Answer:
- 6 is the extraneous solution.
Step-by-step explanation:
Given : [tex]\sqrt{-3x -2} = x + 2[/tex].
To find : Which of the following is an extraneous solution .
Solution : We have given that [tex]\sqrt{-3x -2} = x + 2[/tex].
Taking square both sides
-3x - 2 = [tex](x+2)^{2}[/tex].
On applying identity [tex](a+b)^{2}[/tex] = a² + b² + 2ab
Then ,
-3x -2 = x² + 2² + 2 * 2 *x
-3x -2 = x² + 4 + 4x.
On adding both sides by 3x
-2 = x² + 4 + 4x + 3x
-2 = x² + 4 + 7x
On adding both sides by 2
0 = x² + 4 + 7x + 2
On switching sides
x² +7x + 6 = 0
On Factoring
x² +6x + x + 6 = 0
x ( x+ 6 ) +1 (x +6 ) = 0
On grouping
( x +1) ( x +6) = 0
x = -1, -6.
Let check for x = -6
[tex]\sqrt{-3 (-6) -2} = -6 + 2[/tex].
4 = -4
An extraneous solution is a root of a transformed equation that is not a root of the original equation.
Therefore, -6 is the extraneous solution.
The length of a rectangle is 2 cm less than 6 times the width. find the possibilities for the width of the rectangle such that the area is not more than 840 cm2
To solve this problem, let us first assign the variables. Let us say that:
l = length of rectangle
w= width of rectangle
The given problem gives us the relation that:
l = 6 w – 2 ---> 1
We know that the formula for area of rectangle is given as:
A = l w ---> 2
Substituting equation 1 into 2:
A = (6 w – 2) w
A = 6 w^2 – 2 w
The area must not be greater 840 cm^2, therefore:
840 cm^2 = 6 w^2 – 2 w
w^2 – (1/3) w = 140
By completing the square:
w^2 – (1/3) w + (1/36) = 140 + (1/36)
(w – 1/6)^2 = 5041/36
w – 1/6 = ± 11.83
w = -11.66, 12
Therefore the maximum value that the width can take is 12 cm. Therefore the possibilities of width such that the area does not exceed 840 cm^2 is from 1 to 12 cm.
Answer:
1 cm to 12 cm
15-3 7/8
What is 15 minus 3 and 7 8ths
Solution of equqation 15 - 3 7/8 is 11 1/8.
To solve 15 - 3 7/8, you need to follow these steps:
Convert the mixed number 3 7/8 to an improper fraction.Subtract this fraction from 15.First, convert 3 7/8 to an improper fraction:
3 7/8 = (3 * 8 + 7) / 8 = 31/8Next, convert 15 to a fraction with a common denominator of 8:
15 = 120/8Now you subtract the improper fraction from the whole number fraction:
120/8 - 31/8 = (120 - 31) / 8 = 89/8Convert the result back to a mixed number:
89/8 = 11 1/8So, 15 minus 3 and 7/8 is 11 1/8.
How do you use the additive inverse to evaluate an expression that uses subtraction
Answer:
Additive inverse is the negative of the number, i.e. what you add to the number to get zero.
So the additive inverse of number b is - b
Additive inverse of 4 is - 4.
Then, you can verify the subtraction is the same that add the additive inverse.
For example subtracting 4 from 10 (10 - 4) is the same that adding -4:
10 - 4 = 10 + (-4).
Then given any expression if you have to subtract other expressión you just add the addive inverse of the second expression.
For example: given A(x) = x^2 + 3x + 5 and B(x) = 2x + 4
Find A(x) - B(x) = A(x) + [-B(x)]
=> x^2 + 3x + 5 + (-2x -4) = x^2 + 3x - 2x + 5 - 4 = x^2 + x + 1
Step-by-step explanation:
hope this helped!
Find the volume of a rectangular prism if the length is x, the width is x2, and the height is 5x2 + 4x + 1. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
5x5 + 4x4 + x3
5x4 + 4x3 + x2
6x5 + 4x4 + x3
6x4+4x3+x2
Answer:
A) 5x^5 + 4x^4 + x^3
Step-by-step explanation:
Which of the following points is a solution to the system of linear inequalities?
{y ≤ 2x+1 y>1/2x-4
Answer choices:
A.(2, 6)
B.(2, –3)
C.(2, 3)
D.(2, –6)
You deposit $1400 into a savings account that earns simple annual interest. After 12 years, the balance in the account is $2408. What is the annual interest rate?
ROUND 977.259856871 TO 3 DECIMAL PLACES HELP!
3 decimal places would be where the 9 is, since the next number is 8 , the 9 would become a 0 and the number before it (5) would become a 6
so it would be 977.260
A basketball court is in the shape of a rectangle. It has a length of (x − 7) meters and a width of (x + 3) meters. The expression below represents the area of the court in square meters:
(x − 7)(x + 3)
Which of the following simplified expressions represents the area of the basketball court in square meters?
− 6x + 3
x2 − 21
x2 − 4x − 21
x2 − 7x + 3
The answer is x² - 4x - 21 or C
The area (A) of the rectangle is:
A = l * w (l - length, w - width)
We have:
l = x - 7
w = x + 3
Therefore:
A = (x - 7)(x + 3)
Now, multiply each factor with another:
A = (x - 7)(x + 3) = x * x + x * 3 - 7 * x - 7 * 3 = x² + 3x - 7x - 21 = x² - 4x - 21
Hello, everyone! I am in high school and I need help with my geometry homework! I will also mark you as the brainliest answer if you answer it clearly!
A) #3 y = x+3, if you subtract x from y there is a difference of 3 in all of them.
B) #5 y = -x^2, the y value is the negative value of x raised to the 2nd power
C)#6 y = x^2+3, if you raise the value of x to the 2nd power and then add 3 you get the y value
D)#2 y=3x-1, if you multiply the value of x by 3 then subtract 1 you get the y value
In a genetics experiment on? peas, one sample of offspring contained 402402 green peas and 3838 yellow peas. based on those? results, estimate the probability of getting an offspring pea that is green. is the result reasonably close to the value of 3 divided by 43/4 that was? expected?
The empirical probability of getting a green pea is approximately 91.37%, which is not reasonably close to the expected value of 75% based on Mendel's laws.
Explanation:In this observed pea experiment, there were 402 green peas and 38 yellow peas. To calculate the probability of getting a green pea, we divide the number of green peas by the total number of peas. Therefore, the probability is 402/(402+38) ≈ 0.9137 or 91.37%, which is the empirical probability of getting a green pea.
The expected ratio, which is based on Mendel's genetic laws, is 3/4 for the dominant trait (green peas in this case) but after doing the math, it represents 0.75 or 75%, which is lower than our empirical probability. Therefore, the result is not reasonably close to the value expected (3/4).
It's worth mentioning that this discrepancy can occur due to many reasons including statistical variation, "especially when sample size is not large enough".
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whats pie as in the math equation help me plus thanks
some people use 22/7, some use 3.14
it is used in formulas for circles
(05.03)
Identify the initial value and rate of change for the graph shown
Initial value: 1, rate of change: 2
Initial value: 2, rate of change: 1 over 2.
Initial value: 2, rate of change: 1
Initial value: 1 over 2., rate of change: 2
Answer: Initial value: 2, rate of change: 1
Step-by-step explanation:
From the graph we can see the line is intersecting y axis at (0,2).
Therefore, y intercept of the graph = 2
Therefore, the initial value of the graph = 2
Also there as two point from which line is passing (0,2) and (1,3)
The rate of change of the line is given by :-
[tex]R=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{1-0}=1[/tex]
Hence, for the given graph, the Initial value is 2 and the rate of change is 1 .
Jill has been watching the squirrels that live in her neighborhood. The number of squirrels changes each week.
n f(n)
1 8
2 12
3 18
4 27
Which function best shows the relationship between n and f(n)?
A f(n) = 12(1.5)n
B f(n) = 12(1.5)n−1
C f(n) = 8(1.5)n
D f(n) = 8(1.5)n−1
Find the slope of the line on the graph. Write the answer as a fraction or a whole number, not a mixed number or decimal.
Which of the following is an identity?
A. csc^2 x + cot^2 x = 1
B. (cscx + cotx)^2 = 1
C. sec^2 x sec^2 x + 1 = tan^2 x csc^2 x
D. sin^2 x - cos^2 x = 1
Jackie walks into a convenience store and recognizes the number of lottery tickets she can purchase varies inversely with the price of each ticket. If Jackie buys $5 tickets, she can purchase exactly 6 tickets. If she buys $3 tickets, what is the maximum number of tickets she can purchase?
Answer:
Step-by-step explanation:
10
Find the value of x for which M//N
A.
38
B.
62
C.
102
D.
150
I think the answer is B= 62
Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest thousandth. leg = 9, leg = 12
Choose the correct simplification of (4x3 − 3x − 7) + (3x3 + 5x + 3)
After performing the addition operation on both expressions, the resulting simplified expression is 7x^3+2x-4
Simplification of Algebra ExpressionGiven Data
First expression = (4x3 − 3x − 7) Second expression = (3x3 + 5x + 3)To add both Expression let us open brackets
= (4x3 − 3x − 7) + (3x3 + 5x + 3)
= 4x3 − 3x − 7 + 3x3 + 5x + 3
Collect like terms we have
= 4x^3+3x^3-3x+5x-7+3
= 7x^3+2x-4
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Kate, who is 16, is four times as old as her brother. how old will kate be when she is half as old as her brother?
A customer calls and says that they are upset because they just received their bill and it is for two months service plus a $20 late fee. They have never had a late payment before. They explain that they moved last month and never received their bill. What would you tell them?
Answer with explanation:
The Customer , is irked due to the reason that,he or She hasn't got the last month bill and now they have to pay the bill for two months service plus $ 20 late fee.
Also, the customer is Saying that they moved from that place last month where they were Residing.
I will start Querying with the customer in the following way
Sir, or Madam
1. Have you checked , or asked your Neighbor or Landlord, after leaving that place ,whether they have got this kind of bill ?
2. Secondly , we have your email-ID as well as Mobile number.We message every month about your bill,through email as well as Messaging tool of your mobile.Haven't you Checked your Mail as well as Messaging.
it Shows that Customer is Lying.
So, Sir or Madam
Please , pay the Bill along with late fee.
(03.06 MC) Choose the equation below that represents the line passing through the point (−3, −1) with a slope of 4.
Answer:
The equation of the line is
Y= 4X + 11
Step-by-step explanation:
The equation of the line is equall to
(Y- Y1)/(X-X1) = slope
X1 = -3
Y1= -1
Equation is
(Y-(-1))/(X-(-3))=4
(Y+1)/(X+3) = 4
Y+ 1 = 4X + 12
Y= 4X + 11
The price of gold has increased by 35% per year from 2000. In the year 2000, Harry bought a gold ring for $590. Which of the following functions f(x) can be used to represent the price of the ring x years after 2000? f(x) = 590(1.35)x f(x) = 590(0.65)x f(x) = 35(0.41)x f(x) = 35(1.59)x
A car leaves town traveling 40 mi/h. Two hours later, a second car leaves the same town, on the same road, traveling at 60 mi/h. In how many hours will the second car pass the first car? Use formula d=rt
The area of a square garden is 200 m². How long is the diagonal?
100 m
10 sqrt of 2
200 m
20 m
To find the length of the diagonal of a square garden, you can use the Pythagorean theorem. In this case, the length of the diagonal is approximately 14.14 meters.
Explanation:To find the length of the diagonal of a square garden, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two shorter sides of the right triangle are the sides of the square garden. Let's call each side x. The hypotenuse (the diagonal) will be the side we are trying to find.
Using the Pythagorean theorem, we have: x^2 + x^2 = diagonal^2. Since the area of the square garden is 200 m², we can set up the equation: x^2 + x^2 = 200. Combining like terms, we get: 2x^2 = 200. Dividing both sides by 2, we have x^2 = 100. Taking the square root of both sides, we find that x = 10.
Therefore, each side of the square garden is 10 meters. And using the Pythagorean theorem one more time, we can find the length of the diagonal: diagonal^2 = 10^2 + 10^2. Simplifying, we get diagonal^2 = 200. Taking the square root of both sides, we find that the length of the diagonal is approximately 14.14 meters.
what is the length of a circle that has a central angle of 98 degrees and 6 cm?
What is the equation of the quadratic graph with a focus of (3, −1) and a directrix of y = 1?
A.) f(x) = −one fourth (x − 3)2 + 1
B.) f(x) = −one fourth (x − 3)2
C.) f(x) = one fourth (x − 3)2 + 1
D.) f(x) = one fourth (x − 3)2
When 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4. find the number. j. grossman?
Answer:
its 3
Step-by-step explanation:
The required value of the unknown number x would be 3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have been given that " 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4".
Let the unknown number be x.
7x - 8 = 3x + 4
To solve the equation;
7x - 8 = 3x + 4
Collect the like terms;
7x - 3x = 8 + 4
4x = 12
Divide by 4 on both sides;
x = 12/4
x = 3
Therefore, the required value of the unknown number x would be 3.
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There are 16 boys in an English class of 28 students. The ratio of boys to the total number of students in this class is typical of the whole school. There are 476 students in the school. About how many are boys?
The number of the boys in the school is 272.
What is multiplication?Multiplication is mathematical arithmetic operation. It is also a process of adding same types of expression to some number of times.
Example - 2 × 3 means 2 is added three times or 3 is added 2 times.
Given, the ratio of boys to the total number of students in this class is typical of the whole school.
That means,
16 : 28 = x : 476
where x is the number of boys in the school.
Simplifying,
16/28 = x/476
Using cross multiplication,
x = 16 x 476/ 28
x = 272
Therefore, the number of the boys in the school is 272.
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What is the answer Barbara also works part-time at themepark the radio of the number of hours Barbara works at the park to the money she earns in dollars is 1:9 create a table to show the money earned by Barbara for 5,6,8 hours of work at a theme park