The result matches the given after-tax total, confirming that the pre-tax subtotal is indeed $1,000.00.To calculate the pre-tax subtotal, we need to reverse-engineer the calculation based on the given after-tax total and tax rate.
Let's denote the pre-tax subtotal as "x." The tax rate is 7%, which can be written as 0.07 in decimal form. The after-tax total is $1,070.00.
We know that the tax amount is calculated by multiplying the tax rate by the pre-tax subtotal. So, the tax amount can be expressed as 0.07x.
The after-tax total is obtained by adding the pre-tax subtotal and the tax amount:
After-tax total = Pre-tax subtotal + Tax amount
$1,070.00 = x + 0.07x
To solve for x, we can combine like terms:
$1,070.00 = 1.07x
Now, let's isolate x by dividing both sides of the equation by 1.07:
$1,070.00 / 1.07 = x
Simplifying the calculation:
$1,000.00 = x
Therefore, the pre-tax subtotal is $1,000.00.
To verify the result, we can calculate the tax amount by multiplying the pre-tax subtotal by the tax rate:
Tax amount = 0.07 * $1,000.00 = $70.00
Adding the tax amount to the pre-tax subtotal:
$1,000.00 + $70.00 = $1,070.00
The result matches the given after-tax total, confirming that the pre-tax subtotal is indeed $1,000.00.
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PLEASE HELP PLEASE HELP
Answer:
22
Step-by-step explanation:
You can do it by 220 divided by 10, which gives an answer of 22.
Classical determination of the probability of an event. There are 8 red, 5 white and
6 black balls. One ball is randomly taken from the urn. What is the probability that it will be black?
The probability of drawing a black ball from the urn, with a total of 19 balls (8 red, 5 white, and 6 black), is approximately 0.3158 or 31.58%.
To determine the probability of drawing a black ball from the urn, we need to consider the total number of balls and the number of black balls.
In this case, the total number of balls in the urn is 8 + 5 + 6 = 19, as there are 8 red, 5 white, and 6 black balls.
The probability of drawing a black ball can be calculated by dividing the number of black balls by the total number of balls:
Probability = Number of black balls / Total number of balls = 6 / 19 ≈ 0.3158 (rounded to four decimal places)
Therefore, the probability of drawing a black ball from the urn is approximately 0.3158, or 31.58%.
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1. Consider a simple random sample of 25 newts. The mean tail length of our sample is 5 cm. If we know that 0.2 cm is the standard deviation of the tail lengths of all newts in the population, then what is a 90% confidence interval for the mean tail length of all newts in the population ?
The 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).
How to find 90% confidence interval for the mean tail length of all newts in the populationTo calculate the 90% confidence interval for the mean tail length of all newts in the population, we can use the formula:
Confidence Interval = Sample Mean ± Margin of Error
Given:
- Sample size (n) = 25
- Sample Mean (xbar) = 5 cm
- Standard Deviation of the population (σ) = 0.2 cm
- Confidence level = 90% (which corresponds to a z-score of 1.645 for a two-tailed test at a 90% confidence level)
First, we need to calculate the margin of error:
Margin of Error = (Critical Value) * (Standard Deviation / √Sample Size)
In this case, the critical value for a 90% confidence level is 1.645. Let's substitute the values:
Margin of Error = 1.645 * (0.2 / √25)
Margin of Error = 1.645 * 0.04
Margin of Error ≈ 0.0658
Now, we can calculate the confidence interval:
Confidence Interval = Sample Mean ± Margin of Error
Confidence Interval = 5 ± 0.0658
Confidence Interval ≈ (4.9342, 5.0658)
Therefore, the 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).
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explanation needed i do not undersatnd whats being calculated here
Find the missing side. 42° Y y 18 y = [?] Round to the nearest tenth.
Answer:
Step-by-step explanation: a = o/t
a = 18/tan(42)
a = 19.99
If the HCF of two numbers is 36 and their LCM is 1260 . If one number is 72 find the other one
Hence, The other Number is: B = 630
Step-by-step explanation: EUCLIDS ALGORITHMIf the HCF of two numbers is 36 and their LCM is 1260. If one number is 72 find the other one:
PRIME FACTORS of 1260 are:2, 2, 3, 3, 7
PRIME FACTORS of 72 are:2, 2, 2, 3, 3
Write the formula for HCF and LCM:HCF * LCM = a * b
HCF = 2 * 2 * 3 * 3
= 36
Substitute The Given Values:36 * 1260 = 72 * b
36 * 1260 = 72b
45360 = 72b
Divide Both Sides by 36:1260 = 2 * b
45360 / 72 = 72b/72
b = 630
Divide Both Sides by 2:B = 630
Draw the conclusion:Hence, The other Number is: B = 630
I hope this helps you!
An environmental group is tracking a fast-growing algae's coverage on a nearby pond. When
the group first measured the algae, it covered 3 square meters of the pond. They expect the
area of the pond covered by algae will double each day.
Write an exponential equation in the form = a(b)^x that can model the area of the pond
covered by algae, y, in x days.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How much of the pond is expected to be covered by algae after 4 days?
Answer:
y = 3(2^x)48 m² after 4 daysStep-by-step explanation:
You want an exponential function of the form y = a(b^x) that models algae growth that initially covers 3 square meters of a pond and doubles in area each day.
Exponential functionThe function y = a(b^x) has an initial value of 'a', which the problem statement tells us is 3 (square meters). The value 'b' is the growth factor, which the problem statement tells us is 2 each day.
The desired exponential equation is ...
y = 3(2^x)
4 daysWhen x=4, the function evaluates to ...
y = 3(2^4) = 3(16) = 48 . . . . square meters
After 4 days, 48 square meters of the pond is expected to be covered by algae.
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la edad de Ana es la mitad de jose y dentro de 10 años seran dos tercios ..cual es la edad de jose
La edad actual de José es de 30 años.
Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.
La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.
Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.
Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].
Al resolver la ecuación resultante, encontramos que x = 30.
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HELP ASAP IVE BEEN STUCK ONNTHIS 20 PTS
Answer:
[tex] \sqrt{ {( - 4 - 2)}^{2} + {(1 - 0)}^{2} } = \sqrt{ {( - 6)}^{2} + {1}^{2} } = \sqrt{36 + 1} = \sqrt{37} [/tex]
The number 37 goes beneath the radical symbol.
3
2
1
-1
-2
-3
Determine the period.
V
MAN
6 8 10 12 14
2 4
The period of the function in this problem is given as follows:
5 units.
How to obtain the period of the function?A periodic function is a function that has the behavior repeating over intervals in the domain of the function.
Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.
The distance between peaks of the function in this problem is of 5 units, which represents the period of the function.
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no explanation needed would be nice ytho thnks
The average rate of change in the population between 2002 and 2004 is one thousand per year, and between 2002 and 2006 is 1.75 thousand per year.
Rate of changeTo calculate the average rate of population change, we need to find the difference in population between the given years and divide it by the difference in years.
Between 2002 and 2004:
Population change = 80 - 82 = -2 (decrease of 2, as the population decreased)
Year difference = 2004 - 2002 = 2
Average rate of change = Population change / Year difference
Average rate of change = -2 / 2 = -1 (thousands per year)
Between 2002 and 2006:
Population change = 75 - 82 = -7 (decrease of 7, as the population decreased)
Year difference = 2006 - 2002 = 4
Average rate of change = Population change / Year difference
Average rate of change = -7 / 4 = -1.75 (thousands per year)
Therefore, the average rate of change of population between 2002 and 2004 is 1 thousand per year, and between 2002 and 2006 is 1.75 thousand per year.
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Can I get a help with the second one please!
Answer:
897
Explanation:
Start with replacing all the [tex]t[/tex] with 2.
[tex](t^{2} + 6t+7)(3t^{2} +3)[/tex]
[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]
Deal with the exponent before multiplying and adding.
[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 12+7)(((3)(2))^{2} +3)[/tex]
[tex](23)(((3)(2))^{2} +3)[/tex]
Now I believe here is where you made your mistake, you should first multiply 3 and 2 instead of evaluating the exponent straight away, because [tex]3t[/tex] was squared together.
[tex](23)(((3)(2))^{2} +3)[/tex]
[tex](23)(6^{2} +3)[/tex]
[tex](23)(36 +3)[/tex]
Then after adding, just multiply to get your answer, 897.
[tex](23)(36 +3)[/tex]
[tex](23)(39) = 897[/tex]
solve the following problem
a. The maximum population of the squirrels is 1800.
b. The number of squirrels that were introduced to the island are 200 squirrels.
What is an exponential function?In Mathematics and Geometry, a logistic growth function can be represented by using the following mathematical equation:
[tex]f(x) = \frac{L}{1\;+\;e^{-k(x-x_0)}}[/tex]
Where:
L represents the carrying capacity, maximum value or supremum.x represents the x-value of midpoint.k represents the rate of change or growth rate.Based on the information provided above, the population of squirrels can be modeled by the following logistic growth function;
[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}[/tex]
Part a.
By comparison, the maximum value or supremum population of the squirrels is 1800 squirrels.
Part b.
When t = 0, the initial number of squirrels that were introduced to this island can be calculated as follows;
[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}\\\\P(0) = \frac{1800}{1\;+\;8e^{-0.3(0)}}[/tex]
P(0) = 1800/9
P(0) = 200 squirrels.
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answer QUESTION DOWN BE;LOW IN MID EXPLANANTION TAHNKS
The solution to the composite functions from the graph are:
(f * g)(2) = 16
(f - g)(0) = -5
How to interpret the Function Graphs?Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, then the function “ f of g of x”, is the composition of the two functions.
a) Using the concept of composite functions, we can say that:
(f * g)(x) = f(x) * g(x)
Thus:
(f * g)(2) = f(2) * g(2)
f(2) = 4
g(2) = 4
Thus:
(f * g)(2) = 4 * 4
(f * g)(2) = 16
b) Using the concept of composite functions, we can say that:
(f - g)(x) = f(x) - g(x)
Thus:
(f - g)(0) = f(0) - g(0)
f(0) = 1
g(0) = 6
Thus:
(f - g)(0) = 1 - 6
(f - g)(0) = -5
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How many combinations of poker hands are in a deck of cards?
Find standard deviation.
The table below gives the number of hours spent watching TV last week by a sample of 24 children.
8 5 2 4 4 9
9 7 3 5 2 4
4 7 10 5 1 8
9 8 3 3 8 7
Sample Standard Deviation:
The sample standard deviation for the given data set is approximately 2.77.
Let's calculate the sample standard deviation for the given data set:
Calculate the mean
Sum of all data points = 8 + 5 + 2 + 4 + 4 + 9 + 9 + 7 + 3 + 5 + 2 + 4 + 4 + 7 + 10 + 5 + 1 + 8 + 9 + 8 + 3 + 3 + 8 + 7 = 137
Mean = Sum of all data points / Number of data points = 137 / 24 = 5.71 (rounded to two decimal places)
Subtract the mean from each data point and square the result
(8 - 5.71)^2 = 2.4361
(5 - 5.71)^2 = 0.5041
(2 - 5.71)^2 = 15.1361
(4 - 5.71)^2 = 2.9241
(4 - 5.71)^2 = 2.9241
(9 - 5.71)^2 = 10.3961
(9 - 5.71)^2 = 10.3961
(7 - 5.71)^2 = 1.6641
(3 - 5.71)^2 = 8.2561
(5 - 5.71)^2 = 0.5041
(2 - 5.71)^2 = 15.1361
(4 - 5.71)^2 = 2.9241
(4 - 5.71)^2 = 2.9241
(7 - 5.71)^2 = 1.6641
(10 - 5.71)^2 = 23.7761
(5 - 5.71)^2 = 0.5041
(1 - 5.71)^2 = 21.8441
(8 - 5.71)^2 = 2.4361
(9 - 5.71)^2 = 10.3961
(8 - 5.71)^2 = 2.4361
(3 - 5.71)^2 = 8.2561
(3 - 5.71)^2 = 8.2561
(8 - 5.71)^2 = 2.4361
(7 - 5.71)^2 = 1.6641
Find the sum of all the squared differences
Sum of squared differences = 2.4361 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 10.3961 + 10.3961 + 1.6641 + 8.2561 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 1.6641 + 23.7761 + 0.5041 + 21.8441 + 2.4361 + 10.3961 + 2.4361 + 8.2561 + 8.2561 + 2.4361 + 1.6641 = 174.07 (rounded to two decimal places)
Divide the sum by the number of data points minus 1
Variance = Sum of squared differences / (Number of data points - 1) = 174.07 / (24 - 1) = 7.67 (rounded to two decimal places)
Take the square root of the variance
Sample Standard Deviation = √(Variance) = √(7.67) = 2.77 (rounded to two decimal places)
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Write an equation to state the relationship:
I am thinking of three consecutive integers, Four times the third decreased by on-half, the second is 4
The expression that represent the relationship is 7 / 2 x - 15 / 2 = 4.
How to write an equation to represent a relationship?An equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Therefore, let's find the equation that represents the relationship as follows:
Three consecutive numbers, four times the third decreased by on-half, the second is 4.
Therefore,
Let
x = first number
second number = x + 1
third number = x + 2
Therefore,
4(x + 2) - 1 / 2(x + 1) = 4
4x + 8 - 1 / 2x - 1 / 2 = 4
4x - 1 / 2x + 8 - 1 / 2 = 4
7 / 2 x - 15 / 2 = 4
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one year on venus is equivalent to 224.7 days on earth. How many days on earth, in decimal form are equivalent to 9 1/2 years on venus
9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth.
Explanation:To find how many days on Earth are equivalent to 9 1/2 years on Venus, we need to use the ratio of 224.7 days on Earth to 1 year on Venus. First, we convert 9 1/2 years to a decimal form, which is 9.5 years. Then, we multiply 9.5 years by the conversion ratio: 9.5 years * 224.7 days/year = 2137.65 days on Earth. Therefore, 9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth in decimal form.
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At the zoo for every six adore camel 05 baby camels there are a total of 44 adult and baby camels at the zoo
Using proportions, it is found that the table is completed as follows:
Original Ratio Number in the zoo
Baby camels 5 20
Adult camels 6 24
Total camels 11 44
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
At the zoo, for every 6 adult camels, there are 5 baby camels, hence, out of 11 camels, 5 are baby and 6 are adult.
Thus, out of 44 camels, we have that:
44/11 x 5 = 20, hence there are 20 baby camels.44/11 x 6 = 24, hence there are 24 adult camels.The table is:
Original Ratio Number in the zoo
Baby camels 5 20
Adult camels 6 24
Total camels 11 44
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Your question was incomplete, the complete question is-
At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels at the zoo.
Complete the table.
Original ratio Number in the zoo
Baby camels 5 ?
Adult camels 6 ?
Total camels ? 44
Which of the following could be a real world description of 3x-15
Answer:
three times a number minus fifteen
or
fifteen is less than three times a number
Find the sum of the first 50 terms
t1=91 and t25=374
In an arithmetic sequence where t1=91 and t25=374, the sum of the first 50 terms is 18,425.
How to find sum of arithmetic sequenceFormula for the sum of an arithmetic sequence is given as
[tex]Sn = (n/2) x [2a1 + (n-1)d][/tex]
where
Sn is the sum of the first n terms,
a1 is the first term
d is the common difference and
n is the number of terms.
Given that t1 = 91 and t25 = 374.
To find d, we can use the formula for the nth term of an arithmetic sequence:
[tex]tn = a1 + (n-1)d[/tex]
Substitute n = 25, t25 = 374, and a1 = 91, we get:
374 = 91 + 24d
d = 11
Substitute d in the Sn formula
S₅₀ = (50/2) x [2(91) + (50-1)(11)]
S₅₀ = 25 x [182 + 49 x 11]
S₅₀= 25 x 737
S₅₀ = 18,425
Therefore, the sum of the first 50 terms is 18,425.
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Solve 5 ≥ -5x > 25 and graph the solution set on a number line
I need help please.
Answer:
false
Step-by-step explanation:
Its All Real Numbers
After college, you get a job with a starting salary of $37,000. You have a cousin that works at the same company, but he was hired three years before you. Your contract states you will receive a pay raise each year of 6%. Your cousin tells you that his starting salary three years ago was $50,000 and he has been guaranteed a 4% pay raise each year.
1. Make a table showing your salary for your first five years on the job
1. A table showing your salary for the first five years on the job is shown below.
2. Your cousin's salary would be $56243.2 in the year you started working.
3. A formula for your salary is [tex]P(t) = 37000(1.06)^t[/tex]
A formula for your cousin's salary is [tex]P(t) = 50000(1.04)^t[/tex]
4. A graph of your salary and your cousin's salary is shown below.
It would take about 16 years before your salary exceed your cousin's salary.
How to write an exponential function to model the situation?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]P(t) = I(1 + r)^t[/tex]
Where:
P(t) represent the future value.t represent the time or number of years.I represent the initial amount.r represent the exponential growth rate.Part 1.
We can create a table of values to model your salary for the first five years on the job as follows;
Years 1 2 3 4 5
Salary ($) 39,220 41,573.2 44,067.6 46,711.7 49,514.4
Part 2.
For your cousin's salary three years after, we have:
y = 50,000(1.04)³
y = $56243.2.
Part 3.
We can write a formula for your salary as follows;
[tex]P(t) = 37000(1 + 0.06)^t\\\\P(t) = 37000(1.06)^t[/tex]
For your cousin's salary, we have:
[tex]P(t) = 50000(1 + 0.04)^t\\\\P(t) = 50000(1.04)^t[/tex]
Part 4.
In order to plot a graph of your salary and your cousin's salary, we would use an online graphing tool with a scale of 1 units for 1 year on the x-axis and a scale of 50 units for 1000 dollars on the y-axis.
Since the lines representing both salaries intersect at 15.808, we can logically deduce that it would take approximately 16 years for your salary to exceed your cousin's salary.
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Simplify one over four n-1/2 divided by n over five minus one over 20 n
The simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).
First, let's focus on simplifying the numerator and denominator separately:
Numerator:
The numerator is 1 divided by (4n - 1/2). We can simplify this by finding a common denominator. The denominator of 1/2 is 2, so we rewrite the expression as:
1/(4n - 12) = 1/(4n - 2/4) = 1/(4n - 2/4) = 1/((16n - 2)/4) = 4/(16n - 2)
Denominator:
The denominator is (n/5 - 1/20n). To simplify this, we find a common denominator. The denominator of 1/20n is 20n, so we rewrite the expression as:
n/5 - 1/20n = (20n^2)/(5 * 20n) - 1/(20n) = (20n^2 - 1)/(100n)
Now, let's simplify the entire expression by dividing the numerator by the denominator:
(1/(4n - 1/2)) ÷ (n/5 - 1/20n) = (4/(16n - 2)) ÷ ((20n^2 - 1)/(100n))
To divide by a fraction, we multiply by its reciprocal:
(4/(16n - 2)) ÷ ((20n^2 - 1)/(100n)) = (4/(16n - 2)) * (100n/(20n^2 - 1))
Next, we can simplify the numerator and denominator separately:
Numerator:
4 * 100n = 400n
Denominator:
(16n - 2) * (20n^2 - 1) = 320n^3 - 52n - 40n^2 + 2
Finally, we substitute the simplified numerator and denominator back into the expression:
(4/(16n - 2)) * (100n/(20n^2 - 1)) = (400n)/(320n^3 - 52n - 40n^2 + 2)
Thus, the simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).
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Solve the right triangle.
b=1.98 c=4.63
[tex] \sf \hookrightarrow \: {(BC)}^{2} + {(AC)}^{2} = {(AB)}^{2} [/tex]
[tex] \sf \hookrightarrow \: {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] \sf \hookrightarrow \: {a}^{2} + {(1.98)}^{2} = {(4.63)}^{2} [/tex]
[tex] \sf \hookrightarrow \: {a}^{2} + (1.98 \times 1.98)= (4.63 \times 4.63) [/tex]
[tex] \sf \hookrightarrow \: {a}^{2} + (3.9204)= (21.4369)[/tex]
[tex] \sf \hookrightarrow \: {a}^{2}= (21.4369) - (3.9204)[/tex]
[tex] \sf \hookrightarrow \: {a}^{2}= 17.5165[/tex]
[tex] \sf \hookrightarrow \: a= \sqrt{ 17.5165}[/tex]
[tex] \sf \hookrightarrow \: a= 4.18. Approx[/tex]
Answer: To solve the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's label the sides of the triangle as follows:
The length of the hypotenuse is c = 4.63.
One of the legs is b = 1.98.
Using the Pythagorean theorem, we can find the length of the other leg, which we'll label as a:
a^2 + b^2 = c^2
a^2 + (1.98)^2 = (4.63)^2
a^2 + 3.9204 = 21.4369
a^2 = 21.4369 - 3.9204
a^2 = 17.5165
Taking the square root of both sides, we find:
a ≈ √17.5165
a ≈ 4.1833
So, the length of the other leg (side a) is approximately 4.1833.
Therefore, the sides of the right triangle are approximately:
Side a ≈ 4.1833
Side b = 1.98
Side c = 4.63
Step-by-step explanation:
The surface of the triangle shown in the picture 15.1 is:
A) 6 B) 21 C) 14 D) 12
I'm not sure I've solved it right.
Answer:
The coreect answer o
is 14
how many time can 457 go into 600
Answer:
Once
Step-by-step explanation:
Simple, once. If you do 600-457, you get an answer of 143, which you cannot subtract another 457 because it will turn negative.
Create a table of values for the function graphed below using the plotted points. Remember, table of values are written with the x
-values in order from least to greatest (read the graph from left to right).
there are 5 rows for both problems x,y and 45 points for helping me with this
The table of values of the graphs are
x -2 -1 0 1 2
y -8 -6 -4 -2 0
and
x -7 -2 2 3 4
y 1 -8 3 5 -5
Writing the table of values of the graphs.from the question, we have the following parameters that can be used in our computation:
The graph
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx - 4
Using the points, we have
2m - 4 = 0
This gives
2m = 4
So, we have
m = 2
This means that the equation is y = 2x - 4
So, we have the following table of values
x -2 -1 0 1 2
y -8 -6 -4 -2 0
For the second table, we have
x -7 -2 2 3 4
y 1 -8 3 5 -5
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what is 4.5x-100>125
Answer:
4,5x>225--> x>225:4,5
Step-by-step explanation:
The answer is:
x > 50Work/explanation:
To solve this inequality, begin by adding 100 on each side:
[tex]\sf{4.5x-100 > 125}[/tex]
[tex]\sf{4.5x > 125+100}[/tex]
[tex]\sf{4.5x > 225}[/tex]
Now, divide each side by 4.5.
[tex]\sf{x > 50}[/tex]
Hence, the answer is x > 50.Question is in the attachment↓
pls give proper answer!
i) It has been proven that CD/GH = AC/FG by Corresponding Sides of Similar Triangles
ii) △DCB ∼△HGE by the AA criterion of similarity
iii) △DCA ∼△HGF by the AA criterion of similarity
How to solve similar triangles?In △ABC and △FEG, we are told that they are similar and as such we can denote as:
△ABC ∼ △FEG
Thus, we can say that:
∠ACB = ∠EGF (Corresponding angles of similar triangles)
We are told that, CD and GH are bisectors of ∠ACB and ∠EGH respectively and as such we can say that:
∠ACB = 2∠ACD = 2∠BCD
∠EGF = 2∠FGH = 2∠HGE
Thus, by substitution, we can say that:
∠ACD = ∠FGH and ∠DCB = ∠HGE ...................(1)
Similarly:
∠A = ∠F and ∠B = ∠E ...............(2)
With respect to equations 1 and 2 we can establish that:
△ACD ∼ △FGH by the AA criterion of similarity
Similarly, △DCA ∼△HGF
Thus:
CD/GH = AC/FG (Corresponding Sides of Similar Triangles)
Similarly, In △DCB and △HGE, we can also establish that
△DCB ∼△HGE by the AA criterion of similarity
Read more about similar triangles at: https://brainly.com/question/14285697
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