The speed of River's mom drove for 10 miles distance is 0.234 mph
The speed of River's mom drove for 25 miles is 10.234 mph
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
here, we have,
Given as :
The first distance cover by River's mom = 10 miles
The rate of speed = x mph
The second distance cover by river's mom = 25 miles
The rate of speed = x + 10 mph
The total driving time = 45 min
Now, According to question
Time = speed/distance
So, 45 =10/x + 25/(x+10)
Or, 9 =2/x + 5/(x+10)
Or, 9 × x × ( x + 10 ) = 2 × ( x + 10 ) + 5 x
Or, 9 x² + 90 x = 2 x + 20 + 5 x
Or, 9 x² + 90 x = 7 x + 20
Or, 9 x² + 90 x - 7 x - 20 = 0
Or, 9 x² + 83 x - 20 = 0
Solving this quadratic equation
x = 0.234 , - 9.4567
so, the value is,
I.e x = 0.234 , - 9.4567
now,
We consider x = 0.234
So, The speed for 10 miles distance = x = 0.234 mph
and The speed of 25 miles = x + 10 = 0.234 + 10 = 10.234 mph
Hence The speed of River's mom drove for 10 miles distance is 0.234 mph
and The speed of River's mom drove for 25 miles is 10.234 mph
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Solve x² - 11x - 42 = 0
O x = -3 and 14
O x = -14 and 3
O x = -6 and -7
O x = 6 and 7 < Previous
Answer: a = 1, b = -11, and c = -42.
Step-by-step explanation:
The solutions to the equation x² - 11x - 42 = 0 are x = -6 and x = 7.
You can find the solutions by factoring the equation, or by using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.
In this case, a = 1, b = -11, and c = -42.
Match each pair of points to the slope of the line that joins them.
The slopes for the given pairs are:
(9, 10) and (7, 2) the slope is -4(5, -6) and (2, 3) the slope is -3(4,7) and (6, 2) the slope is -5/2How to find the slopes?If a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by:
a = (y₂ - y₁)/(x₂ - x₁)
Using the first pair of points (9, 10) and (7, 2) the slope is:
s = (2 - 10)/(9 - 7)
s = -8/2 = -4
For the second pair:
(5, -6) and (2, 3)
Here the slope is:
s = (3 + 6)/(2 - 5)
s = 9/3 = -3
The last pair of points is (4,7) and (6, 2) the slope is:
s = (2 - 7)/(6 - 4)
s = -5/2
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Paula bought a ski jacket on sale for $8 less than half its original price. She paid $84 for the jacket. What was the original price?
The original price of the ski jacket is $184.
What is price?
The sum of money paid or the amount of compensation offered by one party to another in exchange for goods or services is known as a price. The cost of production can take on different names depending on the circumstance. If the item is a "good" in a commercial transaction, the cost of the item will probably be referred to as its "price".
Given:
Paula bought a ski jacket on sale for $8 less than half its original price.
She paid $84 for the jacket.
We have to find the original price of the ski jacket.
Let
The original price = x
The amount she bought it = x/2 - 8
She paid $84 for the jacket
Therefore,
84 = x/2 - 8
Add 8 on both sides,
84 + 8 = x/2 - 8 + 8
92 = x/2
x = 184
Hence, the original price of the ski jacket is $184.
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There are 5,280 feet in 1 mile. Which proportion can be used to find the number of miles in 8, 400 feet?
Number of miles in 8,400 feet are 1.6 miles.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, there are 5,280 feet in 1 mile.
Let the number of miles in 8,400 feet be x.
So, 5280/1 = 8400/x
5280x=8400
x= 8400/5280
x= 1.6 miles
Therefore, number of miles in 8,400 feet are 1.6 miles.
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How many solutions does the pair of 6 equations y 0 and y 5 have?
Here, y = 0 is the equation of the x-axis.
Also, y = 5 is the equation of a line parallel to the x-axis.
⇒ y = 0 and y = 5 are parallel to each other
Since the equations are parallel, then they have no solution.
Hence, the pair of equations y = 0 and y = 5 has no solution.
Number of solution in system EquationA linear equation in two variables is an equation of the form ax + by + c = 0 where a, b, c ∈ R, a, and b ≠ 0. When we consider a system of linear equations, we can find the number of solutions by comparing the coefficients of the variables of the equations. Also, we can find the number of solutions by the graphical method.
Three Types of Solutions of a System of Linear EquationsConsider the pair of linear equations in two variables x and y.
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Here a1, b1, c1, a2, b2, c2 are all real numbers.
Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0
1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.
2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables
3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.
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How do you solve factored form?
To solve for the factored form of an equation, you can use a variety of methods, such as grouping, factoring by grouping, factoring by inspection, factoring by using the difference of squares, sum of cubes, or difference of cubes.
Grouping: This method involves grouping the like terms in the equation and factoring out the greatest common factor from each group.
Factoring by grouping: This method involves grouping the terms in the equation and factoring out the common factor that is shared by each group.
Factoring by inspection: This method involves looking at the equation and identifying any common factors that can be factored out of the equation.
Factoring by using the difference of squares, sum of cubes, or difference of cubes.
Factoring by using the quadratic formula.
Once you have factored the equation, you can set each factor equal to zero and solve for the variable.
For example, let's consider the equation x^2 + 5x + 6 = 0. Using the factoring by inspection method, we can see that (x + 2)(x + 3) = 0, so either x + 2 = 0 or x + 3 = 0. Solving for x, we find that x = -2 and x = -3 are the solutions to the equation.
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Name the subset(s) of the real numbers to which each number belongs.
help
The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.
What is mathematical equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."√81 = 9
-√144 = -44
√4/25 = 2/25
√0.36 = 0
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A trapezoid has bases of lengths 12 and 27. Find the trapezoid's area
if its height is 8.
The trapezoid's area if its height is 8 is 156.
What is trapezoid area?Trapezoid area is the area of a four-sided flat shape with two sides that are parallel. It is a type of quadrilateral with two non-parallel sides. To calculate the area of a trapezoid, you need to multiply the sum of the lengths of the two parallel sides by the height of the trapezoid and then divide by two. The formula for trapezoid area is A = (a + b) * h / 2, where a and b are the lengths of the two parallel sides and h is the height of the trapezoid.
The area of a trapezoid is calculated by multiplying the height by the average of the two bases. Therefore, the area of the trapezoid in question is 8 multiplied by the average of 12 and 27, which is 19.5. The final answer is then 156.
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A taxi cab company charges a rate of $2.40 per mile traveled.
Chris wants to determine the cost to travel from his house to the airport in a taxi cab. In order to determine the cost he uses the equation c=(d/2.4)
, where c represents the cost, and d represents the distance in miles between his house and the airport.
Which statement explains why Chris will incorrectly determine the cost of taking the taxi cab to the airport?
A.Chris should have added d to 2.4 as shown by the equation c=(2.4+d).
B.Chris should have divided 2.4 by d as shown by the equation c=(2.4/d)
c.Chris should have divided 2.4 by d as shown by the equation c=(2.4d)
d.
Chris should have multiplied 2.4 by d as shown by the equation c=(2.4d).
The statement explaining why Chris will incorrectly determine the cost of taking the taxi cab to the airport is D. Chris should have multiplied 2.4 by d as shown by the equation c=(2.4d).
What is an equation?An equation is a mathematical statement proving two or more mathematical expressions to be equivalent or equal.
Equations use the symbol (=) to depict the equality of the expressions.
The equation to show the total cost of hiring a tax cab should multiply the distance (miles) by the unit rate.
The tax cab charge (rate) per mile = $2.40
The cost function or equation is C = distance x $2.40
= 2.40d
Thus, the correct cost equation is Option D.
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What is vertical and horizontal line?
In a coordinate plane, a vertical line is an upward and downward straight line perpendicular to the y-axis. Like the x-axis, the horizontal line travels straight, left, and right.
A line that runs horizontally is one that does so from left to right. You are viewing the dawn across a horizontal line when you stare at it beyond the horizon. An illustration of a horizontal line is the x-axis.
A line that runs up and down is called a vertical line. The legs of a table are vertical lines, like in the example to the right. An illustration of a perpendicular line is the y-axis.
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4. Each image shows a quadrilateral in a plane. The quadrilateral has been dilated using a center above the plane and a scale factor between 0 and 1.
Estimate the scale factor that was used for each dilation. (Lesson 5-3)
Dilation A
Dilation B
Dilation C
Given the above image, the estimated scale factor used in the dilation are given as follows:
Dilation A - 3/4
Dilation B - 1/4
Dilation C - 1/2
What is a scale factor?The scale factor is a metric for figures with similar appearances but differing scales or measurements. Assume two circles appear identical but have different radii. The scale factor specifies how much larger or smaller a figure is than the original figure.
When the new and original dimensions are specified, the scaling factor may be determined. The fundamental formula for determining a figure's scale factor is: Scale factor = Dimension of the new shape ÷ Dimension of the old shape.
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What are the 3 kinds of system of linear equation in two variables?
There are three types of systems of linear equations in two variables: Consistent System,Inconsistent System,Dependent System.
What is linear systems?A linear system is a mathematical model of a system of linear equations, in which the variables and constants have a linear relationship. This type of system is widely used in engineering, physics, economics, and other areas of study. Linear systems are often used to find solutions to problems in areas such as optimization or forecasting. They are also used in many machine learning algorithms. Linear systems are characterized by their linearity and they are usually solved using linear algebra techniques.
1. Consistent System: A consistent system of linear equations in two variables has at least one solution. This means that there is at least one set of values for the two variables that will make all equations true.
2. Inconsistent System: An inconsistent system of linear equations in two variables has no solution. This means that there is no set of values for the two variables that will make all equations true.
3. Dependent System: A dependent system of linear equations in two variables has an infinite number of solutions. This means that there is more than one set of values for the two variables that will make all equations true.
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please help!!! find N and M write as simplified rations :D
Answer: n=6, m=12
Step-by-step explanation:
Since the triangle is a 30-60-90 triangle, the ratio of its sides is [tex]2 : \sqrt{3} : 1[/tex].
Since one side is 6[tex]\sqrt{3}[/tex], n is 6 and m is 12, according to the ratio.
We can solve this using sin/cos/tan, too.
A ____ is the intersection of a plane with one or both nappes of a double cone.
Answer: The answer Is conic
Step-by-step explanation:
Mara surveyed her class of 30 students on their favorite genres of books to read. Her results are shown below. 7 liked mystery. There are 500 students at Mara’s school. Based on this sample, about how many students at Mara’s school MOST LIKELY favor mystery?
Answer:
Give more points
Step-by-step explanation:
Determine three points on the line with slope 4 and passing through (-7,6).
Answer: (-8.5, 0), (0, 34), and (2, 42)
Andrea attends the county fair the fair charges for admission and for each ride
A. Use the pattern in the table to find the cost for Andrea to ride 5 rides or 8 rides. Then write an equation for the pattern
The cost of admission to the fair (A) $18 (B) 2.50x +18 (C) Coefficient of x-term represents the cost for each ride ticket and constant term represents the cost of admission to the fair.
How to find the cost of admission?Note that the county fair charges $2.50 per ticket for the rides and Henry bought 15 tickets for the rides.
So, the total cost of the 15 tickets will be: (2.5* 15)r = $37.50
He spent total $55.50 on ride tickets and fair admission.
So, the cost of admission to the fair will be:
(B) If x represents the number of ride tickets and represents the total cost, then the cost for number of ride tickets is 2.50x +18
So, the linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission will be:
(C) In the above linear equation, coefficient of x-term is 2.50, which represents the cost for each ride ticket.
And the constant term is 18, which represents the cost of admission to the fair.
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complete question
The county fair charges $2.50 per ticket for the rides. Henry bought 15 tickets for the rides and spent a total of $55.50 at the fair. Henry spent his money only on ride tickets and far admission. The price of the fair admission is the same for everyone. Use x to represent the number of tide tickets and y to represent the total cost.
(A) Find the cost of admission to the fair. Explain how you found the cost of admission.
(B) Write a linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission.
(C) Explain what the coefficient on x and the constant of your linear equation represent.
Write the equation of the line that has an undefined slope and passes through the point (4, 7).
The equation of the line that has an undefined slope and passes through the point (4, 7) is y = 4.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know if a line has an undefined slope it is parallel to the y-axis and passes through the point (4, 7).
As it is parallel to the y-axis x-coordinate point remains the same.
So, The equation of the line must be, y = 4.
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In triangle, STU, ST = 52, and TU = 39. What is the range of values for the length third side? With decent explanation please.
A)-13 < SU < 13
B) -13 < SU < 91
C) 13 < SU < 52 (It's not this one, I promise you all it is not)
D) 13 < SU < 91
Answer:
D
Step-by-step explanation:
given 2 sides of a triangle then the third side SU is in the interval
difference of 2 known sides < SU < sum of 2 known sides , that is
52 - 39 < SU < 52 + 39
13 < SU < 91
HELP!!! Cindy needs to graph the following equation: y = 2x + 5. Which table can help her correctly graph the equation?
Answer: it is table "a"
explanation:
as the equation is y= 2x + 5 you should substitute each of the x values from -2 to 4 in order to get the y value which will help you decide which table should be used by Cindy to graph the equation.
now, this is how you should substitute the values into the equation and simplify it so that you get the "y" value.
the first x value given is -2 therefore:
you put -2 in the equation instead of putting x, this will allow you to find the y value which you can compare with the choices given.
y= 2x+5 (this is the equation)
y= 2(-2)+5 (here I have replaced the x with -2)
y= -4+5 (you should multiply 2 and -2)
y= 1 (therefore the answer is 1)
you should further continue this way and get the y values which will help you decide which is the correct table to be used. Now you already know that table "a" is the answer.
Answer:
The answer is table A
Step-by-step explanation:
Given:
Form the table of values from x = -2 to x = 4
Hence,
Therefore, the table that can be used for the graph of the equation is;
Table A
HELP I NEEED HELP THANKS
Answer:
70.3
Step-by-step explanation:
7 tenths = 70
Answer:
Option #4 7.3
Step-by-step explanation:
First you multiply 7 by 10 the denominator. (7x10)=70
Second add 3 to the sum. (70+3)= 73
Third divide 73 by 10. (73/10)=7.3
This makes the answer 7.3.
-Hope this helped
if the zeros of the function are -2, 3, and 10 find the corresponding polynomial
Answer:
x³ - x² - 6x + 60
Step-by-step explanation:
you can write the polinom in this form: (x+2) × (x-3) × (x-10)
(x+2 = 0 => x = -2) same for other two zeros
(x² -3x +2x -6) × (x - 10) =
(x³ - 10x - 3x² + 30x + 2x² - 20x - 6x + 60) =
x³ - x² - 6x + 60
People/ 7. The cost for 7 dance lessons is $82. The cost for 11 lessons is $122. Write and solve an equation to find the cost of 4, lessons.
The cost of 4 dance lessons will be $52.
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 the cost for 7 dance lessons is $82 and the cost for 11 lessons is $122.
The given coordinate points are -
(7, 82) and (11, 122)
We can write the equation as -
y = mx + c
Now -
m = (122 - 82)/(11 - 7)
m = 40/4
m = 10
The equation will now become -
y = 10x + c
For the point (7, 82), we can write -
82 = 10 x 7 + c
c = 82 - 70
c = 12
So, the equation representing the cost to the total number of dance lessons is -
y = 10x + 12
For {x} = 4, we can write -
y = 40 + 12
y = 52
Therefore, the cost of 4 dance lessons will be $52.
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Determine the rate of change for a horizontal line.Explain why this rate of change makes sense
The rate of change of a horizontal line is zero, this is because it does not rise vertically (i.e. y1 − y2 = 0).
What is the Rate of Change of a Horizontal Line?A rate of change of a horizontal line is the same as its slope, which is the change in y over the change in x, or rise over run.
For the horizontal line that is shown in the graph below, the rate of change for this line is 0, and this can be confirmed by utilizing the slope calculation method.
This makes sense because the change in y of the line is zero, which means it it does not rise vertically (i.e. y1 − y2 = 0).
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Gina has 22 more barrettes than Holly.
The equation g = 22 + h, where g represents the number of barrettes Gina has, and h represents the number of barrettes Holly has, shows this relationship.
If Gina has 43 barrettes, how many barrettes does Holly have?
Sixty-four students are going on a field trip. There is 1 adult for every 8 students. How many adults are there?
There are 8 adults. This is because 1 adult is needed for every 8 students, so 8 multiplied by 8 is 64, which is the number of students. Therefore, 8 adults are needed.
what is the the ratio of the central angle measure to the circumference?
The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula:
arc measure = central angle measure / circumference
For a given central angle measure in degrees, the formula will be:
arc measure = (central angle measure in degrees) / 360
It's worth noting that this ratio is equal to the fraction of the circumference that the arc of the central angle measures.
For example, if the central angle measure is 90 degrees, the arc measure will be 90/360 = 1/4, meaning that the arc that is formed by the central angle measure is 1/4 of the circle's circumference.
It's also important to note that this ratio is also equal to the fraction of the total area of the circle that the sector formed by the central angle measures.
It's also worth noting that this ratio is always less than 1, since the central angle can't be greater than 360 degrees.
Therefore, The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula: arc measure = central angle measure / circumference
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(a) suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.
The probability of a house valued less than $ 500, 000 is = 0.34 + .37 = 0.71
What is Probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Basic Probability Properties are :
P(E) = [Number of favorable outcomes of E]/[Total number of possible outcomes of E] is the formula for calculating an event's probability.The likelihood of a given occurrence or a sure thing happening is 1.There is no chance that an impossible occurrence will occur.A number P(E) that has the formula 0≤ P(E)≤ 1 represents the probability of an occurrence E. The probability scale is always positive.If events A and B are two occurrences that can never occur together, then P(A∪B) = P(A) + P (B).An basic event is one that has just one result. The total likelihood of such outcomes in an experiment is 1, or 1.The probability of a house valued less than $ 500, 000 is
(P < $500,000) = P(X<$250,000) + P($250,000 <x <$500,000)
= 0.34 + .37 = 0.71
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A cylindrical bucket that is 30 inches tall holds 11,400 cubic inches of water,
What is this bucket's radius? Round to the nearest inch,
The radius of the cylindrical bucket is 11 inches.
Now, According to the question:
We have the given data is :
A cylindrical bucket that is 30 inches tall
A cylindrical 11,400 cubic inches of water.
We have to find the radius of bucket's.
Height (h) = 30 inches tall
Volume of cylinder is 11,400
We know that the:
Volume of cylinder is = [tex]\pi r^2h[/tex]
Plug all the values in the formula.
[tex]\pi =3.14[/tex]
11,400 = 3.14[tex](r)^2[/tex]× 30
11,400 = 94.2[tex](r)^2[/tex]
[tex](r)^2[/tex] = 11400/94.2
r = [tex]\sqrt{121.00}[/tex]
r = 11
Hence, The radius of the cylindrical bucket is 11 inches.
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You look at a local newspaper to post your advertisement. You find it is going to cost you $50 for the first 200 words. Anything over200 words will be an additional $0. 05 per word. You used 84 words. Write this as a piecewise function
If the cost for first 200 words is $50 and anything over200 words will be an additional $0.05 per word , then the piecewise function is [tex]C(x) = \begin{array}{cc} \{ & \begin{array}{cc} 50 & 0\leq x\leq 200 \\ 50+(x-200)\times0.05 & x > 200 \end{array}\end{array}[/tex].
For posting the advertisement in local newspaper , there are two criteria ,
if the advertisement is for 200 words then the cost will be $50 ;
let the number of words be x ;
So , the domain for this in the piecewise function will be [tex]0\leq x\leq 200[/tex] ;
and if there are more than 200 words , then the additional cost is $0.05 per word ,
that means , the domain will be [tex]x > 200[/tex] ;
also given that , we have used 84 words in the advertisement ,
84 lies in this [tex]0\leq x\leq 200[/tex] , So ,the cost will be $50 .
The Piecewise Function can be represented as : [tex]C(x) = \begin{array}{cc} \{ & \begin{array}{cc} 50 & 0\leq x\leq 200 \\ 50+(x-200)\times0.05 & x > 200 \end{array}\end{array}[/tex].
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