[tex]\huge{\color{magenta}{\fbox{\textsf{\textbf{Answer}}}}}[/tex]
x = -1
Step-by-step explanation:
[tex] \sf\frac{x}{x - 2} + \frac{x - 1}{x + 1} = - 1[/tex]
Taking LCM
[tex] \sf \hookrightarrow \frac{x(x + 1) + (x - 1)(x - 2)}{(x - 2)(x + 1)} = - 1 \\ \\ \sf \hookrightarrow \frac{ {x}^{2} + x + {x}^{2} - 3x + 2 }{ {x}^{2} - x - 2} = - 1 \\ \\ \sf \hookrightarrow \frac{2 {x}^{2} - 2x + 2 }{ {x}^{2} - x - 2 } = - 1[/tex]
Cross multiplying
[tex] \sf \hookrightarrow 2 {x}^{2} - 2x + 2 = - 1( {x}^{2} - x -2) \\ \\ \sf \hookrightarrow 2 {x}^{2} - 2x + \cancel2 = - {x}^{2} + x + \cancel2 \\ \\ \sf \hookrightarrow 3 {x}^{2} - 3x = 0[/tex]
Taking 3 common
[tex] \sf \hookrightarrow {x}^{2} - x = 0 \\ \\ \sf \hookrightarrow x(x - 1) = 0 \\ \\ \sf \hookrightarrow x - 1 = 0 \\ \\ \\ \green{\boxed{ \hookrightarrow x = 1}}[/tex]
VerifyingTaking x as 1
[tex] \sf \implies\frac{x}{x - 2} + \frac{x - 1}{x + 1} = - 1 \\ \\ \sf \implies \frac{1}{1 - 2} + \frac{1 - 1}{1 + 1} = - 1 \\ \\ \sf \implies - 1 + 0 = - 1 \\ \\ \sf \implies - 1 = - 1[/tex]
Can someone help me to solve this question? Prove that the quadrilateral ABCD whose vertices are A(-2,-1), B(-2,-3), C( 5,6), and D(5,-1)is a trapezium.Find the area of trapezium ABCD. Also Can you tell how to find the height of trapezium with vertices without knowing the area? Thank you.
If the height of the trapezium is 7 units. Then the area of the trapezium will be 31.5 square units.
What is a trapezium?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.
The quadrilateral ABCD whose vertices are A(-2,-1), B(-2,-3), C( 5,6), and D(5,-1).
The lines AB and CD are parallel to the y-axis. Then the quadrilateral ABCD is a trapezium.
The height of the trapezium will be 7 units.
The area of the trapezium will be
Area = 1/2 (2 + 7) x 7
Area = 0.5 x 9 x 7
Area = 31.5 square units.
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A group of 31 friends gets together to play a sport. First, people must be
divided into teams. Each team has to have exactly 3 players, and no one can
be on more than one team. How many teams can they make? (It is possible
that not everyone can be on a team.)
87
Answer: 10 teams is the answers
Convert the into millimetres.
A. 234cm
B. 15m
C. 25km
A. 234 cm
multiply the given length value ( 234 ) by 10.
[tex]234 \times 10[/tex]
[tex] = 2340 \: mm[/tex]
B. 15m
multiply the given length value ( 15 ) by 1000.
[tex]15 \times 1000[/tex]
[tex] = 15000 \: mm[/tex]
C. 25km
multiply the length value ( 25 ) by 1000000.
[tex]25 \times 1000000[/tex]
[tex] = 25000000 \: mm[/tex]
a)
234 × 10
= 2340 millimeters
b)
15 × 1000
= 15000 millimeters
c)
25 × 1000000
= 25000000 millimeters
Statistical uncertainty in estimates associated with the fact that surveys do not interview every individual in the population of interest is called __________. Group of answer choices measurement error sample bias probability sampling sampling error
Statistical uncertainty in estimates associated with the fact that surveys do not interview every individual in the population of interest is called Sampling Error , Option D is the correct answer.
What is Sampling Error ?Sampling error is the difference between the estimated value and the true value if the whole population was enumerated while doing the sampling.
By following the sampling principles one can keep the sampling error to the minimum.
The knowledge of the sampling error will help in evaluating the sampling process and defining gits efficiency.
The factors that affect Sampling Error are
Sample Size: When the sample size is large , the Sampling error decreases , They do not have a direct proportion.Sample Design : These define how the sample will be taken , cluster , random , stratified , Different methods have different extent of sampling error , The design should be selected according to the population and resources constraints.Population Variability : The variability in the population increases the sampling error as the sampling is then cannot be uniform and cannot represent the entire population , By increasing sample size , the population variability can be minimized and so the sampling error.Statistical uncertainty in estimates associated with the fact that surveys do not interview every individual in the population of interest is called sampling Error.
Therefore , Option D is the correct answer.
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which expression shows the raltinship between 1 and 2 and 6 and 3
Step-by-step explanation:
THREE SOLUTION TO PROVE ITS FALSE
1:2
Multiply by 3 on each side
1*3 : 2*3 = 3:6
This is not the same as 6:3
3 apple:6 bananas is not the same as 6 apples: 3 bananas
1:2 is equivalent to 6:12 not 6:3
because 1x6=6 2×6=12 =6:12
3)
however when we solve mathematically
1/2=6/3
1/2=2
The sides are not equa so its false
I need an equation for the line
Answer:
Y = -(1/3)X
Step-by-step explanation:
Extract two points
P1(6; -2) P2(-6; 2)
Now:
Y=mX+n. n=0 (interception with Y axis) exis)
Y=mX +0. m= (y2-y1) / (x2-x1)
m= (2+2) / (-6-6)
m= -(1/3)
Y=-(1/3)X
sharmar spent at least 30 minutes playing his guitar on saturday he spent 10 minutes longer playing his guitar on saturday than on friday. how many minutes could shamar have played his guitar on friday F?
A circle is placed in a square with a side length of 4 yards as shown below find the area of the shaded region use the value 3.14 for π and do not round your answer be sure to include the correct unit in your answer
Answer:
If the circle touches all 4 sides, the diameter is 2 so the area us 3.14(4) = 12.56.
16 - 12.56 = your answer
Mark brainliest if I am right pls
which equation represents a line which is parallel to the line y=8/7x-6?
Answer: 8x-7y = 56
Step-by-step explanation:
You plan to move to San Antonio. You earn a salary of $42,000 here in McAllen. How much more must you earn in San Antonio if the cost of living is 15% higher?
A factory produces a batch of toy vehicles, 1/3 of which are cars and the rest are trucks. trucks have defective ratio of 0.02 and cars have defective ratio of 0.01. the quality inspector picks a toy vehicle at random from the batch and finds out that it is defective. what is the probability that the vehicle was a truck
Answer:
Step-by-step explanation:
b
When analyzing the relationship in non-linear data as a linear association, when should the strategy of ignoring outliers be used?
If ignoring half of the data points allows the remaining data to be represented by a curved line.
If ignoring one or two data points allows the remaining data to be represented by a straight line.
If ignoring half of the data points allows the remaining data to be represented by a straight line.
If ignoring one or two data points allows the remaining data to be represented by a curved line.
carolyn and emily are searching online for tickets to a concert. two weeks ago, the cost was $20. now the cost is $29. carolyn said the percent increase is 45% and emily said the percent of increase is about 31%. who is correct?
Answer:
Carolyn
Step-by-step explanation:
Carolyn:
45% = 0.45
We multiply the orignal price with 0.45 to see how much it increased.
[tex]20(0.45) = 9[/tex]
We then add it to the original price
[tex]20+9 =29[/tex]
Emily:
31% = 0.31
We multiply the orignal price with 0.31 to see how much it increased.
[tex]20(0.31) = 6.2[/tex]
We then add it to the original price
[tex]20+6.2=26.2[/tex]
That means that Carolyn is correct.
Solve for the value of x -
[tex]5(4x-4)=-60[/tex]
Thanks! ^^
Answer:
x = -2
Step-by-step explanation:
[tex]20x - 20 = -60\\20x = -40\\x = -2[/tex]
hope this helped!!
Answer:
x = -2
Step-by-step explanation:
Divide both sides by 5 :
5/5 (4x - 4) = -60/54x - 4 = -12Add 4 to both sides :
4x - 4 + 4 = -12 + 44x = -8Divide both sides by 4 :
4x/4 = -8/4x = -2You have 10 trees and 5 rows you can only use 4 trees a row
Answer:
You would plant 2 trees in each row instead of 4.
10 divided by 5 = 2
solve system by elimination
-2x+4y=-2
2x+3y=9
Answer:
y=1, x=3 or (3,1)
Step-by-step explanation:
when you add the two equations together the two x's cancel out, which leaves one solvable equation, 7y=7, so y=1, then you can plug y=1 into one of the equations. 2x+3(1)=9 which is 2x+3=9 then solve, x=3.
Additionally if you want to check answers plug both into one equation- -2(3)+4(1)=-2, -6+4=-2, -2=-2 which is correct.
The solution for the given linear system from the elimination method is x=3 and y=1.
System of Linear EquationsSystem of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
You can solve a linear system by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
-2x+4y=-2 (1)
2x+3y=9 (2)
You should sum the equations 1 and 2, for eliminate the variable x.
-2x+4y+2x+3y=-2+9
7y=7
y=1
If y=1 from equation 2, you have:
2x+3*1=9
2x+3=9
2x=9-3
2x=6
x=3
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what is the probability of rolling a 1 and then rolling an even number with one 6 sided die
Answer:
5/6(83.33%) I think this should be the probability of it.
what is the absolute vale of |-18|
Answer:
18
Step-by-step explanation:
the absolute value is 18
-5(8a - b) - 2(-6a + 9b)
Need answer plis
A certain species of bird is in danger of becoming extinct. There were 1500 birds in 2000 and they are
decreasing at an annual rate of 6.5%.
a) If this trend continues, how many birds will be left by 2010?
b) How many birds would there have been in 1990?
a) If this trend continues, how many birds will be left by 2010 will be 525
b) The birds would there have been in 1990 will be 2475
What is rate of increase?Rate of increase or decrease is defined as the increment or decrement in any quantity over a period of time constantly.
Here we have the data that:
There were 1500 birds in 2000 and they are decreasing at an annual rate of 6.5%.
a) If this trend continues, how many birds will be left by 2010
{1500x6.25}/{100}=97.5
So the bird decrement in the one year will be =97.5 so it will be in the 10 years or upto 2010 will be
97.5x10=975
So the birds left till 2010 will be:
Q=1500-975=525
b)The birds would there have been in 1990 will be:-
=1500+975=2475
Hence If this trend continues, how many birds will be left by 2010 will be 525.The birds would there have been in 1990 will be 2475
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-
I
The shaded area shows a patio that Rudy built. He covered the shaded area with square tiles.
1 tile = 1 square foot
What is the area of the patio?
O A. 15 square feet
O B. 18 square feet
OC. 21 square feet
OD. 25 square feet
Answer:In the diagram, there are 28 tiles. You can do that with easy multiplication or just counting. Each square length is 1.5 feet, or 18 inches. You get that by multiplying 12 by 1.5. The area of a square is 324 inches, found by multiplying 18 by 18. Divide 324 by the area of a tile, 36 (6*6), to get 9. There are 9 tiles in each square. Multiply 9 by 28 to get... 252
Step-by-step explanation:
a trapezoid has a perimeter of 14ft what will the perimeter be if each side length id increased by a factor of 7
Answer:
42
Step-by-step explanation:
Trapezoid has 4 lines
If each side increase by 7, 4 lines totally increase by 7*4 = 28
Perimeter will be 14 + 28 = 42
Mr Thando received a statement of water usage from BCM. According to the statement he has to pay a sum of R281,27incl VAT for March consumption. The statement does not reflect the amount of water used. WATER in kilolitres Tariffs in R/kl excl VAT 0-610 Free +6 - 14k1 R6.36 +14 20kl R7.98 +20 - 30k! R10,05 +30 - 45kl R12,25 +45 R15.49 Mr Thando is so confused and as a result he consulted you to help him to calculate the number of kilolitres of water he has been charged for Use the Table above that was shown in the statement for your calculations
It can be estimated that the total amount of water that Mr. Thando used is 40 Kiloliters. See the arithmetic calculation/ explanation below and the reconstructed table attached.
What is the calculation of Mr. Thando's Water Usage?The approximate amount of water that he has been charged for will be given as follows:
The maximum fee for Band A + Maximum fee for Band B + Maximum fee for Band C.
Which is: (0) + (6.36 *14) + (7.98*20) = R248.64
Recall that the total amount he was charged is R281.27.
Hence, because the question does not include the percentage of VAT payable, and the referenced table is unavailable, we are forced to assume that the difference between the amount paid and our calculations above is the VAT.
This figure (that VAT) is: R281.27 - R248.64 = R32.63
Hence, the total amount of water used by Mr. Thando is: 6 + 14 + 20 = 40Kl
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Find the equation of the line that passes through the point (-8,15) and is perpendicular to the equation below.
y = -4/5x + 5
A. y = -5/4x + 5
B. y = -4/5x - 7
C. y = -4/5x + 23
D. y = 5/4x + 25
Please help asap!
Answer:
[tex]y = \frac{5}{4} x + 25[/tex]
Step-by-step explanation:
We were told that the equation of the line we are looking for is perpendicular to
[tex]y = - \frac{4}{5} x + 5[/tex]
We know that the gradient of perpendicular lines when multiplied is equal to -1, therefore
[tex] line \: .1 \times \: line \: .2 = - 1 \\ \\ \frac{4}{5} \times line \: .2 = - 1 \\ \\ line \: .2 = \frac{ - 1}{ \frac{4}{5} } [/tex]
[tex]line\: .2 = \frac{5}{4} \: \: \: \: y = 15 \: \: \: \: x = - 8 \\ \\ y = mx + c \\ \\15 = ( \frac{5}{4} ) - 8 + c \\ \\ 15 = - 10 + c \\ 15 + 10 = c[/tex]
[tex]25 = c \\ \\ therefore \: the \: equation \: of \: the \: line \: is \: \\ \\ y = \frac{5}{4} x + 25[/tex]
Diego has purchased a $159000 home with a 30-year mortgage at 5.05%. He can make a monthly payment if $1300. If he were to make this each month, how long will it take him to pay off his mortgage?
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It will take 308 months for Diego to pay the complete loan.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = P×T×R
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
The interest that will be charged on the principal amount is,
SI = $159,000×30×0.0505 = 240,885
Now, the total amount that Diego needs to pay is the sum of interest and principal, therefore,
Total amount = $159,000 + $240,885 = $399,885
Further, since each month Diego is paying $1300, therefore, the number of months it will take to pay the complete loan is,
Number of months = $399,885/$1300 = 307.6 ≈ 308
Hence, it will take 308 months for Diego to pay the complete loan.
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At summer camp, Rob went on a nighttime nature walk with his troop. During the walk, they saw 3 bats, 1 owl, 2 deer, and 6 squirrels.
Rob had never seen a bat before. What percent of the animals they saw on the walk were bats?
Answer:
25%???
Step-by-step explanation:
I think
What is the mode of the following numbers?
6, 4, 1, 9, 3, 8, 3, 5, 10
Explanation:
The mode is the most frequent number. It is the number that shows up the most.
Sorting the values gets us {1, 3, 3, 4, 5, 6, 8, 9, 10} in which we can see that "3" shows up twice, which is the most compared to any other value. Therefore the mode is 3.
Kate is the captain of a large cruise ship. As she
drives the ship, she sits 50 meters above the sea.
Paul is the captain of a boat. He sits 15 meters
above the sea. If the radius of the earth is
6,371,000 meters, how much further can Kate see
across the horizon than Paul?
Kate can see across the horizon by 3.33 times further than Paul.
What is the shape of the horizon?The assumed shape of the horizon shows that it forms a cone shape. The volume of the cone can be used to determine how far they can see.
The volume of the cone [tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
For Kate:
Height (h) = 50 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}[/tex]
V = 2.12526863 × 10¹⁵ m³
For Paul
Height (h) = 15 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}[/tex]
V = 6.3758059 × 10¹⁴ m³
To determine how much further can kate see across the horizon than Paul, we have:
= Volume of Kate/Volume of Paul
= 2.12526863 × 10¹⁵ m³/6.3758059 × 10¹⁴ m³
= 3.33 times further.
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Et $a_1, a_2, a_3,\dots$ be an arithmetic sequence.
if $a_1 + a_3 + a_5 = -12$ and $a_1a_3a_5 = 80$, find all possible values of $a_{10}$.
Since it's an arithmetic sequence,
[tex]a_2 = a_1 + d[/tex]
[tex]a_3 = a_2 + d = a_1 + 2d[/tex]
[tex]a_4 = a_3 + d = a_1 + 3d[/tex]
and so on, up to
[tex]a_n = a_1 + (n-1)d[/tex]
Now, by substitution,
[tex]a_1 + a_3 + a_5 = -12[/tex]
[tex]a_1 + (a_1+2d) + (a_1+4d) = -12[/tex]
[tex]3a_1 + 6d = -12[/tex]
[tex]a_1 + 2d = -4[/tex]
[tex]\implies a_1 = -4-2d, a_3 = -4, a_5 = -4+2d[/tex]
Then the product [tex]a_1a_3a_5=80[/tex] depends only on d, so that
[tex](-4-2d) \times (-4) \times (-4+2d) = 80[/tex]
Solve for d :
[tex](4+2d) (4-2d) = -20[/tex]
[tex]16 - 4d^2 = -20[/tex]
[tex]4d^2 = 36[/tex]
[tex]d^2 = 9[/tex]
[tex]d = \pm3[/tex]
If d = 3, then the first term in the sequence is [tex]a_1 = -10[/tex], and the tenth term would be [tex]a_{10} = \boxed{17}[/tex].
If d = -3, then the first term would instead by [tex]a_1 = 2[/tex], and the tenth term would be [tex]a_{10} = \boxed{-25}[/tex].
Translation 3 units left and 15 units down
Rotation 270° counterclockwise around the origin
Answer:
W'' (-5,-11) , X'' (-11,-9) , Y'' (-9,-3) and Z'' (-3,-5)
Kindly check the attached image for more reference
Step-by-step explanation:
Given points of WXYZ ( can be identified by looking at the graph )
W : (14,10) X : (12,4)Y : (6,6) Z : (8,12)Applying translation 3 units left , 15 units down
(Note when shifting left , you subtract from the x value , when shifting down, you subtract from the y value.)
Rule for translation (x,y) ===> ( x - 3 , y - 15 )
Applying translation to given points
W : (14,10) ===> (14-3,10-15) ===> (11,-5)X : (12,4) ===> (12-3,4-15) ===> (9,-11)Y : (6,6) ===> (6-3,6-15) ===> (3,-9)Z : (8,12) ===> (8-3,12-15) ===> (5,-3)Applying rotation 270° counterclockwise around the origin
Rotation 270° clockwise rule : (x,y) ===> (y,-x)
Explanation of rule , change the sign of the x values, then swap the x and y values places.
Applying rotation rule to points
W : (11,-5) ===> (y,-x) ===> (-5,-11)X : (9,-11) ===> (y,-x) ===> (-11,-9)Y : (3,-9) ===> (y,-x) ===> (-9,-3)Z : (5,-3) ===> (y,-x) ===> (-3,-5)So the final points of square WXYZ after the two transformations would be W'' (-5,-11) , X'' (-11,-9) , Y'' (-9,-3) and Z'' (-3,-5)
To see this graphed, kindly view the attached image.
The red square represents the square before any transformations
The blue square represents the square following the translation
And the black square represents the coordinates of the square after the full transformation including both the translation and the rotation .
Answer:
Original image:
W = (14, 10)
X = (12, 4)
Y = (6, 6)
Z = (8, 12)
To translate 3 units left, subtract 3 from the x-values (x - 3)
To translate 15 units down, subtract 15 from the y-values (y - 15)
W' = (14 - 3, 10 - 15) = (11, -5)
X' = (12 - 3, 4 - 15) = (9, -11)
Y' = (6 - 3, 6 - 15) = (3, -9)
Z' = (8 - 3, 12 - 15) = (5, -3)
(red square on attachment)
To rotate 270° counterclockwise around the origin (0, 0),
the point (x, y) becomes (y, -x). So, switch x and y and make x negative.
W'' = (-5, -11)
X'' = (-11, -9)
Y'' = (-9, -3)
Z'' = (-3, -5)
(green square on attachment)
