The equation 2(x - 4) = 2x - 8 has infinitely many solutions.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is 2(x - 4) = 2x - 8.
Solving this,
Using the distributive property, a (b + c) = ab + ac, 2(x - 4) = (2 × x) - (2 × 4).
Substituting in the original equation,
(2 × x) - (2 × 4) = 2x - 8
2x - 8 = 2x - 8
2x - 2x = -8 + 8
0 = 0
Right hand side and left hand side are equal if we put any value for x.
So it has infinitely many solutions for x.
Hence the given equation has infinitely many solutions.
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A 7meter flog poce costs a shadow of 5meter. Calculate height of an electric pole that will cost a shadow of 10m under the same condition
The height of the electric pole in order to cast a shadow of 10 m in the same condition as to be 14 m.
The flog poce cast a shadow of 5 metre and itself as a height of 7 m.
Now we have to find the height of an electric pole that will cast the shadow of length 10 m under the same conditions.
The word under the same condition means that the angle of elevation will be same in both the cases, so, we can use the tan theta here,
Tan A = perpendicular/base
Tan A will be equal for both.
Tan A = 7/5
Tan A = H/10
H is the height of the electric pole.
7/5 = H/10
H = 14m
The height of the electric pole will be 14 m.
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I need help, Find the volume of this object. Use 3 for Pi.
The volume of the given 3 - D figure is 156.36 cubic inches.
What is volume?A volume is a collection of a three dimensional coordinate points enclosed by a two dimensional coordinate points.
Given is the 3 - D figure as shown in the image.
We can write the volume as -
V = πr²h/3 + lbh
V = (3.14 x 3 x 3 x 8)/3 + (9 x 9 x 1)
V = 156.36 cubic inches
Therefore, the volume of the given 3 - D figure is 156.36 cubic inches.
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Consider the function as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days.
R(t) = 30t − 3t^2; t = 3
a. Find the average rate of change of R(t) over the time intervals [t, t + h], where t is as indicated and h = 1, 0.1, and 0.01 days. (Use smaller values of h to check your estimates.)
Answer:
-0.061 dollars per day.
Step-by-step explanation:
(R(t + h) - R(t)) / h
We can use this formula to find the average rate of change of R(t) over various time intervals h, starting with t = 3:
For h = 1 day:
R(3 + 1) = 30(3 + 1) - 3(3 + 1)^2 = 27 - 6 = 21
Average rate of change = (21 - 30(3) + 3(3)^2) / 1 = (21 - 27) / 1 = -6
For h = 0.1 day:
R(3 + 0.1) = 30(3 + 0.1) - 3(3 + 0.1)^2 = 29.7 - 8.91 = 20.79
Average rate of change = (20.79 - 30(3) + 3(3)^2) / 0.1 = (20.79 - 27) / 0.1 = -0.61
For h = 0.01 day:
R(3 + 0.01) = 30(3 + 0.01) - 3(3 + 0.01)^2 = 29.93 - 8.9699 = 20.9601
Average rate of change = (20.9601 - 30(3) + 3(3)^2) / 0.01 = (20.9601 - 27) / 0.01 = -0.061
As we can see, as the value of h decreases, the average rate of change approaches a more accurate value. The average rate of change of R(t) at t = 3 days is approximately -0.061 dollars per day.
Your friend is on a weight-loss program and
wants to reach a final goal weight of 160
pounds. His starting weight was 180 pounds. If
he has lost 8% of his body weight so far, how
many pounds does he still have to lose to reach
his final goal.
Answer:
5.6lbs
Step-by-step explanation:
multiply 180 by .08
8%=14.4
14.4-180=165.6
165.6-160= 5.6
There are 150 employees in a factory. （2/3）of the employees are males. Then, 20 male employees and 10 female employees are resigned. A employee is chosen at random from the remaining employees. Find the probability of choosing a female employee.
the price of an item is $90.after the sales tax is added, the final cost is &94.5. which percent of sales tax has been applied to the item?
The percent of sales tax that has been applied to the item is 5%.
What is sales tax?A sales tax is a consumption tax imposed on the sale of items. It is often applied to the selling price of an item.
Here, the original cost is $90 and the final cost is $94.5.
Let, the sales tax rate is r%.
Calculate the percentage of sales tax.
Final price after sales tax = Selling Price×(1 + Rate of sales tax/100)
94.5 = 90(1+r/100)
94.5 = 90 + 0.9r
0.9r = 4.5
r = 5
Therefore, the obtained answer is 5%.
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Which function is represented by the graph?
f(x) = |x – 1| + 3
f(x) = |x + 1| – 3
f(x) = |x – 1| – 3
f(x) = |x + 1| + 3
The function represented by the graph is:
f(x) = |x – 1| + 3
This function takes the absolute value of the difference between x and 1, and then adds 3 to the result. The graph of this function will have a "V" shape centered at x = 1 with the vertex at (1, 3). The left side of the vertex will have a slope of -1, and the right side of the vertex will have a slope of +1. The y-intercept will be 3 units above the x-axis.
Answer: B
Step-by-step explanation: YES
un cuerpo describe un M.A.S de a cuerdo con lo especificado.
x= 2 cos (π/2 T+π) r
Hallar sus elementos en:
T= 2
T= 2/3 seg
K= f/x
The M.A.S motion for two different time periods {T} = 2s and
{T} = 2/3s is calculated above.
What is the general equation of a wave motion?The general equation is -
y{t} = A sin(ωt + Ф)
Given is a body describes an M.A.S according to the function -
{x} = 2 cos{(π/2)T+ π)r
Now -
For {T} = 2, we can write -
{x} = 2 cos{(π/2) x 2+ π)r
{x} = 2 cos{2π}r
{x} = 2 x 1 x r
{x} = 2r
For {T} = 2/3, we can write -
{x} = 2 cos{(π/2) x 2/3+ π)r
{x} = 2 cos{π/3}r
{x} = 2 x -0.33 x r
{x} = - 0.66r
Therefore, the M.A.S motion for two different time periods {T} = 2s and
{T} = 2/3s is calculated above.
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{Question in english -
a body describes an M.A.S according to what is specified.
x= 2 cos (π/2 T+π) r
Find its elements in:
T= 2
T= 2/3 sec
K=f/x}
Kyle is at the end of a pier 30 feet above the ocean. His eye level is 6 feet above the pier.
He is using Binocular to watch a whale surface. If the angle of depression of the whale is
25°, how far is the whale from Kyle's binoculars?
Step-by-step explanation:
Let the distance between them be y
sin20° =
=> 0.342 = [ sin20° = 0.342]
=> y = 33/ 0.342
=> y = 96.5 ft
So, the distance between them is 96.5 ft
whats the answer to this question
Answer:
180 most likely
Camden is working two summer jobs, making $10 per hour babysitting and making $18 per hour lifeguarding. In a given week, he can work no more than 14 total hours and must earn no less than $180. If Camden worked 9 hours lifeguarding, determine the minimum number of whole hours babysitting that he must work to meet his requirements. If there are no possible solutions, submit an empty answer.
Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.
What is the solution to the equation?A solution to an equation is a number that can be substituted for the variable to provide a true number statement.
Let's call the number of hours Camden works babysitting "x".
We know that x + 9 (hours of lifeguarding) cannot be more than 14 and that his total earnings must be at least $180. So we can write two equations based on these conditions:
x + 9 ≤ 14 (hours worked can't exceed 14)
10x + 18 × 9 ≥ 180 (earnings must be at least $180)
Now we can substitute the first equation into the second:
10x + 18 × 9 ≥ 180
10x + 162 ≥ 180
10x ≥ 18
x ≥ 1.8
Since x has to be a whole number of hours, we round up to find that Camden must work at least 2 hours babysitting.
So, Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.
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I mark Brainliest :D (I've been waiting 30 mins please someone answer)
In the figure below, AD=32 cm, CD=24 cm, and points C and D are on the perpendicular bisector of segment AB. What is the perimeter of △ABC?
Answer:
The perimeter of △ABC is 144 cm.
------------------------------
Since points C and D are on the perpendicular bisector of AB, we have:
CD⊥AB;AD = BD;AC = BC.Find the length of AC using Pythagorean:
[tex]AC=\sqrt{AD^2+CD^2}=\sqrt{32^2+24^2} = \sqrt{1600}=40\ cm[/tex]Find the perimeter of ΔABC:
P = AB + BC + AC = 32*2 + 40 + 40 = 64 + 80 = 144 cmif each coded item in a catalog begins with 4 distinct letters followed by 4 distinct nonzero digits, find the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even.
The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is 5/52
probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations.
Given that, if each coded item in a catalog begins with 4 distinct letters followed by 4 distinct nonzero digits
Like the 4 distinct letters be A,B,C,D
4 distinct nonzero digits are 2,3,4,5
The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to the 10/104 = 5/52
Here the probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations and the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to 5/52
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Factor the following expressions.
(a-7)-y(a-7)
8a(x+y)-(x+y)
Answer:
(x+y)(8a - 1)
Step-by-step explanation:
For the first expression:
(a-7) - y(a-7)
We can factor out (a-7) from both terms:
(a-7)(1 - y)
So, the factored expression is:
(a-7)(1 - y)
For the second expression:
8a(x+y) - (x+y)
We can factor out (x+y) from both terms:
(x+y)(8a - 1)
So, the factored expression is:
(x+y)(8a - 1)
Answer: (1-y)(a-7) and (8a-1)(x+y)
Step-by-step explanation:
When the values in the parentheses are the same twice, they reappear only once after grouping. In the first problem, the coefficients are 1 and -y, therefore, the answer becomes (1-y)(a-7).
Hope this helps
MM
how many three-digit numbers satisfy the property that the middle digit is the absolute value of half the difference of the first and the last digits?
A total of [tex]10 + 4 + 4 = \boxed{18}[/tex] three-digit numbers that satisfy the given property.
Let the three-digit number be written as abc, where a, b, and c are the hundreds, tens, and ones digits, respectively. We want b to be the absolute value of half the difference between a and c. In other words, we want b = [tex]\left|\frac{a-c}{2}\right|.[/tex]
Since a, b, and c are digits, we know that [tex]0 \leq a, b, c \leq 9.[/tex] Since b is the absolute value of a number, we know that b is non-negative.
Case 1: [tex]a \geq c[/tex]
If [tex]a \geq c[/tex], then[tex]b = \frac{a-c}{2}[/tex]. Since b must be non-negative, we have two
subcases to consider:
Subcase 1: a=c
In this subcase, b=0, which means that the number abc is of the form a00, where [tex]0 \leq a \leq 9[/tex]. There are 10 such numbers.
Subcase 2: a>c
In this subcase, [tex]b = \frac{a-c}{2}[/tex] is a positive integer. Since a and c must have the same parity (i.e., they are either both even or both odd), we have two
sub-subcases to consider:
Sub-subcase 1: a and c are both even
In this sub-subcase, a and c are both integers between 0 and 8 inclusive (since they are even and cannot be equal to 0 or 9). There are 4 such pairs of values for a and c: (2,0), (4,2), (6,4), and (8,6). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.
Sub-subcase 2: a and c are both odd
In this sub-subcase, a and c are both integers between 1 and 9 inclusive (since they are odd and cannot be equal to 0 or 8). There are 4 such pairs of values for a and c: (9,7), (7,5) , (5,3), and (3,1). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.
Case 2: a < c
If a < c, then[tex]b = \frac{c-a}{2}[/tex]. Since b must be non-negative, we have only one
subcase to consider:
Subcase: c- a is even
In this subcase, c-a is an even integer between 2 and 8 inclusive (since it cannot be equal to 0 or 9). There are 4 such even integers: 2, 4, 6, and 8. For each even integer, the values of a and c that satisfy c-a are uniquely determined, and the value of b is then uniquely determined. So there are 4 corresponding numbers abc.
Putting everything together, we have a total of [tex]10 + 4 + 4 = \boxed{18}[/tex] three-digit numbers that satisfy the given property.
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Please help me answer this question 20 points
Answer:
uhhhh
Step-by-step explanation:
. How many 1/3 cup servings are in 8 cups of granola?
Answer:
24
Step-by-step explanation:
If we convert this problem into "math language", it's basically asking what is 8 divided by 1/3? So, we set this up: [tex]\frac{8}{\frac{1}{3} }[/tex] = 8 * 3 = 24
2.
In isosceles triangle RST shown below, RS = RT,
M and N are midpoints of RS and RT, respectively,
and MN is drawn. If MN = 3.5 and the perimeter
of ARST is 25, determine and state the length of
NT.
The length of the segment NT is 4.5 units
What is isosceles triangle?
An isosceles triangle is one that has two sides of equal length.
The angles opposite to equal sides are equal.
Let RM=x, then MS=RN=NT=x ( because RS = RT )
RS=RT =2x
RST and RMN are two similar triangles
So, we have
ST/MN = RT/NT
=> ST/3.5 = 2x/x
=> ST/3.5 = 2
=> ST = 2*3.5 = 7
Given , perimeter = 25
=> RS+ST+RT = 25
=> 2x+ST+ 2x = 25
=> 4x + 7 = 25
=> 4x= 25-7 = 18
=> x=18/4 = 4.5
NT=x= 4.5 units
The length of the segment NT is 4.5 units
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I need help with this
The angle relationship that will fill the correct angle are given below.
What is an angle relationship?An angle is said to be generated when two or more lines intersect at a point. Thus series of angles which have some common relationship on comparison are formed. Some common angle relationships are; supplementary angles, complementary angles, vertical angles, etc.
The angle relationship to fill the correct angle are:
1. <AXE and <CXD are vertical angles.
2. <AXF and <DXF are supplementary angles.
3. <DXC and <BXC are complementary angles.
4. <CXB and <AXB are adjacent angles.
5. <AXC and <CXD are supplementary angles.
6. <DXE and <AXC are vertical angles.
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allintext:if we have four variables, then how many equations will we have in our system of linear equations?
If we have four variables, then four equations will we have in our system of linear equations.
A linear equation is a mathematical equation that represents a straight line on a graph. It is an equation that can be written in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point where the line intersects the y-axis.
Linear equations can be used to model a wide range of real-world phenomena, from simple physics problems such as calculating the speed of a moving object, to economic models that describe the relationship between price and demand. They are also widely used in fields such as engineering, finance, and statistics.
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12. (A.10.B) A sidewalk was built around a rectangular garden. Find the area of the sidewalk in terms of x
x
3x
2x-1
X+2
The area of the sidewalk in terms of x would be 3 x ² + x + 2
How to find the area of the sidewalk ?The area of the sidewalk would be :
= Area of rectangular area - Area of rectangular garden
Area of rectangular area = 2 x ( 2x + 1 )
Area of rectangular garden = x ( x + 1 )
The area of the sidewalk in terms of x is therefore :
= ( 2 x ( 2x + 1 ) ) - ( x ( x + 1 ) )
= ( 4 x ² + 2 ) - ( x ² + x )
= 4 x ² + 2 - x ² + x
= 4 x ² - x ² + x + 2
= 3 x ² + x + 2
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What is the area of this sign?
The area of the composite figure is 294 cm square.
How to find the area of a composite figure?The figure above is a composite figure. The figure is formed by combining two trapeziums.
Therefore, the area of the figure is the sum of the whole area of the shape.
Hence,
area of the composite figure = area of the trapezium1 + area of the trapezium2.
area of the trapezium1 = 1 / 2 (a + b)h
hence,
area of the trapezium1 = 1 / 2 (12 + 25)6
area of the trapezium1 = 1 / 2 (37)6
area of the trapezium1 = 111 cm²
area of the trapezium2 = 1 / 2 (24 + 37)6
area of the trapezium2 = 3 × 61
area of the trapezium2 = 183 cm²
Therefore,
area of the composite figure = 111 + 183
area of the composite figure = 294 cm²
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explain what is meant by statistical inference. give an example of statisticalinference from everyday life, say, a political poll
It's important to use sound statistical methods and careful analysis to ensure that the inferences drawn are as accurate as possible.
Statistical inference is the process of drawing conclusions or making predictions about a population based on data from a sample of that population. In other words, statistical inference involves using the principles of probability and statistics to make generalizations about a larger group based on information collected from a smaller group.
For example, a political survey may be conducted to gather opinions from a sample of voters about a particular issue or candidate. The data collected from this sample can be used to make inferences about the opinions of the larger population of voters. Statistical inference allows us to estimate the opinions of the larger population based on the information gathered from the smaller sample.
To illustrate this, suppose a survey is conducted on a random sample of 1000 voters in a city, and 600 of them indicate that they support a particular candidate. Based on this sample, the surveyors can use statistical inference to estimate the proportion of voters in the entire city who support that candidate. A confidence interval could be constructed to provide a range of values within which the true proportion of voters who support the candidate is likely to lie. This estimate can be used to inform political strategy and decision-making.
However, it's important to note that statistical inference is subject to certain assumptions and limitations, and there is always a degree of uncertainty associated with making predictions or generalizations based on a sample. Therefore, it's important to use sound statistical methods and careful analysis to ensure that the inferences drawn are as accurate as possible.
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Themba lends 12 000 to his friend to buy a car he requires the loan to be repaid after five years with a payment of 22 109,22 . what was the compound interest rate that he charged
The compound interest rate charged is given as follows:
13% per year.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
P = 12000, A(t) = 22109.22, n = 1, t = 5.
Hence the interest rate is obtained as follows:
22109.22 = 12000(1 + r)^5
(1 + r)^5 = 22109.22/12000
1 + r = (22109.22/12000)^(1/5)
1 + r = 1.13
r = 1.13 - 1
r = 0.13.
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5 Dans chaque cas, calculet une valeur approchée
au dixième près de la longueur, en cm, de chaque
cercle.
2.8 cm
18 m
J’ai besoin d’une réponse au plus vite possible
Two communications companies offer calling plans. With Company X, it costs 25¢ to connect and then 4¢ for each minute.
With Company Y, it costs 15¢ to connect and then 3¢ for each minute. Write and simplify an expression that represents how
much more Company X charges, in cents, for n minutes.
Which of these expressions represents how much more Company X charges than Company Y?
OA. (25+3n)-(15+4n)
B. 25n-4-15n-3
OC. (25n-3)-(15n-4)
Answer: A
Step-by-step explanation:
: 4x+25, 3x+15. x=10
Write the equation in slope-intercept form. y−2=−43(x+6)
The equation can be written in slope-intercept form as y = -43x - 250. This equation has a slope of -43 and a y-intercept of -250.
Subtract 2 from both sides:
y - 2 - 2 = -43(x + 6) - 2
y - 4 = -43(x + 6)
Divide both sides by -43:
(-1/43) * (y - 4) = x + 6
(-1/43)y - (-4/43) = x + 6
x = (-1/43)y + (-38/43)
Add 6 to both sides:
x + 6 = (-1/43)y + (-32/43)
Subtract (-1/43)y from both sides:
x + 6 - (-1/43)y = (-32/43) - (-1/43)y
x + 6 + (1/43)y = (-32/43)
Multiply both sides by -43:
(-43)(x + 6 + (1/43)y) = (-43)(-32/43)
-43x - 250 = -32
Add 250 to both sides:
-43x - 250 + 250 = -32 + 250
-43x = 218
Divide both sides by -43:
x = (-218)/(-43)
x = 5
The equation can be written in slope-intercept form as y = -43x - 250. This equation has a slope of -43 and a y-intercept of -250.
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What is the solution to this equation?
X
= 6
-3
O A. X = 18
O B. X=-18
C. X = 2
O D. X= -2
The solution to the equation is (b) x = -18
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
X
= 6
-3
Represent the equation properly
So, we have the following representation
x/-3 = 6
Cross multiply the equation
This gives
x = -3 * 6
Evaluate the products
x = -18
Hence, the solution is (b) x = -18
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Find X then find angle BD
Applying the Two Tangents Exterior Angle Theorem, the value of x is: 12.
m(BD) = 120°
What is the Two Tangents Exterior Angle Theorem?If you draw two tangents from a point outside a circle, the size of the angle they form is equal to half of the difference between the sizes of the two arcs they intercept inside the circle, based on the Two Tangents Exterior Angle Theorem.
Therefore, we have:
6x - 12 = 1/2[(-12 + 21x) - (12x - 24)] (according to the Two Tangents Exterior Angle Theorem)
Solve for x:
6x - 12 = 1/2[(-12 + 21x - 12x + 24)
2(6x - 12) = -12 + 21x - 12x + 24
12x - 24 = 9x + 12
12x - 9x = 24 + 12
3x = 36
x = 36/3
x = 12
m(BD) = 12x - 24 = 12(12) - 24
m(BD) = 120°
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Calculate x in the following ratio: x : 4 = 54 : 3
Answer:
x = 72
Step-by-step explanation:
x : 4 = 54 : 3
express the ratios in fractional form
[tex]\frac{x}{4}[/tex] = [tex]\frac{54}{3}[/tex] = 18 ( multiply both sides by 4 to clear the fraction )
x = 4 × 18 = 72
