The rate if he went three years without an accident based on the information about the insurance is $552.15.
How to calculate the insurance?From the information given, his basic insurance cost is $613.50 per year and his insurance company offers a typical "safe-driver discount.
The amount will be:
= 613.50 - (20.45 × 3)
= 552.15
In conclusion, the rate is $552.15.
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Coordinate grid shows from -2 to positive two on x-axis and -2 to positive two on y-axis. There are increments I have one over four for each grid line on each of the two axes. Only the whole numbers are labeled on either side of the axis. A point A is shown at the intersection of 5 grid lines to the right of the y-axis and 3 grid lines below the x-axis. What are the coordinates of point A?
The coordinates of point A are ( 5/4, -3/4)
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
x - coordinate = 5 grid lines to the right of the y-axis
y - coordinate = 3 grid lines below the x-axis.
The point A is in the 4th quadrant
(x,y) = ( + 5 grid lines, -3 grid lines )
There are increments I have one over four for each grid line on each of the two axes
This means,
(x,y) = ( + 5 * 1/4, -3*1/4 ) = ( 5/4, -3/4)
So, the coordinates of point A are ( 5/4, -3/4)
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In this activity, you are investigating the financial viability of the martingale betting strategy that was introduced in class.
Recall how a martingale works. You place a bet on any "even money" event (that is, a wager where winning means gaining the money bet). If you win, you stop — you have won money. If you lose, you keep doubling the bet until you win, and then stop. Your winnings will cover the previous losses. Unfortunately, a long losing streak means that you run out of money and can no longer bet – hence losing a lot.
Balph Snerdwell has $31 in his wallet. He is going to be betting on red or black, at the roulette table. Recall that, in an American casino, there are 38 numbers — 18 red and 18 black (plus 0 and 00). So Balph has an 18/38 probability of winning, each time he bets.
a) Balph plays a martingale — doubling his bet after each loss. What’s the maximum number of times he can lose? Why?
b) Recall that Balph might win a dollar from playing a martingale … or he might lose all $31 in his wallet. What’s the probability that he wins a dollar? That he loses everything?
c) And so, what is the expected value of Balph’s net winnings, from one martingale?
d) Sometimes Balph will bet only one dollar. But sometimes he will bet three dollars (if he loses, then wins). Or seven dollars (lose, lose, win). Or some other amount. What are the possible values for total amount wagered? Their probabilities? Therefore, what is the expected value of the numbers of dollars wagered?
e) In Part D you found how much money Balph won, on average. In Part E, you found how much money Balph bet, on average. How much did Balph win, per dollar bet? (Does this number look familiar?)
The answers are:
b) 0.9596, 0.0404
c) expected value of dollars won = -$0.29236
d) expected value of dollars wagered = $5.55475
Can someone please break it down and explain how they got the answers
Answer:
a) Balph can lose a maximum of 6 times in a row before running out of money and not being able to place any more bets. This is because if he loses 6 times in a row, he would have to bet $64 (1+2+4+8+16+32) which is more than the $31 he has in his wallet.
b) The probability that Balph wins a dollar is 0.9596 and the probability that he loses everything is 0.0404. These probabilities are calculated by assuming a 18/38 probability of winning each bet and using the martingale betting strategy.
c) The expected value of Balph's net winnings from one martingale is -$0.29236. This means that on average, Balph can expect to lose $0.29236 each time he plays the martingale betting strategy.
d) The possible values for the total amount wagered are $1, $3, $7, $15, $31, and $64. These values correspond to the amount wagered after losing 0, 1, 2, 3, 4 and 5 times in a row. The probability of each value depends on the probability of losing that many times in a row, calculated using the 18/38 probability of winning each bet. The expected value of the number of dollars wagered is $5.55475.
e) The amount Balph wins per dollar bet is -0.0527. This number is calculated by dividing the expected value of Balph's net winnings by the expected value of the number of dollars wagered. This number is less than zero, indicating that on average, Balph will lose money for every dollar he bets.
Cuando se calcula la potencia de un producto, que sucede con el exponente en los factores del producto, se.
Según el álgebra de números reales, la potencia del producto es el producto de las potencias.
¿Cómo determinar la potencia de un producto de dos números reales?
De acuerdo con la pregunta, tenemos el caso del producto de dos números reales a, b elevados a un potencia n, cuya descripción matemática se presenta a continuación:
(a · b)ⁿ
De acuerdo con el álgebra de números reales, este caso tiene la siguiente equivalencia:
(a · b)ⁿ = aⁿ · bⁿ
De modo, pues, que la potencia de un producto de dos números reales es igual al producto de las potencias de los números reales.
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what expression represents 5 less than one half of x
Answer:
5 < 1/2x
5 is less than 1/2 of x
the table of ordered pairs (x y) gives an exponential function write an equation for the function
The equation of the function is found to be y = [tex]2^{2x+3}[/tex].
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
y = 2⁽ᵃˣ⁺ᵇ)
x = - 1 y = 2 = 2¹
=> ax + b = 1 => -a + b = 1
=> b -a = 1
x = 0 y = 8 = 2³
=> ax + b = 3 => 0 + b = 3
=> b = 3
b -a = 1
=> 3 - a = 1
=> a = 2
checking for others
x = 1 y = 32 = 2⁵
ax + b = 2(1) + 3 = 5
x = 2 y = 128 = 2⁷
ax + b = 2(2) + 3 = 7
The equation is y = [tex]2^{2x+3}[/tex]
Hence the equation of the function is found to be y = [tex]2^{2x+3}[/tex].
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7. The average comic book sold for $2.25 in 1994 and for $3.99 in 2016.
a) Write a linear function that approximates the average cost of comic books
over time (t) starting in 1994.
b) Predict the average cost of a comic book in 2020.
- c) In about what year will the average cost have gone over $5?
The linear function to find average cost will be A=$(2.25+0.079t), average cost of a comic book in 2020 = $4.3, Average cost will be $5 in year 2029.
what is a linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0. Although the linear functions are also represented in terms of calculus as well as linear algebra. The only difference is the function notation. Knowing an ordered pair written in function notation is necessary too. f(a) is called a function, where a is an independent variable in which the function is dependent. Linear Function Graph has a straight line whose expression or formula is given by;
y = f(x) = px + q
It has one independent and one dependent variable. The independent variable is x and the dependent one is y. P is the constant term or the y-intercept and is also the value of the dependent variable. When x = 0, q is the coefficient of the independent variable known as slope which gives the rate of change of the dependent variable.
Now
Initial value = $2.25 in 1994
cost in 2016 = $3.99
Therefore
3.99=2.25+2.25*r*22/100
r=0.079
where r=rate
then
Average cost=initial value+0.079t
Hence
A=$(2.25+0.079t)
where t=time (given year - 1994)
cost in 2020=$(2.25+0.079*26)
cost in 2020=$4.3
Now for A=$5
5=2.25+0.079t
t=35years
Hence Average cost will be $5 in year 2029.
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In a certain country, there are about 7.0 million people. Of those,
1.9 million do not have access to safe drinking water. Solve the equation
p+1.9=7.0 to find p, the number of people (in millions) who have
access to safe drinking water.
By linear algebra , we can find that number of people having access to safe drinking water is 6.1 million.
What is the purpose of linear algebra?The solution of linear systems of differential equations is facilitated by the use of linear algebra in conjunction with calculus. Analytic geometry, engineering, physics, the natural sciences, computer science, computer animation, and the social sciences all use methods from linear algebra (particularly in economics).
It is simpler to analyze linear systems involving differential equations by combining calculus with linear algebra. Techniques from linear algebra are used in many fields, including the social sciences, engineering, physics, computer science, and computer animation (particularly in economics).
equation,
p+1.9=7.0
p=7.0-1.9
p=6.1
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Find the length of an arc on a circle of radius 7 corresponding to an angle of 45∘.
Arc length =
Give an exact answer as a fraction, not a decimal approximation.
The length of the arc is 5½ units
What is length of an arc?The length of an arc is the distance covered at a particular angle on the circumference of a circle.
A circumference is the external body of a circle. it is also called the perimeter of a circle
Length of an arc is given as :
l = 2 π r × (θ/360°)
where θ = angle subtended
therefore l = 45/360 × 2 × 22/7 ×7
dividing through by 45
= 1/8× 2 × 22/7 ×7
dividing through by 7
= 1/8 × 2 × 22
= 44/8
dividing through by 4
= 11/2
therefore l = 5 ½ units
This means that the length of the arc is 5 ½ unit
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easy please help area of a trapezoid using decomposition
The area of the trapezoid is calculated as: D. 90 square units.
How to Find the Area of a Trapezoid By Decomposing?To find the area of the trapezoid that is shown in the image above, we can decompose the trapezoid into three shapes which are one rectangle and two identical triangles.
Area of triangle = 0.5 * base * height
Area of rectangle = length * width.
Given the following:
x = 8 units
y = 2 units
h = 9 units
Area of the 2 triangles = 2(0.5 * y * h) = 2(0.5 * 2 * 9) = 18 units²
Area of rectangle = x * h = 8 * 9 = 72 units²
Area of trapezoid = 18 + 72 = 90 units²
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The function f is defined on the closed interval [-5,4]. The graph of f consists of three line segments and is above in the figure above. Let g be the function defined by g(x) = integral_2_-3 f(t) dt. a. Find g(3) b. On what open intervals contained in -5 lessthan x lessthan 4 is the graph of g both increasing and concave down? c. The function h is defined by h(x) = g(x)/5x. Find h'(3). d. The function p it defined by p(x) = f(x^2 - x). Find the slope of the line tangent to the graph of p at the point where x = -1.
a. g(3) = -2
b. g is increasing and concave down on the intervals (-3 <= x < 2) and (2 <= x <= 4).
c. h'(3) = 0
d. The slope of the tangent line to the graph of p at x = -1 is -3.
a. The function g is defined as the definite integral of f(t) with respect to t from -3 to 2. Therefore, g(3) = integral_2^3 f(t) dt. From the graph, we can see that:
f(t) = 2 for -5 <= t < -3f(t) = -t for -3 <= t < 2f(t) = 2t - 8 for 2 <= t <= 4.Therefore, g(3) = integral_2^3 (-t) dt + integral_2^3 (2t - 8) dt
= -1/2(3^2 - 2^2) + 1/2(3^2 - 2^2 - 8(3 - 2)) = -5/2 + 1/2 = -2.
b. The graph of g is increasing and concave down when the graph of f is concave down and when the definite integral of f is increasing. From the graph of f, we can see that f is concave down on the intervals (-5 <= t < -3) and (2 <= t <= 4). Therefore, g is increasing and concave down on the intervals (-3 <= x < 2) and (2 <= x <= 4).
c. The function h is defined by h(x) = g(x)/5x. To find h'(3), we need to use the quotient rule for derivatives. h'(x) = (5xg'(x) - g(x)5)/5x^2.
Since g(x) = integral_2_-3 f(t) dt, it is not a function of x, so g'(x) = 0. Therefore, h'(3) = (530 - 05)/53^2 = 0.
d. The function p is defined by p(x) = f(x^2 - x). To find the slope of the line tangent to the graph of p at the point where x = -1, we need to find the derivative of p at -1. Using chain rule: p'(x) = f'(x^2-x)(2x-1) so p'(-1) = f'(-1) * (2(-1)-1) = (2(-1) -1) = -3.
Therefore, the slope of the tangent line to the graph of p at x = -1 is -3.
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Find the vertical asymptotes (VA), removable discontinuities (RD),
horizontal (HA) or slant asymptote (SA) and intercepets (Int)
x2-10x+9
for graph of the rational function
x²-9x
Therefore , the solution to the given problem of function comes out to be slant asymptotes are y = x -4.
What does the term function mean?Numbers and their variants, equations & related structures, and geometry and their regions and potential applications are all mathematical topics. The link between a group of input, each of which generates a related output, is referred to as a "function." A function is a relationship between outputs and inputs where each input results in a single, distinct output. Each procedure has a domain and a city / municipality, which are frequently referred to as a scope. Functions are usually represented by the letter f. (x). The input is X. On activity, one-to-one activities, many-to-one activities, throughout operations, as well as on functions are the four main categories of supplied functions.
Here,
There are no limitations on the type of rational function, therefore it is feasible to construct one with each of the three asymptotes.
This is depicted in the attached graph, along with the graph of the rational function it represents. These are the asymptotes of the function.
Vertical asymptotes are x = -4,
horizontal asymptotes are y = 0 and
slant asymptotes are y = x -4.
Additional remarks
We employ an exponential function in our example function. Although it can be expressed as a polynomial of infinite degree, that is not often regarded as a polynomial. The proportion of polynomials is how most authors describe a rational function.
Therefore , the solution to the given problem of function comes out to be slant asymptotes are y = x -4.
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Not sure on this question
Answer:
It will take 250 seconds for 30 liters to pass through the pipe.
Step-by-step explanation:
Let's use just the units only to help us set up and equation.
liters/sec × sec = liters
This works. Fill in the numbers we know.
.12 l/sec × ?sec = 30liters
Use a real variable and let's leave off the units so we can write an neater equation to solve.
.12 l/sec × x sec = 30liters
.12x = 30
That's a good equation. Divide by .12 to solve.
x = 30/.12
x = 250
Remember x was seconds. We were asked to find the seconds.
It will take 250 seconds for 30 liters to pass through the pipe.
(In case they ask later, that's 4minutes and 10 seconds)
Solve the following inequality
2 x + 1 < 9
Answer:
2x+1<9
collecting the like term
2x<9-1
2x<8
divide both sides by 2
x<4
Solve the proportion
The value of the proportion x is 10. When determining if two ratios or fractions are equivalent, the proportion formula is utilized.
What is proportion formula?When determining if two ratios or fractions are equivalent, the proportion formula is utilized. By dividing the supplied numbers, we may determine the missing value. One way to express the percentage formula is as a: Whereas a and d are the extreme terms and b and c are the mean terms, b::c: d = a/b = c/d.
1)Cross, multiply, and spread
2) Be sure to alter the signs when you move the x to one side and the numbers without the x to the other.
3)solve
4)x=
x - 2 /4 = x + 4 /2
2x-4 = 4x+ 16
-20= 2x
x=10.
The value of the proportion x is 10.
The complete question is
Solve the proportion : x - 2 /4 = x + 4 /2
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The revenue of a certain company increased by 10% in the first quarter, decreased by 6% in the second quarter, decreased by 12% in the third quarter, and increased by 11% in the fourth quarter.
Did revenue increase or decrease overall?
It increased
It decreased
What is the average rate of growth or decline? Enter your answer as a positive number in percent form, rounded to one decimal places.
The company overall revenue net percentage change is increased by 89.2%.
What is net percentage change?
Two or more percentage changes applied to a quantity consecutively are covered by the idea of successive percentage changes. As the base changes after the first adjustment, the total change in this instance is not simply the addition of the two percentage changes.
If a number N changes by x% and then y%, what will the net percentage change is [tex]x+y+\frac{xy}{100}[/tex] %.
Now in first quarter = 10% increase
In second quarter = 6% decrease
In third quarter = 12% decrease
In fourth quarter = 11% increase.
Now over all percentage change is ,
=> [tex]10-6-12+11+\frac{10.6.12.11}{100}[/tex]
=> 3+79.2
=> 82.2%
Hence the company revenue is increased by 82.2%.
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14. Damian is building a display case to hold
75 model cars. The case will have fewer
than 10 shelves, and each shelf will hold
no more than 15 cars. If Damian wants
each shelf to have the same number of
cars, how many shelves should he put in
the display case?
Damian should put 5 shelves in the display case to hold 75 model cars and ensure that each shelf has the same number of cars.
What is the unit value?
Unit value is a measure of the price of a single unit of a good or service. It is calculated by dividing the total cost of the good or service by the number of units purchased. It is also known as unit cost.
To determine how many shelves Damian should put in the display case, we can use the following steps:
Divide the total number of cars by the maximum number of cars per shelf. In this case, 75 model cars / 15 cars per shelf = 5
If the number of shelves is not a whole number, round up to the next whole number. In this case, 5 shelves is already a whole number, so we don't need to round up.
Check that the number of shelves is less than 10. In this case, 5 shelves are less than 10 shelves.
Hence, Damian should put 5 shelves in the display case to hold 75 model cars and ensure that each shelf has the same number of cars.
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Mitch plays chess with his aunt every Friday.
He's won 12 matches and lost 3 matches.
What is the experimental probability that Mitch will win the next match?
The answer is 4/5
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: Mitch won 12 matches and lost 3 matches.
Thus the theoretical probability of him winning the next match is 12/15=4/5
Hence, The answer is 4/5
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Please help me! Thank you so much!
The mean of the numbers, given the stem and leaf plot of the number of classrooms in each school in the city, is 84 classrooms
How to find the mean ?To find the mean of the schools, you first need to add up the number of classrooms in each school and then divided this sum by the number of schools that Evelyn used in the social studies project.
When using a stem and leaf plot in this instance, the stem is the tens figure and the leaf is the ones figure.
This means that a stem of 7 and lead of 7 means 77 classes.
The sum of the number of classrooms is therefore :
= 77 + 77 + 81 + 81 + 82 + 82 + 83 + 84 + 84 + 85 + 85 + 87 + 90 + 90 + 92
= 1, 260 classrooms
The mean is therefore :
= 1, 260 / 15 schools
= 84 classrooms
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What is the slope of the line shown below? (6, 2); (- 2, - 3); 8/5; 5/8; - B/5 D. - 5/8
The slope of the line shown below is -5/8.
What is slope?Slope is the measure of the steepness or incline of a line or surface. It is calculated by measuring the ratio of the vertical change over the horizontal change between two points. It is a mathematical concept used in algebra, geometry, and calculus to measure the rate of change of a function or line. Slope is also used to identify the direction of a line or surface. It is represented by the variable ‘m’ and is calculated by dividing the vertical change by the horizontal change between any two points on a line or surface.
This can be determined by using the formula for slope, which is (y2 - y1)/(x2 - x1). In this equation,
(y2 - y1) = -3 - 2 = -5 and (x2 - x1) = -2 - 6 = -8. Thus, the slope of the line is -5/8.
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What are the slope and y-intercept of the equation 2x - 5y = -10?
Answer:
slope 2/5
y-intercept (0,2)
Step-by-step explanation:
a) Work out the minimum number of hikers who could have walked between 8 miles and 19 miles.
b) Work out the maximum number of hikers who could have walked between 8 miles and 19 miles.
Answer:
B
Step-by-step explanation:
8 = 3 a - 4
Nmbvcxzstyhvff
The value of a in the equation 8 = 3a - 4 is
What are linear equations?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
The equation 8 = 3a -4 is an example of linear equation with only one variable. The variable here is a. And the value of this variable can be found using mathematics principle.
8 = 3a - 4
collect like terms
3a = 12
divide both sides by 3
a = 12/3
a = 4
therefore the value of a in 8 = 3a -4 is 4
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Use the quadratic formula to find the solutions to the quadratic equation below x^2-5x-4=0
Answer:
comparing given quadratic equation x²-5x-4=0 with ax²+bx+c=0 we get,
a=1,b=-5,c=-4
Now,
x={-b±√b²-4ac}/2a
={-(-5)±√(-5)²-4×1×-4}/2×1
={5±√25+16}/2
=(5±√41)/2
Hence,B.is the correct option
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Which of the following is an example of a variable measured at the nominal level of measurement?
A. Location in which respondent was born
B. Religiosity measured as not religious, somewhat religious, and very religious
C. Time in seconds in which a subject completes a given task D. Number of respondents' first cousins
E. Level of education in years completed
Religion is an example of a variable measured at the nominal level of measurement. Thus, option B is correct.
Nominal values are those that cannot be quantified by numbers, such as when calculating age or tallying academic accomplishments. As opposed to the ordinal, interval, or ratio measurements, it is the level of measurement representing a variable that just has distinct properties.
Since the 'characteristic' or 'identity' we are interested in is just named, the nominal level of measurement is the least accurate and illuminating. In nominal variables, the numerical values just "label" the attribute in a distinctive way. The numerical value is just a label in this instance.
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solve to find solutions no solution or infinte solution
6n+7+-2n+-14=5n+1
The given expression has one solution which is n = -8.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is,
6n + 7 + -2n + -14 = 5n + 1
Doing the operations of like terms,
6n - 2n + 7 - 14 = 5n + 1
4n - 7 = 5n + 1
Again grouping with like terms,
4n - 5n = 1 + 7
-n = 8
n = -8
Hence the given expression has solution n = -8.
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Answer:
n = -8
Step-by-step explanation:
6n+7+ -2n + -14=5n +1
=6n -2n -5n =1 -7 +14
=-n = 8
=-n/-1 = 8/-1
=n = -8
Hence the value for n is -8.
Aella Iniko and Loki played a game. Aella scored 2/5 of the points, and Loki scored 1/3 of the point. What part of the points did Iniko score?
The part of the points that Iniko score will be 4/15.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, Aella Iniko and Loki played a game. Aella scored 2/5 of the points, and Loki scored 1/3 of the point.
The part of the points that Iniko score will be
= 1 - (1/3 + 2/5)
= 1 - (5/15 + 6/15)
= 1 - 11/15
= 4/15
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5
432-
1
--5-4-3-2-1 1
ENTY
-2
-3-
-4
Mark this and return
23
45x
Which function is represented by the graph?
Of(x)=-x-31 +4
Of(x) = -x + 3) +4
O f(x) = -x-41+3
Of(x) = -x +41 +3
Save and Exit
Next
4
27
Submit
On solving the provided question, we can say that the value of the equation here is f(2) = -29 and f(3) = -41
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation here is
f(x)=-x-31 +4
f(2) = -29
f(x) = -x-41+3
f(3) = -41
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this is factorizing by looking for the common factor i have no idea how to answer any of them and i need it for tomorrow please help (im in algebra 2)
Answer:keep dividing
Step-by-step explanation:
keep dividing till you get a common factor
Can someone help me ASAP? Plsss I need this grade
Answer:
11 units
Step-by-step explanation:
Diagonals in a rectangle are congruent.
WY and XZ are both diagonals of the rectangle WXYZ.
Therefore, their values are congruent or equal.
6x-7 = 3x+2
Subtract 3x from both sides and add 7 from the left side to isolate the x's equal to a constant.
You get 3x = 9
Divide both sides by 3 to isolate x by itself.
x = 3
Next, plug in the value of 3 for x in any of the equations and you will get 11 units.
Hope this helps!
Xochitl went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Alonso went into the same movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. Determine the price of each bag of popcorn and the price of each drink.
The price of each bag of popcorn and the price of each drink is $7.5 and $4 respectively.
How to calculate the equation?Let the drinks be represented as d.
Let the popcorn be represented as p.
From the information, Xochitl went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Thus will be:
6p + 4d = 65
Alonso went into the same movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. This will be:
9p + 8d = 107.50
Equating the equation
6p + 4d = 65 ..... i
9p + 8d = 107.50 ..... ii
Multiply equation i by 8
Multiply equation ii by 4
48p + 32d = 520
36p + 32d = 430
12p = 90
Divide
p = 90/12
= 7.5
6p + 4d = 65 .
6(7.5) + 4d = 65
4d = 65 - 45
4d = 20
d = 20/4 = 5
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