Answer:
7/20Step-by-step explanation:
Frequency of Section 1 is 28 and total number of frequencies is 80.
P(Section 1) = 28/80 = 7/20Answer:
the frst person id wight!
Step-by-step explanation:
h(x) = -3(x²)
describe the transformation
Answer:
The parent function is the simplest form of the type of function given.
g
(
x
)
=
x
2
The transformation being described is from
g
(
x
)
=
x
2
to
h
(
x
)
=
−
3
x
2
.
g
(
x
)
=
x
2
→
h
(
x
)
=
−
3
x
2
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
h
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
h
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
h
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
h
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
In this case,
k
=
0
which means that the graph is not shifted up or down.
Vertical Shift: None
The graph is reflected about the x-axis when
h
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: Reflected
The graph is reflected about the y-axis when
h
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: Stretched
Compare and list the transformations.
Parent Function:
g
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: Reflected
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
image of graph
The parent function is the simplest form of the type of function given.
g
(
x
)
=
x
2
The transformation being described is from
g
(
x
)
=
x
2
to
h
(
x
)
=
−
3
x
2
.
g
(
x
)
=
x
2
→
h
(
x
)
=
−
3
x
2
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
h
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
h
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
h
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
h
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
In this case,
k
=
0
which means that the graph is not shifted up or down.
Vertical Shift: None
The graph is reflected about the x-axis when
h
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: Reflected
The graph is reflected about the y-axis when
h
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: Stretched
Compare and list the transformations.
Parent Function:
g
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: Reflected
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
image of graph
Step-by-step explanation:
Put the steps in order. *
5 points
1st 2nd 3rd 4th 5th
Get Constant on other side of equal sign (+ or -)
Combine Like Terms on EACH side of equations.
Get rid of Coefficient (divide or multiply)
Get Variable on one side of equal sign (+ or - )
Get rid of any grouping symbols -({[]}) - use Distributive Property
Answer:
5,4,1,3,2
Step-by-step explanation:
There's no problem doing these out of order.
Need help ASAP Tysm
Answer:
20
Step-by-step explanation:
Plug in the variables
2(-4)^2 + 4(-3)
32 + -12
= 20
A cafe sells smoothie bowls that are 4 ounces or larger, up to a maximum of 10
ounces. A 4 ounce smoothie bowl costs $5. Each additional ounce costs $0.75, and each
topping added to it costs $0.50.
Write an equation that represents the cost of a smoothie bowl. Be sure to specify what
the variables represent.
Answer:
5 + (.75 * x ) + y = z
Step-by-step explanation:
X = number of added ounces
Y = toppings added
Z = cost of smoothie bowl
$5 the cost of minimum bowl.
Then add that to the .75 cents multiplied by the number added ounces.
Then add that to the .50 if you get toppings.
The .50 equals the y but it could be 0 to so that's why I added Y.
Expand the expression 9(2t-8)
Answer:
18t-72
Step-by-step explanation:
Is 6.7825.. reapeating or terminating
You wrote "6.7825.."
Typically, a non-terminating decimal has three dots, so I'm not sure what is intended by only two dots.
As for repeating, a repeating pattern should be established before the ... if that is intended to be repeating.
So, 6.782578257825... would be a repeating decimal, while
6.7825... does not indicate any repeating pattern.
the difference of eight and twice a number
Answer:
8-2x
Step-by-step explanation:
What is the equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line represented by y=34x−8?
Answer:
The equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line is:
\(y=-\frac{1}{34}x+\frac{91}{17}\)Step-by-step explanation:
We know the slope-intercept form of the line equation
\(y=mx+b\)
where m is the slope and b is the y-intercept
Given the line
\(y=34x-8\)
comparing with the slope-intercept form of the line equation
The slope m = 34
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 34
Thus, the slope of the the new perpendicular line = – 1/m = -1/34 = -1/34
Using the point-slope form
\(y-y_1=m\left(x-x_1\right)\)
where m is the slope of the line and (x₁, y₁) is the point
substituting the values of slope = -1/35 and the point (12, 5)
\(y-y_1=m\left(x-x_1\right)\)
\(y-5=-\frac{1}{34}\left(x-12\right)\)
Add 5 to both sides
\(y-5+5=-\frac{1}{34}\left(x-12\right)+5\)
\(y=-\frac{1}{34}x+\frac{91}{17}\)
Therefore, the equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line is:
\(y=-\frac{1}{34}x+\frac{91}{17}\)In ΔABC, m∠B = 90°, cos(C) =
, and AB = 16 units.
Based on this information, m∠A =
°, m∠C =
°, and AC =
units.
A major credit card company requires monthly payments equal to or greater than 8% of the total balance.A consumer has a credit card balance of $320. Write an inequality that represents acceptable payment amounts.
Answer:
320 x 0.08 = X
In the case, a payment equal to or greater than $ 25.60 would be considered acceptable by the company.
Step-by-step explanation:
Given that a major credit card company requires monthly payments equal to or greater than 8% of the total balance, and a consumer has a credit card balance of $ 320, the following calculations must be performed to determine an inequality that represents acceptable payment amounts:
320 x 0.08 = X
25.6 = X
Thus, in the case, a payment equal to or greater than $ 25.60 would be considered acceptable by the company.
Please help me I need to answer this before tomorrow!
Answer:
Quadrant IV or D
Step-by-step explanation:
It is Quadrant IV or D, since it is a positive x (meaning it must be 1 or 4) and it has a negative y (so 3 or 4). You then find the common answer which is 4 or IV.
FILL IN THE BLANK. if it is impossible for events a and b to occur simultaneously, the events are said to be mutually exclusive. for such events, p(a or b) _________.
If it is impossible for events A and B to occur simultaneously, the events are said to be mutually exclusive. For such events, P(A or B) is equal to the sum of the individual probabilities of events A and B.
In other words, if A and B are mutually exclusive events, the probability of A or B occurring is equal to the sum of the probabilities of A and B individually.
Mathematically, P(A or B) = P(A) + P(B).
This holds true because when two events are mutually exclusive, the occurrence of one event excludes the possibility of the other event happening at the same time. Therefore, there is no overlap in the outcomes, and we can simply add their probabilities to calculate the probability of either event occurring.
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Mathematics for the practical man explaining simply and quickly all the elements of algebra, geometry, trigonometry, logarithms, coördinate geometry, calculus
"Mathematics for the Practical Man" is a book that aims to provide a simplified and quick explanation of various mathematical concepts such as algebra, geometry, trigonometry, logarithms, coordinate geometry, and calculus.
The book is targeted towards individuals who may not have a strong background in mathematics, but need to understand these concepts for practical purposes.
The book is divided into chapters that cover each topic in depth, providing clear explanations and examples for the reader to follow. The language used in the book is simple and easy to understand, without sacrificing the accuracy and rigour of the mathematical concepts being taught. Overall, "Mathematics for the Practical Man" is a useful resource for anyone who needs to quickly and easily learn or refresh their knowledge of key mathematical concepts.
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1.) Max is driving 42 miles per hour. A dog dog runs into the street and max reacts in about three quarters of a second. What is his approximate reaction distance
Answer: \(14.07\ m\)
Step-by-step explanation:
Given
Max is driving at a speed of \(42\ mph\)
It took him three-quarters of a second i.e. \(0.75\ s\)
Speed in meter per second is \(18.77\ m/s\)
Distance is given by
\(d=v\times t\)
Reaction distance is
\(d=18.77\times 0.75=14.07\ m\)
what is the answer to
3n=n-2
Answer:
- 1
Step-by-step explanation:
Step 1:
3n = n - 2
Step 2:
2n = - 2
Answer:
n = - 1
Hope This Helps :)
Find a particular solution to the differential equation y′′ + 3y = -9
To find a particular solution to the given differential equation, we can assume a constant value for y and solve for it.
The given differential equation is y′′ + 3y = -9. To find a particular solution, we assume y = k, where k is a constant. Substituting this assumption into the differential equation, we get k'' + 3k = -9. Since k is a constant, its second derivative is zero, so the equation simplifies to 3k = -9. Solving for k, we find k = -3.
Therefore, a particular solution to the given differential equation is y = -3. This means that for this particular value of y, the second derivative of y is zero, and when we substitute it into the differential equation, it satisfies the equation.
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Draw a ratio box for this problem. Then solve the
problem using a proportion.
her piano students and that 40% of the
Ms. Smith noted that there were 12 girls among
students were boys. How many piano students
did Ms. Smith teach?
There are total 30 students in the piano class.
What is Ratio and Proportion ?When a number can be divided by another number then they can be written as p : q , when two ratios can be equated using an equal sign then they are said to be in proportion.
It is given that the total number of girls is 40% of the total students
The ratio of total students to girls is 100 :40
= 10 :4
= 5 : 2
It is also given that in the total number of students 12 were girls
Let total students be x
Then the ratio is x : 12
As both the ratio are same and so can be equated and the proportion will be
5 : 2 = x : 12
5/2 = x /12
x = 30
Therefore there are total 30 students in the piano class.
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3/6 over 4 simplified?
Answer:
I think its 1/8
Step-by-step explanation:
Keep Switch Flip
Keep the 3/6 switch the symbol and flip the 4
3/6 x 1/4 = 1/2 x 1/4 = 1/8
From a point on the ground the angle of elevation of the top of a tower is x°. Moving 150 meters away from that point the angle of elevation was found to be y° .If tan x=3/4 and tan y=5/7 find the height of the tower.
Answer:
2250m
Step-by-step explanation:
Step 1
Since
Hence,
tan x = 3/4
tan y=5/7
tan x = BA/ CA where BA = height and CA = distance
3/4 = h/ d
4h = 3d
h = 3d/4.......... Equation 1
tan y = BA / DA + 150m
5/7 = h/d + 150
7 × h = 5(d + 150)
7h = 5d + 750............ Equation 2
Since h = 3d/4
7(3d/4) = 5d + 750
21d/4 = 5d + 750
Multiply both sides by 4
21d = 4(5d + 750)
21d = 20d + 3000
21d -20d = 3000
d = 3000
Distance (d) = 3000m
Substitute 3000m for d in equation 1
h = 3d/4
h = 3 × 3000/4
h = 2250m
Answer:
2250mStep-by-step explanation:
\(tangent=\dfrac{opposite}{adjacent}\)
We have:
\(\tan x^o=\dfrac{3}{4}\\\\\tan y^o=\dfrac{5}{7}\)
By definition of tangent, we have:
\(\tan x^o=\dfrac{AB}{AC}\\\\\tan y^o=\dfrac{AB}{AC+150}\)
Therefore we have the system of equations:
\(\left\{\begin{array}{ccc}\dfrac{AB}{AC}=\dfrac{3}{4}&(1)\\\\\dfrac{AB}{AC+160}=\dfrac{5}{7}&(2)\end{array}\right\)
From (1)
\(\dfrac{AB}{AC}=\dfrac{3}{4}\) cross multiply
\(3AC=4AB\) divide both sides by 3
\(AC=\dfrac{4AB}{3}\)
Substitute it to (2):
\(\dfrac{AB}{\frac{4AB}{3}+150}=\dfrac{5}{7}\\\\\dfrac{AB}{\frac{4AB}{3}+\frac{3\cdot150}{3}}=\dfrac{5}{7}\\\\\dfrac{AB}{\frac{4AB}{3}+\frac{450}{3}}=\dfrac{5}{7}\\\\\dfrac{AB}{\frac{4AB+450}{3}}=\dfrac{5}{7}\\\\AB\cdot\dfrac{3}{4AB+450}=\dfrac{5}{7}\)
\(\dfrac{3AB}{4AB+450}=\dfrac{5}{7}\) cross multiply
\((3AB)(7)=(5)(4AB+450)\\\\21AB=(5)(4AB)+(5)(450)\)
\(21AB=20AB+2250\) subtract 20AB from both sides
\(AB=2250\)
Such a tower height is rather impossible, but this is the solution.
as a seismologist, janet understands the devastating effects that earthquakes can have. so, she keeps her basement stocked with canned food, like chili. janet buys cans of chili from an online retailer that charges a shipping fee plus the cost of each can of chili. this table shows the relationship between the number of cans of chili janet buys, x, and the total cost (in dollars), y. x (cans) y (dollars) 12 $26.40 44 $56.80 66 $77.70 100 $110 according to the values in the table, do x and y have a proportional relationship?
As a seismologist, Janet understands the devastating effects that earthquakes can have. so, she keeps her basement stocked with canned food, like chili. This table shows the relationship between the number of cans of chili Janet buys, x, and the total cost (in dollars), y.
\(\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}\)
According to the values in the table, x and y have not a proportional relationship.
Prove x and y have a proportional relationshipTable
\(\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}\)
Specifies the gradient (m) in rows 1 and 2
m₁ = \(\displaystyle \frac{56.80 - 26.40}{44-12}\)
m₁ = \(\displaystyle \frac{30.40}{32}\)
m₁ = \(\displaystyle \frac{19}{20}\)
Specifies the gradient (m) in rows 2 and 3
m₂ = \(\displaystyle \frac{77.70 - 56.80}{66-44}\)
m₂ = \(\displaystyle \frac{20.9}{22}\)
Because the values of m₁ and m₂ are not the same \(\displaystyle \frac{19}{20}\) ≠ \(\displaystyle \frac{20.9}{22}\), then x and y have not a proportional relationship.
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How long will it take any sum to double itself a. With a 14 percent simple interest rate? b. With a 14 percent interest rate, compounded annually? c. With a 14 percent interest rate, compounded continously?
a. Simple interest: around 14.29 years.
b. Annual compound interest: about 5 years.
c. Continuous compound interest: roughly 4.95 years.
a. With a 14 percent simple interest rate, the time it takes for a sum to double can be calculated using the formula:Time = (100 / interest rate) * 2
In this case, the interest rate is 14 percent, so the time it takes for the sum to double is:Time = (100 / 14) * 2 = 14.29 years (approximately).
b. With a 14 percent interest rate compounded annually, the time it takes for a sum to double can be calculated using the compound interest formula:Time = log(2) / log(1 + (interest rate / 100))
Substituting the values, the time it takes for the sum to double is:
Time = log(2) / log(1 + (14 / 100)) = 5.00 years (approximately).
c. With a 14 percent interest rate compounded continuously, the time it takes for a sum to double can be calculated using the formula:
Time = ln(2) / (interest rate / 100)
Using the values, the time it takes for the sum to double is:
Time = ln(2) / (14 / 100) = 4.95 years (approximately).
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estimate the error that is made by approximating the sum of the given series by the series the fitst 5 terms 1/k^3
The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.
To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.
The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.
That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.
The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.
The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.
The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.
So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.
The error involved in this approximation is very small and can be neglected.
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1. Solve the system by the elimination method.
3x−5y=4
−9x+3y=−24
A. (2, −2)
B. (3, 1)
C. (1, −1)
D. (8, 4)
2. Manny says he should multiply the first equation in the system of equations below by 3 and the second equation by 2, then add to eliminate x. Is there a more efficient way to solve this system? Explain your answer.
−2x+y=15
3x+4y=−12
A. No, there isn't a more efficient way to solve this system.
B. Yes, a more efficient way is to multiply the first equation by −4
add to eliminate y, then solve for x.
C. Yes, a more efficient way is to multiply the first equation by −4
add to eliminate x, then solve for y.
D. Yes, a more efficient way is to multiply the first equation by 4
add to eliminate y, then solve for x.
Answer:
x = 3 and y = 1
Step-by-step explanation:
A) most efficient way is to multiply the first equation by 3 to eliminate the 'x' terms and get 9x - 15y = 12
if you add this to -9x + 3y = -24 you will get -12y = -12
y = 1
substitute 1 for 'y' to get 'x': 3x - 5 = 4
3x = 9
x = 3
When you listen to the sound of a bouncing ping-pong ball that has been dropped onto a cement floor, what mathematical pattern do you hear? Explain,
A drop of water is denser than a ping-pong ball.
Usually, water is made of particles that are firmly pressed together. In differentiation, plastic (the material ping pong balls are made of) may be a lightweight fabric and the particles are not as firmly stuffed together.
The thickness of a ping pong ball is 0.0840 g/cm³, though water’s thickness is 997 kg/m³. Subsequently, ping pong balls aren’t about as thick as water and will continuously coast and surface greatly quickly.
The ping pong ball appears to oppose gravity and coast within the air.
Ping-pong balls drift within the water since they are amazingly lightweight, empty, and filled with air. Too, the water’s surface pressure makes it simple for the ping pong ball to drift.
In expansion, water is denser than ping pong balls, making them look for the most noteworthy point of water.
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The sound which we hear when the pig pong ball is bounced on the floor
is 19.48 DB
The repeating of sounds, especially in rhyme, is the form of repetition that most people connect with poetry. Alliteration, assonance, and onomatopoeia are other sound patterns in poetry that give additional meaning in addition to rhyme. Every one of these audio elements has a certain purpose in a poem.
a) \(\sum \ log(n)\)
by expanding the series for each value of n is
log (1) + log (2) + log(3) + log (4) + ......... + log ( 96)
simplify the expanded form we get
0 + 0.3010 + 0.4771+0.6020 ......................... + 1.982
=> 149.9963
b) \(\sum_{n=0}\) to infinity \(\sqrt{0.9^n}\)
formula for the sum of number in geometric progression
is a/1-r
to find the ratio of the successive terms
plugging into the formula
r = \(\frac{a_{n+1}}{a_n}\)
r = \(\frac{\sqrt{0.9^{n+1}} }{\sqrt{0.9^n} }\)
=> r = \(\frac{\sqrt{0.9^n \times 0.9} }{\sqrt{0.9^n} .1}\)
=> r = \(\frac{\sqrt{0.9} }{1}\)
=> r = \(\sqrt{0.9}\)
=> a = \(\sqrt{0.9^0}\)
=> a = \(\sqrt{1}\)
=> a= 1
by applying the formula having the value a =1 is
\(\frac{1}{1-\sqrt{0.9} }\)
rationalize the denominator by multiplying with \(1+\sqrt{0.9}\)
=> \(\frac{1+\sqrt{0.9} }{(1-\sqrt{0.9} ) (1+\sqrt{0.9}) }\)
=> 19.4868
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The population of a municipality in the beginning of 2071 B.S. was 1,80,000 and at
the end of 2073 B.S. was 2,39,580. Find the rate of growth of population per year.
what is the mass of a cubic meter of air at room temperature (20°c)?
The mass of a cubic meter of air at room temperature (20°C) depends on various factors such as atmospheric pressure and humidity. However, as a rough estimate, at standard atmospheric conditions, the mass of dry air in a cubic meter is approximately 1.2 kilograms.
What is cubic meter?
A cubic meter is a unit of volume in the metric system. It represents the amount of space occupied by a cube that measures one meter on each side. It is commonly used to measure the volume of solids, liquids, or gases.
The mass of air can be calculated by considering its density. At standard atmospheric pressure (101.325 kilopascals) and temperature (20°C), the approximate density of dry air is about 1.2 kilograms per cubic meter. This value may vary depending on factors such as altitude, humidity, and temperature deviations from the standard conditions.
It's worth noting that including water vapor in the air would increase the mass further. Therefore, the given estimate of 1.2 kilograms represents the mass of dry air, neglecting the presence of water vapor.
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please finish these 4 I need help pls
Find the slope and y -intercept of each line.. y=0.4-0.8 x
The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Given: y = -0.8x + 0.4
As we know that the slop-intercept form of the equation of a line is given by: y = mx + c, where
m = slope of the linec = y-intercept of the lineOn comparing the given equation of line with the above form of equation of line, we get: m = -0.8 and c = 0.4.
Hence, The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.
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factorise 12d²-19d+5
Answer:
4d99982726629161619172928227
Step-by-step explanation:
di ko alam Ang sagot
Answer two questions about Equations A and B: A. 5x-2+x=x-4 B. 5x+x=x-4 How can we get Equation B from Equation A?
Answer:
The answer is below
Step-by-step explanation:
To be able to get equation B from equation A, we have to compare equation A with equation B. Given that equation A. is 5x-2+x=x-4 and equation B is 5x+x=x-4.
Equation B: 5x+x=x-4.
Equation A: 5x-2+x=x-4.
Simplifying equation A to be in the form of equation B:
5x -2 + x = x - 4
Adding 2 to both sides:
5x + x -2 + 2 = x - 4 + 2
5x + x = x - 4 + (+2)
= equation A + 2
But 5x+x=x-4 = equation A
Therefore Equation B is the same as Equation A + 2
Answer:ADD/SUBTRACT A QUANTITY TO/FROM ONLY ONE SIDE
And part 2: is NO