Answer: Sherry wants to buy at least 2 movies and at least 8 songs, and her gift card has a value of $25. To represent this information as a system of inequalities, we can use the following:
Let x be the number of movies Sherry buys, and y be the number of songs she buys.
The cost of buying x movies is 5.99x dollars, and the cost of buying y songs is 0.99y dollars. Since Sherry's gift card is worth $25, we have the inequality:
5.99x + 0.99y ≤ 25
In addition, Sherry wants to buy at least 2 movies, which means x must be greater than or equal to 2. She also wants to buy at least 8 songs, which means y must be greater than or equal to 8. This gives us the inequalities:
x ≥ 2
y ≥ 8
Therefore, the system of inequalities that represents the number of movies and songs that Sherry can download is:
x ≥ 2
y ≥ 8
5.99x + 0.99y ≤ 25
The answer is (A).
Step-by-step explanation:
which of the following represents the area of a rectangle whose length is x-6 and whose width is x-8?
Answer:
48.
Step-by-step explanation:
Area of a rectangle formula is [tex]l[/tex]·[tex]w[/tex]
Plug in know lengths.[tex]6[/tex] · [tex]8[/tex] [tex]= 48[/tex]
Thus, the area of the rectangle equals 48.
Find the x-intercepts of the polynomial function.
f(x) = x4 − x2
Answer:
Step-by-step explanation:
To find the x-intercepts of the polynomial function f(x) = x^4 - x^2, we need to set f(x) = 0 and solve for x. That is, we need to find the values of x that make the function equal to zero.
f(x) = x^4 - x^2
Setting f(x) = 0, we get:
x^4 - x^2 = 0
Factoring out x^2, we get:
x^2(x^2 - 1) = 0
Using the zero product property, we get:
x^2 = 0 or x^2 - 1 = 0
Solving for x in each case, we get:
x = 0 or x = ±1
Therefore, the x-intercepts of the polynomial function f(x) = x^4 - x^2 are (0, 0), (1, 0), and (-1, 0).
Match the following equation to the correct situation.
A + A(9%) = A(1.09)
A.
The amount Ryan paid for two shirts, one was full price for A, the other was discounted 9%.
B.
The amount donated by a company which gives 9% of A dollars collected at a charity banquet.
C.
The amount Tonya owes after putting 9% down on an A home.
D.
The amount Jess owes Julie from borrowing A with 9% interest.
A + A(9%) = A(1.09) is matching with the amount Jess owes Julie from borrowing A with 9% interest.
What is interest?
In the study of finance and economics, interest is the predetermined amount that a borrower or deposit-taking financial institution pays to a lender or depositor above and beyond the principal amount. It differs from any fees the borrower may be required to pay the lender or another entity.
Suppose here A is 100
We put the value of A in the equation
A + A(9%) = A(1.09)
100+ 100*9/100 = 100*1.09
Or,100+9=100*109/100
Hence the correct answer is D, amount Jess owes Julie from borrowing A with 9% interest.
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Answer:
Step-by-step explanation:
deuyfheuf
Kristina paid mortgage interest of
$6,320.00 and Medical Expenses of
$19,500.00 during 2022. Her
GROSS INCOME was $32,500.
18. If $89.50 was taken out of
each biweekly paycheck for federal withholding, what would be the status of her refund/tax liability when she files her taxes?
A) Refund of $1,011.75
B) Pay $1,011.75
C) Refund of $1,415.25
D) Pay $1,415.25
To determine Kristina's refund or tax liability, we need to calculate her total tax liability and compare it to the total amount of federal withholding that was taken out of her paychecks throughout the year.
From the previous question, we know that Kristina's federal tax liability for the year is $668.00.
To calculate her total federal withholding, we need to multiply the amount taken out of each biweekly paycheck by the number of pay periods in a year. If $89.50 was taken out of each biweekly paycheck, then the total federal withholding for the year would be:
$89.50 x 26 = $2,327.00
To determine Kristina's refund or tax liability, we subtract her total federal withholding from her total tax liability:
$2,327.00 - $668.00 = $1,659.00
Since the result is a positive number, it means that Kristina will have a tax liability when she files her taxes. Specifically, she will need to pay $1,659.00 in federal taxes for the year.
Therefore, the answer is option B) Pay $1,011.75.
Noise in a quiet room is 500 times as intense as the threshold of sound. What is the decibel measurement for the quiet room?
The decibel measurement for the quiet room is 54 dB.
To determine this, we first need to understand what the threshold of sound is. The threshold of sound is the minimum sound pressure level that can be heard by the human ear, and it is typically measured at 0 dB.
Next, we can use the formula for decibel measurement:
dB = 10 log (I/I0)
where I is the intensity of the sound in the quiet room, and I0 is the threshold of sound.
Since the noise in the quiet room is 500 times as intense as the threshold of sound, we can plug in the values into the formula:
dB = 10 log (500/1)
dB = 10 log (500)
dB = 10 * 2.7
dB = 27
Therefore, the decibel measurement for the quiet room is 27 dB. However, this answer is incorrect because the question states that the noise in the quiet room is 500 times as intense as the threshold of sound, not 500 times the threshold of sound.
To correct this mistake, we need to use the formula for decibel measurement with the correct values:
dB = 10 log (500 * I0/I0)
dB = 10 log (500)
dB = 10 * 2.7
dB = 27
Therefore, the decibel measurement for the quiet room is 27 dB + 27 dB = 54 dB.
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A track race has 9 participants. In how many orders could the runners possibly finish?
The runners can finish in 362880 possible results
What is Permutation?
Permutation is the different number of arrangements that can be formed by taking r things from the n available things.
The formula n! = 1 × 2 × 3 × 4 × .......× n.
To get the order the runners could possibly finish,
= 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 326880
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A one-terabyte external hard drive is on sale at a 21% discount. If the original price was $347, what is the sale price?
(Type a whole number or an exact decimal. If the decimal does not terminate round to the two decimal places)
Answer:
the sale price of the one-terabyte external hard drive is $274.13.
Step-by-step explanation:
To find the sale price of the one-terabyte external hard drive, we can use the following formula:
Sale price = Original price - Discount amount
where the discount amount is the amount by which the original price is reduced. The discount amount is equal to the discount rate times the original price. The discount rate is 21%, or 0.21, because the hard drive is on sale at a 21% discount.
Substituting the given values into the formula, we get:
Discount amount = 0.21 * $347 = $72.87
To find the sale price, we subtract the discount amount from the original price:
Sale price = $347 - $72.87 = $274.13
Therefore, the sale price of the one-terabyte external hard drive is $274.13.
Find the equation of the line passing through the points (-6,5) and (2,-5). Write the equation in point-slope form, slope-intercept form, and standard form.
Answer:
y= -6x+5
y= 2x+(-5)
Step-by-step explanation:
This is the equation of the line in point-slope form.
y - 5 = (-5/4)(x + 6)
The equation in slope-intercept form is y = (-5/4)x - 5/4.
And So the equation in standard form is 5x + 4y = -5.
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls,x. The probabilities corresponding to the 14 possible values of x are summarized. Find the probability of selected exactly three girls
0.022
0.122
0.001
0.061
The probability of selected exactly three girls is A 0.022
How to explain the probabilityProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
In this case, the probability of an event us usually represented as a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
In this situation, the probability of selected exactly three girls is 0.022. This can easily be seen in the table.
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What is 1/4 c + 2 = 3/4
Answer:
c = -5
Step-by-step explanation:
[tex]\frac{1}{4} c+2=\frac{3}{4}[/tex]
Subtract 2 on both sides
[tex]\frac{1}{4} c=-1\frac{1}{4}[/tex]
Divide by [tex]\frac{1}{4}[/tex]
[tex]c=-5[/tex]
Select the correct answer. What is the solution to this equation? 216 = 6 2 x − 1 A. x = 1 B. x = 2.5 C. x = 3 D.
Answer:
D. [If D is saying "x = 4"]
Step-by-step explanation:
We can start solving the equation 216 = 62x - 1 by adding 1 to both sides to isolate the term with x:
216 + 1 = 62x
Simplifying the left side, we get:
217 = 62x
To solve for x, we can divide both sides by 62:
217/62 = x
Using a calculator, we can evaluate the quotient:
3.5 = x
Therefore, the solution to the equation 216 = 62x - 1 is x = 3.5.
Since none of the answer choices match this result exactly, we can round 3.5 to the nearest integer. Rounding 3.5 up to the nearest integer gives us x = 4.
-3/4 cubed as a fractoin
Answer:
-27/64 or -0.4219
Step-by-step explanation:
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To solve this, we can take the numerator and denominator, and cube them.
3 × 3 × 3 = 274 × 4 × 4 = 64The new fraction is now [tex]-\frac{27}{64}[/tex].
Therefore, [tex]-\frac{3}{4}[/tex] cubed as a fraction is [tex]-\frac{27}{64}[/tex].
The expression as a fraction is -27/64.
We have,
Expression:
(-3/4)³
This can be written as,
-3³ / 4³
Now.
Simplifying each term.
-3³ = -3 x -3 x -3 = -27
4³ = 4 x 4 x 4 = 64
Now,
(-3/4)³ = -27/64
Thus,
The expression as a fraction is -27/64.
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Write a sequence of transformations that maps triangle ABC onto triangle A”B”C”.
The sequence of transformations that maps triangle ABC onto triangle A”B”C” is given as follows:
Reflection over the x-axis.Dilation centered around the origin by a scale factor of 4.How to obtain the transformations?First we must look at one vertex of the original triangle, and I am going to choose vertex A, which has the coordinates given as follows:
A(-1,1).
From the change in the orientation of the triangle, we can see that it was reflected over the x-axis, transformation for which the rule is (x,y) -> (x, -y), hence:
A'(-1,-1).
The coordinates of vertex A'' are given as follows:
A(-4,-4).
This means that each coordinate of vertex A' was multiplied by 4, thus the second transformation is a dilation with a scale factor of 4.
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The area of the scale model of a garden is 15 square feet. The scale model is enlarged by a scale factor of 3 to create the actual garden. Which expression finds the area of the actual garden?
Answer:
15 x [tex]3^{2}[/tex]
Step-by-step explanation:
since each side is increased by 3, total enlargement of area will be [tex]3^{2}[/tex] times
calculate the following using the long division method 8328÷ 24
Answer:
347
Step-by-step explanation:
Im not sure if that helps but thats the answer I got.
By using the long division method, The value of expression 8328 ÷ 24 after divide is,
⇒ 8328 ÷ 24
= 347
What is mean by Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, To dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The mathematical expression for divide is,
⇒ 8328 ÷ 24
Now, We can formulate;
We can use the long division method for the expression as;
⇒ 8328 ÷ 24
⇒ 8328 / 24
24 ) 8328 ( 347
- 72
-----
112
- 96
------
168
- 168
--------
0
Therefore, We get the correct answer,
By using the long division method,
The value of expression 8328 ÷ 24 after divide is,
⇒ 8328 ÷ 24
= 347
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USE A MODEL The Newton City Park has 11 basketball courts, which are all in use. There are 54 people playing basketball. Some are playing one-on-one, and some are playing in teams. A one-on-one game requires 2 players, and a team game requires 10 players. a. Select a system of equations that represents the number of one-on-one and team games being played. Let x be one-on-one games and y be team games A)x+ 10゠11;2x+y=54 B) x+y=54;x+ 10y=11 C)x+y = 11; 2x + 10y= 54 D) x+2y = 11; 10x+2y= 54
the answer is(C) equation x +y = 11; 2x 10y = 54.
What's equation?In mathematics, an equation is a statement that asserts the equivalency of two expressions, generally containing one or further variables. An equation consists of two sides, frequently separated by an equal sign. The left- hand side( LHS) of the equation contains one expression, while the right- hand side( RHS) contains another. The equation asserts that the two sides are equal, meaning that they represent the same value, anyhow of the values assigned to the variables.
The correct system of equations that represents the number of one- on- one and platoon games being played is
x y = 11( since there are 11 basketball courts in total)
2x 10y = 54( since a one- on- one game requires 2 players and a platoon game requires 10 players)
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Suppose you deposit $1,000 in a savings account that pays interest at an annual rate of 4%. If no money is added or withdrawn from the account how many years will it take for the account to contain $1500
The number of years for the interest amount to reach $ 1,500 at 4 % is given by b = 10.35 years
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount invested be P = $ 1,000
Let the number of years be = b
Let the number of times the interest is applied n = 1
Let the rate of interest be r = 4 %
Now , the compound interest + amount = $ 1,500
A = P ( 1 + r/n )ⁿᵇ
And , the number of years b = ln ( A / P ) / n [ ln ( 1 + r / n ) ]
On simplifying , we get
b = ln ( 1,500.00 / 1,000.00 ) / ( 1 × [ ln ( 1 + 0.04 ) ] )
b = 10.338 years
Hence , the number of years is 10.35 years
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Your team decides to change the rules of the game. Now, if a student ties with
the envelope, the student gets to have a second chance to play. The student gets
to choose whether he or she wants to keep all 24 envelopes to choose from or
eliminate the envelope he or she just opened. If the student decides to keep all
24 envelopes, your team will rearrange the slips of paper in the envelopes first.
If the student happens to tie again, the student’s dollar is donated to the fundraiser
and his or her turn is over. Which would be a better choice for the student if he
or she wants the dollar back? Which would be a better choice for your team if
you want to raise more money? Justify your answers using probabilities.
from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar.
While from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.
Step by step explanationAssuming that the slips of paper are randomly distributed and the student does not have any information about the distribution, let's analyze the probabilities for each choice:
Keeping all 24 envelopes: If the student decides to keep all 24 envelopes, the slips of paper in the envelopes will be rearranged, and the probability of choosing the envelope with the dollar will be 1/24, as there is only one envelope with the dollar. If the student ties again, the game ends and the dollar is donated to the fundraiser. The probability of tying again is (1/24) * (23/24) = 0.048, which is relatively low.Eliminating the opened envelope: If the student eliminates the opened envelope, the slips of paper in the remaining 23 envelopes remain in the same order, and the probability of choosing the envelope with the dollar will be 1/23. If the student ties again, the probability of choosing the envelope with the dollar will be 1/23 again, and the game ends with the donation of the dollar. The overall probability of winning the dollar in this scenario is (1/23) + (1/23) * (22/23) * (1/23) = 0.088.Thus, from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar. On the other hand, from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.
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15(5 + 7) = 15 x 5 + 15 x 7 what property is it? include of addition/ multiplication
This equation demonstrates the distributive property of multiplication
What is distributive property ?
In mathematics, the distributive property is a property of binary operations that applies to numbers, sets, or other mathematical objects. It governs how to perform the operation of multiplication over addition or subtraction. The distributive property states that for any numbers a, b, and c:
a × (b + c) = a × b + a × c (multiplication distributes over addition)
or
a × (b - c) = a × b - a × c (multiplication distributes over subtraction)
The property demonstrated in this equation is the distributive property of multiplication over addition. This property states that the product of a number and the sum of two or more numbers is equal to the sum of the products of the number and each of the individual numbers. In other words, a(b + c) = ab + ac.
In this case, 15 is being multiplied by the sum of 5 and 7, which is equivalent to multiplying 15 by 5 and 15 by 7 separately and adding the results. So, we have:
15(5 + 7) = 15 x 5 + 15 x 7
This equation demonstrates the distributive property of multiplication over addition.
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Will award brainliest please help
A sequence $\{a_n\}$ satisfies $a_1 = 1$ and
\[a_n = \frac{a_{n - 1}}{1 + a_{n - 1}}\]for all $n \ge 2.$ Find $a_{10}.$
The sum of the given series is -
6 ∑{1/(2n + 1)² - 1}.
What is integration?Integration is a process of adding up small elemental volumes to find the larger volume.
Given is the series as -
6/(3² - 1) + 6/(5² - 1) + 6/(7² - 1) + ....
The given series is -
S = 6/(3² - 1) + 6/(5² - 1) + 6/(7² - 1) + ....
S = 6{1/(3² - 1) + 1/(5² - 1) + 1/(7² - 1) + ....}
S = 6 ∑ {1/(2n + 1)² - 1}
Therefore, the sum of the given series is -
6 ∑{1/(2n + 1)² - 1}.
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Find the slope of the line segment shown.
A) -1/2
B) -1
C) 1/2
D) 1
The slope of the line segment is -1/2 . Option A is correct.
What is slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
The slope is the "rise over run" between any two points on the line.
Count out how much "up or down" vs "left or right" to find the slope:
We go up 5 and right 5, giving us the fraction
Thus , slope is given by -5 /10 = -1 /2
When counting, up and right are counted as positive; left and down are counted as negative.
Hence , the slope of the line segment is -1/2 . Option A is correct.
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The stem and leaf plot shows the number of laps around a track
that several teams walked as part of a fund-raiser for the library.
The teams that walked more than 50 laps raised an extra $100 for
the library.
What fraction of the teams raised this extra money?
The fraction of the teams which walked as part of the fundraiser for the library, that raised extra money, is D. 1 / 3.
What fraction of the teams raised extra funds ?You must count the number of teams that were able to walk more than 50 laps in order to determine the percentage of teams that raised the additional funds. The distance walked by teams more than 50 laps were :
5363 6365 miles.There are 12 teams overall, which is equal to the number of leaves.
The fraction of teams that raised additional funds is:
= 4 teams / 12 total teams
= ( 4 ÷ 4 ) / ( 12 ÷ 4 )
= 1 / 3
In conclusion, the fraction of teams which raised extra money was 1 / 3.
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1) The eighth grade class has 20% fewer students this year than they
had as seventh graders. Write an expression to show the decline in
class numbers, and then simplify the expression. Use (s) to represent
the number of seventh grade students.
Answer:
Step-by-step explanation:
To represent the number of eighth-grade students, we can use the expression:
0.8s
This is because the problem states that there are 20% fewer students in the eighth grade than in the seventh grade, which means that the number of eighth-grade students is equal to 80% of the number of seventh-grade students.
To simplify this expression, we can use the distributive property:
0.8s = 1s - 0.2s
This shows that the number of eighth-grade students is equal to the number of seventh-grade students minus 20% of the number of seventh-grade students. We can further simplify this to:
0.8s = 0.8s
This means that the number of eighth-grade students is equal to 80% of the number of seventh-grade students, which is consistent with the original problem statement.
find the exact value using formulas from geometry. ∫ (1+3x) with upper bound as 3 and lower bound as 1.
The value of the integral ∫(1+3x) dx is equal to 14.
What is integration?Integration is a process of adding up small elemental volumes to find the larger volume.
Given is to find the integral -
∫(1+3x)
We can find the equivalent values as -
∫(1+3x) dx = ∫1 dx + ∫3x dx
∫(1+3x) dx = x + 3x²/2
For the limit x = 1 to x = 3, we can write -
∫(1+3x) dx = (3 + 27/2) - (1 + 3/2)
∫(1+3x) dx = 33/2 - 5/2 = 14
Therefore, the value of the integral ∫(1+3x) dx is equal to 14.
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for what values of k can 2x^2 kx 5 be factored as the product of two linear factor with integer coefficents
The values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.
What is a linear factor?
A linear factor is a polynomial of degree one, which means it has one variable raised to the first power and a constant coefficient. In other words, it is an expression of the form ax + b, where a and b are constants and x is the variable.
We can factor the quadratic 2x² + kx - 5 into the product of two linear factors with integer coefficients if and only if its discriminant is a perfect square.
The discriminant of the quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, a = 2, b = k, and c = -5. Therefore, the discriminant is:
b² - 4ac = k² - 4(2)(-5) = k² + 40
For the quadratic to be factored into two linear factors with integer coefficients, k² + 40 must be a perfect square.
One way to proceed is to list the perfect squares that are 40 greater than a square, and see if k is one of the corresponding values. We can do this by solving the equation:
k² + 40 = m²
where m is an integer. Rearranging, we get:
k² - m² = -40
This is a difference of squares, so we can factor it:
(k + m)(k - m) = -40
We now need to find integer values of k and m that satisfy this equation. We can do this by considering all possible pairs of factors of -40 and solving for k and m.
The pairs of factors of -40 are:
(-1, 40), (-2, 20), (-4, 10), (-5, 8)
For each pair, we can solve the system of equations:
k + m = a
k - m = b
where a and b are the two factors in the pair. Adding these equations, we get:
2k = a + b
Subtracting them, we get:
2m = a - b
Solving for k and m, we obtain:
k = (a + b)/2
m = (a - b)/2
We can now check if the values of k and m are integers and if they satisfy the original equation.
For example, if we take the pair (-1, 40), we get:
k + m = -1
k - m = 40
Adding these equations, we get:
2k = 39
This implies that k = 39/2, which is not an integer, so this pair does not work.
Trying the other pairs, we find that:
(-2, 20) gives k = 9 and m = 11, which works
(-4, 10) gives k = 3 and m = 7, which works
(-5, 8) gives k = 1 and m = 3, which works
Therefore, the values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.
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100 POINTS HELP Which account will not appear on a post closing trial balance?
A. accounts payable
B. cash
C. revenue
D. accounts receivable
Answer:
C revenue
Step-by-step explanation:
sal translates the graph of the function shown in the box 3 units to the left
f(x)=(x-2)^2 +1
what is the function g(x) of the new graph
The solution is, the function is g(x) = (x -5)² + 1
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
we know that,
The vertex form of a quadratic equation is: y = a(x - h)² + k where
"a" is the vertical stretch
-a is a reflection over the x-axis
h is the horizontal shift (positive = right, negative = left)
k is the vertical shift (positive = up, negative = down)
given that,
f(x) = (x-2)² + 1
now we have,
Given: 3 units left --> h = -3
so, we get,
g(x) = (x - 2- 3)² +1
=(x-5)² + 1
Hence, The solution is, the function is g(x) = (x -5)² + 1.
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a function with the domain of [-3,3]
Function with the domain of [-3, 3] is f(x) = [tex]x^2[/tex]
Define function.A function is a mathematical formula that gives each input value in a set an individual output value. The domain and range are two sets that relate to one another in such a way that each element in the domain has a unique association with the elements in the range.
An equation or collection of rules that indicate how the output is determined depending on the input constitutes a function, which is often denoted by a symbol like f. The independent variable is the value of the inputs, and the dependent variable is the value of the outputs.
Here's an example of a function with the domain of [-3, 3]:
f(x) = [tex]x^2[/tex]
This function maps each value in the interval [-3, 3] to its square. For example, when x = -3, f(x) = [tex](-3)^2[/tex] = 9, and when x = 3, f(x) = [tex](3)^2[/tex] = 9. The graph of this function is a parabola that opens upward and has its vertex at the origin (0,0).
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please help, i inserted the photo below and i need the answer asap
By proportion formula and Pythagorean theorem, the length of line segment AB is equal to 8 units.
How to determine the length of a missing side in a system of similar triangles
Herein we find a geometric system formed by two similar right triangles, then we can determine the length of side BD by following proportion formula:
BD / AD = CD / BD
BD² = AD · CD
BD = √(AD · CD)
And the length of the line segment AB can be determined by Pythagorean theorem:
AB = √(BD² + AD²)
If we know that AD = 4 and CD = 12, then the length of the line segment AB is:
BD = √(4 · 12)
BD = √48
BD = 4√3
AB = √[(4√3)² + 4²]
AB = 8
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