thus, a = -39 is the solution to the equation -a = 4b-7 when (a, -8) is a solution
What's equation?An equation is a fine statement that asserts the equivalency of two expressions. It generally consists of two sides, with an equal sign between them. Equations are used to describe connections between variables, and to break problems in colorful fields, including mathematics, wisdom, engineering, and economics.
Given by the question.
the equation given is -a = 4b - 7.
We are also told that (a, -8) is a solution to this equation. This means that if we substitute a for x and -8 for y, the equation will be true.
Substituting the given values, we get:
a = 4b - 7 (Given equation)
a = 4(-8) - 7 (Substituting b = -8, since (a, -8) is a solution)
a = -32 - 7 (Simplifying)
a = -39 (Final answer)
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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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What is the value of 2.7 liters in ounces
One liter is equal to 33.814 ounces, so 2.7 liters is equal to 90.772 ounces. This can be calculated using the following formula, which is multiplying 2.7 by 33.814: 2.7 x 33.814 = 90.772.
To calculate the number of ounces in a given amount of liters, this formula can be used. This can be calculated using the following formula, which is multiplying 2.7 by 33.814: 2.7 x 33.814 = 90.772.This is useful for quickly and accurately converting between liters and ounces, which can come in handy when measuring liquids or other substances. For example, if a recipe calls for 2.7 liters of a certain ingredient, you can easily convert that to ounces using the formula.
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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.
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
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
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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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
A parallelogram is drawn on a centimetre grid.
Find the area of the parallelogram
Answer: 15
Step-by-step explanation:
Base x Height = Area
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!
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
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 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 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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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
I need help with my homework please help
The formulas for the rigid transformations of the figures are listed below:
Case 1: (x, y) → (x - 10, y + 9)
Case 2: (x, y) → (- y, x)
Case 3: (x, y) → (- x, y)
Case 4: (x, y) → (- y, x)
Case 5: (x, y) → (x, - y)
Case 6: (x, y) → (x, y + 10)
How to determine the transformation rule for each case
In this question we find six cases of rigid transformations applied on figures. The most common rigid transformations are listed below:
Translation: (x, y) → (x + a, y + b), where a, b are real numbers.Reflection about x-axis: (x, y) → (x, - y)Reflection about y-axis: (x, y) → (- x, y) Rotation: (x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ), where θ is the angle of rotation.Then, by direct inspection, we derive the following rigid transformations:
Case 1 (Translation)
(x, y) → (x - 10, y + 9)
Case 2 (Rotation)
(x, y) → (x · cos (- 270°) - y · sin (- 270°), x · sin (- 270°) + y · cos (- 270°))
(x, y) → (- y, x)
Case 3 (Reflection about y-axis)
(x, y) → (- x, y)
Case 4 (Rotation)
(x, y) → (x · cos 90° - y · sin 90°, x · sin 90° + y · cos 90°)
(x, y) → (- y, x)
Case 5 (Reflection about x-axis)
(x, y) → (x, - y)
Case 6 (Translation)
(x, y) → (x, y + 10)
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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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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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Many sheet materials used in construction, such as plywood or drywall, measure 8 feet by 4 feet. What are these dimensions in inches?
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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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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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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Two friends shop for fresh fruit. Elena buys a watermelon for $8.55 and 5 pounds of cherries. Taniy buys a pineapple for $4.45 and 4 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more Elena spent.
The expression to represent how much more Elena spent is 4.1 + p.
How to find the expression to represent a situation?Two friends shop for fresh fruit. Elena buys a watermelon for $8.55 and 5 pounds of cherries. Taniya buys a pineapple for $4.45 and 4 pounds of cherries.
Therefore, the expression to represent how much more Elena spent can be represented as follows:
hence,
p = price in dollars, per pound of cherries.
Hence,
amount Elena spent more = 8.55 + 5p - (4.45 + 4p)
amount Elena spent more = 8.55 + 5p - 4.45 - 4p
amount Elena spent more = 8.55 - 4.45 + 5p - 4p
Therefore,
amount Elena spent more = 4.1 + p
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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.
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
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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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.
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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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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