If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
What is a quadrilateral?A quadrilateral is a closed shape that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The sum of quadrilateral interior angles is always 360 degrees. A quadrilateral is a four-sided polygon with four edges and four corners in geometry.
A parallelogram is formed when both pairs of opposite sides of a quadrilateral are congruent. A parallelogram is formed when one pair of opposite sides of a quadrilateral are parallel and congruent.
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find an equation of the tangent plane to the given parametric surface at the specified point. x = u v, y = 8u2, z = u − v; (2, 8, 0)
The equation for the normal line B gives us :
L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R
Find the solution ?
Full question is:
Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7e(xyz) at a specified point (0, 0, 7)
If we have a level surface, then it will give us
f(x,y,z) = x+y+z = 7e(xyz). where f is the function of the x, y, and z coordinates.
Now let us calculate the ∇ gradient of f at point (0,0,7):
∇ = (fx,fy,fz) = (1−7yz,1−7xz,1−7xy)
= (1, 1, 1)
We get the equation for the tangent plane A:
A: 1(x−0) + 1(y−0) + 1(z−7)=0
This can also be written as:
x+y+z = 7 ------------------------------------------------------------------(a)
The equation for the normal line B gives us :
L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)
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Line segment su is dilated to create s'u' using point q as the center of dilation. the scale factor of the dilation is
The scale factor of the dilation is 2 which can be shown in the details given below.
In geometry, a line segment is bounded with the aid of using awesome factors on a line. Or we are able to say a line phase is a part of the road that connects factors. A line has no endpoints and extends infinitely in each the course however a line phase has constant or particular endpoints.
QS : QS'
= 4 : 8
= QU : QU'
= 5 : 10
= 1 : 2
Then the scale factor is of the dilation is 2 (magnification).
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Complete question
Line segment SU is dilated to create S'U' using point Q as the center of dilation.
The scale factor of the dilation is:
3 Question* (1 Point) 3) The volume of Lake Superior is approximately 1.22 x 10 4 cubic kilometers. The volume of the Pacific Ocean is approximately 6 x 10 8 cubic kilometers. Write About It! About how many times larger is the Pacific Ocean than Lake Superior? Write a mathematical argument that can be used to defend your solution.
Answer:
The Pacific Ocean is approximately 4.9 times larger than Lake Superior in terms of volume. This can be shown through the following mathematical argument:
First, divide the volume of the Pacific Ocean by the volume of Lake Superior to determine the size ratio:
6 x 10^8 cubic kilometers / 1.22 x 10^4 cubic kilometers = 4.9
This shows that the Pacific Ocean is approximately 4.9 times larger than Lake Superior.
To defend this solution, we can use the concept of ratio and proportion. We know that the ratio of the volumes of the two bodies of water is equal to the ratio of their respective sizes. Therefore, by finding the ratio of the volumes, we can determine the size ratio.
In this case, the ratio of the volumes is 6 x 10^8 cubic kilometers / 1.22 x 10^4 cubic kilometers, which simplifies to 4.9. This means that the Pacific Ocean is 4.9 times larger than Lake Superior in terms of volume.
This solution can be further supported by the fact that the Pacific Ocean is the largest ocean in the world, while Lake Superior is one of the Great Lakes and is much smaller in size.
Step-by-step explanation:
SELF EXPLANATORY
define the level of significance. multiple choice it is the probability of a type ii error. it is the probability of a type i error. it is a z-value of 1.96. it is the beta error.
By information provided in the question, we can say that It is the probability of a Type I error.
what is probability?The proportion of favorable outcomes to all possible outcomes for an event is known as the probability. The quantity of positive outcomes in an experiment with 'n' outcomes is represented by x. The following equation can be used to determine the likelihood of an event:
Probability (event) = positive outcome / overall outcome = x/n
It refers to the likelihood of a Type I mistake.
The likelihood that a Type I error will occur, or the likelihood that a null hypothesis will be rejected when it is true, determines the degree of significance.
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like terms onto each other to simplify fully.
6+3x-6+4+5y
The simplified form of the given expression is 3x+5y+4. Here only the constants are simplified since there are no like terms in the expression.
What are like terms?An expression is the combination of terms with any of the arithmetic operations in between them. Here the terms are formed by a coefficient and a variable.In an expression, if two or more terms with the same variable with the same power are said to be like terms otherwise they are said to be unlike terms.The like terms undergo addition and subtraction operations.But the unlike terms can't be added or subtracted.Calculation:The given expression which is to be simplified is 6+3x-6+4+5y.
Here to simplify the given expression, we need to add or subtract the like terms.
In the given expression, the variables x and y.
They are unlike terms. So, we cannot add or subtract them. But there are three constants. Then, we can add or subtract them.
Thus, the simplified expression for the given expression is
6+3x-6+4+5y = 3x+5y+4
Here 6 and -6 are added so that we get 0.
Hence the answer is 3x+5y+4.
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. finding numbers the sum of two nonnegative numbers is 20. find the numbers if (a) the sum of their squares is as large as possible; as small as possible. (b) one number plus the square root of the other is as large as possible; as small as possible.
When the sum of their squares is as largest as possible the numbers are 0 and 20, when the sum of their squares is as small as possible, the numbers are 10 and 10
Sum of the two numbers = 20
First we have to find the sum of their squares is as large as possible
Consider the first number as x and second number as y
To get the largest values the value of x or the value of y should be zero
Then the two numbers are 0 and 20
To get the small as possible
x^2 + (20-x)^2 = x^2 + x^2 - 20x +400
= 2x^2 -20x + 400
= 2(x^2 - 10x + 100)
The one number will be 10 and the other number will be 10
Therefore, to get the largest value the numbers will be 0 and 20 and to get the smallest value the numbers will be 10 and 10
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Use I=PRTI=PRT to find the total amount in the savings account. Type in "money form".
$4500.00 at 8% for 3 years
The total amount earned after 3 years at 8% rate is $5580
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money.
Given that, $4500 is invested at 8% for 3 year,
SI = PxRxT/100
= 4500x8x3/100
= 1080
Amount = interest + principal
Amount = 1080 + 4500 = 5580
Hence, The total amount earned after 3 years at 8% rate is $5580
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Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
Please answer all four questions (they are simple and go with the diagram)
(1) The measure of the angle CFD = 48°.
(2) The measure of the angle AFE = 48°.
(3) Pair of supplementary angles: Angle BFC and angle CFD.
(4) Pair of adjacent angles: Angle AFB and angle BFD.
What are the properties of angles?
The angle properties of lines are:
Vertically opposite angles are equal, for example, a = d, b = c.
Adjacent angles add to 180, for example, a + b = 180, a + c = 180. Corresponding angles are equal, for example, a = e, b = f, c = g, d= h.
(2) In the given figure, m∠BFC = 42°
By using the property of linear pair, we can write
∠BFC + ∠CFD = 180
42 + ∠CFD = 180
∠CFD = 58.
(2) Angle CFD and angle AFE are opposite angles and opposite angles are same in measurement so we can write
m∠AFE = 58°.
(3) Pair of supplementary angles: Angle BFC and angle CFD.
(4) Pair of adjacent angles: Angle AFB and angle BFD.
Hence,
(1) The measure of the angle CFD = 48°.
(2) The measure of the angle AFE = 48°.
(3) Pair of supplementary angles: Angle BFC and angle CFD.
(4) Pair of adjacent angles: Angle AFB and angle BFD.
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for each graph caculate the slope of each line
Answer:
m=-1/3
Step-by-step explanation:
How do you convert 2−2i to polar form?
2 - 2i can be written in polar form as [tex]2\sqrt{2} \ cis\frac {-3\pi}{4}[/tex]
To convert a complex number in Cartesian form (such as 2 - 2i) to polar form, you can use the following steps:
Find the magnitude (or absolute value) of the complex number. This is the distance from the origin to the point representing the complex number in the complex plane. The magnitude of 2 - 2i is approximately 2.83.Find the argument of the complex number. This is the angle between the positive real axis and the line connecting the origin to the point representing the complex number in the complex plane. To find the argument, you can use the inverse tangent function (also known as arctangent or atan). The argument of 2 - 2i is approximately -135 degrees, or -2.356 radians.Combine the magnitude and argument to express the complex number in polar form. In polar form, a complex number is written as "magnitude (angle)", where the angle is expressed in either degrees or radians. So, the polar form of 2 - 2i is approximately 2.83 (-135 degrees) or 2.83 (-2.356 radians).To learn more about complex number, visit:
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2.5kg of potatoes cost £1.40
work out the cost of 4.25kg
The 2.5kg of potatoes cost £1.40 so the cost of 4.25 kg of potatoes is £2.38.
What is Cost ?A cost is an outlay needed to create, market, or prepare an asset for regular use. In other words, it's the cost incurred to produce a good, buy inventory, sell goods, or prepare equipment for use in a business process.
Given,
2.5 kg of potatoes = £1.401 kg of potatoes
cost = 1.40/2.5
= £0.56
To find the cost of 4.25 kg of potatoes is: Then,
1 kg = £0.564.25 kg
= 0.56 x 4.25
= £2.38
Thus from the above conclusion we can say that the cost is £2.38.
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I need to simplify the exponent for my math test asap.
An element with mass 420 grams decays by 11.8% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram
An element with mass 420 grams decays by 11.8% per minute. the amount of the element remaining after 16 minutes is 56.3 grams
What is an exponential function?This is a type of function that are of 3 main parts
the starting or initial value base function the exponentsA mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.
Considering the given problem,
the starting = 420 grams
the base = 1 - r = 1 - 11.8% = 1 - 0.118 = 0.882
the exponents = 16
amount remaining = 420 (0.882)^16
= 56.330895
= 56.3 to the nearest tenths
the amount left is 56.3 g
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20
Use the box and whisker plot to answer the following question.
73
81 84
70
→
65 70 75
80
Low temperatures (°F)
85
87
王
90
What is the interquartile range IQR of the data set? (IQR = Q3 - Q1)
The interquartile range IQR for the given data set is IQR=10
What is block and whisker plot?A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.
How do you calculate box and whisker plot?Finding the median, lower quartile, and upper quartile of a given set of data (Q2, Q1, and Q3) is the first stage in creating a box-and-whisker figure. Now that you know how to calculate the interquartile range (IQR). The distance between the upper and lower quartiles is known as the interquartile range.
Lower data set:
70 73 81 84
Q1=73+81/2=77
Middle data set
65 70 75 80
Q2= 70+75/2=72.5
Upper data set
85 87 90
Q3=87
IQR=Q3-Q1=87-77=10
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e altitude of a triangle is increasing at a rate of 1 cm!min while the area of the triangle is increasing at a rate of 2 cm !min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area i
The base of the triangle is decreasing at the rate of 1.6 cm/min.
Given
dh/dt = 1 cm/min
dA/dt = 2 cm2/min
When A = 100 cm2, h = 10 cm
We know that
A = 1/2 × b × h
b = 20 cm
Let us differentiate both sides
dA/dt = 1/2 [b dh/dt + h db/dt]
Substituting the values
2 = 1/2 [20 × 1 + 10 × db/dt]
By further simplification
4 = 20 + 10 db/dt
db/dt = -1.6 cm/min
Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.
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Calculate the distance between the points Q=(1,0) and B= (-2.-3) in the coordinate plane.
Round your answer to the nearest hundredth.
Answer: QB≈4.24
Step-by-step explanation:
Q(1,0) B(-2,-3) QB=?
[tex]\boxed{L=\sqrt{(x_2-x_1)+(y_2-y_1)^2} }\\\\x_1=1\ \ \ \ x_2=-2\ \ \ \ y_1=0\ \ \ \ y_2=-3[/tex]
Hence,
[tex]QB=\sqrt{(-2-1)^2+(-3-0)^2} \\\\QB=\sqrt{(-3)^2+(-3)^2} \\\\QB=\sqrt{9+9} \\\\QB=\sqrt{18} \\\\QB=\sqrt{9(2)} \\\\QB=\sqrt{3^2(2)} \\\\QB=3\sqrt{2} \\\\QB\approx4.24[/tex]
queuing system a has a utilization of 80 percent, and queuing system b has a utilization of 90 percent. both have a single server. say the utilization of both systems increases by 5 percent; that is, a increases from 80 percent to 85 percent while b increases from 90 percent to 95 percent. which system is likely to experience the bigger change in the average time in queue?
For queuing system B, the average time in queue ids going to change significantly as a result of increased utilization.
This is because queuing system B is initially heavily loaded and has less capacity to handle more requests. As a result, an increase in utilization can cause a significant increase in average queue latency on system B compared to system A.
Average Queue Time is a measure of the time a customer or request spends being processed by a server. It is affected by several factors such as server load, customer or request arrival rate, and server service rate. As the load on the queuing system increases, it means that the server is being used more frequently and is no longer available to process incoming requests. This will increase the average time in the queue as more requests accumulate and have to wait to be processed. The greater the increase in occupancy, the greater the impact on average latency.
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Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x=98.13, y=100.6, r=0.904, P-value=0.000, ŷ=14.68+0.88x, where x represents the IQ score of the twin born first. Find the best predicted value of ModifyingAbove y with caret given that the twin born first has an IQ of 104? Use a significance level of 0.05.
The predicted value of the twin born first has an IQ of 104 is 106.2..
We have given that,
sample size n = 10
x = 98.13
y = 100.6
r = 0.904
p-value = 0.000
y'= 14.68 + 0.88x
significance level = 0.05
and we have to find predicted value of the twin born first has an IQ of 104.
We know that x represents the IQ score of the twin born first.
Therefore value of x is 104.
Hence the predicted value P will be,
P = 14.68 + 0.88(104)
= 14.68 + 91.52
P = 106.2
Therefore the best predicted value of the twin born first has an IQ of 104 is 106.2.
The positive predicted value is the probability that a test gives result for a true statistic. The negative predictive value is the probability that a test gives a false result for a false statistic.
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what number multiplied by 3 and subtracted by 2 equals 40
The number multiplied by 3 and subtracted by 2 equals 40 is 14.
Linear Equation:The Equation that is used to find an unknown value is known as Linear Equation. To find an unknown value or quantity, first form a linear equation according to the conditions that are given the problem, here we use variables like x, y, etc. to represent the unknown value.
Here we have
A Number is multiplied by 3 and subtracted by 2 equals 40
Let the number be x
Given that 'x' is multiplied by 3 (3x); subtracted by 2 (3x-2) equals to 40
=> 3x - 2 = 40
Add 2 on both sides
=> 3x - 2 + 2 = 40 + 2
=> 3x = 42
Divide by 3 into both sides
=> 3x/3 = 42/3
=> x = 14
Therefore,
The number multiplied by 3 and subtracted by 2 equals 40 is 14.
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8y−5<3 = ??
please help me im so confused
Answer:
It looks like you have an inequality equation with one variable, but the equation is incomplete. In order to solve the inequality, we need to have a complete equation with a left-hand side and a right-hand side.
For example, if we wanted to solve the inequality 8y - 5 < 3, we could complete the equation by adding 5 to both sides:
8y - 5 + 5 < 3 + 5
8y < 8
Then, we could divide both sides of the inequality by 8 to solve for y:
8y/8 < 8/8
y < 1
Therefore, the solution to the inequality 8y - 5 < 3 is y < 1.
peterson's solution is a valid solution to the critical section problem on modern multi-core systems. true false
Therefore, Peterson's solution is not a valid solution to the critical section problem on modern multi-core system so it is false.
What is multi core system?A multicore processors is an electronic component that has two or more processor cores attached for higher performance and lower power consumption. These processors also enable more efficient execution of numerous activities, such as with parallelization and multithreading.
Here,
It is because of the following disadvantages:
Although Peterson's technique is effective for two processes, it is the best plan for the important part in user mode.
Additionally, this solution involves busy waiting, wasting CPU time. So that “SPIN LOCK” problem can emerge. And any busy waiting solution may encounter this issue.
Therefore, Peterson's solution is not a valid solution to the critical section problem on modern multi-core system so it is false.
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a farmer plans to fence a rectangular pasture adjacent to a river (see figure). the pasture must contain 405,000 square meters in order to provide enough grass for the herd. no fencing is needed along the river. what dimensions will require the least amount of fencing?
If the farmer plans to fence a rectangular pasture adjacent to a river than the dimensions that is required for the least amount of fencing is length = 900 m and width = 450 m .
In the question ,
it is given that ,
the farmer is planning to fence the rectangular pasture adjacent to the river ,
the area of the pasture is = 405000 square meter .
let the length of the pasture = "y"
let the width of the pasture be = "x" ,
since only three side is fenced , the required perimeter is = 2x + y ;
given that area ⇒ x*y = 405000
y = 405000/x ;
So , the perimeter equation becomes ;
p = 2x + 405000/x
differentiating and equation to 0 we get ;
p' = 2 - 405000/x²
2 - 405000/x² = 0 ;
2x² = 405000
x² = 202500 ;
x = 450 , putting in perimeter equation ,
we get ; y = 900 .
Therefore , the dimension is length = 900 m and width = 450 m.
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An oil company fills 1 over 12 of a tank in 1 over 4 hour with gasoline. At this rate, which expression can be used to determine how long it will take for the tank to fill completely? (1 point)
Group of answer choices
1 over 4⋅ 1 over 12
1 over 12⋅ 4
1 over 4⋅ 12
12 ⋅ 4
The expression that can be used to determine how long it will take for the tank to fill completely is C. 1 over 4 . 12.
How to illustrate the rate?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.
In this case, the oil company fills 1 over 12 of a tank in 1 over 4 hour with gasoline.
The rate will be:
= 1/4 ÷ 1/12
= 1/4 × 12
= 3
The correct option is C
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there
Write an equivalent expression for 6a + a + 8b + b.
A
Answer:
7a+9b
Step-by-step explanation:
If f(x) = (x ^ 2 - x + 1)/(x - 1) find f(- 1/2)
Answer:
[tex] \frac{7}{6} [/tex]
Find the 21st term in the arithmetic sequence.
3, 7, 11, 15, 19, ...
The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.
What is the nth term of an arithmetic series?The nth term of an arithmetic sequence is calculated by the formula
aₙ = a + (n - 1) · d
Here the first term is 'a' and the common difference is 'd'.
Calculation:The given sequence is an arithmetic sequence.
3, 7, 11, 15, 19, ....
So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.
Thus, the required 21st term in the sequence is
a₂₁ = 3 + (21 - 1) × 4
⇒ a₂₁ = 3 + 20 × 4
⇒ a₂₁ = 3 + 80
∴ a₂₁ = 83
So, the 21st term in the given arithmetic sequence is 83.
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Please help!!
Find the y-intercept
Answer:
-2,0
very simple it is so easy
the area of the compound shape below is 30mm^2.
Calculate the value of x.
If your answer is a decimal, give it to 1 d.p
Answer:
x = 2.5 mm-------------------------------------
Set equation for area of given shape:
x*4 + x*(2x + 3) = 30Simplify and solve for x:
4x + 2x² + 3x = 302x²+ 7x = 302x² + 7x - 30 = 0x = [-7 ± √(7² - 4*2*(-30))] /4x = (-7 ± √289)/4x = (-7 ± 17)/4x = (10/4) and x = (- 24)/4 (discarded as negative number for the segment length)x = 2.5 mmAnswer:
x = 2.5 mm
Step-by-step explanation:
A compound shape is made up of two or more basic shapes.
From inspection of the given compound shape, we can see that it is made up of two rectangles.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a rectangle}\\\\$A=w \cdot l$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]
Dimensions of the smaller rectangle:
w = xl = 4 mmDimensions of the larger rectangle:
w = xl = (2x + 3) mmTherefore, the equation for the area of the compound shape is:
[tex]\begin{aligned}\implies \textsf{Area}&=x \cdot 4 + x \cdot (2x+3)\\&=4x+x(2x+3)\\&=4x+2x^2+3x\\&=2x^2+7x\end{aligned}[/tex]
Given the area of the compound shape is 30 mm², substitute this value into the found equation for area and solve for x:
[tex]\begin{aligned}\implies 2x^2+7x &=30\\2x^2+7x-30&=0\\2x^2+12x-5x-30&=0\\2x(x+6)-5(x+6)&=0\\(2x-5)(x+6)&=0\\\\2x-5&=0 \implies x=2.5\\x+6&=0 \implies x=-6\end{aligned}[/tex]
As length is positive, x = 2.5 mm only.
The word problem below has too little information. Read carefully, then
choose the fact or facts needed to solve the problem.
In the reptile tent, there are albino alligators, saltwater crocodiles, and
freshwater crocodiles. How many more crocodiles than alligators are there in
the reptile tent?
A. All 6 crocodiles were in one large pool.
B. The two alligators were completely white.
C. Albino alligators are very rare.
D. Freshwater crocodiles have thin snouts.
C. Albino alligators are very rare.
What is crocodiles ?
Crocodiles are large reptiles found in tropical regions of Africa, Asia, the Americas and Australia. They are members of the order Crocodilia, which also includes caimans, gharials and alligators.
crocodiles are more than alligators in the reptile tent because Albino alligators are very rare. according to the passage there are more types of crocodiles ans less alligators.
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-4-0.2x+11=-0.8x+10
please help meeeeeee i need the answerrrr
The solution of the expression - 4 - 0.2x + 11 = - 0.8x + 10 is 28.33.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A numerical expression and we have to solve for x or find the value of x.
- 4 - 0.2x + 11 = - 0.8x + 10.
- 0.2x - 7 = - 0.8x + 10.
- 0.2x + 0.8x = 10 + 7.
0.6x = 17.
x = 17/0.6.
x = 28.33.
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