The equation of a line perpendicular to line y = 8/3x-5 in slope-intercept form that contains point (-2, -2) is y = -3x/8 - 11/4.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
8/3 × m₂ = -1
m₂ = -3/8.
At data point (-2, -2), a linear equation of this line can be calculated in point-slope form as follows:
y - (-2) = -3/8(x - (-2))
y + 2 = -3/8(x + 2)
y = -3x/8 - 3/4 - 2
y = -3x/8 - 11/4
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10. Find the distance of the line segment RS with R(-2, 3) and S(4, 5) in simplest radical form.
The distance between the points in simplest radical form is equal to 2√10 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given parameters into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-2))² + (5 - 3)²]
Distance = √[6² + 2²]
Distance = √[36 + 4]
Distance = √40
Distance = 2√10 units.
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The position of a ball after it is thrown is modeled with the
function f(x) = -2(x - 1)² + 7 in vertex form, where y is
the height, in feet, above the ground and x is the horizontal
distance, in feet, of the ball from where it is thrown.
A. Write the function in standard form.
B. What is the height of the ball when it is thrown?
C. What is the horizontal distance from the point where the ball is thrown to the highest point that the ball reaches?
(a) The function in standard form is f(x) = -2x² + 4x + 5.
(b) The height of the ball when it is thrown is 5 feet.
(c) The horizontal distance from the point where the ball is thrown to the highest point that the ball reaches is 1 foot.
What is the function of ball's motion?
To write the function in standard form, we need to expand the square and simplify the expression:
f(x) = -2(x - 1)² + 7
f(x) = -2(x² - 2x + 1) + 7
f(x) = -2x² + 4x - 2 + 7
f(x) = -2x² + 4x + 5
B. The height of the ball when it is thrown is the y-intercept of the function, which occurs when x = 0. So we can find the height by plugging x = 0 into the function:
f(0) = -2(0)² + 4(0) + 5
f(0) = 5
C. The highest point that the ball reaches is the vertex of the parabola, which occurs at x = 1 (from the given vertex form). To find the height of this point, we can plug x = 1 into the vertex form of the function:
f(1) = -2(1 - 1)² + 7
f(1) = -2(0) + 7
f(1) = 7
Therefore, the highest point that the ball reaches is 7 feet above the ground. The horizontal distance from the point where the ball is thrown to this point is the distance between the point (0,5) and the vertex (1,7), which is 1 unit.
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If the vertex of the graph of y = −1(x − 2)2 + 3 is (a,b) what is the value of b?
Answer:
the value of b is 3.
Step-by-step explanation:
The vertex of the graph of a parabola in the form y = a(x - h)^2 + k is given by (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
So in this case, the vertex of the graph of y = -1(x - 2)^2 + 3 is (2, 3), and the value of b is 3.
Answer:
b=3
Step-by-step explanation:
[tex]y=a(x-h)^2+k\\y=-1(x-2)^2+3[/tex]
If we compare the vertex-form equation of a parabola to our given function, we can see the vertex is [tex](2,3)[/tex], which means that b=3.
20 In a village the number of houses and the number of flats are in the ratio 7:4 the number of flats and the number of bungalows are in the ratio 8: There are 50 bungalows in the village. How many houses are there in the village? 77
The number of houses is there in the village will be 25.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
In a village, the number of houses and the number of flats is in the ratio 7:4 the number of flats and the number of bungalows is in the ratio 8: There are 50 bungalows in the village.
Let 'x', 'y', and 'z' be the number of houses, flats, and bungalows, respectively. Then the equations are given as,
x / y = 7 / 4
y = (4/7)x ...1
y / z = 8 / 6
z = 6y / 8
z = 3x / 7 ...2
x + y + z = 50 ...3
From equations 1, 2, and 3, then we have
x + (4/7)x + (3/7)x = 50
7x + 4x + 3x = 350
14x = 350
x = 25
The number of houses is there in the village will be 25.
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At Santorini's Shakes, a regular milkshake costs $3.50. A larger milkshake can be purchased for an additional $0.40 per ounce above the regular size.
If x represents the number of ounces above the regular size, which inequality shows how much can be added to the regular size for a milkshake that costs under $5.00?
Answer:
5=0.40x+3.50
He can get 3 extra ounces
Step-by-step explanation:
5.00-3.50=1.50 so an extra $1.50 to spend on extra ounces
1.50/0.40=3
0.40(3)+3.50= $4.70
So the most ounces he can get is 3
He will have $0.30 left
x^-5y^3 negative exponents
The solution is x^-5y^3 = y^3/x^5.
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
given that,
x^-5×y^3
[ as, the power of x is negative 5, so, we make it positive 5 by dividing}
=1/x^5 * y^3
=y^3/x^5
Hence, The solution is x^-5y^3 = y^3/x^5.
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The budget for a project on voting trends includes $3200 for hiring undergraduate students, graduate students, and faculty members to conduct interviews on the day before an election. Each undergraduate student will conduct 30 interviews for $100. Each graduate student will conduct 32 interviews for $150. Each faculty member will conduct 33 interviews for $200. No more than 20 interviewers can be hired.
(a) How many of each type of interviewer should be hired in order to maximize the number of interviews?
(b) What is the maximum number of interviews?
To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics
Simplex Method:In 1947, George Dantzig invented an algorithm that allows us to take a system of equations and find its maximum or minimum values that make the equations most efficient. This method is used in linear programming to determine optimization.
If n = the number of interviews, then let x = the number of undergraduate students hired, y = the number of graduate students employed, z = the number of faculty members hired.
Maximization of n = 30x + 32y + 33z
The limitations are: x + y + z 20; 100x + 150y + 200z 3200; and 0;
The answer is 644 because x = 0, y = 16, z = 4.
To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics given.
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Select the equation that should be used to solve for x. Responses 8x−14+2x+10=90 8 x minus 14 plus 2 x plus 10 is equal to 90 8x−14+2x+10=180 8 x minus 14 plus 2 x plus 10 is equal to 180 8x−14=2x+10 8 x minus 14 is equal to 2 x plus 10 8x−14+2x+10=360 8 x minus 14 plus 2 x plus 10 is equal to 360
The value of x is 9.4 in the equation 8x−14+2x+10=90.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 8x−14+2x+10=90
Eight times of x minus forteen plus two times of x plus ten equal to ninety.
In the given equation x is the variable
Plus and minus are the operators.
Add the like terms
Ten times of x minus four equal to ninety
10x-4=90
Add 4 on both sides to cancel four on the left hand side.
10x-4+4=90+4
10x=94
Divide both sides by 10
x=94/10
Divide numerator and denominator by 10.
x=9.4
Hence, the value of x is 9.4 in the equation 8x−14+2x+10=90.
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The complete question
Solve the equation 8x−14+2x+10=90
Determine the, LCM, of the following three terms: 3st,4s2,5t2
60 s²t² is the lowest common multiple of 3st, 4s^2, 5t^2
Finding the LCM of expressionsLCM is known as the lowest common multiple. This is the smallest number that is a multiple of both of two numbers is called the least common multiple.
Given the terms 3st, 4s^2, 5t^2
Find the factors
3st = 3 * s * t
4s² = 4 * s * s
5t² = 5 * t * t
The LCM is calculated as thus:
LCM = (3*4*5) * s²t²
LCM = 60 s²t²
Hence the LCM of the terms 3st, 4s^2, 5t^2 is 60 s²t²
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Which shapes from the Clade Race would be considered autoapomorphic?a. Arrow b. Circle c. Moon d. Triangle e. Square f. Crossg. Star h. Heati. Hexagon
Answer:
Step-by-step explanation:
f
pls help asap!!!
The table shows the proportional relationship between the number of tickets required per game at a carnival.
Games 4 7 10
Tickets 24 42 60
Determine the constant of proportionality.
3
6
16
30
Today hugo got a new credit card, and he made a purchase of $1400. The card offers an introductory apr of 0% for the first 5 months and a standard apr of 30. 8% thereafter. If the card compounds interest monthly, how much money will the introductory apr save hugo in interest over the first 5 months? (assume that hugo will make no payments or additional purchases during the first 5 months, and ignore any possible late payment fees. ).
$189.13
That's the correct answer On Ax
Answer:
$189.13
Step-by-step explanation:
You want to know the interest saved if interest at 30.8% compounded monthly on a balance of $1400 is waived for 5 months.
Compound interestThe balance with interest compounded would be ...
A = P(1 +r/12)^n
where P is the principal earning interest at annual rate r for n months.
The amount of interest earned in that time is ...
I = P((1 +r/12)^n -1) = $1400(1 +0.308/12)^5 -1) ≈ $189.13
Hugo will save $189.13 in interest charges for the first 5 months.
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Write some examples of interval variables
An interval variable is a type of quantitative variable, where the difference between two values of the variable is meaningful and the values can be ordered.
Examples of interval variables include temperature (in Celsius or Fahrenheit), time (in seconds, minutes, hours, etc.), and dates. You can calculate the difference in temperature between two points, the length of time between two events, or the number of days between two dates. For example, let's say that the temperature outside is 25°C at noon and 29°C at 4 pm. The interval variable is the temperature, and the difference between the two temperatures is 4°C (29°C - 25°C = 4°C). Another example is the length of time between two events. Let's say that Event A began at 1 pm and Event B began at 2 pm. The interval variable is the length of time between the two events and the difference between the two times is 1 hour (2 pm - 1 pm = 1 hour). Finally, let's say that Date A is January 1, 2020 and Date B is January 10, 2020. The interval variable is the number of days between the two dates, and the difference between the two dates is 9 days (January 10,)An interval variable is a type of quantitative variable, where the difference between two values of the variable is meaningful and the values can be ordered.
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What is the LCM of 9 and 27?
Answer: 27
Step-by-step explanation: in order to find out the LCM, you have to list out the multiples of 9 ( 9: 9, 18, 27, 36, etc.) and 27 ( 27: 27, 54, etc). Then you find the least common multiple which in this case is 27.
What are the domain and range of this linear function? f(x)=2x-5
Answer:
The Domain : {(−∞,∞), {x/x∈R} and Range : {(−∞,∞), {y/y∈R} of the function f(x)=2x-5
What is a function?
A relation is a function if it has only One y-value for each x-value.
We have to find the domain and range of f(x)=2x-5
The domain of the expression is all real numbers except where the expression is undefined.
In this case, there is no real number that makes the expression undefined.
Interval Notation:(−∞,∞)
The range is the set of all valid y values.
Domain : {(−∞,∞), {x/x∈R}
Range : {(−∞,∞), {y/y∈R}
Hence, the Domain : {(−∞,∞), {x/x∈R} and Range : {(−∞,∞), {y/y∈R} of the function f(x)=2x-5
Have a wonderful day! :-)
The September price of a computer was $1000. Later, an October price was obtained by raising the September price by 20%. Then a November price was obtained by lowering the October price by 20%. What was the November price in dollars?
Answer:
Step-by-step explanation:
1200
Answer:
$960
Step-by-step explanation:
September = 1000
20% * 1000 = 200
1000+200 = 1200
October = 1200
20% * 1200 = 240
1200-240 = 960
November = 960
What are the three components of research questions?
A research question is an inquiry that a study or research project aims to resolve. Quantitative and Qualitative research questions are the components of questions.
Descriptive research questions are used to determine how the population of the study will react to one or more variables or to describe the factors that the study will evaluate. These questions typically begin with "what."
Comparative research questions aim to identify differences between two or more groups for an outcome variable. These inquiries could possibly be the cause. A comparison between two groups, one in which a certain variable is present and the other in which it is not, may be made, for instance.
Relationship research themes aim to find patterns and interactions between two or more variables. The phrases "association" and "trends," as well as dependent and independent variables, are commonly used in these enquiries.
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Jimmy is an accountant who also works part-time as a museum tour guide. Information from his tax worksheet is wages from accounting job, $75,937.84; wages from museum job, $14,937.92; interest, $839.40; and dividends, $123.45. What is Jimmy’s total income?
Jimmy’s total income is $91838.61
How to determine Jimmy's income?
You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period
The given parameters that will help us to determine the income are
wages from accounting job, $75,937.84;interest, $839.40wages from museum job, $14,937.92; dividends, $123.45.Therefore Jimmy's total income is the sum of all the incomes
$(75,937.84 + 839.40 + 14,937.92 + 123.45)
Total income = $91838.61
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The side lengths of a triangle are 6, 8, and 10. Is this a right triangle?
OA. Yes, because 62 +82 > 10².
B. No, because 62 +82 # 10².
C. Yes, because 62 +82 = 10².
OD. No, because 6 + 8 + 10.
SUBMIT
Is this a right triangle: C. Yes, because 6² + 8² = 10².
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < n < b + c
Where:
n, b, and c represent the side lengths of this triangle.
By applying Pythagorean theorem, the possible side lengths of the triangle's third side is given by:
10² = 6² + 8²
100 = 36 + 64
100 = 100 (True).
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A. x = 80 degrees
B. x = 60 degrees
C. Cannot be determined
D. x = 30 degrees
The measure of the angle is 60 degrees. Option B
How to determine the value of the variableIt is important to value of the angle, we have to take note of the following;
The sum of angles on a straight line is equivalent to 180 degreesThe pair of angles are also supplementary to each otherFrom the information given, we have that;
The angles 80,690 and x are on a straight line, that is, the sum of the angles is 180
This is represented as;
60 + 80 + x = 180
collect like terms
x = 180 - 140
substract the like terms
x = 60 degrees
Hence, the value is 60 degrees
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what a unit of measurement equal to one thousand meters?
A unit of measurement equal to one thousand meters is called a kilometer.
The prefix "kilo" means one thousand, so a kilometer is a unit of length in the metric system that is equal to 1000 meters. Kilometers are commonly used to measure longer distances, such as the distance between cities or countries, or the length of a marathon race. In contrast, smaller distances may be measured in meters, centimeters, or millimeters, which are all smaller units of length in the metric system.
a metric measurement of length that is equal to 1,760 yards or 5,280 feet. A thousandth of a liter is the same as a metric unit of capacity. a length measurement in meters that is one-thousandth of a meter. a time interval that is frequently used and equates to 60 seconds and 1/60 of an hour.
The complete question is:-
What word goes with a unit of measurement equal to one thousand meters?
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Karen drove 335 miles in 5 hours.
At the same rate, how many miles would she drive in 11 hours?
Answer: 737 miles
Step-by-step explanation: 335/5=x/11.
Cross Multiply and divide to get x=737
The box plots shows the number of books read by students in Mrs. Long's class
this summer. What is the median number of books read in Mrs. Long's class?
O 3 books
O 6 books
O 8 books
O 9 books
Answer:
8 books
Step-by-step explanation:
On a box plot, there is a line in the middle that says where the median is. In this situation, the median is 8.
Write an equation in slope-intercept form of the line with slope −1 that contains the point (5,−2).
A. y = x + 5
B. y = −x + 5
C. y = −x + 3
D. y = −x − 2
Answer:
Below
Step-by-step explanation:
y = mx = b is slope intercept form
m= slope b = y-axis intercept ..... sub in the values given
-2 = (-1)(5) + b shows b = 4
y = -x + 3
Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically.
Answer:
There is exactly one solution: (3, 1)
Step-by-step explanation:
To graph these equations, you need to change them to slope intercept form:
x + y = 4 in slope intercept form is y = -x + 4 (subtract x frok both sides).
x - y = 2 in slope intercept form is y = x - 2 (subtract x from both sides then divide both sides by -1)*.
Now, all you have to do is graph both and find the point they cross at (the solution) which is (3, 1).
* = y can never be negative, which is why you divide by a -1 after subtracting x.
Hope this helps!
A parallelogram is drawn on a centimetre grid.
Find the area of the parallelogram
Answer: 15
Step-by-step explanation:
Base x Height = Area
An airplane takes 7 hours to fly 2800 kilometers against the wind. The return trip with the wind takes only 4 hours. What is the speed, in kilometers per hour, of the airplane in still air?
Answer: Let's call the speed of the airplane in still air "x".
Since the airplane takes 7 hours to fly 2800 kilometers against the wind, its speed against the wind is 2800/7 = 400 km/hr.
Since the return trip with the wind takes only 4 hours, the speed of the wind must be 400 - x.
The total speed of the airplane on the return trip is x + (400 - x) = 400 km/hr.
So, we have:
400 = x + (400 - x)
Expanding the right side:
400 = 400
Therefore, x = 400 km/hr, which is the speed of the airplane in still air.
Step-by-step explanation:
Say you have a single pair of pants and a single shirt. In this case you'd only have 1 outfit option.
If you have 2 pairs of pants and 2 shirts, you now have 4 unique outfit options.
How many pairs of pants and shirts would you need in order to have a unique outfit for each day of the week?
What if you wanted a unique outfit each day for a month? for a year? for your whole life
To have a unique outfit for each day of the week, you would need at 3 pairs of pants and 3 shirts.
To have a unique outfit for a month you would need at 6 pairs of pants and 5 shirts.
To have a unique outfit for each day of the year, you would need 26 pairs of pants and 15 pairs of shirts.
How to find the unique outfits ?To find the unique outfits, you need to have enough clothes to have a unique outfit made from those clothes.
There are 7 days in a week. If you had 3 pairs of pants and 3 shirts, the unique outfits would be :
= 3 x 3
= 9 unique outfits
For a month :
= 6 x 5
= 30 unique outfits
For a year :
= 26 x 15
= 390 unique outfits for 365 days
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A family wants to rent a car to go on vacation. Company A charges $30.50 and 8 cents permile. Company B charges $ 65.50 and 13 cents permile . How much more does Company A charge for x miles than ?
The amount of money Company A charge more for x miles, 35 - 0.05x dollars
What is subtraction?In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.
For example, if we take 4 pencils out of 10 then remaining pencils are 6
so this process is called subtraction.
Let's call the number of miles the family wants to travel "x".
The cost for Company A is $30.50 plus 8 cents per mile, so the total cost for Company A is,
30.50 + 0.08x.
The cost for Company B is $65.50 plus 13 cents per mile, so the total cost for Company B is,
65.50 + 0.13x.
To find out how much more Company A charges, we can subtract the cost for Company B from the cost for Company A:
= (30.50 + 0.08x) - (65.50 + 0.13x)
= 35 - 0.05x
So, Company A charges 35 - 0.05x dollars more than Company B for x miles.
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what are the coordinates of the top right corner of the screen?
The coordinates of the top right corner of the screen (1280, 720).
The coordinates usually consist of two or three values, depending on whether you're working with a two-dimensional or three-dimensional system.
To answer your question, we need to know which coordinate system we're using. In this case, we're assuming that we're dealing with a two-dimensional system, which means that we only need to specify two coordinates: the x-coordinate and the y-coordinate.
The top right corner of the screen is located at a specific position that can be determined by measuring the distance from the origin (usually the bottom left corner) to that point. If we assume that the origin is located at (0, 0), then we need to find the x and y values that correspond to the top right corner.
The x-coordinate of the top right corner depends on the width of the screen, which can vary depending on the device you're using. For example, if the width of the screen is 1280 pixels, then the x-coordinate of the top right corner would be 1280.
The y-coordinate of the top right corner also depends on the height of the screen, which again can vary depending on the device. If the height of the screen is 720 pixels, then the y-coordinate of the top right corner would be 720.
Therefore, the resulting coordinates would be (1280, 720).
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