The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)
Given equation y = 3x + a / 2x - 5
= y(2x - 5) = 3x + a
= 2xy - 5y = 3x + a
= 2xy - 3x = a - 5y
= x(2y-3) = a - 5y
Hence, x = (a - 5y) / (2y - 3)
First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).
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Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
Submit Answer
+
2
Ń
9.
The mapping diagram above
where there
Set B
5
C
a function since
C
in
attempt 1 out of 2
-8 + 2x - 9 + 3x - 10 = 21
The variable x of the equation is 9.6.
How to solve equations?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
We have to solve the equation for the variable x .
A variable is a number represented with a letter in an equation.
Therefore, let's find the variable x in the equation.
-8 + 2x - 9 + 3x - 10 = 21
combine the like terms
-8 + 2x - 9 + 3x - 10 = 21
- 8 - 9 - 10 + 2x + 3x = 21
-27 + 5x = 21
add 27 to both sides of the equation
-27 + 5x = 21
-27 + 27 + 5x = 21 + 27
5x = 48
divide both sides by 5
5x / 5 = 48 /5
x = 48 / 5
Therefore,
x = 9.6
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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after 11 hours of burning, a candle has a height of 19.4 centimeters. after 23 hours of burning, its height is 12.2 centimeters. what is the height of the candle after 15 hours?
The height of the candle after 15 hours of burning is 17 cm.
According to the question,
We have the following information:
Height of the candle after 11 hours of burning = 19.4 cm
Height of the candle after 23 hours of burning = 12.2 cm
Now, we will find the rate at which the height of the candle is decreasing. It means that we will find the decrease in height per centimeter.
Difference between hours and height:
23-11 = 12 hours
19.4-12.2 = 7.2 cm
So, we have:
12 hours = 7.2 cm
1 hour = 7.2/12
1 hour = 0.6 cm
So, the height is decreasing at the rate of 0.6 cm per hour.
Now, we have to find the height after 15 hours.
Height at 11 hours = 19.4 cm
Difference between 15 hours and 11 hours is 4 hours.
Change in height = 0.6*4 cm
Decrease in height = 2.4 cm
So, the height after 15 hours:
19.4-2.4
17 cm
Hence, the height of the candle after 15 hours of burning is 17 cm.
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Compare and Explain: Are they equivalent?
3 hours worked for $12; 9 hours worked for $36
Answer:
Yes they are equivalent.
Step-by-step explanation:
$12 divided by 3 is $4
$36 divided by 9 is also $4
Therefore they are equivalent.
Your welcome
Answer:
Yes!
Step-by-step explanation:
You divide 3 by 12 because that's how much they work for an hour. That means they make $36 for 9 hours.
12 ÷ 3 = 4
36 ÷ 9 = 4
They have the same answer which makes them equivalent.
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Dimensions of the area enclosed is 800 * 800 and the maximum area = 6,40,000 square yards.
Given:
Liana has 3200 yards of fencing to enclose a rectangular area.
Let l and b be the length and width.
we know that:
perimeter of rectangle = 2(l+b)
2l + 2b = 3200
l+b = 1600
b = 1600 - l
Area of rectangle A = lb
= l*1600-l
= 1600 l - l^2
Apply derivative:
dA/dl = 1600 - 2l
1600 - 2l = 0
1600 = 2l
l = 1600/2
l = 800
l+b = 1600
b = 1600 - 800
= 800
Area = 800*800
= 6,40,000
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James knows that he eventually wants to buy a motocycle, and the model he has in mind cost $5000. he has found a bank that will let him open a saving account with 7% interest that is compounded monthly. if he wants to buy his motocycle in 5 years ( he's still nervious) how much money should he invest in the account now
He should invest $86.29 in the account now, which has a 7% interest compounded monthly.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded monthly, and t is the time in number of months
Based on the given information, P is the unknown and
B = $5000
t = 5 years = 60 months
r = 7% = 0.07
n = 1
Plug in the values and solve for P or the amount that should be invested today.
B = P(1 + r/n)^t
$5000 = P(1 + 0.07/1)^60
$5000 = P(1.07)^60
P = $5000/(1.07)^60
P = $86.29
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The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is 45° more than three times the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
The measure of each angle of this isosceles triangle is equal to 27°, 27°, and 126°.
What is an isosceles triangle?An isosceles triangle can be defined as a type of triangle that has two (2) of its sides equal in length and two (2) equal angles. This ultimately implies that, an isosceles triangle comprises two (2) angles that have the same measure or are equal in magnitude.
Let the variable x represent the angles that have the same measure or are equal in magnitude. Therefore, the sum of the measures of the angles of this isosceles triangle is given by this mathematical expression:
x + x + (45° + 3x) = 180°.
5x + 45° = 180°.
5x = 180° - 45°
5x = 135°
x = 135°/5
x = 27°
Therefore, the measure of each angle of the isosceles triangle is given by:
First angle = 27°.
Second angle = 27°.
Third angle = 45° + 3(27) = 126°.
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find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
1. 2, (3,9) 2. 5, (1,8)
Answer:
1. y=2x+3
2. y=5x+3
Step-by-step explanation:
1. to find equation of the line we need the gradient and y-intercept
gradient=2
y=mx+c where m is gradient,x and y are coordinates and c is the y-intercept
input given coordinates and gradient in the equation to find c:
9 = 2(3)+c
9 = 6+c
9-6 = c
c = 3
to write the equation we only input gradient and y-intercept:
y=2x+3
2. to find the equation of the line we need the gradient and y-intercept
gradient=5
y=mx+c where m is gradient,x and y are coordinates and c is the y-intercept
input given coordinates and gradient in the equation to find c:
8 = 5(1)+c
8 = 5+c
8-5 = c
c = 3
to write equation we only input gradient and y intercept:
y=5x+3
You have 7,160 grams of a radioactive kind of bismuth. How much will be left after 10 days if
its half-life is 5 days?
grams
The solution is 1790 grams
The amount of bismuth left after 10 days if the half life is 5 days will be
1790 grams
What is half-life of an element?
The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
Let the half life of the element be represented as t½
The value of t½ = 5 days
Now , the initial amount of bismuth N₀ = 7160 grams
The number of days t = 10 days
The amount of bismuth left after 10 days = N( t )
Now , the value of N( t ) is given by the formula ,
N( t ) = N₀ ( 1/2 )^ t/ t½
Substituting the values in the equation , we get
N( t ) = 7160 ( 1/2 )^10/5
N( t ) = 7160 ( 1/2 )²
N( t ) = 7160 / 4
N( t ) = 1790 grams
Therefore , the value of N( t ) is 1790 grams
Hence , the amount of bismuth left is 1790 grams
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Match the following definitions with the correct term.
Answer:
that's biology but
Step-by-step explanation:
autotrophs make their owner food
heterotrophs can't make their own food
photosynthesis is the 3rd one
photosynthesis happens in the chloroplast
photosynthesis makes glucose
I can go in depth about any of these, ask me if needed
consider tbe graph of a function that is positive over its entire domain. can the graph have an x-intercept?
The graph whose domain is positive will not have any x - intercept.
What is graph of a function?
At first it is important to know about function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Graph of a function is the set of all points of the form (x, f(x)).
The graph is positive in its entire domain
f(x) > 0 for all x
So the graph will never cut the x axis at any point.
So the graph will not have any x intercept.
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it is known that 15% of the calculators shipped from a particular factory are defective. what is the probability that exactly four of ten chosen calculators are defective?
With the help of probability we can conclude our answer.
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, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, whereC5 3= 5!/3/2=4*5/2=10p is the probability that one randomly selected calculator is defective= 10%=0.1q is the probability that one randomly selected calculator is non-defective.q=1-p=1-0.1=0.9So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081learn more about probability click here:
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time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)
We utilize the z statistic to find the probability percentage. Calculating the z value and then looking up the p value using the common probability tables is the process to follow. The z score formula is:
Z = (x - )/ ( / sqrt(n)
where,
x=11, sample score.10 is the sample mean.Standard deviation equals 2
sample size, n With n = 5, calculating the z and p values:
z =(11 - 10) / (2 / sqrt(5))z = 1.12The tables show that p(5) = 0.8686.
For n = 6, calculate the z and p values as follows:
z =(11 - 10) / (2 / sqrt(6))z = 1.22The tables show that p(6) = 0.8888.
If both days to occur, the probability that each day will last no more than 11 minutes is as follows:
p total = p(5) * p(6)p total = 0.8686 * 0.8888p total = 0.772learn more about probability click here:
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NEED HELP PLEASE AS FAST AS YOU CAN
Answer:
3.87
Step-by-step explanation:
b =
[tex] \sqrt{8 ^{2} -7 ^{2}} [/tex]
Divide. Write 5/8 as a fraction, a whole number, or a mixed number.
Answer: 5/8
Step-by-step explanation:
5/8 is already a fraction
This stem-and-leaf plot shows the number of Australian road fatalities in April for the years 2009 to 2019. Find the range of the data. Stem Leaf 7 2 889 9 10 11 15 4 1 2 6 1 3 4 3 Key 13 0=130
What is the slope of the line that passes through the points (0, -10)(0,−10) and (-4, -11)(−4,−11)? Write your answer in simplest form.
The slope of the line that passes through the points is 1/ 4
What is slope?The gradient or slope of a line is a value or number describing both the direction and the steepness of a line.
The formula for calculating the slope of a line is expressed as;
Slope, m = y₂ - y₁/ x₂ - x₁
Where;
y₁ is the first point on the y - axis y₂ is the second point on the y - axisx₁ is the first point on the x - axisx₂ is the second point on the x - axisNow, substitute the values, we have;
Slope, m = (-11 - ( -10)/ ( -4 - 0)
expand the brackets
Slope, m = - 11 + 10/ -4
Add the values
Slope, m = -1/ -4
Divide the values
Slope, m = 1/ 4
Hence, the value is 1/ 4
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Answer:
1/4
Step-by-step explanation:
find the ratio of 2 meters to 76 centimeters
The ratio of 2 meters to 76 centimetres is 50: 19.
How to find ratios of units?In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.
In simpler terms, a ratio compares values.
Let's find the ratio of 2 meters to 76 centimetres as follows:
We have to first convert the units so they will be same.
Hence,
1 cm = 0.01 m
76 cm = ?
cross multiply
length in metres = 76 × 0.01
length in metres = 0.76 metres
Therefore, let's multiply the 2 units by 100.
0.76 × 100 = 76 metres
2 × 100 = 200 metres
In ratio, 200 : 76 will be simplified as 50 : 19
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which shape has a larger area: a rectangle that is 7 inches by 3/4 inch, or a square length 2 1/2 inches? Show your reasoning
The area of the of the rectangle is 5.25square inch and the area of the square is 6.25square inch. Therefore the square has larger area.
What is area of plane shape?The area of a shape is the “space enclosed within the perimeter or the boundary” of the given shape. We calculate the area for different shapes using formulas.
Area formula in rectangle is L× W and in square is L^2. This happened in square becos square has all it's sides equal. Where L and W are length and Width respectively
The area of rectangle with dimension 7inches by 3/4 inch is 7×3/4= 5.25 square inches
The area of the square with dimension 2 1/2 inches is( 5/2)^2= 25/4= 6.25m
Therefore the square has larger area
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PLEASE HELP ME !!!!!!!
Answer:ok
Step-by-step explanation:
Answer: 1/5 25/48
maybe?
A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 50 meters and a standard deviation 100 meters. What is the probability that the measured distance will be smaller than the true distance?.
Check answer below in the image.
The mean temperature for the first 4 days in January was 3°C.
The mean temperature for the first 5 days in January was 1°C.
What was the temperature on the 5th day?
The temperature on the fifth day in January is -7°C.
What is mean?It should be noted that a mean simply means the average of a set of numbers that are given.
Since the mean temperature for the first 4 days in January was 3°C. The rural temperature will be:
= 4 × 3°C
= 12°C
The mean temperature for the first 5 days in January was 1°C. The total temperature will be:
= 5 × 1°C
= 5°C
The temperature of the fifth day will be the difference between the temperature. This will be:
= 5°C - 12°C
= -7°C
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14.9 - 15.1 EVALUATE PLEASE.
Answer:
-0.2
Step-by-step explanation:
14.9-15.1= -0.2
To do equations like this in the beginning I used to switch the terms and then add a negative symbol in front of it
I would solve it like this
15.1-14.9
.2
And now since I switched the terms I change the sign to negative
-0.2
Hopes this helps please mark brainliest
each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite edge. the choice of the edge pairing is made at random and independently for each face. what is the probability that there is a continuous stripe encircling the cube?
The probability that there is a continuous stripe encircling the cube is 3/16.
A single, thin stripe is painted from the center of one edge to the center of the other edge on each face of a cube. Each face's edge pairing is selected independently and at random.
For each of the cube's six faces, there are two possible stripe orientations, resulting in a total of 2 x 6 = 64 possible stripe permutations. Since there are three sets of parallel faces, the stripe orientation for the remaining faces is determined uniquely by the pair of faces that does not contribute to the encircling stripe. Additionally, there are two possible orientations for the stripe on each face that is non-contributing.
A continuous stripe surrounds the cube as a consequence of a total of
3 * 2 * 2 = 12 stripe variations.
The necessary probability is 12/64, which equals 3/16.
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Can yall help me on this?
x-intercept is (-250, 0) and y-intercept is (0, 100)
What is x-intercept and y-intercept
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.
First, find x-intercept
For x-intercept it means y = 0
observe the graph and see the blue line cuts the x-axis when y = 0
We see, x = -250
so, the x-intercept is = (-250, 0)
Now, same thing do to find y-intercept
For y-intercept it means x = 0
observe the graph and see the blue line cuts the y-axis when x = 0
We see, y = 100
so, the y-intercept is = (0, 100)
Therefore, x-intercept is (-250, 0) and y-intercept is (0, 100).
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Let the function f be defined as p (x) = -5 (-3x + 4) and function g be
defined as m (x)= 5x - 2 (5x - 6). What value of x satisfies the
equations m (x)= p (x)?
If the functions are equal. Then the value of the variable 'x' will be 1.6.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let the capability f be characterized as p(x) = - 5(- 3x + 4) and work g be characterized as m(x) = 5x - 2(5x - 6).
If the functions are equal. Then the value of the variable 'x' will be given as,
m(x) = p(x)
- 5(- 3x + 4) = 5x - 2(5x - 6)
15x - 20 = 5x - 10x + 12
15x - 20 = - 5x + 12
20x = 32
x = 1.6
If the functions are equal. Then the value of the variable 'x' will be 1.6.
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The length of a living room is 12 feet and its width is 1012 feet. The length of the room is being expanded by x feet. What expression could you create from that problem?
Options C and E are correct. The expression can be written in the forms of
C. 10.5(12 + x) square feetE. (126 + 10.5x) square feetHow to solve for the expressionWe have the length of the room as 12 feet
The width of the room = [tex]10\frac{1}{2}[/tex] feet
The expansion of the = 12 +x
What is the area of a rectangle?
The area of a rectangle is given as lw = length x width
Hence we would have the following:
(12+x)10.5 = area
We would have to open the bracket as well
126 + 10.5x
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Complete question
1012 feet. The length of the room is being expanded by x feet. Choose an expression to represent the new area of the living room in square feet and the expanded form of the expression. Select all that apply.
A. 10.5(12x) square feet
B. (10.5 + 12 + x) square feet
C. 10.5(12 + x) square feet
D. 126x square feet
E. (126 + 10.5x) square feet
F. (22.5 + x) square feet
Can somebody help me on this please
Since it is labeled that this triangle has two equal sides, it is isosceles. Isosceles triangles' acute angles are always congruent, so we can infer that there are two angles with a measurement of 29 degrees. Knowing that all of the angles in a triangle add up to 180 degrees, we can set up this equation:
2*29 + 11x - 65 = 180
58 + 11x - 65 = 180
-7 + 11x = 180
11x = 187
x = 17
Knowing that "x = 17" we can find the measurement of the obtuse angle:
11*17 - 65
= 187 - 65
= 122
At the gym on Saturday, Reese ran 5 miles in the treadmill and then the completed 1 mile in the elliptical machine and burned 725 calories. On Sunday she ran 3 miles on the treadmill and completed 1 mile in the elliptical, and burned 505 calories. Write and solve a linear system to find the number of calories Reese burns on the machine
Answer:The equations are 5t + e = 725 and 3t + e = 505
Step-by-step explanation:Subtract equation (2) from equation (1) and you arrive at;
2t = 220
Divide both sides of the equation by 2
t = 110
Having calculated the value of t, substitute for the value of t into equation (1)
5t + e = 725
5(110) + e = 725
550 + e = 725
Subtract 550 from both sides of the equation
e = 175
The above calculations shows that the calories burned on each gym equipment are;
Treadmill = 110 per hour
Elliptical = 175 per hour
What is the inverse of this function? f(x)=1/3x-2
The inverse of the function f(x) = 1/3x-2 is f^-1(x) = (1 + 2x)/3x.
Inverse of a functionA function f is has an inverse if it is both one-to-one and onto.
Given the function f(x) = 1/3x-2
we replace f(x) with y and make x the subject of the formula to derive the inverse function f^-1(x) as follows ;
y = 1/3x - 2
by cross multiplication
3x - 2 = 1/y
add 2 to both sides of the equation
3x = 1/y + 2
3x = (1 + 2y)/y
divide both sides of the equation by 3
x = (1 + 2y)/y ÷ 3
x = (1 + 2y)/3y
So, f^-1(x) = (1 + 2x)/3x
Therefore, the inverse of the function f is derived by interchanging the value of x for y and vice versa, that is f^-1(x) = (1 + 2x)/3x.
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