Given a right triangle with the longer leg three less than three times the shorter leg and the hypotenuse
is seven less than four times the shorter leg. What are the lengths of the three sides of the triangle? Be
sure to check both solutions to answer the question correctly.
So there are two possible triangles:
(10.5, 35.5, 37) and (35.5, 10.5, 37).
Step by step explanationLet's call the length of the shorter leg x. Then, the longer leg would be 3x - 3, and the hypotenuse would be 4x - 7.
Using the Pythagorean theorem, we have:
x^2 + (3x - 3)^2 = (4x - 7)^2
Expanding and simplifying, we get:
x^2 + 9x^2 - 18x + 9 = 16x^2 - 56x + 49
Combining like terms, we have:
7x^2 - 74x + 40 = 0
Using the quadratic formula, we find the solutions for x:
x = (74 ± √(74^2 - 4 * 7 * 40)) / (2 * 7)
x = (74 ± √(2744 - 560)) / 14
x = (74 ± √2184) / 14
x = (74 ± 46.56)/14
x = (35.5, 10.5)
So there are two possible triangles:
(10.5, 35.5, 37) and (35.5, 10.5, 37).
These are the two solutions for the lengths of the sides of the triangle.
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Which of the following are solutions to the equation below?
Check all that apply.
4x2 - 12x+ 9 = 5
Answer:
x = 3 + √5 / 2
Step-by-step explanation:
4x²-12x+9=5
4(x²-3x+1=0)
x²-3x+1=0
(quadratic formula)
a=1 b=-3 c=1
x= -(-3)+√(-3)²-4x1x1 / 2x1
simplify:
x = 3+√5 / 2
Vito uses 999 liters of water to water 242424 flower pots. He is wondering how many liters of water (w)(w)left parenthesis, w, right parenthesis it would take to water 404040 flower pots. He assumes he'll use the same amount of water on each pot.
Vito can not use same amount of water for 40 flower pots, as it would take 15 liters of water.
Vito uses 9 liters of water 24 flower pots.
To find: the amount of liters of water (w) it would take to water 40 flower pots.
This means, 9 liters is to 24 pots as w liters is to 40 pots
We write above statement as :
9:24::w:40
So, we get an a proportion,
9/24 = w/40
We solve above equation for w.
24w = 9(40)
24w = 360
w = 360/24
w = 15 liters
Therefore, 15 liters of water it would take to water 40 flower pots.
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The complete question is:
Vito uses 9 liters of water 24 flower pots. He is wondering how many liters of water (w) it would take to water 40 flower pots. He assumes he'll use the same amount of water on each pot. Which portion could Vito use to model this situation? Solve the proportion how many liters of water it takes to water 40 flower pads
Find the volume of cuboid which is 9cm multiply 4cm multiply 5cm
The volume of cuboid with dimensions 9cm × 4cm × 5cm is 180 cm³
We know that the formula for the volume of the cuboid is:
V = l × w × h
where, V is the volume of the cuboid
l is the length of the cuboid
w is the width of the cuboid
and h is the height of the cuboid
Here, the length of the cuboid is l = 9 cm,
the width of the cuboid is w = 4 cm
and the height of the cuboid is h = 5 cm
Using above formula,
V = l × w × h
V = 9 × 4 × 5
V = 180 cubic cm
Therefore, the required volume is 180 cubic centimeters
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there are four red balls and two white balls in a jar. one ball is randomly removed and replaced with a ball of the opposite color. the jar is then shaken and one ball is randomly selected. what is the probability that this ball is red? express your answer as a common fraction.
The probability that this ball is red after the jar is then shaken and one ball is randomly selected is 11/18.
There are four red balls and two white balls in a jar
P(white removed and then red is chosen)'
P = 2/6 * 5/6
= 10/36
P= 5/18
Probability that the white removed and then red is chosen is 5/18.
P(red removed and then white is chosen)
P = 4/6 * 1/2
= 4/12
= 1/3
P = 6/18
Probability that the red removed and then white is chosen is 6/18.
The probability that this ball is red,
P(red is chosen) = 5/18 +6/18 = 11/18
Therefore, The probability that this ball is red is 11/18.
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f(x)=2/3x^2 domain and range
The domain and range of function f(x) = 2/3x² are respectively, real numbers and non-negative numbers
What is Domain and Range ?The domain of a function is the set of all input values (independent variable) for which the function is defined and produces a valid output (dependent variable).
The range of a function is the set of all possible output values of the function. It represents the set of all possible values of the dependent variable.
Given that,
The domain of the function f(x) = 2/3x² is all real numbers except x = 0, since division by 0 is undefined.
The function f(x) = 2/3x²
The range of the function f(x) = 2/3x² is all non-negative real numbers.
It is because for any real number x,
the value of 2/3x² will always be non-negative.
To see this, consider the case where x > 0.
In this case, 2/3x² is positive,
and for x < 0, 2/3x² is still positive.
So, the domain of the function f(x) = 2/3x² is all real numbers except x = 0 and the range of the function is all non-negative real numbers.
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Topic 3 proportional relationships
Raven needs new winter boots. Both ShoeTown and LaceUp shoe stores carry the boots she wants to buy.
The boots are regularly priced $85.95, but both stores are running sales. ShoeTown has the boots marked
down 15%. LaceUp has the boots marked down 10%, plus Raven has a $5 coupon she can use on the
boots after the markdown is applied.
Raven’s friend Becca tells Raven there is an online shoe store called Run, Don’t Walk that has the boots she
wants for only $71.99. If Raven buys the boots in a local store, she will have to pay 7.16% sales tax on her
purchase. If Raven buys the boots online, she won’t have to pay sales tax, but she will have to pay $6.50 for shipping.
Shoe Town provides the finest ultimate price, so Raven should purchase the boots there.
Equal in proportional to what?possessing an identical or consistent ratio or connection between two quantities: If y/x = k, in which k is the proportionality constant, then the numbers y and x are proportionate.
To determine which one is the best store for Raven let's calculate the price in each case.
Shoe Town
Total price:
Initial price - Mark down + Sales tax
85.95 - 15% + 7.16 %
85.95 - 12.89 + 7.16 %
73.06 + 7. 16%
73.06 + 5.23 = 78.29
Lace Up
Total price:
Initial price - Mark down - Coupon + Sales tax
85.95 - 10% - 5 + 7.15%
89.95 - 8.99 - 5 + 7.15%
80.96 - 5 + 7.15%
75.96 + 7.15%
75.96 + 5.43 = 81.39
Run, Don't Walk
Total price:
Initial price + shipping
71.99 + 6.50 = 78.45
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Problem 1
A ladder 15ft in length leans against a vertical wall, with the bottom of the ladder 5ft from the
wall on the horizontal floor. If at that time the bottom end of the ladder is being pulled away at
the rate of 2ft/s at what rate does the top of the ladder slip down the wall.
The top of the ladder slips down the wall at the rate of 5.6 ft/sec.
What is a rate?
The ratio of two related quantities expressed in several units is known as a rate. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
Here, we have
Given: A ladder 15ft in length leans against a vertical wall, with the bottom of the ladder 5ft from the wall on the horizontal floor. If at that time the bottom end of the ladder is being pulled away at the rate of 2ft/s .
Let: x = the distance from the base of the ladder to the base of the wall
y = the distance from the tip of the ladder to the base of the wall, we have:
x² + y² = 15²
y² = 15² - 5² = 225 - 25 = 200 => y = 14.14 ft
2x dx/dt + 2y dy/dt = 0
2 * 5 * dx/dt + 2 * 14.14 * (-2) = 0
10 dx/dt = 56.56
dx/dt = 5.6 ft/sec
Hence, the top of the ladder slips down the wall at the rate of 5.6 ft/sec.
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Which of the points lies on the line y = 3x – 5? Explain how you are thinking.
A: (0, 3 ) B: (1, ‒2) C: (2, 2) D: (2, 0) E: (‒1, ‒8)
Answer:
B(1,-2)
Step-by-step explanation:
b is the answer from the above explanation
professor grok draws two cards from ms. q's deck at random without replacement. what is the probability that the first card grok draws has an even number, and the second card grok draws has a multiple of $3?$
The likelihood of drawing an average even number first, followed by a number that is a multiple of 3, is frac1850 cdot[tex]$frac1649 = $frac2882450$[/tex].
Since the two events are independent of one another, the likelihood of drawing an even number first and then a multiple of 3 equals the product of the probabilities of the two events. In a deck of 50 cards, there are 18 even numbers and 16 multiples of 3, hence the likelihood of getting an even number is [tex]$frac$[/tex]1850 and the likelihood of drawing a multiple of 3 is frac1650. The likelihood of drawing an even number first, followed by a multiple of 3, is frac1850 cdot frac1650 = frac2882450 because these are separate events
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One positive number is 5 times another number. The difference between the two numbers is 1016, find the
numbers.
Answer:
Let's call the two numbers x and 5x. We know that their difference is 1016:
5x - x = 1016
Expanding and solving for x:
4x = 1016
x = 254
So, the two numbers are 254 and 5 * 254 = 1270. These are the two numbers that have a difference of 1016 and satisfy the given condition.
Step-by-step explanation:
Answer:
1+5x=1016
Step-by-step explanation:
which of the tables is the appropriate table of conditional percentages to discover if the region where one lives affects whether or not one has health insurance?
Table A of conditional percentages answers the question of whether the region where one lives affects whether or not one has health insurance.
Table A is the appropriate table of conditional percentages to discover if one's region of residence influences if they have health insurance.
Table A provides the overall percentage of individuals who are insured and uninsured in each region of the country. It gives a clear picture of the proportion of people in each region who have health insurance coverage. The data in this table allows us to compare the percentage of uninsured individuals across different regions.
In contrast, Table B provides the percentage of uninsured individuals among the total number of insured and uninsured individuals in each region. This type of table does not give us a clear understanding of the overall proportion of insured and uninsured individuals in each region.
Table C provides the percentage of uninsured individuals among the total population in each region. However, it does not provide a clear picture of the proportion of insured individuals in each region, which is crucial information to determine if the region where one lives affects whether or not one has health insurance.
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Complete Question: Table image has been uploaded.
(1/64)^x/2+1 = (1/16)^x/3-3
Therefore , the solution of the given problem of expression comes out to be there is no value of x which can make equation true.
Explain the expression.Mathematical operations like addition, multiplication, variables and proliferation, and division are necessary. They result in the following when combined: An equation, some information, and a mathematical operator Values, parameters, and operations like additions, subtraction, multiplication, and division are all included in a statement of fact. Different sentences and words can be contrasted and compared.
Here,
Given :
Expression is :
=> (1/64)ˣ / 2 + 1 = (1/16)ˣ / 3 -3
=> (1/64)ˣ / 2 + 4 = (1/16)ˣ / 3
=> ( (1/64)ˣ + 8 ) / 2 = (1/16)ˣ / 3
=> (1/64)ˣ + 8 = (1/16)ˣ 2 / 3
=> (1/4)³ˣ + 8 = (1/4)²ˣ * 2/3
=> 8 = (1/4)²ˣ ( 2/3 + (1/4)ˣ )
So,
We found that there is no value of x which can make equation true.
Therefore , the solution of the given problem of expression comes out to be there is no value of x which can make equation true.
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# 25-29) A cast iron cylinder serves as a counterbalance that is used in a window
manufacturer's double-hung window design. The cylinder has a height of 7.45 in and a
diameter of 2.7in. The weight density of cast iron is 0.259 lbs/in³.
What is the volume of the cylinder?
Volume = 42.63374
What is the surface area of the cylinder?
Surface area =
What is the weight of the cylinder?
Weight =
V=7₂².h
3.14 (1.352). 7.45
= 42.63374
2.7÷2=1.35
3.14(
W=dw.v
W=
The surface area and weight of the cylinder is 45.1805 in² and 11.107 lbs respectively.
Describe Cylinder?A cylinder is a three-dimensional geometric shape that has two parallel circular bases and a curved lateral surface connecting the bases. The bases are located at opposite ends of the cylinder, and they have the same diameter. The lateral surface is a rectangle that has been bent around the circumference of the circular bases.
The height of a cylinder is the distance between the two bases, and the diameter of the bases is the distance across the circle through its center. The volume of a cylinder can be calculated by multiplying the area of one of its bases by its height. The formula for the volume of a cylinder is:
V = πr²h
where r is the radius of the circular base and h is the height of the cylinder.
Cylinders are commonly used in many real-world applications, such as in the design of pipes, cans, and other containers. They are also commonly used in mathematics and physics, where they can serve as models for objects with cylindrical symmetry, such as pipes and wires.
In summary, a cylinder is a three-dimensional shape with two parallel circular bases and a curved lateral surface connecting the bases. The height of the cylinder is the distance between the bases, and its volume can be calculated using the formula V = πr²h. Cylinders are commonly used in real-world applications and in mathematics and physics.
The following formula can be used to determine the cylinder's volume:
V = π × r² × h = π × (d/2)² × h = π × (1.35²) × 7.45 = 42.63374 in³
The following formula can be used to get the cylinder's surface area:
A = 2πr² + 2πrh = 2π × r² + 2π × r × h = 2π × (1.35²) + 2π × 1.35 × 7.45 = 45.1805 in²
The cylinder's weight can be determined using the formula below:
W = d × V = 0.259 lbs/in³ × 42.63374 in³ = 11.107 lbs.
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Substitution of 1/2x + 2y = 8 and 3x - 2/3y = 1
The solution to the system of equations in this problem is given as follows:
x = 1.16, y = 3.71.
How to solve the system of equations?The system of equations for this problem is defined as follows:
x/2 + 2y = 8.3x - 2y/3 = 1.Multiplying the first equation by 2, we have that:
x + 4y = 16
x = 16 - 4y.
Replacing into the second equation, the solution for y is obtained as follows:
3(16 - 4y) - 0.67y = 1
48 - 12y - 0.67y = 1
12.67y = 47
y = 47/12.67
y = 3.71.
Then the solution for x is of:
x = 16 - 4(3.71)
x = 1.16.
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A ramp is 16ft long rises to a platform that is 12ft off the ground, find X, the angle of elevation of the ramp. Round your answer to the nearest tenth of a degree
Answer:
x = 48.6°
Step-by-step explanation:
see photo for explanation
x²(x+y)³ - 2xy²(x + y)²
Can you please factorize this for me the answer is x(x + y)²(x+2y)(x - y) but I don’t know how to get it
The equation be x²(x + y)³ - 2xy²(x + y)² then the factorization be x(x + y)²(x - y)(x + 2y).
What is meant by factorization?In mathematics, the term "factorization" or "factoring" refers to the splitting apart or "factoring" of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together yield the original number, matrix, etc.
Factoring is a useful skill in real life. Examples of typical uses include splitting something into equal portions, exchanging money, comparing costs, understanding time, and performing calculations while traveling.
Let the equation be x²(x + y)³ - 2xy²(x + y)²
Factor out common term [tex]$x(x+y)^2= x(x+y)^2\left(x(x+y)-2 y^2\right)$[/tex]
[tex]$=x(x+y)^2\left(x(x+y)-2 y^2\right)$$[/tex]
Expand [tex]$x(x+y)-2 y^2= x^2+x y-2 y^2$[/tex]
simplifying the above equation, we get
[tex]$=x(x+y)^2\left(x^2+x y-2 y^2\right)$$[/tex]
Factor [tex]$x^2+x y-2 y^2=(x-y)(x+2 y)$[/tex]
= x(x + y)²(x - y)(x + 2y)
Therefore, the factorization be x(x + y)²(x - y)(x + 2y).
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on a 7 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
The probability of getting at least one question wrong on a 7 question multiple-choice test with two answers for each question is 1 - (1/4)^7, which is approximately 99.2%.
The probability of getting one question wrong on a 7 question multiple-choice test with two answers for each question is 1/4. This is because there are two options for each question, and if you choose the wrong one, you get the question wrong. Therefore, the probability of getting all 7 questions wrong is (1/4)^7, or one in 16,384. The probability of getting at least one question wrong on the test is 1 - (1/4)^7, which is equal to 1 - 1/16,384, or approximately 99.2%. To calculate the probability of getting at least one question wrong, you subtract the probability of getting all 7 questions correct from 1. This is because if you do not get all 7 questions correct, then you must have gotten at least one question wrong.
The complete question: On a 7 question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong? Give your answer as a fraction
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6. A figure has an area of 9 square units. The equation y = √√represents the
scale factor of y by which the solid must be dilated to obtain an image with
area of x square units. Select all points which are on the graph representing
this equation. (Lesson 5-5)
(A.) (0, 0)
(B.) (1, 1)
(1,3)
D.) (3, 1)
E. (9,1)
(F.) (9, 3)
G.) (18,2)
(H.) (36, 2)
The graph represents the function that maps the area of the original figure to the area of the dilated figure. If the original area is 9 square units and the dilated area is x square units, then the equation y = √√x represents the relationship between the two areas. Points (B), (F), (G), and (H) are on the graph because they satisfy the equation y = √√x. Points (A), (C), and (E) are not on the graph because they do not satisfy the equation.
2) 1.6 ft 1.6 ft
what is the answer
The solution to the perimeter is 6.4 feet
How to determine the perimeter of the squareFrom the question, we have the following parameters that can be used in our computation:
Side length = 1.6 ft
Shape = Square
Using the above as a guide, we have the following:
Perimeter = 4 * Side length
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 4 * 1.6 ft
Evaluate
Perimeter = 6.4 ft
Hence, the perimeter is 6.4 ft
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Complete question
2) Determine the perimeter of a square with side length 1.6 ft
what is the answer
if you draw a random sample of 1,000 observations, what is the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24?
The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.
If the sample size is large enough (typically, n >= 30), we can assume that the sample mean is approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.
Therefore, if we know the population mean and standard deviation, we can calculate the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24. Let's denote the population mean as mu and the population standard deviation as sigma. Then, the standard deviation of the sample mean is sigma / sqrt(n), where n = 1000 is the sample size.
We can standardize the sample mean using the z-score formula:
z = (x - mu) / (sigma / sqrt(n))
where x is the sample mean.
For the sample mean to be greater than 3,011.76, we have:
z = (3,011.76 - mu) / (sigma / sqrt(n)) > 0
And for the sample mean to be less than 2,988.24, we have:
z = (2,988.24 - mu) / (sigma / sqrt(n)) < 0
To find the probability, we need to find the area under the standard normal curve to the right of z for the first case, and to the left of z for the second case. These probabilities can be found using a standard normal table or a statistical software package.
Unfortunately, without knowledge of the population mean and standard deviation, it is not possible to determine the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24.
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Someone please help!!!
The components of the vector in rectangular form given magnitude and angle can be found as : x= |56| cos83°, y = |56| sin 83° .
How to determine the magnitude and angle of a vector?Let be a vector in rectangular form, that is, a vector of the form (x, y). The magnitude can be found by applying the square root of the dot product of the vector or the Pythagorean theorem and the direction is determined by applying inverse trigonometric functions:
here, we have,
Magnitude (linear algebra approach)
|r|=√(x,y). (x.y) (1)
Magnitude (algebra approach)
|r|=√(x²+y²) (2)
Direction
θ = tan⁻¹ (y/x) (3)
And the components of the vector can be found by applying the following formulas:
|r|=xcos θ (4)
|r|= y sinθ (5)
The components of the vector in rectangular form given magnitude and angle can be found as: x= |56| cos83°, y = |56| sin 83° ., .
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Can anyone help,
The function f and g each represent the population of two different kinds of bacteria,where x is the time(in hours) and f and g are the number of bacteria(in thousands)
Bacteria A:f(x)=36x
Bacteria B:g(x)=3*
A)Between the first and fourth hour,which bacteria had a faster rate of growth?Explain how you determined your answer
B)Explain whether or not the population of g will ever exceed the population of f
It would help if you answer me
According to the information, it can be inferred that the F bacterium had a greater growth over time. Additionally, the population of G si will exceed the population of F because it has an x exponent.
What do the functions express?The functions express the relationship between the number of bacteria and time. In accordance with the above, the function of the bacterium A, expresses that the number of bacteria grows 36 individuals every hour.
36 * 1 = 3636 * 2 = 7236 * 3 = 10836 * 4 = 144On the other hand, the function of B expresses that the individuals grow exponentially in 3. According to the above, at some point the exponent of 3 will be so great that it will be able to exceed the number of individuals of A. (not in the first four hours).
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Please help I’m stuck
We can solve the inequality |8x - 7| < 9 to get the compound inequality:
-1/4 < x < 2
How to solve the inequality?Here we have an absolute value inequality:
|8x - 7| < 9
The absolute value part can be "broken" into two parts, these are:
(8x - 7) < 9
(8x - 7) > -9
Now we need to solve these two.
The first one gives:
8x - 7 < 9
8x < 9 + 7
8x < 16
x < 16/8
x < 2
The other gives:
(8x - 7) > -9
8x > -9 + 7
8x > -2
x > -2/8
x > -1/4
Then we have the compound inequality:
-1/4 < x < 2
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Which scatter plot represents the data shown in the table?
The scatter plot is given in the attached image below.
The correct option is D.
What is a trend line?The straight line on a scatter plot closest to the points is called a trend line. Two points on a trend line can create an equation in slope-intercept form.
Given:
The data are shown in the table.
From the table:
When the value of x = 1, then y = 11.
And when x = 3, then y = 30.
Similarly, all the values are placed as per the data.
The scatter plot is given in the attached image.
Therefore, the plot is given below.
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Two functions are shown.
f(x)=x+2
g(x)=x²-x-3
What is (gof)(x)?
A x²-x-1
Bx²-x+3
C x² + 3x +3
Dx² + 3x - 1
danielle has taken five math tests so far this year. the tests are out of twenty points, and she has gotten the following scores. 17, 19, 20, 14, 16 what is the mode of her scores? which of the central tendancy would danielle wnat her teacher to use in order to describe her test scores
Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that the tests are out of twenty points, and she has gotten the following scores. 17, 19, 20, 14, 16
The mode of a set of data is the value that occurs most frequently. In this case, Danielle's scores are: 17, 19, 20, 14, 16.
There is no mode value.
Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average.
Hence, Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average.
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a regulation-sized gymnasium is 80 feet wide and 100 feet long. if a scale model of the gymnasium is 12 inches long, how wide is the model?
A scale model of a regulation-sized gymnasium that is 12 inches long would be 10 inches wide.
To determine the width of a scale model of a regulation-sized gymnasium, you need to determine the scale factor used to create the model. The scale factor is the ratio of the size of the model to the size of the actual object.
In this case, the length of the model is 12 inches, while the length of the actual gymnasium is 100 feet, or 1200 inches. So, the scale factor is: 12/1200 = 1/100.
To find the width of the model, you would multiply the width of the actual gymnasium, 80 feet, by the scale factor, 1/100. This gives you a width of:
80 × 1/100 = 0.8 feet = 10 inches.
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I already asked this question but could not see the answer
All the correct expression in each steps are,
⇒ Step 1; (m³ + m²n + mn² - m²n - mn² - n³)
( By multiplication distributor )
⇒ Step 2; m³ - n³
( By combine like terms)
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression to prove is,
⇒ (m - n) (m² + mn + n²)
Now, We can simplify as;
⇒ (m - n) (m² + mn + n²)
Step 1;
⇒ (m³ + m²n + mn² - m²n - mn² - n³)
( By multiplication distributor )
Step 2;
⇒ m³ - n³
( By combine like terms)
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The value of x include the following: B. 52/3.
What is the basic proportionality theorem?In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
By applying the basic proportionality theorem to the given triangle, we have the following:
3x/4x = (3x + 7)/(5x - 8)
By cross-multiplying, we have the following:
3x(5x - 8) = 4x(3x + 7)
15x² - 24x = 12x² + 28x
3x² = 52x
3x = 52
x = 52/3.
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