2
Janet solved the inequality and was asked to express her answer in set notation. Determine ifshe made a mistake, correct the mistake if she made one and create the correct expression inset notation.-X - 2 <-3-x < -1x < -1Set Notation: {x | x < -1}
Answers
It is given that:
[tex]\begin{gathered} -x-2<-3 \\ -x-2+2<-3+2 \\ -x<-1 \\ x>1 \end{gathered}[/tex]So she made a mistake in the last step.
The answer should be x>1
The set notation will be:
[tex]\mleft\lbrace x|x>1\mright\rbrace[/tex]Silvia manages a sub shop and needs to prepare smoked turkey sandwiches. She has 1- lb of turkey in the cooler, and each sandwich requires001Ib of turkey. How many sandwiches can she make?
Answers
The total amount of turkey available to make the sandwiches is 1 1/2lb. Each sandwich requires 1/2lb of turkey. To determine how many sandwiches can be made you have to divide the total amount by the amount needed per sandwich:
[tex]1\frac{1}{2}\div\frac{1}{2}[/tex]First, you have to express the mixed number as a fraction:
-Divide the whole number by 1 and add 1/2
[tex]\frac{1}{1}+\frac{1}{2}[/tex]-Multiply the first fraction by 2 to express it using the same denominator and add 1/2
[tex]\frac{1\cdot2}{1\cdot2}+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex]Now you can write the division as follows:
[tex]1\frac{1}{2}\div\frac{1}{2}=\frac{3}{2}\div\frac{1}{2}[/tex]To divide two fractions, you have to multiply the dividend by the reciprocal (inverse) fraction of the dividend. So, switch 1/2 upside down and multiply both fractions:
[tex]\frac{3}{2}\div\frac{1}{2}=\frac{3}{2}\cdot\frac{2}{1}=\frac{3\cdot2}{2\cdot1}=\frac{6}{2}=3[/tex]Silvia can make 3 sandwiches with the smoked turkey available.
Write the following in standard form: 423_13x4 + 7x + 11x2-2. 0-13.24 + 4.3 + 11x2 + 7æ - 2 O 13.04 + 403 + 11x2 + 72 – 2 11x2 + 7x + 423 – 2 – 13.4 – 13.4 – 4.3 + 11x2 + 7x – 2 +
Answers
The standard form of any polynomial is
[tex]ax^n+bx^{n-1}+cx^{n-2}+\cdots+d[/tex]That means arranging the powers of the variable from greatest to smallest and putting the numerical term at last
The given polynomial is
[tex]4x^3-13x^4+7x+11x^2-2[/tex]The greatest power is x^4, then it should be the first term
The next term is with x^3
The next term is with x^2
The next term is with x
The numerical term at last
Then the standard form is
[tex]-13x^4+4x^3+11x^2+7x-2[/tex]The answer is A (first choice)
If x = 3 is specifically a vertical asymptote (nonremovable discontinuity) of f(x), then what must be true about g(3) and h(3)? Explain your reasoning.
Answers
g (x)
and
h (x)
are the values of f(x)
g(3) is at right of asymptote x= 3
h(3) is at left of asymptote x= 3
then
g(3) = f (3) is + infinite
And
h(3) = f (3) is - infinite
A road sign reads "Speed Limit 30." Which statement best represents the allowed driving speeds (x) on this road?
Answers
hello
this question involves a simple multiplication of numbers
Answer:
Step-by-step explanation:3xp23
x
A map that was createdusing a scale of 1 inch : 3 milesshows a lake with an area of18 square inches. What is theactual area of the lake?
Answers
The scale 1 inch : 3 miles means that 1 square inch is proportional to 9 square miles. Then:
[tex]18\text{ sq in}\cdot\frac{9\text{ sq miles}}{1\text{ sq in}}=162\text{ sq miles}[/tex]The actual area of the lake is 162 square miles
Ged test how do I determine the value of x?
Answers
D) 26"
1) Similar triangles have proportional sides and congruent angles.
2) As the picture state that these two triangles are similar, then we can write out the following ratios:
[tex]\frac{x}{8}=\frac{19\frac{1}{2}}{6}=\frac{32\frac{1}{2}}{10}[/tex]But notice that, since we have Mixed Numbers it is easier to convert them to Improper fractions:
[tex]\begin{gathered} 32\frac{1}{2}=\frac{2\times32+1}{2}=\frac{65}{2} \\ 19\frac{1}{2}=\frac{2\times19+1}{2}=\frac{39}{2} \\ \end{gathered}[/tex]To convert it keep the denominator and multiply that by the whole number and then add to the numerator.
2.2) Now we can plug them back, but we just need two ratios the one with the missing length and a ratio with known length:
[tex]\begin{gathered} \frac{x}{8}=\frac{19\frac{1}{2}}{6}\Rightarrow\frac{x}{8}=\frac{\frac{39}{2}}{6} \\ \frac{x}{8}=\frac{\frac{39}{2}}{6} \\ 6x=8\cdot\frac{39}{2} \\ 6x=156 \\ \frac{6x}{6}=\frac{156}{6} \\ x=26 \end{gathered}[/tex]Hence, the line segment AB is 26inches long