The solutions to the quadratic function y = x² + 4x + 3, using the quadratic formula, are given as follows:
x = -1 and x = -3.
How to solve a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
In which the leading coefficient a must assume a value different of zero.
The solutions to the quadratic function ax² + bx + c = 0 are obtained using the quadratic formula, as follows:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic function for this problem is defined as follows:
x² + 4x + 3 = 0.
Hence the coefficients are:
a = 1, b = 4, c = 3.
The first solution is:
[tex]x = \frac{-4 - \sqrt{4^2 - 4(1)(3)}}{2} = -3[/tex]
The second solution is:
[tex]x = \frac{-4 + \sqrt{4^2 - 4(1)(3)}}{2} = -1[/tex]
Missing InformationThis problem was incomplete, hence the quadratic formula is used to solve y = x² + 4x + 3, as an example.
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Molly and Liza are exercising. Molly does
10 push-ups at the same time
as Liza
does 15 push-ups. When Molly does
40 push-ups, how many push-ups does
Liza do?
Answer:
25
Step-by-step explanation:
so molly and liza are exercising right?.so 10 push-ups at the same time wich means they do 10 push-ups together and liza push-ups 15 and molly does 40 pushups so. its addition so 10+15=25 so thats the answer.
How do you know how many real solutions?
The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.
What are real solutions of an equation?A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.
How many real solutions does the discriminant have?When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.
So that we can find real solution of quadratic equation by finding discriminant of given equation.
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The sides of a triangle are 68, 61, and 46. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
Answer: Acute
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex]. A and b are legs while c is hypotenuse. Hypotenuse is also the longest side. Let's plug them in and see if they are equal to each other.
[tex]46^2+61^2=68^2[/tex] [exponent]
[tex]2116+3721=4624[/tex] [add]
[tex]5837\neq4624[/tex]
Since they are not equal, then it is not a right triangle.
To tell is a triangle is acute, if the sum of the two shorter sides squared is greater than the longest side squared, then the triangle is acute.
At the end of the Pythagorean Theorem, we got 5837≠4624. 5837>4624, so that tells us that the triangle is acute.
A sookeeper weighted an African elephant to be 9 x 10 (to the 3rd power) pounds, and an African lion to be 4 x 10 (to the second power) pounds. Hiw many times greater is the weight of the elephant than the weight of the lion
2.25×10 times greater is the weight of the elephant than the weight of the lion.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a zookeeper weighted an African elephant to be 9 x 10³ pounds.
An African lion to be 4 x 10² pounds
We need to find how many times greater is the weight of the elephant than the weight of the lion
Now, Divide the weighed an African elephant with weighed an African lion to determine times greater is the weight of the elephant than the weight of the lion,
N=9×10³/4×10²
=2.25×10
Hence, 2.25×10 times greater is the weight of the elephant than the weight of the lion.
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Find the length of the third side. If necessary, round to the nearest tenth
Answer:
6.3
Step-by-step explanation:
This is a right triangle, so in order to solve you can use the Pythagorean theorem; which is a² + b² = c² (The hypotenuse, or the longest side, equals C. A and B equal the legs, or the shorter sides.) So once you plug in the values, your equation should look like this:
3² + b² = 7²
Square each side, or in other words multiply it by itself.
9 + b² = 49
Subtract 9 from both sides.
b² = 40
Take the square root of 40 and your done!
b = 6.3
I hope this helped you! :)
Is N2 the same as 2N?
Therefore, N2 and 2N are not equal, they are different mathematical expressions.
What are expressions?A finite collection of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
What are symbols?A mark, sign, or term that denotes, denotes, or is taken to denote a concept, an item, or a connection is known as a symbol. By connecting seemingly unrelated ideas and events, symbols let individuals look beyond the known and the visible.
No, N2 and 2N are not the same.
N2 is the square of N, which means it is N multiplied by itself. For example, if N = 5, then N2 = 5*5 = 25.
2N, on the other hand, is N multiplied by 2. For example, if N = 5, then 2N = 5*2 = 10.
So, N2 and 2N are not equal, they are different mathematical expressions.
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What does the slope of a log-log graph represent?
The Slope of log - log graph represents the power of the relationship, and a straight line which indicates that there exists a definite power relationship .
What is Logarithm ?
The Logarithm is defined as power to which a number must be raised to get some other number .
A log-log plot is the plot in which both the x-axis and y-axis use a log scale.
The plot of logarithms of variables helps in extracting the information about the power relationship. The case of freely falling object is used to illustrate a log - log plot.
A plot of the logarithm of freefall distance as a function of logarithm of time gives a straight line of slope 2.
Therefore , The slope of log-log plot gives the power of relationship, and a straight line indicating that a definite power relationship exists.
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How do u work this out ?
Answer:
[tex]\frac{d}{c}[/tex]
Step-by-step explanation:
[tex]\frac{cxcxdxdxd}{cxcxcxdxd}[/tex] You can cross out 2 c's from the top and the bottom and 2 d's from the top and the bottom. It now looks like this
[tex]\frac{d}{c}[/tex]
The medical treatment cost $3000, and the insurance pays 90% less deductible of $300. Write how much money the patient pays and how much the insurance company pays. Describe the mathematics involved.
Based on the question above, the patient pays $600 and the insurance company pays $2400.
What is the arithmetic operations about?To calculate how much the patient pays, we first need to calculate how much the insurance pays. We can do this by taking the total cost of the treatment ($3000) and multiplying it by the percentage that the insurance pays:
(90% = 0.9).
$3000 x 0.9 = $2700
This means that the insurance pays $2700 of the cost of the treatment. But we also need to subtract the $300 deductible from this amount.
$2700 - $300
= $2400
So the insurance pays $2400 for the medical treatment.
To find out how much the patient pays, we can subtract the amount paid by the insurance from the total cost of the treatment:
$3000 - $2400
= $600
Therefore, the mathematics involved in solving this problem is very straightforward. We used basic arithmetic operations such as multiplication and subtraction to find the amounts paid by the insurance company and the patient.
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f(n) = 2n-1 find the arithmetic sequence ?
An arithmetic sequence is a sequence of numbers in which the difference between any two successive members of the sequence is a constant value. The general form of an arithmetic sequence is:
a, a + d, a + 2d, a + 3d, ...
where "a" is the first term of the sequence, and "d" is the common difference between successive terms.
Given the function f(n) = 2n - 1, we can see that the function outputs a sequence of integers, with a common difference of 2. So f(n) is not an arithmetic sequence.
Arithmetic sequence is a list of numbers in which each number is the sum of the previous number and a constant number.
Example: 1,3,5,7,9 is an arithmetic sequence because the constant difference is 2.
If you have any other question feel free to ask.
5 whole 1/7- 2 whole 5/21
The value of 5 1/7 minus 2 5/21 will be 2 19 / 21.
How to solve the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Based on the information, the value of 5 1/7 minus 2 5/21 will be:
= 5 1/7 - 2 5 / 21
= 5 3/21 - 2 5 / 21
= 2 19 / 21
The value is 2 19/21.
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When Edna's phone is fully charged, it can operate for up to 18 hours before running out of battery. It has been 6 hours since Edna's phone was fully charged. Let x represent how many more hours Edna's phone can operate without running out of battery. Which inequality describes the problem? 6 + x < 18 6 +xs 18 Solve the inequality. Then, complete the sentence to describe the solution. Edna's phone can operate for up to more hours without running out of battery.
Edna's phone can operate for up to 12 more hours without running out of battery.
In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
fully charged
T = 18Hr
It has been 6 hours since Edna's phone was fully charged.
remaining battery =18- 6= 12Hr
x=12Hr
6 + x < 18
6 +x > 18
neither nor.
both equations are wrong.
6 +x = 18
Edna's phone can operate for up to 12 more hours without running out of battery.
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Is 10 12 15 a Pythagorean triple?
No, 10 12 15 is not a Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, and c such that a^2 + b^2 = c^2.
To determine whether 10 12 15 is a Pythagorean triple, we need to calculate a^2 + b^2.
In this case, 10^2 + 12^2 = 100 + 144 = 244. Since 244 ≠ 15^2, 10 12 15 is not a Pythagorean triple. We can also confirm this by plugging 10, 12, and 15 into the Pythagorean Theorem, a^2 + b^2 = c^2.
10^2 + 12^2 = 100 + 144 = 244
244 ≠ 15^2
Therefore, 10 12 15 is not a Pythagorean triple.
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How do you find the sides of an acute triangle?
To find the missing side length of the acute angled triangle apply the cosine law as follow:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
As given in the question,
Given triangle is acute angled triangle.
Let us consider the measure of two sides and its included angle of the acute angled triangle is given.
Let the triangle be ABC,
Side opposite to ∠A, ∠B , and ∠C are a , b, and c respectively.
Apply cosine law to find the measure of the missing side in the acute angled triangle:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
Therefore, to get the measure of the missing side length in the acute angled triangle apply cosine law.
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Angle AOB is a central angle with a measure of 110 degrees.
What is the measure of its arc AB?
The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
Given that,
In the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
We have to find the measure of the ACB arc.
We know that,
Suppose that AB is the minor arc that is m(arc AB) = 110°
We know that measure of the major arc is 360°- measure of minor arc.
m(arc ACB)= 360- m(arc AB)
m(arc ACB)= 360-110
m(arc ACB)= 250°
Therefore, The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
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A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.
What are the odds against exactly 5 cars passing over the bridge in that time?
Answer: The odds against an event occurring are the ratio of the probability that the event will not occur to the probability that the event will occur. To find the odds against an event, you can use the formula:
Odds against = (1 - probability of event occurring) / probability of event occurring
In this case, the event is that exactly 5 cars will pass over the bridge in a 4-minute period. The probability that this event will occur is 0.16. Therefore, the odds against this event occurring are:
Odds against = (1 - 0.16) / 0.16
= 0.84 / 0.16
= 5.25
So, the odds against exactly 5 cars passing over the bridge in a 4-minute period are 5.25 to 1.
It means that there are 5.25 times more likely that it will not happen compare to happen.
Step-by-step explanation:
the survey is a research method in which: group of answer choices individuals are carefully observed in their natural environments. a representative, random sample of individuals are questioned regarding their attitudes or behaviors. an individual is studied in great depth. an investigator determines the extent to which two variables influence each other.
The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.
B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.
C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.
D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.
Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
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What linear equation means?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1 or 0. A linear equation is an algebraic equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
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The points (-5, 5) and (5, u) fall on a line with a slope of 3/10 What is the value of u?
Thank you!
Answer:
u = 8
Step-by-step explanation:
calculate the slope of the line passing through the 2 give points using the slope formula, then equate to the given slope.
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 5 ) and (x₂, y₂ ) = (5, u )
m = [tex]\frac{u-5}{5-(-5)}[/tex] = [tex]\frac{u-5}{5+5}[/tex] = [tex]\frac{u-5}{10}[/tex] , then equating the 2 expressions gives
[tex]\frac{u-5}{10}[/tex] = [tex]\frac{3}{10}[/tex] ( cross- multiply )
10(u - 5) = 30 ( divide both sides by 10 )
u - 5 = 3 ( add 5 to both sides )
u = 8
Step-by-step explanation:
(u - 5)/(5 + 5)= 3/10
(u - 5)/10= 3/10
10u - 50 = 30
10u = 80
u = 8
Choose the equation that represents the line passing through the point (-3,-1) with a slope of 4.
y=4x-11
y = 4x + 11
y = 4x + 7
y=4x-7
On solving the provided question, we can say that - in the linear equation here the value will be
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
y = 4x + 11
x = 8
y = 32 + 11
y = 43
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Rob collects model planes one of his planes uses a sacks in which 1 inch represents 1. 5 feet if the length of the model airplane is 12 inches find the length of the actual airplane on feet
If 1 inch represents 1.5 feet, we can use this conversion factor to find the length of the actual airplane in feet. Thus 12 inches of model airplane represents an actual length of the actual airplane of 18 feet.
Therefore the answer is 18 feet.
To convert the length of the model airplane (12 inches) to feet, we can multiply it by the conversion factor (1 inch = 1.5 feet)
= 12 inches × 1.5 feet/inch
= 18 feet
So the length of the actual airplane is 18 feet.
It is important to pay attention to the units of measurement when performing conversions and make sure to use the correct conversion factor. And also it's a good practice to always check your answer to make sure it makes sense in the context of the problem.
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If f(x)=3x, g(x)=x+4, and h(x)=x2-1, find the value of h[f(5)]
Answer:
29
Step-by-step explanation:
The local sports team donated 200 meal vouchers and 24 jerseys for a fundraising event. 125 vouchers and 20 jerseys were part of a raffle . The ratio of tickets sold to raffled items was 8:1; each ticket was sold for $3.50. How much money was raised from the raffle
On solving the provided question, we can say that by linear equation $249.67 money was raised from the raffle
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
the linear equation that can be formed is
200x + 24 y = 3.50
125 x + 20y = 5
ratio = 8:1
so, $249.67 money was raised from the raffle
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If sin 0<0 and cos0>0, then the terminal point determined by 0 is in :
Answer: The statement "if sin 0 < 0 and cos 0 > 0" is not true, as both the sine and cosine of an angle of 0 degrees are equal to 0. Therefore, the statement is not meaningful and the question cannot be answered.
It is important to note that sine, cosine, and all the trigonometric functions are defined in radians and not degrees and the value of sin(0) and cos(0) is not zero but 1
Please provide more context or specify what you are asking about in order to give a more accurate answer.
Step-by-step explanation:
During a particularly dry growing season in a southern state, farmers noticed that there is a delicate balance between the number of seeds that are planted per square foot and the yield of the crop in pounds per square foot. The yields were the smallest when the number of seeds per square foot was either very small or very large. What is the explanatory variable for this relationship
The number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.
The explanatory variable for this relationship is the number of seeds per square foot. The number of seeds per square foot is the variable that is being manipulated or changed by the farmers in order to observe the effect on the yield of the crop in pounds per square foot.
The farmers observed that the yields were the smallest when the number of seeds per square foot was either very small or very large, this means that there is an optimal number of seeds per square foot that yields the highest crop.
So, the number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.
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When a=-1/2 and b=6, which expression:
has the largest value?
has the smallest value?
is the closest to zero?
When a=12 and b=-6, which expression:
has the largest value?
has the smallest value?
is the closest to zero?
When a=-6 and b=-12, which expression:
has the largest value?
has the smallest value?
is the closest to zero?
For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.
For a=-1/2 and b=6, the expression with the largest value is a+b, which is equal to 5.5. The expression with the smallest value is a-b, which is equal to -7.5. The expression closest to zero is a+b, which is equal to 5.5.
For a=12 and b=-6, the expression with the largest value is a+b, which is equal to 6. The expression with the smallest value is a-b, which is equal to 18. The expression closest to zero is a-b, which is equal to 18.
For a=-6 and b=-12, the expression with the largest value is a+b, which is equal to -18. The expression with the smallest value is a-b, which is equal to 6. The expression closest to zero is a+b, which is equal to -18.
For an expression containing two variables, a and b, the expression with the largest value is a+b, the expression with the smallest value is a-b, and the expression closest to zero is either a+b or a-b, depending on the values of a and b.
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A regular pentagon is a pentagon with five sides of the same length. If the length of one side of the pentagon is represented by 2X -1, what expression would represent the perimeter of this pentagon
Step-by-step explanation:
one side : 2x - 1
so, 5 sides (the perimeter is the sum of all sides) :
5 × (2x - 1) = 10x - 5
Question 1 : (2.3 × 10^4) × (1.5 × 10^-2)
Question 2: (3.6 × 10^-5) ÷ (1.8 × 10²)
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expressions are given below.
(2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
Simplify the expression (2.3 × 10⁴) × (1.5 × 10⁻²), then the value of the expression will be given as,
⇒ (2.3 × 10⁴) × (1.5 × 10⁻²)
⇒ 345
Simplify the expression (3.6 × 10⁻⁵) ÷ (1.8 × 10²), then the value of the expression will be given as,
⇒ (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
⇒ 2 × 10⁻⁷
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
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Find the inverse of y = √x + 8, y ≥ 8
To find the inverse of a function, you can follow these steps:
Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.
Solve the equation for y. In this case, you would get:
x = √y + 8
y = x - 8
Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:
f^-1(x) = x - 8
This is the inverse function of y = √x + 8.
Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.
After my salary was increased by $16\%,$ it was $\$52{,}200$. What was my salary before the increase
%, a relative figure signifying hundredths of any amount. Before the raise, I was making $45,000.
What is percentage?A percentage that represents a tenth of a quantity. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).
Calculating a percentage involves dividing an item by its sum and multiplying the result by 100.
Considering the query
It was $52,200 after a 16% raise in my pay.
In light of the conditions stated, come up with
[tex]$=\frac{52200}{1+16 \%}$$=\frac{52200}{1+0.16}$$=\frac{52200}{1.16}$$=\frac{5220000}{116}$[/tex]
= $45000
Before the raise, I was making $45,000.
Therefore, the answer is $45,000.
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