The directrix of the parabola defined by the equation (x+9)²= -16(y-5) is x=-16(y-5)+9.
What is equation?Equation is a physical and mathematical statement that describe physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variables may be pointed such as you energy.
The directrix of a parabola is the line which is perpendicular to the axis of symmetry and is equidistant from the focus of the parabola. In this case, the axis of symmetry is y=5 and the focus is (9,-16).
The equation of a line perpendicular to the axis of symmetry is y=mx+b where m is the slope of the line and b is the y-intercept. The slope of the line perpendicular to the axis of symmetry is given by the negative reciprocal of the slope of the axis of symmetry. The slope of the axis of symmetry is 0, so the slope of the perpendicular line is undefined.
Using the point-slope form of the equation of a line, we can represent the equation of the directrix as x=-16(y-5)+9. This is because the point (9,-16) is equidistant from the directrix, so the y-intercept of the directrix is -16(5-5)+9 = 9.
Therefore, the directrix of the parabola defined by the equation (x+9)² = -16(y-5) is x=-16(y-5)+9.
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Yes or no please helpp
Answer:
Step-by-step explanation:
No, the point is not (1,0)
What is the conversion of 65f to c ?
65 °F is equal to 18.3333 °C.
A temperature unit developed from the SI (International System of Units) is Celsius (symbol: °C).
Prior to the adoption of the metric system, Fahrenheit (symbol: °F) was a commonly used measurement of temperature.
To convert a temperature from Fahrenheit (°F) to Celsius (°C),
We can use the following formula:
°C = (°F - 32) x 5/9
Where °C is the temperature in Celsius
°F is the temperature in Fahrenheit.
Substituting 65 for °F,
We get:
°C = (65 - 32) x 5/9
Simplifying the expression:
°C = 33 x 5/9
°C = 18.3333333333
Therefore, 65 degrees Fahrenheit is equal to nearly 18.3333 degrees Celsius (rounded to four decimal places).
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4( – 4n2–n–1) Find the product. Simplify your answer.
The simplified answer is [tex]-16n^2 - 4n - 4.[/tex]
Describe Simplification?In mathematics, simplification refers to the process of simplifying an expression or equation without affecting its fundamental meaning or value. Using mathematical tools and rules to simplify an equation makes it simpler to manipulate or solve.
In algebra, simplification might take the form of factoring out common factors, grouping like concepts, or distributing multiplication across addition or subtraction. For instance, merging two like terms will simplify the formula 2x + 4x to 6x. The same strategy can be used to reduce the expression 3(x + 2) - 2(x - 1) to 3x + 4 by spreading out the multiplication and combining related terms.
Other types of mathematical simplification include determining the square root of a number, simplifying trigonometric functions, and reducing fractions to their simplest forms. In order to solve difficulties and comprehend mathematical concepts, simplification is a crucial step that removes superfluous complexity and facilitates understanding of the underlying structure of an equation or problem.
To find the product of 4 and the expression [tex](-4n^2 - n - 1),[/tex] we can distribute the 4 to each term inside the parentheses:
[tex]4(-4n^2 - n - 1) = -16n^2 - 4n - 4[/tex]
Therefore, the simplified answer is [tex]-16n^2 - 4n - 4.[/tex]
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what is integral of secx?
The integral of sec(x) is ln |sec(x) + tan(x)| + C.
The integral of sec(x) is:
∫sec(x) dx = ln |sec(x) + tan(x)| + C
where C is the constant of integration.
To solve this integral, you can use the method of substitution. Let u = sec(x) + tan(x). Then [tex]du/dx = sec(x)tan(x) + sec^2(x)[/tex], which can be simplified to du/dx = u tan(x). Rearranging, we get du/u = tan(x)dx.
Substituting these expressions into the integral, we have:
∫sec(x) dx = ∫(sec(x) + tan(x))/(sec(x) + tan(x)) dx = ∫(1/u) du
Integrating this expression gives:
∫(1/u) du = ln |u| + C = ln |sec(x) + tan(x)| + C
Therefore, the integral of sec(x) is ln |sec(x) + tan(x)| + C.
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suppose that a flaw in a certain computer chip installed in computers was discovered that could result in a wrong answer when performing a division. the manufacturer initially claimed that the chance of any particular division being incorrect was only 1 in 11 billion, so that it would take thousands of years before a typical user encountered a mistake. however, statisticians are not typical users; some modern statistical techniques are so computationally intensive that a billion divisions over a short time period is not outside the realm of possibility. assuming that the 1 in 11 billion figure is correct and that results of different divisions are independent of one another, what is the probability that at least one error occurs in one billion divisions with this chip? (round your answer to four decimal places.)
In 1 billion, the probability of division being incorrect would be : {1/(11 x 10⁹)²}.
What is probability?In science, the probability of an event is a number that indicates how likely the event is to occur.
Given is that the manufacturer initially claimed that the chance of any particular division being incorrect was only 1 in 11 billion.
The probability of division being incorrect would be -
P{incorrect} = (1/11 x 10⁹)
In 11 billion, the probability of division being incorrect is (1/11 x 10⁹).
Then, in 1 billion, the probability of division being incorrect would be -
{1/(11 x 10⁹)²}
Therefore, in 1 billion, the probability of division being incorrect would be : {1/(11 x 10⁹)²}.
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Answer:
Step-by-step explanation:
0.0869
one condition of a well-defined probability density function of a continuous random variable x is that f(x) is multiple choice question. greater than zero for all values of x. not greater than zero for all values of x. less than zero for all values of x. greater than four for all values of x.
The correct answer is:
greater than zero for all values of x.
What is Probability ?Probability is a way of evaluating how likely something is to happen. Several things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. One is the probability of every event in a sample space.
Now in the given question ,
A probability density function (PDF) of a continuous random variable x is a function that describes the relative likelihood of x taking on different values in a continuous range. The PDF is defined such that the area under the curve between any two values a and b represents the probability of x being in that range, i.e., P(a ≤ x ≤ b).
Since probabilities are non-negative, the PDF of a continuous random variable must also be non-negative. That is, f(x) > 0 for all values of x. This condition ensures that the area under the curve is non-negative, which is necessary for it to represent a valid probability distribution.
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Which expression is equivalent to 5(3x + 4) + 2(3x − 7)
Answer:
21x + 7
Step-by-step explanation:
See picture below :)
What is antiderivative of sin?
The antiderivative of sin is -cos(x) + C.
The antiderivative of a function is the inverse operation of differentiation which is is also known as its indefinite integral.
So, the integral of sin
∫sin(x) = -cos(x) + C
where C = constant of integration.
This can be verified by differentiating -cos(x) + C with respect to x, which gives sin(x).
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what is the nominal ordinal interval ratio?
Nominal, ordinal, interval, and ratio are measurement scales used in statistics to categorize and rank data.
Nominal, ordinal, interval, and ratio are four sorts of information estimation scales utilized in measurements.
Nominal scales are utilized to mark or classify information into particular gatherings, where each gathering is fundamentally unrelated and altogether comprehensive. Instances of ostensible information incorporate orientation, race, and occupation.
Ordinal scales include positioning information in a particular request, however the distinctions between values are not significant. Instances of ordinal information incorporate positioning motion pictures in view of their prominence or understudy execution on a test.
interval scales include positioning information in a particular request, however the distinctions between values are significant, and there is no obvious zero point. Instances of stretch information incorporate temperature, intelligence level scores, and time.
ratio scales are like span scales, however they have a genuine zero point, implying that values can be duplicated and partitioned. Instances of proportion information incorporate weight, level, and pay.
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The complete question is:
what is the nominal, ordinal, interval and ratio?
¿Cuáles de las siguientes opciones tienen el mismo valor que el
, de
81
?
The correct answer is option B and it is equal to 30% of 81 because it shows 0.30 x 81.
We have to find that how much is equal to the 30% of 81.
We can use the percentage formula here and that is,
%age = Obtained value/total value x 100
Here in this case, we have to find the obtained value and the total value is 81 and the percentage that we are going to get is equal to 30.
So, putting all the values, we get,
obtained value = 30 x 81/100
obtained value = 0.30 x 81
Hence, the value 0.30 x 81 is equal to 30 % of 81. hence option B is the correct answer.
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Complete question - Which of the following options have the same value as 30% of 81?
A. 0.03 x 81
B. 0.3 x 81
C. 0.03 x 81
D. 3 x 81
A pole 8 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Maya measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
A: 111 ft long. (Student pressed "see solution" instead of submitting an answer) (As the op i can't upload it as an Answer, so i am leaving it here in my edited question).
108ft is the length of the of the guy wire
Similar trianglesTriangles are known to be similar if the ratio of the similar sides of the triangle are equal.
From the given diagram, we need to determine of the guy wire. Using the similarity theorem of a triangle;
8/2 = l/25+2
8/2 = l/27
2l = 8 * 27
l = 4 * 27
l = 108 ft
Hence the length of the of the guy wire, to the nearest foot is 108ft
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HELP ASAP!
Moesha is looking at a graph that shows a line drawn between two points with a slope of -5. One of the points is smudged and she cannot read it. The point as far as she can tell are (3,5) and (x,10). What must the value of x be? Explain.
The value of x is 2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The point as far as she can tell are (3,5) and (x,10).
Slope is -5.
-5=10-5/x-3
-5=5/x-3
-5(x-3)=5
Apply distributive property
-5x+15=5
Substitute 15 from both sides
-5x=-10
Divide both sides by 5
x=2
Hence, the value of x is 2.
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the diagram shows a sector OPQR of a circle, centre O and radius 8 cm. OPR is a triangle. work out the area of the shaded segment PQR. give your answer correct to 3 significant figures
the shaded segment PQR will be 18.265m².
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
the diagram shows a sector OPQR of a circle, centre O and radius 8 cm.
Area of shaded part = Area of quadrant − Area of triangle
=πr²/ 4 - 1/2 bh
= π × 8²/ 4 - 1/ 2 × 8× 8
= 18.265m².
Hence the shaded segment PQR will be 18.265m².
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Please help me answer this quickly!!!! Give a thorough explanation and answer every part! Thank youuuuu :) (will give brainliest)
The features of the sine function are given as follows:
Midline: y = 1.Maximum value: y = 4.Minimum value: y = 2.Amplitude: 3 units.Period: 8 units.Frequency: 1/8 units. (one divided by the period).The equation is given as follows:
y = 3sin(0.25πx) + 1.
How to define the sine function?The standard definition of a sine function is given as follows:
y = Asin(Bx) + C.
The parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.The minimum value is of -2, while the maximum value is of 4, hence the midline is given as follows:
y = (-2 + 4)/2
y = 1.
The difference between the minimum and the maximum value is of 6 units, hence the amplitude is obtained as follows:
2A = 6
A = 3.
The function with no vertical shift would oscillate between -A = -3 and A = 3, while this function oscillates between -2 and 4, hence the vertical shift is given as follows:
C = 1.
The shortest distance between repetitions of the function is of 8 units, hence the period is of 8, the frequency is of 1/8, and the coefficient B is given as follows:
2π/B = 8
8B = 2π
B = π/4.
B = 0.25π.
Hence the function is defined as follows:
y = 3sin(0.25πx) + 1.
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A pizza restaurant charges for each pizza and adds a delivery fee. The cost (c), in dollars, to have any number of pizzas (p) delivered to a home is described by the function c = 8p + 3. Which statement is true?
Each pizza costs $3 and the delivery fee is $8.
The cost of 3 pizzas is $14.
The cost of 8 pizzas is $11.
Each pizza costs $8 and the delivery fee is $3.
Answer:a
Step-by-step explanation:
Help me please I need to turn this in
Answer: look at the image for the answer and explanation
Step-by-step explanation:
Compound Interest
1. If $1,800 is deposited into an account earning 6% interest, how much wll be in the account at
the end of 18 years if the interest is compounded with the following frequencies:
b) weekly
At the end of 18 years, there will be a total of $5,890.37 in the account.
Compound interest is a powerful financial tool that can help you grow your money over time.
In the case of the $1,800 deposited into an account earning 6% interest compounded weekly, the total amount in the account at the end of 18 years can be calculated as follows:
Let P be the principal balance, r be the interest rate, n be the number of times the interest is compounded per year, and x be the number of years. Using the compound interest formula, we can calculate the amount in the account at the end of 18 years:
A = P(1 + (r/n))ⁿˣ
A = 1800 * (1 + (0.06/52))⁵²ˣ¹⁸
A = 5,890.37
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what is 32.32 x 2.1 6th grade math
Answer:
67.872
Step-by-step explanation:
a surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect it t/f
The statement that "a surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect" is true.
The surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect it is called a torus. The torus is a three-dimensional surface that can be thought of as a doughnut shape. The curve that generates the torus is called the generator, and the line about which the curve is rotated is called the axis of rotation. The torus has the interesting property that it has a hole in the center, and the distance from any point on the surface to the center of the torus is constant.
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Please help what’s the answer for what the question is asking me
Answer:
Unit rate = 0.6
y = 0.6x
x= 24
Step-by-step explanation:
I cannot see the headings to the table, but on examining the questions, the first column contains the values for variable x and the second column the values for variable y
Unit Rate
Unit rate = increase in y for a unit increase in x
We see that the rate is constant for every unit increase in x and is = 0.6
Unit rate = 0.6
Equation
The equation therefore is y = 0.6x
Value of x when y = 14.4
When y = 14.4, plugging into the equation gives:
14.4 = 0.6x
or
0.6x = 14.4 by switching sides - no effect on equation
Divide both sides by 0.6
0.6x/0.6 = 14.4/0.6
x= 24
The ratio of employees who
play musical instruments to
employees who play sports is
3:20. If there are 40
employees who play sports,
how many employees play
musical instruments?
There are 6 employees who play musical instruments.
What is the ratio?
A ratio is a relationship between two quantities, indicating how many times the first quantity contains the second. Ratios are often expressed as a fraction or in the form "a:b", where "a" and "b" are the two quantities being compared.
The given ratio of employees who play musical instruments to employees who play sports is 3:20. This means for every 3 employees who play musical instruments, there are 20 employees who play sports.
We are given that there are 40 employees who play sports. We can use this information to find the number of employees who play musical instruments as follows:
Let's start with the ratio of employees who play sports to employees who play music, which is 20:3. This means that for every 20 employees who play sports, there are 3 employees who play music.
We know that there are 40 employees who play sports, so we can set up a proportion to find the number of employees who play music:
20/3 = 40/x
where x is the number of employees who play music.
To solve for x, we can cross-multiply:
20x = 3 * 40
20x = 120
Then, we can solve for x by dividing both sides by 20:
x = 6
Therefore, there are 6 employees who play musical instruments.
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What is the conversion of 70f in c?
70 degrees Fahrenheit is equal to approximately 21.1111 degrees Celsius (rounded to four decimal places).
The Celsius (symbol: °C) is an SI (International System of Units) derived unit of temperature.
The Fahrenheit (symbol: °F) is a unit of temperature that was widely used prior to metrication.
To convert a temperature from Fahrenheit (°F) to Celsius (°C),
We can use the following formula:
°C = (°F - 32) x 5/9
Where °C is the temperature in Celsius and °F is the temperature in Fahrenheit.
Substituting 70 for °F, we get:
°C = (70 - 32) x 5/9
Simplifying the expression:
°C = 38 x 5/9
°C = 21.1111111111
Therefore, 70 degrees Fahrenheit is equal to approximately 21.1111 degrees Celsius (rounded to four decimal places).
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What is result of 7 x 4
Answer: 7 x 4 = 28
Step-by-step explanation: 7 + 7 + 7 + 7 = 28
Pania ate a quarter of the pizza. Pita ate one sixth of what remained. Paula ate two fifths of what remained after Pita had eaten. What fraction of the pizza was left for penny?
Answer:
Penny had 13/20 of the pizza left.
Step-by-step explanation:
Let's start with the whole pizza, which we can represent as 1.
Pania ate a quarter of the pizza, leaving 3/4 (since 1/4 + 3/4 = 1) for Pita and Paula.
Pita then ate one sixth of what remained, which is one sixth of 3/4 or 3/24, leaving 21/24 (or simplifying to 7/8) for Paula.
Paula then ate two fifths of what remained after Pita had eaten, which is two fifths of 7/8 or 14/40, leaving 26/40 (or simplifying to 13/20) for Penny.
Therefore, Penny had 13/20 of the pizza left.
I hope this helps! And if you could label my answer brainliest that would be awesome.
- Dante
Answer:
3/8 of the pizza was left for Penny.
Step-by-step explanation:
Pania ate 1/4 and left 3/4.
Pita ate 1/6 (of the 3/4) and left 5/6.
Paula ate 2/5 (of the 5/6) and left 3/5.
What was left?
3/5 of 5/6 of 3/4
"of" means times
3/5•5/6•3/4
(cancel the 5s and a 3 with the 6, leaving a 2)
= 3/8
But see the illustrated story, it makes way more sense! See image
1.5 Cheaters, study components: Researchers studying the relationship between honesty, age, and self-control conducted an experiment on 160 children between the ages of 5 and 15. Participants reported their age, sex, and whether they were an only child or not. The researchers asked each child to toss a fair coin in private and to record the outcome (white or black) on a paper sheet, and said they would only reward children who report white. Half the students were explicitly told not to cheat and the others were not given any explicit instructions. In the "no instruction" group the probability of cheating was found to be uniform across groups based on a child's characteristics. In the group that was explicitly told to not cheat, girls were less likely to cheat, and while rate of cheating didn't vary by age for boys, it decreased with age for girls (Ritz et al. 2000). Identify the following
a) What are the cases?
_____all children ages 5 to 15
_____the 160 children between the ages of 5 to 15
_____the coin flips
_____boys or girls
b) What are the variables and their types?
_____The variables and types are age (discrete), sex (regular categorical), whether they were an only child or not (regular categorical)
_____The variables and types are age (discrete numerical), sex (ordinal), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical)
_____The variables and types are age (discrete), sex (regular categorical), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical)
_____The variables and types are age (discrete), sex (ordinal), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical)
c) What is the main research question?
_____Do girls cheat more or less often than boys?
_____What is the effect of age, sex, only child status, and whether or not children were given instructions on the rate of cheating in a game?
_____Do children follow directions?
160 children between the ages of 5 and 15 comprise the cases.
Age and sex child cheated are the variables and types.
What impact do age, sex, being an only child, and whether or not kids received instructions have on the frequency of cheating in games?
a) What are the cases?
The cases are: the 160 children between the ages of 5 to 15.
b) What are the variables and their types?
The variables and types are: age (discrete numerical), sex (regular categorical), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical).
c) What is the main research question?
The main research question is: What is the effect of age, sex, only child status, and whether or not children were given instructions on the rate of cheating in a game?
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What’s 5/32 divided by 25/4 as a fraction in its simplest form?
Work Shown:
5/32 divide 25/4
(5/32) * (4/25)
(5*4)/(32*25)
(5*4)/(8*4*5*5)
(1)/(8*5)
1/40
The height in feet of a thrown football is modeled by the equation f(t) = 6 + 30t - 16t, where t is measured in seconds.
a. What does the constant 6 mean in this situation?
b. what does the 30t mean in this situation?
c. How do you think the squared term -16t^2 affects the value of the function f? what does this term reveal about the situation?
In the given equation, the constant 6 represents the initial height of the football when it was thrown. This means that before the football was thrown, it was already at a height of 6 feet above the ground.
Define an equation.A mathematical equation proves the equality of two expressions by using symbols, numbers, and/or variables. Equations can be used to illustrate relationships between several numbers or to locate unknown values in order to solve problems.
An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equal sign (=). The LHS and RHS can contain constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
a. The constant 6 in equation f(t) = 6 + 30t - 16t represents the initial height of the football when it was thrown.
b. The term 30t in the equation represents the vertical distance covered by the football per second due to its initial velocity. This term is calculated by multiplying the initial velocity of the football by the time t.
c. The squared term -16t^2 in the equation represents the effect of gravity on the height of the football. This term is calculated by multiplying half the acceleration due to gravity (-16 feet per second squared) with the square of time t. The negative sign indicates that the height of the football is decreasing as time passes due to the influence of gravity.
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What is online calculator of variable cost ?
Online calculator of variable cost is used to Total Variable Cost = Total Cost-Fixed Costs to calculate the Total Variable Cost.
A variable cost is an expense that changes as a company's production output rises and falls. Variable expenses vary according on the amount of output produced. Basic variable costs include, in large part:
Raw materialsPackagingLabourTransportation fee, commissionUtility billsVariable costs are frequently employed in business and are a crucial component of the analysis of the company's break-even point. The revenue or unit that must be sold to cover all costs is examined using the break-even approach.
The following calculation is the break-even point:
Break-even point in units = Fixed costs/(Sales price per unit – Variable cost per unit)
Variable costs are crucial for successful investors because they help them calculate the proportion of the set price and predict how the company will respond to various operational scenarios.
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Kim donated half of her pants to charity, and kept her 7 favorite pants. When she was done, she was left with 35 pairs of pants. How many pairs of pants did she have in the beginning?
The answer is 84 pairs of pants.
Explanation:
According to the problem, she donated half of her pants to charity, which means she donated (1/2)x pairs of pants.
After donating half of her pants, she kept her 7 favorite pairs of pants. So, the number of pairs of pants she kept is 7.
The problem states that she was left with 35 pairs of pants after donating half of her pants and keeping her 7 favorite pairs. This means that the remaining number of pairs of pants is (x/2) - 7 = 35.
Solving for x, we get:
(x/2) - 7 = 35
x/2 = 42
x = 84
Therefore, Kim had 84 pairs of pants in the beginning.
Answer:
my guess is 17 .,.
Step-by-step explanation:
The school is 100 m from Jason's house the following describes his most recent trip he walked 50 m towards school and 2 minutes he realized that he left his book at home he turned around and walked home at the same speed he spends one minute looking for his books he walked all the way to school and it twice his original speed finish a graph that actually represents Jason's trip
Answer:
Step-by-step explanation:
left a book at home. He turned around and walked home at the same speed.