State the equation of the function whose graph is shown. (I'm needing help finding the equation from the graph (pic attached))
Answers
The quadratic function graphed is defined as follows:
y = -x² + 6x - 8.
How to define the quadratic function?A quadratic function of roots x' and x'' is defined as follows:
y = a(x - x')(x - x'').
From the graph, the roots of the function are the x-intercepts, which are the values of x for which the graph crosses the x-axis, hence they are given as follows:
x = 2 and x = 4.
Hence:
y = a(x - 2)(x - 4)
y = a(x² - 6x + 8).
In which a is the leading coefficient.
The vertex is at (3,1), meaning that when x = 3, y = 1, hence the leading coefficient a is obtained as follows:
1 = a(3² - 6(3) + 8)
-a = 1
a = -1.
Hence the function is defined as follows:
y = -x² + 6x - 8.
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Related Questions
(CO 2) You flip a coin 3 times. The sample space is \{HHH, HHT, HTH, THH, HTT, THT, TTH. TTT\}. Which of the following is a compound event? A. You get exactly 2 tails B. You get exactly 3 tails C. This is not an event D. You get exactly 3 heads
Answers
A compound event is a combination of multiple simple events that can occur simultaneously or independently. When talking about coin flipping, the sample space is the set of all possible outcomes of the experiment, which in this case is flipping a coin 3 times. In this case, the sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.
Option A, You get exactly 2 tails, is a compound event because it consists of three simple events, THT, HTH, and TTH. These events can happen independently of one another and therefore, it is a compound event.
Option B, You get exactly 3 tails, is not a compound event because it only consists of one simple event, TTT. This event is not a combination of other simple events and is, therefore, not a compound event.
Option C, This is not an event, is not a valid option as it is not a possible outcome.
Option D, You get exactly 3 heads, is also a compound event because it consists of one simple event, HHH. This event can happen independently of other simple events and it is, therefore, a compound event.
Hence, options A and D are compound events as they are a combination of multiple simple events that can happen independently or simultaneously.
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Given sides b, c, and angle d
state the area of the triangle.
Answers
The area of triangle with three sides a,bc is equals to
√[s × (s – a) × (s – b) × (s – c)].
What is triangle ?
Triangle can be defined as in which it consists of three sides, three angles and sum of the three angles are 180 degrees always.
Given
in the triangle with three sides a,b,c.
Let ABC be a triangle such that the length of the 3 sides of the triangle is AB = c, BC = a and CA = b.
The semi-perimeter of triangle ABC = s = (a + b + c)/2
Then, the area of triangle ABC = √[s × (s – a) × (s – b) × (s – c)].
Therefore, The area of triangle with three sides a,bc is equals to
√[s × (s – a) × (s – b) × (s – c)].
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Diego has 3 pencils, 4 pens, and 2 highlighters in his pencil case. What is the ratio of pencils and highlighters to pens in Diego's pencil case?
O 3:6
O
O
4:9
O 5:4
07:2
Answers
Then, ratio to amount of pens
Solution:
Sum of pencils n highlighters = 3 + 2 = 5
Pens = 4
Thus,
The ratio is:
5:4
what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.
Answers
The angle θ measures 53.13⁰ with the east direction.
What is tangent of any angle?The tangent of an angle is a trigonometric function that is defined as the ratio of the side opposite the angle to the side adjacent to the angle in a right triangle. In other words, it is a measure of the steepness of a line that is tangent to a point on a function's graph and is represented by the symbol tan. It is one of the three main trigonometric functions, along with sine and cosine. The value of tangent is always positive in the first and fourth quadrants.
let the angle made be θ degree to the north of east from the post office to the grocery shop
so tan θ = p/b
where p is perpendicular , b is base of the triangle
so tan θ = 3/4
=> θ = 53.13 degree
so the angle θ measures 53.13⁰ with the east direction.
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Complete question :
what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.
When looking east, the angle is 53.[tex]13^{0}[/tex] degrees.
What does a tangent to any angle mean?
The ratio of a right triangle's side opposite to its side next to the angle is known as the tangent of an angle, which is a trigonometric function. It is a measurement of the steepness of a line that is tangent to a point on the graph of a function, and it is denoted by the symbol tan. One of the three primary trigonometric functions, together with sine and cosine, is it. In the first and fourth quadrants, tangent's value is always positive.
Let the angle formed between the post office and the grocery store be degrees to the north of east.
so tan θ = p/b
where p is perpendicular , b is base of the triangle
so tan θ = 3/4
=> θ = 53.13 degree
so the angle θ measures 53.13⁰ with the east direction.
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Complete question :
What is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.
State if the two triangles are congruent. If they are, state how you know.
Select the correct response:
Yes by SAS
They are not congruent.
Yes by AAS.
Yes by ASA.
Answers
The two triangles are not congruent
What does triangular congruency mean?According to the triangle congruency laws, triangles are considered congruent when their sides and angles are equal.
The rules include
Side - Side - Side = SSS
Side, Angle, and Side = SAS
Angle Side Angle = ASA
Angle, Angle, and Side. = AAS
Hypotenuse and one leg. = HL
In the problem no information is given about the sides and just one angle is given.
Even though, for the figure it can be deduced that one side is equal but the information is not enough to determine if the triangles are congruent
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An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 120 g of an alloy That contains 42% copper with 200 g of pure copper
Answers
The mixture is 78.25% copper for the given alloy.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
To solve the given situation, we utilize material balancing before and after mixing.
Let the total amount of material after mixing is 320.
Let x be the percent copper of the mixture and applying copper balance,
⇒ (0.42)(120 g) + (1)(200) = 320x
Solving the above equation, we get the value as
⇒ x = 0.7825
Thus, the mixture is 78.25% copper.
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find the volume v of the described solid s. the base of s is the triangular region with vertices (0, 0), (5, 0), and (0, 5). cross-sections perpendicular to the x-axis are squares.
Answers
Using the disk method, it can be concluded that the volume of the solid is 125π /3 cubic units.
Disk Method is a method used to determine the volume of a solid formed by revolving the region about the x-axis and the interval [a, b]. The volume of the solid is the integral of the area of the base times dx.
V = π ∫ Ax dx
From the question, we know that the base of the figure is a triangular region and the coordinates are (0,0), (5,0), and (0,5).
The square is perpendicular to the x-axis. Thus, we can find the side of the square, that is the straight line passing through (5,0) and (0,5) which meet the y = mx + b equation.
First, we determine the slope of the line (m).
m = (y₂ - y₁) / (x₂ - x₁)
= ( 5 - 0 ) / ( 0 - 5 )
= 5 / -5
= -1
To find b, we input the value of m into the equation for point (5,0):
y = mx + b
0 = -1*5 + b
0 = -5 + b
b = 5
So we got the side of the square:
y = mx + b
y = -x + 5
y = 5 - x
Thus the area of the square is:
A = side²
= (5 - x)²
= 25 + x² - 10x
The volume of the solid can be calculated as follows:
V = π ∫ Ax dx
= π ∫₀² (25 + x² - 10x) dx
= π (25x + 1/3x³ - 5x² |₀⁵)
= π (25*5 + 1/3*5³ - 5*5² - 0)
= π (125 + 125/3 - 125 - 0)
= 125π /3 cubic units
Thus, the volume of the solid is 125π /3 cubic units
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Use the information below to find the value of y. Explain your steps
Answers
Step-by-step explanation:
2y+y=180(Sum of supplementey angle)
3y=180
y=180\3
y=60Explain why these triangles are congruent by AAS (Angle-Angle-Side) and not ASA (Angle-Side-Angle).
Answers
The triangles are congruent by AAS (Angle-Angle-Side) and not by ASA (Angle-Side-Angle)
Properties of congruent triangles.When the corresponding length of sides or measure of the internal angles of two or more triangles are equal, then the triangles are said to be congruent. The congruency can be expressed in terms angles, sides, or the combination of sides and angles. An example is the SAA (Side-Angle-Angle) property which implies that a side that is not an included angle and other angles are congruent.
Considering triangles ABC and CDE, it can be seen that two angles are congruent and a side of both are congruent. Since the congruent side is not an included angle, then the congruent relations is AAS (Angle-Angle-Side).
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Kayden and his children went into a grocery store where they sell apples for $ 0.75 each and mangos for $2 each. Kayden has $20 to spend and must buy a minimum of 16 apples and mangos altogether . Also, he must buy no less than 16 apples. If represents the number of apples purchased and y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution .
Answers
The system of inequalities is:
x + y ≥ 16
x*0.75 + y*2 ≤ 20
And its graph can be seen below, there we can see that one possible solution is (14, 2)
How to write and solve the system of inequalities?
Let's define the variables:
x = number of apples.
y = number of mangos.
Kayden needs to buy not less than 16 items, so the first inequality is:
x + y ≥ 16
And he can spend at most $20, then:
x*0.75 + y*2 ≤ 20
The system of inequalities is then:
x + y ≥ 16
x*0.75 + y*2 ≤ 20
To graph it just graph the two lines and shade the region correspondent, for the first inequality shade the region above the line, for the second one shade the region below the line.
You should get.
The solution set is the region where both shaded areas intercept. Then a possible solution is:
x = 14
y = 2
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A point is the measurement of the distance around a shape. * 1 point True False you will get brainless pls help
Answers
Answer:true
Step-by-step explanation:
? ÷ 2/5 = 4
Draw a diagram to represent the situation.
Answers
Given expression ?/(2/5)=4 where ?=x gives x=8/5.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression ? ÷ 2/5 = 4
let x=?
Therefore,
x=4*2/5
x=8/5
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Car A is rated at 33 mi/gal (miles per gallon) for city driving and 28 mi/gal for highway driving. Car B is rated at 29 mi/gal city and 33 mi/gal highway. How many gallons of gas would each vehicle consume for the following amounts of driving? (a) 300 mi of city driving plus 100 mi of highway driving (b) 100 mi of city driving plus 300 mi of highway driving
Answers
The gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving is 12.66 gallons
The gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving is 13.37 gallons
The gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving is 13.74 gallons
The gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving is 12.54 gallons
How many gallons is consumed?Gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving = (300 / 33) + (100 / 28)
= 9.09 + 3.57 = 12.66 gallons
Gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving = (300 / 29) + (100 / 33)
= 10.34 + 3.03 = 13.37 gallons
Gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving = (100 / 33) + (300 / 28)
= 3.03 + 10.71 =13.74 gallons
Gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving = (100 / 29) + (300 /33)
= 3.45 + 9.09 = 12.54 gallons
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Help with all please
Answers
Answer:
A is ST, PR, and UV
B is rays SQ and QT
C is point Q
D is Points S, Q, and T
In addition, the balance of common stock at the beginning of the year was $550,000, and the balance of retained earnings was $46,000. During the year, the company issued additional shares of common stock for $32,000 and paid dividends of $24,000. Required: Prepare an income statement. Prepare a statement of stockholders’ equity.
Answers
Answer: Income Statement:
Revenue: _________
Expenses: _________
Net Income: _________
Statement of Stockholders' Equity:
Beginning Balance:
Common Stock: $550,000
Retained Earnings: $46,000
Total: $596,000
Additions:
Common Stock: $32,000
Total: $628,000
Deductions:
Dividends: $24,000
Total: $604,000
Ending Balance:
Common Stock: $550,000
Retained Earnings: $50,000
Total: $600,000
Note: I've left the Revenue, Expenses and Net Income section in the income statement blank as it is not provided in the question. It is also important to note that these are just examples and the numbers may not match with the actual financial statement.
Step-by-step explanation:
find the 100th derivative of P(x)=(x^5+x+x^7)^10 (1+x^2)^11 (x^3+x^5+x^7)
Answers
The 100th derivative of P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷) will be zero.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
A polynomial,
P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷).
To find the degree:
(x⁷)¹⁰(x²)¹¹(x⁷) = x⁹⁹.
The polynomial has a degree of 99.
If we think about it intuitively,
Therefore, if we were to multiply it all out,
the leading word would be x⁹⁹.
The term's first derivative is 99x⁹⁸,
followed by 99(98)x⁹⁷,
and 99(98)(97)x⁹⁶.
And finally,
the 99th derivative is 99×98×97×96×...4×3×3×2×1× (x⁰)
=99!
So, the 100th derivative will be zero.
Therefore, by the 100th derivative, all terms will cancel out.
100th derivative will be zero.
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Find the range and standard deviation of the set of data.
11, 8, 5, 11, 25
The range is
(Simplify your answer.)
Answers
The Range and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.
What is mean ?
Mean can be defined as the ratio sum of the observations and total number of observations.
Given
set of data,
11, 8, 5, 11, 25
we have to find the range and standard deviation,
We know that,
range = max - min
here max = 25
min = 5
range = 25-5
range = 20
Standard deviation ,
= √( ( Σx^2 - (Σx)^2 / n ) / (n-1) )
= √( ( Σ11^2+8^2+5^2+11^2+25^2 - (Σ60)^2 / 5 ) / (5-1) )
= √( ( 956 - (3600)^2 / 5 ) / (5-1) )
= √( ( 956 - 720) / 4 )
= √( 59 )
= 7.68
Hence, The Range and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.
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Read the following prompt and type your response in the space provided.
Create a real-life representation of the following multiplication problem. Explain what the result represents in the problem.
15 (2/5)=6
Answers
Answer: In a real-life representation of the multiplication problem "15 (2/5) = 6," we can imagine a bag of 15 items, each of which is 2/5 of a whole. To find out how many whole items are in the bag, we can multiply 15 (the number of items) by 2/5 (the fraction of each item that is a whole).
The result of 6 represents the number of whole items in the bag.
Step-by-step explanation:
A soda company would like to replace the label on a can of soda with a radius of 2 and three fourths cm. If the label touches end to end with no overlap, what is the length of the label? Use 22 over 7 for π.
121 over 7 cm
121 over 14 cm
121 over 28 cm
121 over 56 cm
Answers
The length of the perimeter will be 121/7 cm.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a soda company would like to replace the label on a can of soda with a radius of 2 and three fourths cm. The label touches end to end with no overlap.
Perimeter of a circle is the length of the boundary of the circle. It is given by : P = 2πrThe length of the label will be its perimeter. We can write -
P = 2πr
P = 2 x 22/7 x 11/4
P = 2 x 22/7 x 11/4
P = 22/7 x 11/2
P = 11 x 11/7
P = 121/7
Therefore, the length of the perimeter will be 121/7 cm.
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ions of a
use to make
vill she need
hi
↑
3 in.
Go Online You can complete your homework online.
2 A group of students is painting the flag of
Brunei for a geography project. Joseph is
responsible for painting only the
background colors of the flag. How many
square inches will he cover with white paint?
(Example 1)
4=bh t=72631
yellow
white
black
yellow
A=6120
81⁄2 in.
7 in.
Answers
The required area of the white part of the flag is 612 Square inches.
What is Rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
According to question:We have,
Width = 8(1/2) = 17/2 In
Length = 72 In
Area of the white part of the flag is
= 17/2 × 72
= 612 Square inches
Thus, required area is 612 Square inches.
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The white portion of the flag must have a 612 square inch area.
What is a rectangle?A rectangle is a quadrilateral with parallel sides that are equal to one another and four equal vertices. Due to this, it is also known as an equiangular quadrilateral. Due to their equal and parallel opposite sides, rectangles are also known as parallelograms.The following is what we have:width = 8 (1/2) = 17 (2 inches).72 inches longThe white portion of the flag's area is= 17/2 × 72612 Square Inches612 square inches are therefore needed.To learn more about the area of square refer:
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The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ? The mean is 20 and the standard deviation is 102.A) The mean is 20 and the standard deviation is 50.B) The mean is 22 and the standard deviation is 102.C) The mean is 22 and the standard deviation is 100.D) The mean is 22 and the standard deviation is 50.
Answers
By multiplying the mean of random variable X by two to four, the random variable Y's mean is calculated to be 20. (5). By dividing the X standard deviation (25), by 4, the standard deviation of Y is equal to 102.
The random variable X has a mean of 5 and a standard deviation of 25. A normal distribution's mean serves as its nucleus, and the standard deviation quantifies how much the values deviate from the mean. Y = 2 + 4X is the definition of the random variable Y. By adding 2 to the mean of X (5), we can determine the mean of Y, which equals 20. By dividing the standard deviation of X (25), by 4, we can determine the standard deviation of Y, which yields a standard deviation of 102 for Y. As a result, the standard deviation is 102 and the mean of Y is 20.
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A door frame that appears to be rectangular has a height of 213 cm, width of 92 cm, and one diagonal that measures 231 cm. Determine if the door frame is rectangular. Explain your thinking.
Answers
The door frame is not rectangular.
Is the door frame rectangular?If the door frame is rectangular, the sum of the square of the height and the width would be equal to the square of the diagonal.
Height² + width = diagonal²
213² + 92²
45,369 + 8,463 = 53,833
231² = 53,361
53,833 ≠ 53,361
The door frame is not rectangular because the sum of the height and the width is not equal to the diagonal.
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Select the statement regarding ethical considerations in experimental designs that is not necessarily true: A. If a research team treats two consenting groups such that one group receives a dose of a drug, and the other group receives a placebo, the team must inform the test subjects after the experiment whether they received the drug or the placebo. B. It is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent. C. A national survey, asking respondents about drinking and smoking habits, should remain confidential with regards to the identity of respondents when reporting its findings.
D. If a medical group is going to apply a treatment to a person, that person should be notified and should agree to the treatment first.
Answers
The statement regarding ethical considerations in experimental designs that is not necessarily true is that it is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent.
Therefore the answer is option B. It is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent.
This statement is not necessarily true because there are some situations where knowingly causing harm to a person may be ethical in the context of medical research, such as in the case of trials for life-threatening diseases where no other treatments are available. However, in such cases, strict ethical review and oversight is usually required to ensure that the risks are minimized and that the participants are fully informed of the risks involved.
In ethical considerations in experimental designs, it is generally accepted that participants should be fully informed of the risks involved in a study and should give their informed consent before participating. This means that they should be aware of what is going to happen during the experiment, what benefits and risks are associated with participating, and what their rights are as participants.
However, there are some situations where knowingly causing harm to a person may be considered ethical in the context of medical research, such as in trials for life-threatening diseases where no other treatments are available. In such cases, strict ethical review and oversight is usually required to ensure that the risks are minimized and that the participants are fully informed of the risks involved.
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Simplify using the order of operations.
25) 25 ÷ 5 + 4 × 3 – 3
Answers
Answer: 14
Step-by-step explanation:
What is the value of x in this triangle?
Answers
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
83°Step-by-step explanation:
As it is a triangle , so we know that sum of all angles of a triangle = 180°
therefore,=> 44 + 53 + x = 180
=> 97 + x = 180
=> x = 180 - 97
=> x = 83°
______________________________Hope it helps you ~Use the distributive property to write each expression as an equivalent
algebraic expression.
-2(x-4)
Answers
Answer:
the equivalent algebraic expression is -2x -8 after applying the distributive property.
Step-by-step explanation:
The distributive property states that for any real numbers a, b, and c, a(b+c) = ab + ac.
To apply the distributive property to the expression -2(x-4), we can distribute the -2 across the parenthesis, like this:
-2(x-4) = -2x + (-2)(-4)
Simplifying the last part of the expression:
-2(x-4) = -2x -8
So, the equivalent algebraic expression is -2x -8 after applying the distributive property.
1.
2.
3.
4.
7. Given: ZBAC = ZEDC, BC = EC
Prove: AABC = ADEC
Stat
EUC
3. Given: JK = LM, ZJKM = ZLMK
YO
1.
2.
3.
4.
B
Reasons
E
L
Answers
The triangles are congruent if two of one triangle's sides and its included angle are the same as the corresponding sides and angles of another triangle.
How may a triangle's congruency be demonstrated?Triangles lining up, When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved.The triangles are congruent if two of one triangle's sides and its included angle are the same as the corresponding sides and angles of another triangle.Triangles lining up, When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent.The complete question is,
To what extent can the congruence of the triangles be demonstrated?
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What is the intersection of y=2x-2 and y= -2x^2 +4x+ 3?
Answers
The intersection of equations y=2x-2 and y= -2x^2 +4x+ 3 is y = 3
How to determine the intersection of the linesThe general formula for the equation of a line is expressed as;
y = mx + c
Where the parameters are;
c is the intercept of the line on the y - axism is the slope of the linex is a point on the x-axisy is a point on the y -axisFrom the information given, we have the equation of the lines as;
y=2x-2 y= -2x^2 +5x+ 3Now, equate the lines, we have;
2x - 2 = -2x² + 5x + 3
collect the like terms
2x -5x + 2x² - 2 - 3 = 0
add the iike terms
2x² -3x - 5 = 0
Factorize the quadratic equation
2x² - 5x + 2x - 5 = 0
Group in pairs
(2x² - 5x) + (2x-5) = 0
x(2x -5) + 1(2x - 5) = 0
The intersection for when x = 5/2
y = 2x - 2
y = 2(5/2) - 2
y = 3
Hence, the value is 3
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What is the decimal expansion of the following fraction 1/3
Answers
The decimal expansion of the following fraction 1/3 would be; 0.33
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We need to find the expression of 1 divided by 3.
A negative divided by a negative is positive, then;
1/3 = 0.33
Therefore, The value of expression 1/3 would be; 0.33
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Krystal drove at an average speed of 50 mi/h from her home in Houston to visit her sister in Philadelphia.
She stayed in Philadelphia 25 hours, and on the trip back averaged 60 mi/h. She returned home 46 hours
after leaving. How many miles is Houston from Philadelphia?
a) Write an equation using the information as it is given above that can be solved to answer this question.
Use t as your variable to represent the amount of time Krystal spent driving from Houston to Philadelphia.
Equation:
b) How many miles is Houston from Philadelphia?
Answer:
miles
Give your answer to the nearest mile
Answers
Answer: a. The equation using the information as it is given above that can be solved to answer this question is:
distance = speed x time
Let t be the amount of time Krystal spent driving from Houston to Philadelphia.
distance = 50t + 60(46 - 25 - t)
b. To find the distance between Houston and Philadelphia, we can substitute the known values into the equation and solve for t.
distance = 50t + 60(46 - 25 - t)
distance = 50t + 60(21) - 60t
distance = 50t + 1260 - 60t
distance = -10t + 1260
To find the total distance, we can set t = 25
distance = -10(25) + 1260
distance = -250 + 1260
distance = 1010
Therefore, Houston is 1010 miles from Philadelphia, to the nearest mile.
Step-by-step explanation: