The figure shows △ABC . BD is the angle bisector of ∠ABC .
What is AD ?
Enter your answer in the box as a fraction.
____ units
Answers
[tex]\dfrac{|AD|}{|DC|}=\dfrac{|BA|}{|BC|}\\\\\\\dfrac{|AD|}{|DC|}=\dfrac{8}{10}=\dfrac{4}{5}[/tex]
Moreover:
[tex]|AD|+|DC|=6[/tex]
so:
[tex]|DC|=6-|AD|[/tex]
and
[tex]\dfrac{|AD|}{|DC|}=\dfrac{4}{5}\\\\\\\dfrac{|AD|}{6-|AD|}=\dfrac{4}{5}\qquad\qquad\text{cross multiplying}\\\\\\ 5\cdot|AD|=4\cdot\big(6-|AD|\big)\\\\5\cdot|AD|=24-4\cdot|AD|\\\\5\cdot|AD|+4\cdot|AD|=24\\\\9\cdot|AD|=24\qquad|:9\\\\\\|AD|=\dfrac{24}{9}=\boxed{\dfrac{8}{3}}[/tex]
The length of AD is [tex]\dfrac{8}{3}[/tex].
Given:
BD is the angle bisector of the triangle ABC.
The figure of the triangle ABC.
To find:
The length of AD.
Explanation:
According to the Angle Bisector Theorem, the angle bisector of a triangle divides the opposite side in the same proportion of the other two sides.
Let [tex]x[/tex] be the length of AD. Then, the length of DC is [tex]6-x[/tex].
Using the Angle Bisector Theorem, we get
[tex]\dfrac{8}{10}=\dfrac{x}{6-x}[/tex]
[tex]\dfrac{4}{5}=\dfrac{x}{6-x}[/tex]
[tex]4(6-x)=5(x)[/tex]
[tex]24-4x=5x[/tex]
[tex]24=5x+4x[/tex]
[tex]24=9x[/tex]
[tex]\dfrac{24}{9}=x[/tex]
[tex]\dfrac{8}{3}=x[/tex]
Therefore, the length of AD is [tex]\dfrac{8}{3}[/tex].
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Related Questions
Describe how the graph of y= [tex]x^{2} [/tex] can be transformed to the graph of the given equation.
y = [tex](x-12) ^{2} [/tex] + 3
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
with that template in mind, let's see
[tex]\bf y=(x-12)^2+3\implies y=\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{-12})^2\stackrel{D}{+3}[/tex]
A = 1, so no change there from the parent.
B = 1, no change there either
C = -12, now, C/B is -12/1 or -12, that means a horizontal right shift of 12
D = +3, this means, going up by 3 units.
Madison wants to make cookies for her little sisters birthday party. She is cutting a roll of cookie dough into pieces that are 1/2 inch thick. If the roll is 13 inche long, how many cookies can she make
Answers
Answer:
26 cookies
Step-by-step explanation:
13 times 2
Which property justifies this statement?
x−4=x−4
A. Substitution Property of Equality
B. Transitive Property of Equality
C. Reflexive Property of Equality
D. Symmetric Property of Equality
Answers
Answer:
C. Reflexive Property of Equality
Step-by-step explanation:
[tex]x-4=x-4[/tex]
A. Substitution Property of Equality
Some value is substituted for any variables. In the given equation, the value for x is not substituted.
B. Transitive Property of Equality
If [tex]c=b+1 \ and \ b+1=4[/tex] then c=4. Given equation does not represent transitive property.
C. Reflexive Property of Equality
When both sides are equal , then it is reflexive property
[tex]x-4=x-4[/tex] represents reflexive property of equality
D. Symmetric Property of Equality
If [tex]1+2=a[/tex] then [tex]a=1+2[/tex]
Given equation does not represents symmetric property
What is the playing surface called where the college basketball semi- finals are played
Answers
The playing surface where the college basketball semi-finals are played is called the court. It is rectangular in shape and has various markings such as the three-point line and free-throw line.
Explanation:The playing surface where the college basketball semi-finals are played is called the court or the basketball court. The court is rectangular in shape with a length of 94 feet and a width of 50 feet. It is divided into two halves with a midcourt line and has markings such as the three-point line, free-throw line, and key.
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convert 0.000064 to scientific notation
Answers
At a discount grocery store, Jessica paid 0.72 for an 8-ounce bottle of spring water. What is the cost of the spring water per ounce?
Answers
The cost of the spring water per ounce is .09.
How?
You just divide. .72/8= .09
Annette drives her car 120120 miles and has a mean of a certain speed. if the mean speed had been 3mph3mph more, she could have traveled 128128 miles in the same length of time. what was her mean speed?
Answers
Let's make 2 equations to represent Annette's speed.
T*S = 120
Where
T = the time Annette has been driving.
S = her mean speed.
120 = number of miles she's traveled.
and another equation that's
T*(S+3) = 128
So we now have 2 equations with 2 unknowns. They are
T*S = 120
T*(S+3) = 128
Let's divide the top equation by S on both sides and the bottom equation by (S+3) on both sides giving
T = 120/S
T = 128/(S+3)
So we now know that 120/S is equal to 128/(S+3). So let's make that equation and solve for S
120/S = 128/(S+3)
Multiply both sides by S(S+3)
120(S+3) = 128S
Distribute the 120 on the left
120S + 360 = 128S
Subtract 120S from both sides
360 = 8S
And divide both sides by 8
45 = S
So Annette's speed was 45 mph.
What are the odd numbers between 3497 and 3511?
Answers
3497
3499
3501
3503
3505
3507
3509
3511
what’s the slope for x+5=y
Answers
[tex]y = mx+b[/tex]
Where the m is the slope. Here, m=1.
What is the 8th term in the sequence?
an=25−3n
Enter your answer in the box.
Answers
Hence, the 8th term of the sequence is:
[tex]a_8=1[/tex]
Step-by-step explanation:We are defined the nth term in the sequence with the help of the relation or expression as:
[tex]a_n=25-3n-------(1)[/tex]
We are asked to find the 8th term of the sequence i.e. we are asked to find the value of [tex]a_n[/tex] when n=8.
so, we will put n=8 in the given expression (1).
[tex]a_8=25-3\times 8\\\\a_8=25-24\\\\a_8=1[/tex]
Hence, the 8th term of the sequence is:
[tex]a_8=1[/tex]
What is the value of x? Enter your answer in the box.
Answers
The value of x from the equilateral triangle is x = 12 and the side is 38
What is an Equilateral Triangle?
An equilateral triangle is a triangle in which all three sides have the same length.
Let the triangle be ΔABC , and
∠A = ∠B = ∠C = 60° and AB = BC = CA
Given data ,
Let the triangle be represented as ABC
Now , the triangle ABC is an equilateral triangle with
∠A = ∠B = ∠C = 60°
The measure of side AB = 4x - 10
The measure of side BC = 3x + 2
The measure of side AC = 5x - 22
And , the sides of the triangle will also be the same
So ,
Side AB = Side BC = Side CA
Substitute the values in the equation , we get
4x - 10 = 3x + 2 be equation (1)
On simplifying the equation , we get
Adding 10 on both sides of the equation , we get
4x = 3x + 12
Subtracting 3x on both sides of the equation , we get
x = 12
And ,
5x - 22 = 3x + 2
Adding 22 on both sides of the equation , we get
5x = 3x + 24
Subtracting 3x on both sides of the equation , we get
2x = 24
Divide by 2 on both sides of the equation , we get
x = 12
Hence , the value of x is 12
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what is 5 divided by 9374
Answers
A baker sells bread for $5 a loaf and rolls for $1 each. The baker needs to sell $35 worth of baked goods by the end of the day. Enter a linear equation that describes the problem.
Answers
Explanation:
Cost of 1 loaf of bread = $5
Cost of 1 roll = $1
The baker needs to sell both items and it should be worth $35.
To find the linear equation, Suppose, the baker sells “b” loaves of bread and “r” rolls.
Then the total cost of the sales has to be $35.
So, the linear equation will be:
5b + 1r = 35
Identify the values of a b and c in the quadratic function y = 3x -5x +2
Answers
12/25 x 5/18 !!!!!!!!!!
Answers
(12*5)/(25*18) = 60/450
Then to simply you find a common number, the largest number you can divide into 60 and 450 and still be left with a interger (whole number), in this case it is 30. Then you divide the top and bottom by it:
(60/30)/(450/30) = 2/15
Hope this helps! :)
Value of 12/25 x 5/18 in the simplest form is 2/15.
What is Simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given a equation 12/25 x 5/18 we need to simplify this
Using PEMDAS
12/25 * 5/ 18
=> (12 * 5)/ 25 *18
=> 2 / (5 * 3)
=> 2/15
Therefore, Value of 12/25 x 5/18 in the simplest form is 2/15.
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Megan's DVD club membership, which is $8, is deducted automatically from her bank account every month. Which expression shows the total deductions for the year?
1. (−$8) ÷ 12
2. (−$8) ⋅ 12
3. (−$8) − 12
4. (−$8) + 12
Answers
Hello,
100% CorrectThe correct answer is B) (-$8) × 12
Hope this helps!!!! :)
(Took the Math test)
**(Vanessa)**
Put the numbers in order from least to greatest.
17
, 4.12, 41
10
, 42
15
A) 17
, 4.12, 41
10
, 42
15
B) 41
10
, 17
, 4.12, 42
15
C) 41
10
, 4.12, 17
, 42
15
D) 42
15
, 4.12, 17
, 41
Answers
4/3 of a number is 20. What is the number?
Answers
[tex] \frac{4x}{3} = 20[/tex]
Now solve:
[tex]4x = 60[/tex]
[tex]x = 15[/tex]
Hope this helps!
Using the order of precedence for arithmetic operators, these two formulas will calculate the same result: =22/2*5 =22/(2*5).
Answers
22/2 x 5 = 11 x 5 = 55
22/(2 x 5) = 22 / 10 = 2.2
So, you see both have different answers.
Graph this equation on this graph
Answers
Now let's solve for the vertex form.
y=2x^2-8x+5
y-5=2x^2-8x
y-5=2(x^2-4x)
y-5+8=2(x^2-4+4)
y+3=2(x-2)^2
Thus the vertex is at (2,-3)
Now that you know this, plug in values(-1,0,1,2,3,4,5) to get (15,5,-1,-3,-1,5,15) respectively
For anyone taking or has taken vlacs algebra one, I really need a paragraph describing what was in module #1 for a discussion based assessment. Please help :!
Answers
What is equal to 3log2 + log4
Answers
Log Rule #2: log(x^y) = y*log(x)
Using those log rules, we can say...
3*log(2) + log(4) = log(2^3) + log(4) <-- use log rule #2
3*log(2) + log(4) = log(8) + log(4) <-- simplify 2^3 to get 8
3*log(2) + log(4) = log(8*4) <-- use log rule #1
3*log(2) + log(4) = log(32) <-- simplify 8*4 to get 32
So the expression simplifies to log(32)
Find the greatest possible value of the product xy, given that x and y are both positive and x + 2y = 30
Answers
x + 2y = 30, x = 30 - 2y
xy = (30-2y)y = 30y-2y^2
so if -2y^2+30y = 100, then we can take out a (-2), so: y^2-15y=-50, y^2-15y+50=0
(y-5)(y-10)=0
y-5=0, y=5
y-10=0, y=10
Now we can "plug n play": plug each into x = 30-2y
x = 30-2(5) = 30-10 = 20
x = 30-2(10) = 30-20 = 10
So if we make x=20, y=5... xy = 100
And if x=10, y=10... xy = 100
Now we need to try other number variations to see if they can make xy > 100
if y=6, then x = 30-2 (6) = 30-12 = 18
xy = (18)(6) = 108. Ooh! there's a better choice, but let's keep going
if y=7, then x = 30-2(7) = 16, xy = 7*16 = 112
Even higher! But let's check others
If y=8, then x = 30-16=14, so xy = 112
But from here, the higher y gets the product of xy starts to decrease again
So the greatest possible value comes from 7*16 and 8*14, in which x*y was the maximum it could be at 112
Answer: The maximum value of the product x*y is 112.5
Step-by-step explanation:
We have that x + 2y = 30
so we can isolate one of the variables and get:
x = 30 - 2y
now, the product of x*y can be written as:
x*y = (30 - 2y)*y = 30y - 2y^2
now, we want to find the maximum of 30y - 2y^2
because the leading coeficient is negative (-2), we know that the hands of the quadratic function will go downwards, so the zero of the derivate of this quadratic equation will give us the value where the equation has a maximum:
f(y) = -2*y^2 + 30*y
f'(y) = -4*y + 30 = 0
y = -30/4 = 7.5
So the maximum value is:
f(7.5) = -2*7.5^2 + 30*7.5 = 112.5
I WILL MARK BRAINLIEST ANSWER
What is the equation of the following graph in vertex form?
y = (x − 3)2 − 1
y = (x + 3)2 − 1
y = (x − 4)2 − 2
y = (x − 4)2 + 8
Answers
Answer:
y = (x + 3)2 − 1
:)
Mike and Julie surveyed students to determine how many had a grade of A in math. They recorded their findings for each survey in the table below.
Students with an A in Math
Number of A grades Number of students surveyed
20
4
40
8
60
12
80
16
What is the constant of proportionality of the ratio of students surveyed to the number of A grades?
0.2
0.5
2
5
Answers
20/4 = 5
40/8 = 5
60/12 = 5
80/16 = 5
Answer is 5
Answer:
Option D 5
Step-by-step explanation:
Mike and Julie surveyed students to determine how many had a grade of A in math as given in the table.
We have to find the proportionality constant of the ratio of students surveyed to the number of A grades.
Since proportionality constant = [tex]\frac{\text{Students Surveyed}}{\text{number of A grades}}[/tex]
=[tex]\frac{20}{4}=5[/tex]
Similarly we can get the constant form other data which is equal to 5.
Therefore, Option D. 5 is the correct option.
The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?
Answers
Perimeter is the sum of all sides of a polygon. For this case, the perimeter is expressed as: P=a+b+c. It has been said that the longest side is twice that of the shortest side. Let's assume that a is the longest side and b is the shortest side. So, the equation for the shortest side is,
6.2 = 2c
c = 3.1
14.5 = 6.2 + 3.1 + b
14.5 = 9.3 + b
I take no credit for this answer. It was solved by Taskmasters.
A 3-cup bottle of dish soap costs $5.28. What is the price per fluid ounce?
Answers
3 cups = 24 fluid ounces
To find the unit price, divide the price by the number of fluid ounces.
($5.28)/(24 fl oz) = $0.22/fl oz
Answer:A 3-cup bottle of dish soap costs $3.36. What is the price per fluid ounce.
Step-by-step explanation:
How can I tell if they are none transversal?
Answers
A non-transversal line in geometry is a line that does not intersect two or more lines at distinct points. Similarly, in geology, folds with a horizontal axial line, called non-plunging folds, can be analogous to non-transversal lines as they don't intersect with another structure at a distinct point.
Explanation:In mathematics, specifcally in geometry, transversal is a line that passes through two lines in the same plane at two distinct points. If a line does not intersect two or more lines at distinct points, it can be considered as a non-transversal line.
According to the information provided, in the context of folds in geology, the axial line becomes a key concept. The axial line refers to an imaginary line drawn along the crest of a fold. If the axial line is horizontal, the fold is referred to as a non-plunging fold and it could be analogous to a non-transversal line in geometry, as it doesn't intersect with another structure at a distinct point.
However, if the axial line is tilted (plunging), it might be considered as a transversal in the sense that it 'intersects' the horizontal plane at a distinct angle. Similarly, if a line in geometry is tilted and intersects two or more lines at distinct points, it is a transversal line.
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Evaluate 32 + (7 − 2) ⋅ 4 − 6 / 3.
a. 24
b.54
c.27
d.28
Answers
For some reason I keep getting the result 50.
Determine the exponential function that satisfies the given conditions:
The initial mass is 1.4g and it is halving every 4 days.
Answers
To determine the exponential function, use the general form of an exponential function and substitute the given values. The equation is y = 1.4 * (1/2)^(x/4).
Explanation:An exponential function represents exponential growth or decay. In this case, the given information states that the initial mass is 1.4g, and it is halving every 4 days. We can use the general form of an exponential function, y = ab^x, where a is the initial value, b is the growth/decay factor, and x is the time in days.
Since the mass is halving every 4 days, the decay factor is 1/2, since the mass is halving. The equation becomes y = 1.4 * (1/2)^(x/4).
This equation represents the exponential function that satisfies the given conditions.